# James Beck

##### Jim Beck

### James L. Beck

*George W. Housner Professor of Engineering and Applied Science, Emeritus, Caltech*

##### By David Zierler, Director of the Caltech Heritage Project

May 18, 26 and June 8, 2022

**DAVID ZIERLER:** This is David Zierler, director of the Caltech Heritage Project. It is Wednesday, May 18, 2022. I am delighted to be here with Professor James L. Beck. Jim, it's great to be with you. Thank you for joining me today.

**JAMES L**.** BECK:** Thank you, David.

**ZIERLER:** Jim, to start, can you please tell me your title and affiliation here at Caltech?

**BECK:** I am the George W. Housner Professor of Engineering and Applied Science, Emeritus. As of 2017, I went Emeritus.

**ZIERLER:** What departments were you affiliated with?

**BECK:** I was affiliated with the Mechanical and Civil Engineering Department, and also the Computer and Mathematical Sciences Department.

**ZIERLER:** Was that a dual appointment or was one of them your home department and it was a courtesy in the other?

**BECK:** It was really a dual appointment. I had joint offices for a while, but that didn't turn out practical. They were upgrading the Thomas building**;** it is now the Thomas-Gates building. They closed it, and I never got an office back again. I never asked for one. My office was over with the CMS group, which was where my interests were more in the latter years of my research.

**ZIERLER:** Jim, were you the inaugural holder of the George Housner Chair?

**BECK:** Yes, I was, and I must say it was a great honor because I knew George. He was much older than me, but he continued to come into Caltech until he was 90. I had a lot of respect for him. He was just an amazing guy. I was very pleased to be appointed in that role.

**ZIERLER:** Was it his family that set up the chair? Did Caltech take care of it?

**BECK:** No. George was a very smart man, and he turned out to be smart at investing. He made a lot of money, and he gave multiple millions to Caltech in his will. Caltech decided to do various things with it. One of them was to honor him with this endowed chair. Another was an undergraduate program that I think sends students overseas. Also, there was money put in a research fund for earthquake engineering, which is what George requested.

**ZIERLER:** Do you see any intellectual connection between what Housner did and what you've done over the course of your career?

**BECK:** Yes, I do. We talk about Housner—and I don't know how much you know about him; Tom might have mentioned him—as the grandfather of earthquake engineering. He was, for many years, the Chair of the National Research Council Committee on Earthquake Engineering. He belonged to the National Academy of Engineering and the National Academy of Science. I was actually like his academic grandson. Paul Jennings, who later became provost at Caltech for a number of years, was my advisor**,** and George Housner was Paul's advisor. I got to write a paper with George when I was a graduate student. The first summer I was at Caltech, George said that I might be interested in looking at whether the 1975 Oroville earthquake was triggered by the weight of water in the Lake Oroville reservoir, which had been filled to the highest level since it was impounded. I did some analysis which proved the water weight hypothesis was not the case**;** it didn't apply. Whether it was induced by the reservoir or not is still an open question**,** but the major hypothesis, I was able to discount, and that was through George's suggestion, and that led to a paper in the *Seismological Bulletin* of the Seismological Society of America. By the way, this is George; he said he didn't want to be co-author, that it was all my work, and he just had the idea, so I am the only author on that paper.

**ZIERLER:** Was it George specifically who had the idea to honor you with this chair, or that came from administration?

**BECK:** It came from administration. They held it up for a few years. I think I got the Chair in 2012 and George died in 2008 at the age of 98. The estate had to be wrapped up, but then Caltech sat on it for a while, I think to just boost it up a bit or something. They finally gave it to me. Now, the former executive officer of the Mechanical and Civil Engineering Department is the George W. Housner Professor.

**ZIERLER:** Since you have gone Emeritus, how have you remained connected to Caltech?

**BECK:** I have been more connected with my former students and collaborators. I continue to collaborate with them. I always was the person who preferred to work in cafes with a latte or a coffee and not be bothered. I can shut out all of the noise around me. If I am in my office, I am liable to have people knocking on the door. I continued to do that, and I must say that I don't frequent my office all that often. When I first retired, I used to go to Caltech functions, but I spend time up here in Lake Oswego, and I move around. As time has gone on, I have been less and less attending these functions.

**ZIERLER:** Absent teaching responsibilities and all of the service or committee work, what is some of the science and the engineering that is most interesting to you these days that you might keep up with just for fun?

**BECK:** The fun side is quantum mechanics. I actually published two papers, if you also count an arXiv.org preprint that I put out last August. When I was an undergraduate in New Zealand, my bachelor's was in math and physics. I always was intrigued by quantum mechanics because I understood the math but the meaning was not clear. I later found out that hardly anyone understands what it's all about. Even Richard Feynman said, "I don't think anybody fully understands quantum mechanics." In the last couple of decades, I would play around with it and I educated myself until I had some really strong ideas. I have written a couple of papers on that. That was sort of like a hobby, because it excited me. Of course, professionally, I was doing a lot of stuff in the mainstream, so this was a side thing. Intellectually, it was very interesting for me.

**ZIERLER:** There are so many titles and affiliations and collaborations. Between your educational trajectory and what you have done over the course of your career, are you fundamentally a civil engineer? Is this the best term to describe what you have done?

**BECK:** I should say that, because this year I have been recognized by ASCE as a distinguished member. I am one of ten out of 150,000 members for 2022. My roots were mathematics, so people think of me as a mathematical engineer, because I got interested in earthquake engineering. That story we'll go into later. I really think that I am a bridge between the two. CMS is primarily mathematical, applied mathematics. I was in the control and dynamical systems group when CMS was formed. I was involved in its foundation. That's how I got there. I was interested in control of systems, particularly what's called system identification. My roots were in mathematics. Then I moved into earthquake engineering, but in later years, I moved more into mathematical data analysis**,** sophisticated data-based modeling. I am a proponent of what's called Bayesian data analysis, a very early proponent in engineering. I view myself as an applied mathematician, but very interested in the applications like earthquake engineering, for example, or structural health monitoring, which is a very important area that I worked in. I am certainly not your typical civil engineer. I have been introduced once with "As you will see from his talk, he is very strong mathematically for a civil engineer."

**ZIERLER:** [laugh]

**BECK:** A guy I know was introducing me.

**ZIERLER:** Have all of your research endeavors had a translational or specific application approach, or sometimes are you after fundamental research, just understanding how things work?

**BECK:** Initially, it was more application driven. As time moved on, after a couple of decades, I moved more into fundamental science. I started with "What is probability? What does it really mean?" Then when I got into this Bayesian stuff, it turns out it is computationally difficult to implement, so I got into algorithms to improve it. Now, Bayesian analysis is all over the place. Everyone is doing it. But there was no one in engineering doing it—practically no one I know about—when I started in the late 1980s.

**ZIERLER:** Jim, you may have heard that Friday there is a memorial event in honor of Bob Grubbs who we recently lost. I have been going through some of his papers. He mentioned that one of the wonderful things about Caltech, as you've said, is that you can go into new directions as a professor. I wonder if being at Caltech encouraged you in some ways to do that.

**BECK:** Oh definitely. That's my natural bent. I love to get into something new, understand it, and push it. Of course, if I had been at other institutions, I would have been more confined. Caltech was just open. Just look at me; I'm in Mechanical, I'm in Civil, I'm in Computing and Mathematical Sciences. That doesn't happen at many institutions, or many universities, I should say. It has given me the freedom to do what I like. That's the nice thing about being a professor in general; you can explore your ideas as long as you can get students interested in it, graduate students, as long as you can raise some money. That's what I have done. You will see the arc of my research over the years, it has moved from more looking at novel seismic designs in earthquake engineering, over to, towards the end, very much algorithm generation. The buzzwords now are like machine learning and so on, I wouldn't say I am an expert in that, but the basic tools are the same in some ways.

**ZIERLER:** What have been some of the key advances in computational power that might have fostered your interest to do more modeling-type work?

**BECK:** Just the continual increase in speed is one aspect of it. The other is, starting back in the early 1990s, this MATLAB software started to come out. It was started by a professor at Stanford. It is an extremely powerful, high-level language. Most of my own research when I was younger was done with Fortran, which is a compiled language and not very efficient to program. When I was doing research, you punched your lines of Fortran code on cards, and they went over to the computing center at Caltech. The development of software, particularly MATLAB, and of course the fact that everybody got computers in their offices, students and all, made an enormous difference to the computational power, which we really needed, especially for this Bayesian stuff.

Both the increase in speed and the software that allows you to quickly examine results and quickly develop software**,** is amazing.

**ZIERLER:** Some nomenclature questions, some terms that I know will come up repeatedly—I would like to get both your definition and also your understanding of how you apply these in your research. Let's start first with stochastic dynamics. What is that?

**BECK:** It is another way of saying probabilistic dynamics. Probabilistic is a bit of a mouthful. It means that you are modeling uncertainty—and I'll describe the source of that— uncertainty in dynamic systems using probability. You might think, "Doesn't everybody?" but no, there are other uncertainty mathematics. Especially you may have heard of "fuzzy sets." That was strong at one stage, but it is fading out now that people realize Bayesian probability can do a lot more than that. Stochastic is synonymous with, for me, probabilistic. Some people believe it is a property. They will say "That phenomenon is stochastic." To me that is not the correct way of speaking. It is "We are uncertain about this phenomenon, so we are going to model it with probability," so it is in that sense stochastic.

Now, where is this uncertainty? This is one of the important parts of what I did. Way back, George Housner and Paul Jennings were modeling the uncertainty in the ground motion from earthquakes, because we do not know what the next earthquake shaking is going to look like. That was around, and in the early days it was called random vibrations, vibrations of the structure under some sort of random excitation. Now, it's all part of stochastic dynamics. I meddled a bit in that. You could have the more traditional understanding of probability to handle that. But then, in my thesis, I kind of got stuck because I was buildings models of real structures with data from the structures. There are lots of uncertainties associated with this. How good is the model? How good is the predictions? I ended up pondering that for quite a while and finally got into this Bayesian stuff. Now, stochastic dynamics includes both the input or excitation uncertainty and the modeling uncertainty. The modeling uncertainty, only in about the last twenty years has that been addressed. It's a major uncertainty and very difficult to deal with. You cannot do it with a traditional so-called frequentist approach to probability. You need a Bayesian approach to do it. You need to understand probability differently. The axioms are the same, but you need to understand what it means differently.

**ZIERLER:** Jim, we see in your research Bayesian and then the next word which modifies it—Bayesian probability, Bayesian states, Bayesian learning—the list goes on. First, what is the catch-all for Bayesian from which all of the sub-models or sub-disciplines flow? What is that umbrella term?

**BECK:** Bayesian comes from the Reverend Thomas Bayes, who wrote a paper, wasn't sure about it, left it on his desk and died. His friend came in, saw it, submitted it to the Royal Society and it was published in 1763. The key thing is that the probability axioms are used in a way to do a sort of inverse. That is, if you are given data, what can you learn about a model; and not, if you have a model, what can you predict with uncertainty. It's called Bayes' Theorem, but that's probably not really fair. He had a very special case in his paper. The guy that really broadened it was Laplace, a famous French mathematician, who came up independently with so-called Bayes' Theorem about ten years later in France.

Bayesian probability is using probability in a way that is completely different for how it was understood for a hundred years or so. But the original idea, the way I look at it now, is that it's really a logic. Probability is really a logic for quantitative plausible reasoning. If we are on computers, then we have to do it quantitatively, numerically, and probability is just ideal for that. When you say Bayesian, people immediately know, Oh, you're not using what used to be the standard interpretation. You've got this kind of new—not really new; it's several 100 years old—but it's using probability quite differently.

There used to be a lot of kickback to my work. People get passionate—and I am passionate about being Bayesian—by what probability means. Once you have latched onto it, it is hard to let go. I was pleased to see over the years that some of my colleagues who were against it, but who worked in dynamics, gradually came around. One of them, who was really strong against it at the beginning, even sent one of his PhD students, a woman—he was an Austrian professor—to come and work with me on the topic. I thought, "Okay, this guy is converted."

**ZIERLER:** Jim, what are the kinds of problems for which a Bayesian approach makes a lot of sense? What are some problems that it is not particularly relevant?

**BECK:** The way I look at it, if you want to use probability, if you want to quantify uncertainty, use a Bayesian approach. A lot of people think, "Oh, but with the frequentist approach, you could do the so-called forward problem, which is like the random vibrations problem I talked about, predicting what is going to happen. But they see the value of the inverse problem. That is, given some data from a system, what's the model that is appropriate; rather than, given the model of a system, what's going to be the output, what's going to be the response? I have published papers on this where we show that it is just a very general way of handling any uncertainty and it doesn't need to be limited only to so-called inverse problems, which are worked on by many people because they are fundamental in science and engineering. Inverse problems: trying to learn something from data that you have got.

**ZIERLER:** Jim, what would be a case where you use Monte Carlo simulations?

**BECK:** Whenever you have probability and you are trying to predict, say, the response of a system, in theory you can write down mathematical equations, usually involving integrals, that predict the result. But you look at these integrals and you don't know what they are telling you. They are not simple functions or anything. They are just a mathematical operation. Monte Carlo simulation is a way to show what it's telling you by samples. You're going to end up with a probability distribution on, say, the response of one floor of a structure or something. By Monte Carlo simulation, you run the forward problem many times, and you get samples. For the more probable response, you will get more samples of that type, so you build up a picture.

The key word is actually simulation. You simulate the system with a model. The Monte Carlo part is that you randomly select something from your input distributions, your uncertain ground motion from an earthquake, and you take a sample of that, and you run it through the system. Each sample is so-called deterministic. It's just a calculation on a computer. But as you sample randomly—and there's a whole other theory there—you pull up different inputs. You run it through your system, you get different outputs, you build up a picture of what's going on. You can do some sort of analysis on that, like what's the mean, what's the standard deviation, things like that. Monte Carlo simulation is a sampling technique to get at the basic results that you have anyway, but you don't understand what they are telling you.

**ZIERLER:** Jim, do you see computational structural dynamics as a subset of structural dynamics, or is it its own discipline?

**BECK:** It's a subset, but it has almost subsumed the superset, because nowadays, even in structural design offices, a consultant structural engineer will run software, so-called finite element programs, to simulate how the proposed design is going to behave under some earthquake ground motions. The code will tell him to take so many—it doesn't tell him which ones—but to take so many samples of input and so on. For very simple buildings, they can do calculations almost on the back of an envelope. But any structure that has some height to it or has something different about it, they do a dynamic analysis, a computational analysis.

**ZIERLER:** Your work on system identification, what are the systems that are being identified?

**BECK:** It's very general, in that what I always say is that I am looking at dynamic systems. Dynamic systems just means that time plays a significant role. I come out, of course, of structural dynamics, how earthquakes affect structures, but once you start writing down what's the fundamental framework, what's the fundamental equations, you see that just about everything falls in there. You can look at biological systems changing in time, and there's a whole chemical kinetics theory too. Lots of different areas. My home base, to keep me anchored somewhere in reality, is structural response, and mainly due to earthquakes. I also did some wind excitation, but mainly earthquakes, because New Zealand is earthquake country, and California is earthquake country. At Caltech, I was in the earthquake engineering group. That was my primary home.

**ZIERLER:** Jim, your expertise in Bayesian probability, do you see this approach as getting us closer to earthquake prediction? Is that relevant at all?

**BECK:** It is. In fact, you mentioned you talked to my colleague Tom Heaton. Tom came over on that, too, about essentially looking at it with the Bayesian approach. Because for earthquake prediction, you need data, something that's going to cause triggering, some indicator of something. You also need a lot of prior information. That's another thing about the Bayesian approach that I should add. It naturally combines your understanding from prior information—it has to be quantified in some way—with your models that you use to predict outcomes, your dynamic models. It's a probabilistic combination. It just comes out of the probability axioms. Tom got convinced about that. I should say that Tom had quite an influence on me at different times. I sort of dilly-dallied in looking at various what might almost be called seismological things.

In the last decade before I retired, I got involved in Tom's big project on earthquake early warning systems. Again, lots of uncertainty, right? You make a prediction that the earthquake is going to come and it's going to be so strong, and it's on its way. It's full of uncertainty. We worked on that. I had a student that also was interested in the engineering applications of earthquake early warning. Not just that we duck under a desk or something, but what can you do? Shut down a nuclear power plant? Maybe. Withdraw surgery equipment, if they are using automated stuff on a patients, or that sort of thing. How do you do a cost/benefit analysis of that? How do you predict what is going to happen? But pure earthquake prediction? I am not a believer that we will probably ever be able to do that. Probably Tom would agree. There was a lot of excitement way back in the 1980s, but that seems to have dissipated.

**ZIERLER:** It's almost a philosophical question, but the belief in earthquake prediction rests on the need to understand or believe that the Earth *itself* knows when an earthquake is going to happen. I wonder if there is a Bayesian approach that might shed light on if that's even possible, that the Earth knows, let alone if we can know?

**BECK:** I don't know. It's an interesting question. The word I was struggling for before was actually "precursors," is what they talk about. Is the Earth telling us with some precursors it's feeling something, there's something there, so we can pick up on it? Does it know? Maybe we don't know, we don't see it, but there is something going on there, because it is deep down. Who knows? They instrumented faults that were very active and they found that earthquakes suddenly occurred with nothing on their instruments. Of course, they are all on the surface, not down deep where the earthquakes start. It is a really very interesting question of why earthquakes start when they do, and some spread a long way, and some don't. People looking at the fundamental aspects of that are people like Nadia Lapusta over in Mechanical Engineering, because she is modeling their intricacies, friction laws for the slip on the faults and all that, trying to figure this out. People ask me a lot about earthquake prediction, just because it would be reassuring if you could predict earthquakes. I say I think it is doubtful, but early warning is for sure, it's here, and I tell them about that. You get a few minutes, maybe, or only a few seconds of warning.

**ZIERLER:** Do you see your approach as contributing specifically to making earthquake early warning better?

**BECK:** Oh, definitely, I have. One of my papers from five years ago, or a little bit longer, was with a former PhD student from Caltech who was in seismology, works at USGS, We said, "Okay, you've got all these different algorithms now, competing kinds of algorithms for early warning. Can we collect them, harness them, and integrate them to get an overall prediction? How do you do that?" Because they're all really probabilistic. We worked on that. We have a paper on that. I felt that was a very nice contribution. One of my students was involved too: the early warning guy. I've contributed there.

We also looked at cost/benefit analyses that can be used to harness what is coming out of all of these early warning systems in a way that would be useful to society, other than just protecting ourselves. We went into decision theory and things like that. That was a whole new area that was quite interesting. I don't think that has made much impact, at least not yet. I think the integrating of the early-warning algorithms, though, I am hoping—I haven't talked to Tom, but I am hoping that that will actually be implemented in the California system, because they have the Berkeley one, they have the Caltech/USGS algorithm, and there was another one floating around.

**ZIERLER:** Jim, I am curious what sensors or data-capturing sites have been most important over the course of your research career.

**BECK:** Definitely the instruments inside structures to record what happens during an earthquake. That is how I got started. Paul Jennings, my advisor, suggested to me, "Look, we are getting this data now from inside structures during earthquakes. It's telling us something about structural behavior, structural dynamics. How can we go about this in a systematic way to learn about improving our modeling?" For example, I arrived at Caltech in 1974, and in 1971 there was the San Fernando earthquake. Because of a city bylaw, due to Housner's leadership, any new structures beyond a certain height were to be instrumented. They were simple—well, I don't know if they were simple instruments, but they recorded on 35mm film and were triggered when the acceleration, the shaking, got strong enough to—not potentially damaging, but certainly testing the structures a bit.

You've heard of seismometers, or seismographs. We had accelerographs. They were the earthquake engineers' sensors. The seismologists had the seismographs. They could record an earthquake that occurred around the other side of the world. Of course, we weren't interested in that. We wanted to know what's potentially damaging to structures. Those were called accelerographs. That data were being looked at, but not in a systematic way, not by using these system identification frameworks, just by the seat-of-the-pants sort of thing. Engineers looked at the data after 1971, and then in 1974, when I got into my PhD research, I started looking at how to do this more systematically.

**ZIERLER:** Tell me about your work with convection and porous media. First, what kind of media?

**BECK:** Porous media is basically the Earth. As we will talk about later, my arc of research was quite interesting in my early years just because of my mathematical abilities. I worked at a physics and engineering lab. They said, "What are you interested in?" and I worked on different things. The work on convection in a box of porous material is modeling a geothermal area. New Zealand had several geothermal power systems. The idea was to understand them at a fundamental level. When does convection occur in the Earth? If you have a fluid sitting in a box and you heat it from below, whether it's a porous media in there or not, it's going to initially, when the temperature gradient is not that large, it's just going to conduct, just conduct the heat through. But, because there is a fluid in there, at a certain critical temperature difference, it will start convecting. The fluid will start rising up, because it is heated and getting less dense, and then letting the heat go at the surface, and then coming back down. I looked at, if you have a box of earth and you've got water in it, and you are heating it up from below, at what critical temperature difference does it start to convect? If you are heating from the bottom and you're cooling at the top and the walls were insulated. It turns out, mathematically, this is what is called a bifurcation problem, partial differential equations with bifurcation, and there is a critical parameter called the Rayleigh parameter, it's a non-dimensional temperature gradient. You want to know, what's the value that causes the fluid to suddenly become unstable? The conduction solution becomes unstable, and the fluid starts flowing. What does it flow like? I don't know if you can see my hands, but it kind of just does cylindrical rolls like this. It comes up, goes around, then down like this. That's how I got involved in it. It was a nice piece of work, but then I got interested in earthquake engineering and I kind of left that area. That paper is out there and it is fairly well cited, too. I was only I think 23 when I wrote that.

**ZIERLER:** Jim, your work in structural health monitoring, we hear so much about the aging infrastructure in the United States, of roads and bridges. I am curious if some of the methods you've developed have been useful in those budgetary, zero-sum games about what to renovate, what to fix, what to tear down.

**BECK:** Not directly my stuff. It's kind of fundamental and hasn't really got out there or had much impact yet. You have to get the maintenance people interested in it because they are the only ones with a budget to put instruments on the bridges. Maintenance people have procedures in place for many, many years. But more and more there is interest, although I don't think any of our methods have been used to actually detect damage. Then again, it doesn't happen very often that you actually get damage. These systems may be monitoring but maybe nothing is going on for years and years, especially in the earthquake problem. That's the nature of structural health monitoring.

System identification theory is a basis for that. One thing we have done is looked at how natural frequencies of buildings change when they are damaged. We have proved that we can do that, but so far, I don't think on the building side, it has been used to detect damage. In offshore platforms, it has. In fact, I'll soon learn more about that, because there is a Danish project that I am just getting involved with in an advisory committee role, where they are actually looking at offshore platforms and monitoring them to detect if damage occurs. They are particularly worried about large waves, so-called rogue waves coming through and hitting their offshore platforms. There has been loss of life in the North Sea where there have been collapses, and so on. They are trying to use these ideas on the offshore platforms. But I can't really point directly to my own work having a practical impact. It's a challenging inverse problem. It's very difficult. Everybody realizes that. It's one thing to put instruments on and see changes in the dynamic response, but what does that mean? Is it damaged, and if so, where? That's an inverse problem that's very challenging. This is where my contribution is —I said, "You've got to use Bayes' Theorem here." That was way back. That's how we got what we call Bayesian structural health monitoring.

**ZIERLER:** Jim, we talked earlier about your more recent interest in quantum mechanics. I am sure you have been following the quantum science revolution at Caltech and beyond, between your interest in simulation and the offers, the promises, that quantum computers might have, and also the excitement around quantum sensors. We are living, of course, in a classical world. Where do you see these things headed as the technologies become more advanced and applicable?

**BECK:** Quantum computing would mean that a lot of the computations that may take several days even with the fastest computers, the promise is that they would be solved really quickly. Maybe that means you could do very computationally intensive inverse problems very quickly and know, "Oh, the structure is damaged" rather than it taking forever to compute it. But we are nowhere near there and I feel a skepticism about it. It uses quantum superposition. I need to be careful how I speak about it, because I am not an expert in that area. Maybe it will be beyond my lifetime that we will see these huge speed-ups in computational power that they talk about. We've not yet seen that.

**ZIERLER:** When you work in design optimization, what are you looking to optimize?

**BECK:** You can do the whole structure, but we were looking at, suppose you add in some sort of damping devices to dissipate vibrational energy, which got very popular in recent years. You have "artificial" damping—it's not a natural part of the structure—you put these big damping devices in. How do you choose them? Because maybe a bigger damper is better, but it's also more costly**.** The optimization was a cost/benefit analysis over lifecycle costs of the structure. You put dampers in it and it's an upfront cost. What does it gain you? Nothing unless an earthquake comes. Is an earthquake going to come? Well, who knows? It's very probabilistic and you have to be careful how you do the cost/benefit analysis. We look at lifecycle costs. A bridge may have a 50-year lifecycle, so, you look over 50 years and you do this probabilistic analysis, how frequent the earthquakes will be, and how big they will be, and all this sort of stuff. I had a very good Greek student, who is now a professor at Notre Dame, who made some good contributions with me on how to do that sort of optimization.

**ZIERLER:** Some questions as they relate to teaching undergraduates and mentoring graduate students—for the graduate students who've been attracted to work with you, what have been some of the key areas that they have been interested in and what kinds of fields have they gone into?

**BECK:** I think I had 25 or 26 students. In my CV, I list them and their thesis title and the year. It is very interesting to look at the title because it captures the essence of it. You will see initially it is mainly earthquake engineering and then it moves over to Bayesian stuff. The early people went off not necessarily in earthquake engineering. They went off in areas where their structural dynamics understanding was utilized. For example, my second student was a French woman who works at JPL. She looks at the vibrations of big space telescopes induced by thermal effects. They go from hot to cold and back since they move around the Earth so at times they are sheltered from the Sun, and so on. A number of my PhD students went into industries where dynamics of systems was important, but some of the early guys also saw where I was going and even if they didn't do it for their theses, they ended up working, at least the academia ones, in areas like structural health monitoring and Bayesian stuff. Just about all my students in academia, even if they preceded my interest in Bayesian stuff, they are now using it and contributing to the research field. Some are really good. One guy who is a professor in Greece is doing some amazing stuff. He has research collaborations all over the place. He joins forces with many researchers from different European countries.

**ZIERLER:** What about industry? What kinds of industry have your students gone on to? Or have most of them pursued more academic-type careers?

**BECK:** I think roughly about half of them have gone to academia and half to industry. One guy, a very smart guy in the late 1990s, went to a startup company where they were modeling the human body biochemistry to understand reactions to drugs. If you are working on a new drug, you give it to rats or something and they eventually get to people, but the idea was to have a virtual human that you could basically give the drugs to. He worked a number of years in that. I have kind of lost track of him. I don't know what happened to the company. It was very interesting.

Another one went a more traditional route and looked at the structural control of radar systems. Radar antennas, if you re-orient them, they will vibrate and all that, but you want them to quickly come to rest so you don't distort your imaging. He worked on vibration control systems for a company that built big radar antennas. Another guy ended up working for Ford Motor Company. He got interested in wheel traction. He actually works for the funding agency for the Army now. He got interested in military vehicles and traction in mud and all that sort of thing. It's kind of getting right down into some really good geotechnical engineering there.

If they don't go off to academia, some of them have gone off to government labs, like JPL or Sandia National Labs. It's like an academic setting, they are doing fundamental research, but related to nuclear weapons or some other application. One of our guys in earthquake engineering—actually wasn't mine, but I was on his committee—he ended up working at IBM on the dynamics of shocks in their computers. You drop a computer, and it shocks. What about these boards, the semiconductors and everything**?** How can you protect them? He did earthquake engineering for his PhD. He ended up getting interested in business, did a business degree on the side, an MBA. He ended up on Wall Street doing bond derivatives, doing the analysis, the risk for Standard & Poor, one of the big companies that do assessment of financial risk. How do you assess the risk of a bond derivative? They are complicated financial instruments. He ended up with his own company and just before the big collapse in 2008, he saw what was coming and he sold out, and he retired and he was only like in his fifties, and he went back to Chile. Now he is a professor of finance in Chile, even though his PhD is in earthquake engineering. It just shows that, coming out of Caltech, everybody has really strong analytical skills.

**ZIERLER:** To get a sense of the kinds of thesis research you have supervised and your own work, are there any physical laboratory experiments that you have done, or is it all data analysis, computational pen-and-paper kind of research?

**BECK:** Not so much in the lab, though we had a dynamics lab for many years which was a joint thing with several faculty. We did go out in the field and do so-called ambient vibration testing where we record the motions of the structures. Structures are vibrating all of the time, just from wind and microtremors and all that sort of stuff. We would go out and measure them and determine their fundamental frequencies and the so-called damping ratios of their modes of vibration. There is a mode of vibration for each natural frequency. We determined what the mode shapes look like as the structure vibrates, and so on, from ambient vibration. We were interested in when an earthquake comes, how does that change, because it becomes stronger motion and it becomes less linear. It becomes what they call non-linear dynamics. We did do field testing like that.

A very interesting project actually was in 1994, when the Northridge earthquake occurred, and they discovered that steel structures formerly considered the best and safest buildings had a fundamental flaw. The welds at the joints, where a beam comes into a column, the welding turned out to be brittle and was failing prematurely. A steel structure under strong shaking is meant to go so-called 'plastic.' It yields. It absorbs tremendous amount of energy. But because earthquakes are doing this back and forth, not just in one direction, it doesn't just fall over. These welds failed. The question was—it came back to structural health monitoring. These are hidden defects. You have architectural features; you have fire retardant material over them. How do you know? We didn't know until months after the earthquake. None of them collapsed.

I got interested in that and I had the great opportunity of going into an 11-story steel structure in Westwood, a bank, and doing ambient vibrations. I think something like 30% of the connections had failed. They started taking their fire retardant off and looking at them—** "**Oh, it failed." They went to another one, and so on. They started going through and they found 30%. Then they fixed them. They put in a retrofit at these joints, at these welds. They put in more steel and made sure the welding was different, and then we went back. We sort of had it back to front. We had the healthy structure afterwards and the damaged structure before, whereas usually, we are interested in doing it the other way around, finding a previously healthy structure and trying to find if it is damaged. That was not in the lab, but it is experimental testing with real data and with major implications. We also have, still to this day—it's no longer called Millikan Library; I forget what it's called now.

**ZIERLER:** Caltech Hall.

**BECK:** Up on top is a building shaker. It has lead weights in counter-rotating baskets, and we can control the frequency at which they are rotating. You can slowly increase the forcing frequency and you can see the building resonate at its fundamental frequency, and it starts getting a stronger response, enough that if we have a lot of weights in the basket, people get nervous in the building. They can feel it. We used to have an Experimental Methods in Earthquake Engineering class for many years before that died down, that whole area. We used to have to notify the Caltech Library in the building that we were going to do the shaking for that week or whatever. We showed the students that you can really see how these buildings resonate at certain frequencies, and you can compute the damping of the building's modes of vibration and so on from some inverse analysis.

That was kind of a long story. We don't do that much in the way of the lab work, but we did do field work. With the French woman who went up to JPL, I got involved in a nice project up there where they had a big space antenna in the lab. Scaled, but still big. They were looking at what are the modes of vibrations, their natural frequencies, and how it vibrated and all that, and I got involved in that. That was in the lab, but similar to what we do in the field with real structures.

**ZIERLER:** Your work with differential equations and partial differential equations, is that two different methods of looking at the same problem, or are these really separate approaches?

**BECK:** No. Any dynamic system involves things changing in time, so you need differential equations. Differential equations involve derivatives of quantities, time derivatives, say, and possibly spatial derivatives. People talk about ordinary differential equations meaning essentially that it is only changing in time. It can be a vector of quantities that is changing, so you have equations to describe how they change in time. Partial differential equations just normally means you are also looking at spatial variations for structures. You are not only looking at what's happening at a point in a structure with time, predicting what is going to happen, but also how is that going to change across the structure, across a floor or different floors or so on. Partial differential equations occur all over the place. If you look at temperature distributions in a plate or something like that, you have to solve the partial differential equation. People in applied math at Caltech are pretty much always working with partial differential equations, different non-linear challenging ones. Differential equations just means that the model involves a change either in time or space. In ordinary differential equations its usually just in time, but if it is partial differential equations, you have more than one dimension; you have got time and one, two, or three spatial dimensions, for example. That's the difference.

**ZIERLER:** What about Applied Operator Theory? How is that relevant in your work?

**BECK:** It is a bit of a misnomer, but it was to try to say, "We're not a mathematics department; we're not just teaching operator theory, we are applying it." We would show some examples of where it's used in control and so on. Operator Theory is just a higher level. We were talking about partial differential equations, ordinary differential equations. You can view them as being operators on a function space, the function space being functions in time, some quantity changing in time, or in space. The operators, you can select operators that do things. They operate and change this function into another function, mathematically. Differential operators are a very important class of operators, but even integral operators, which are the opposite of differential—differential you have derivatives and gradients; integrals you are averaging, you are summing up, so they are integral operators. Just about anything we did, if you abstract it enough, it's Operator Theory. There are some advantages in showing students that there's this umbrella thing that sits over the top and then you delve down and it has a structure to it and so on. Within the operators you can divide it up, for example, into bounded operators and unbounded operators and normed operators, so there is a whole theory that you can then take down to your specific applications.

**ZIERLER:** One Bayesian that we haven't talked about yet is Bayesian updating, which you taught. What is that?

**BECK:** That's just another way of saying, different from Bayesian statistics, where they just have empirical models straight out, some regression model or something, we always have, in engineering, prior information. We have like Newton's Second Law, which is a law of mechanics, and so on. We have some models that could predict how the structure is going to behave, but we know they are not very good. We would like to have some data and update these models. The word "updating models" precedes the use of it. I was one of the first people to say, "This is a Bayesian problem. We should do Bayesian inversion." People used to do non-linear least-squares updating and so. The basic idea is that you have a model, typically it comes from a finite element model of a structure, and you get some data from the structure. The model doesn't agree with the data, doesn't predict the correct natural frequencies exhibited in the data, for example. Then you modify the model in some way, so that it is consistent. Of course, that gives a non-unique answer. You could model it in many different ways. I always made the point that there isn't a unique solution. Different solutions have different probabilities based on your prior model and your data. That is what we were doing in Bayesian updating.

**ZIERLER:** I am interested in a larger story among undergraduates at Caltech. You've been around long enough that you knew that physics was the dominant major for undergraduates in the 1960s and 1970s. Today, of course, the tide has shifted towards computer science. I wonder if you have any insight or perspective as to what accounts for this shifted interest and how your own research interests have fared with this transition.

**BECK:** I think that the computer science shift comes because the excitement of technology, iPhones, starting with—I saw it coming, starting, when microcomputers came in the early 1980s. We shifted from these giant computers and people started to have them at home and this sort of thing. It also comes about because of the huge increase of sensor data. Everything now has got sensors on it almost. Your car has a thousand sensors or something ridiculous. You are getting this enormous amount of data; how do you take advantage of it? This is the inverse problem. People talk about machine learning and so on. Computer science at Caltech, I think it's fair to say it's mainly algorithmic. It's not computer engineering. They are not looking at how a computer operates and improving that. They are basically looking at what are the algorithms that we can use to improve our ability to drive cars autonomously, or whatever machine learning stuff.

I just think that the technology excitement is there, whereas in physics, it is old-school. Yes, there is some interesting stuff going on in physics with gravitational waves, for example, in the last few decades, the detection of that, or quantum optics, or quantum computing, or these sorts of things. We have groups in Computer Science that are interested in quantum computing. I just think that young people see around them all of this new technology and it's just a more exciting area than physics in general. But physics is an underpinning of many of the things, right? We talk about bringing physics models together with data. I am really combining these two areas. The physics models, you need to have understanding of the physics. You come up with some sort of model that is generally not going to be perfect. Then you are collecting all of this data and it is telling you something about the system. How can we incorporate these in a systematic way? This is the updating or learning. It is the same thing. Machine learning and Bayesian updating are very similar.

**ZIERLER:** Jim, have you had opportunity to interact much with undergraduates over the course of your career?

**BECK:** Initially I taught undergraduates, but because I was one of the few engineers that was good at the mathematics, I ended up teaching engineering mathematics for many, many years. I did have some applied math undergraduates in the class. They were always a minority among my graduate students. This was graduate engineering mathematics, I should say, that I was teaching. I didn't have a lot of contact in later years, but in the earlier years, I was teaching them in dynamics and statics and so-called strength of materials. That was in the 1980s. I was on UASH, which is Undergraduate Academic Standards and Honors, which is a kind of grueling committee because you were the ones that decide if a student should continue or not, or that they could be rehabilitated and come back, if they start failing. I got involved with students in that way, and then I got on the curriculum committee, which decides the undergraduate curriculum. I ended up being chair of that for several years. Then, after I got off of that, I got back on UASH. I was also an advisor to undergraduates in mechanical engineering for many years. So, for probably 20 or 25 years, I did have interactions with undergraduates, but not so much in teaching, except for this handful that would be in my graduate class.

**ZIERLER:** Some questions as they relate to service work and also your engagement in professional societies; what are the professional societies that have been most important in your career?

**BECK:** Early on it was earthquake engineering societies. In fact, if you looked at my early CVs you would see affiliations at like—oh, like Seismological Society of America, the Earthquake Engineering Research Institute. That's a misnomer, by the way; it's a national society for earthquake professionals, originally more engineers. Those organizations were important in the early years. As soon as I got on the faculty, I joined the American Society of Civil Engineers, but these other more specific earthquake engineering societies were more important to me back then. But then, it turns out there is a very nice group within the American Society of Civil Engineers that is essentially all academics, that used to be called the Engineering Mechanics Division. I ended up chair of the Dynamics Committee. There was also a Probabilistic Methods Committee. There is a Fluid Mechanics Committee. The sort of fundamental mechanics that are used in engineering was our area of interest. I happened to be on the Executive Committee for the so-called Engineering Mechanics Division when we proposed that we become a semi-autonomous institute. We made the case, and the ASCE Board approved the creation of the Engineering Mechanics Institute. I was on the founding governing board and I later became vice president before I stepped down.

This group was my peers, basically, these people in engineering mechanics. The membership is somewhere between two and three thousand, whereas in structural engineering it is between twenty and thirty thousand or maybe even more. It is a small group, but really dedicated because this is a research-oriented group. This is your peers. These are the guys who review your papers and that sort of thing. That was my home, and I spent a lot of years doing different service in that. I think that is partly reflected in my distinguished membership of ASCE, the amount of service I did there, but also my contributions in structural health monitoring and some other areas of civil engineering.

I also got involved in international associations that were natural homes to me. One was the International Association of Structural Safety and Reliability. Every four years they organized an international conference on this topic—structural safety and reliability. They honored me with an award in 2005. I was involved in that for many, many years. Also, the International Association of Structural Control and Monitoring, which is structural health monitoring, I was involved in that and was on the Board of that. In more recent years, the last 10 or 15 years, those were the predominant ones that I was giving my time to. I had done my service in engineering mechanics. I had still felt that that was my home, but I wasn't being active on committees in engineering mechanics of ASCE. It was more these international groups.

**ZIERLER:** On the publication side, over the course of your career, what are some of the most prestigious journals to publish in?

**BECK:** Early days there was only a few, then it proliferated. The *Journal of Engineering Mechanics* of ASCE was prestigious and used to be the first choice for many people. Over the years, other niche ones came in and took stuff away. *Probabilistic Engineering Mechanics* is also another, not related at all, not part of ASCE. My former officemate at Caltech is the editor. It is a very good journal and I have published quite a bit in that. There is another journal that is one of the leading journals in earthquake engineering called *Earthquake Engineering and Structural Dynamics*, run for many, many years by a professor at Berkeley in structural engineering. He is long retired, but still runs the journal. It is still affiliated with the International Association of Earthquake Engineering, I guess. *Probabilistic Engineering Mechanics* just stands on its own in that it is a private journal published by Elsevier. The one affiliated with IAEE is published by Wiley. Those are the big ones—*Probabilistic Engineering Mechanics*, *Journal of Engineering Mechanics*, and *Earthquake Engineering and Structural Dynamics*.

More recently, MSSP in the last couple of decades has come to the fore. It is *Mechanical Systems and Signal Processing*. You can see that that is kind of a natural home for me, too. Then there is the journal that is associated with the International Association of Structural Control and Monitoring called *The Journal of Structural Control and Health Monitoring*. I have published there. That is a nice journal, too, run by an Italian woman professor in civil engineering.

**ZIERLER:** For the last part of our talk today, I want to cover some of the ways that you have been honored by your colleagues in your more recent career. I would like to start first—I assume it was on the occasion of your retirement in 2017, the symposium held in your honor. Let's start first with the title: *Making Rational Decisions Under Uncertainty and Model Complexity*. I wonder if you could translate that for me and what some of the themes might be that are buried in that title.

**BECK:** This whole Bayesian thing, the uncertainty, modeling that. Ultimately in engineering you have to make decisions. Design is a decision. How do you make these decisions in a rigorous, quantitative way, treating all of the uncertainties? There's optimal design, Bayesian optimal design, all that, Bayesian system identification. All of these things wrap into that title. The complex systems is just to say these are not simple mathematical equations; these are models of structures, and they have what's called many degrees of freedom. Nowadays you might create a model of a structure that has 50,000 or 100,000 degrees of freedom, meaning all of these parts that can move, producing strains and stresses, and so on. That's your model complexity part.

Making decisions under uncertainty basically is a key thing that I was doing. I concentrated on parts of that, but even the whole umbrella thing with the probabilistic cost/benefit analysis is that you don't know what the benefits are going to be in the future. You know the costs up front quite well but you don't know exactly what the benefits are, so it is a tricky business. We spent a lot of time trying to figure all of that out. Of course, I don't say that we did all this just in my group. This is a general thing that comes out of operations research. But we were incorporating these sorts of theories into structural engineering, into earthquake engineering.

**ZIERLER:** The speakers' list, in what way did that represent all of your accomplishments both as a mentor and as a collaborator with your peers?

**BECK:** There was an organizing committee, and they came up with people who were some former students and my peers that were known to be currently doing topics that they could talk about that were relevant to the symposium. Of course, the committee ran them by me to see that I agreed. Everybody there is working in one of my areas that I had worked in. Some were colleagues and others were former students who are now professors.

**ZIERLER:** What were some of the intellectual through lines in the talks that put together an amalgam of your research over the years?

**BECK:** I think pretty much the underlying thing is probability; uncertainty, if you like, and quantifying it through probability. I can't remember all of the topics at the moment—they are listed on my webpage—but I think you will find that the common thread is dealing with uncertainty and doing it with probability. Various aspects, either the forward problem, where you are predicting what is going to happen, or the inverse problem, where you have some data, and you want to learn about the models that you use for prediction.

I think one of my students said something like, "Jim is the father of Bayesian probability in structural engineering, and he is passionate about it." Everyone laughed. Because I was always a proponent and talking with people and saying, "You should do it like this and this." I tried to be gentle, but I was convinced that I had the right answer.

I think the underlying thing is some probability. It's dynamic systems, typically structures. I am not sure if everyone was talking about structures and dealing with uncertainties and making predictions with them.

**ZIERLER:** The Hojjat Adeli Award in 2010—who was Hojjat Adeli?

**BECK:** He is still around. He is a professor, almost the same age as me, so he is Emeritus. He started a journal called *Computer Aided Civil and Infrastructure Engineering* that is very good in some respects because he has a broad mind. He's not going to try and put you in a box. If you are doing something that is a little way out in civil engineering but it's still rigorous, that journal would look at it and get it reviewed and so on. He is a bit of a promoter. Who is behind it? I think Wiley publishes it. He started the journal but has Wiley as a publisher. Wiley comes out with this Adeli Award, which I suspect is funded by Adeli. He puts money in for this award. But it doesn't matter. It is a prestigious award. It is associated with that journal. The journal has the highest impact factor of any civil engineering journal. It's quite prestigious. It had just started. I can't remember if I was the first or not. I had a very good paper with a student who is now a professor in Hong Kong that we put in there, and they chose it to get the award that year. I am actually on the editorial board of the journal, and he still calls on me, and I usually deflect it, because now that I am retired, I don't want to do too much in the way of reviewing. I do an occasional one there.

I am also organizing with different people, special issues of this journal, particularly on structural health monitoring. We just started another one. We had some email this week. I have got a guy in Italy and a guy at Berkeley and the three of us are guest editors for a special issue on structural health monitoring in this journal. We have done a number of them, and I have had different partners in the past. I am fairly well-connected with that journal, more so I think since that special award. I may have had some involvement before. That was 2010.

**ZIERLER:** In 2013, when you were named a Fellow of the Engineering Mechanics Institute, what was that in recognition of?

**BECK:** My research effort, I think, more than your service, because plenty of people do a lot of service but don't end up a Fellow. It's looking inside and seeing that you make some nice research contribution in engineering mechanics, so it's a recognition of that. That's the Engineering Mechanics Institute, which is a semi-autonomous and under the umbrella of American Society of Civil Engineers. Now that I am a distinguished member of ASCE, that's kind of like higher up and saying, "Hey look, we see all the service you did for us, we see how you are well-recognized by your peers, we think you are a very distinguished member, so we want to give you this award." There were ten of us this year, out of the whole field of civil engineering. I didn't look to see if there are any others in structural engineering. There might have been.

**ZIERLER:** We talked about Housner all the way at the beginning of our conversation. Tell me what it was like to be named in his honor for structural control and monitoring.

**BECK:** That's like me getting the professorship in his name. It's a real honor because I knew George well, had enormous respect for him. We used to chat quite often about things. I had an office next door to him. He retired just before I joined the faculty, but he would still come for 20-some years into his office. He is well-recognized throughout the earthquake engineering and structural dynamics community. If you get that award, people know that is a prestigious award. To me, it was personal, too, because I knew George and really enjoyed him. He was a real gentleman. A good sense of humor.

**ZIERLER:** What were his skills? What made him so successful?

**BECK:** He had great engineering intuition. Amazing. He wasn't that great with mathematical skills or anything, but—he also was very smart on how to get people—he was definitely not an operator by the way, he wasn't pushing himself, but he would get people behind him. The International Association of Earthquake Engineering is basically founded by him and a few other guys. The International Association of Structural Control and Monitoring, it was him and a couple of other guys that got it going. Actually, it was primarily him. He went to a Japanese professor who was very eminent in that area, structural control and monitoring, and they got together and decided to have the first international workshop on the topic in Hawaii. Then they had the first world conference in Pasadena in 1994. He had these skills in just getting people to get together.

I remember him saying with the structural control and monitoring, because in 1994 he was 84 years old; most people are retired—he said, "I think this is a promising area for young people in academia, this whole area of structural control and monitoring in civil engineering. It is a good area. We need some home for them. We need some infrastructure for them" so he proposed starting this international association. It had already been formed as a national committee, because of him by the way and a professor at USC. He had those organizing skills.

I want to get back to his engineering intuition. There's a really interesting little booklet that my colleague John Hall put together based on George's notes from the Second World War. He was involved in the—was it the OAS?—it was for the Air Force. He was looking at how to improve bombing skills, accuracy and things like this. He was like a consultant to the Air Force during the Second World War. He was just smart advisor. One of the articles I remember is about bombing bridges. It seems sensible that they would go parallel to the road or railway line and go down the bridge and drop the bombs. Of course, if they are off a bit, all of the bombs missed it because they were flying parallel to the thing. George said, "No, fly perpendicular to it," and then they thought, "That's dumb because most of the bombs will miss it." No, but if you fly perpendicular to it and you release a lot of bombs, you are more likely to hit the bridge. That was a simple thing.

He did something very interesting. I will just tell you quickly. The Germans took over the Romanian oil fields. They put up these large balloons tethered by steel cables so that planes couldn't come down low and bomb the infrastructure for the oil fields. George did some calculations and said, "Don't worry, the plane's wings will just slice through the steel cables". Well, that's not obvious. Pilots would be really concerned with that. George had these calculations. He made a few assumptions, and he had this theory and these equations, and he calculated the stresses and it would just yield it, and it would go plastic, and it would slice through without damaging the wings. My colleague John Hall thought, "Where did George get those assumptions from? Just intuition, so how good were they?" He then went and did a detailed finite element model analysis, as we would do nowadays, and found that George was right. He did all this refined analysis on the computer, and he got the same results that George got. So, yeah, he just had an amazing intuition.

He did some great things on rocking of structures during earthquakes after going to Chile in 1960. He made a model of how to predict whether it is going to fall over or not, if it's not tied down. That was just some simple ideas, simple physics, and sure enough, people have done more sophisticated rocking analysis with full dynamics and all that, and George seems to be right. It's just intuition. He was just born with it, I guess. He was a really smart guy. Maybe if he was born a few generations later he would have ended up going into law or something. He was born in 1910. He was raised on a farm. His father died when he was one year old. Maybe being around all of the farm equipment and everything, he got interested in engineering. He went to the University of Michigan. Great intuition. Just a remarkable character and a remarkable person.

**ZIERLER:** Last question for today. We already talked about the fact that you are a brand new Distinguished Member, Class of 2022 for ASCE. Masanobu Shinozuka Medal. Who was Shinozuka and what were you being recognized for with this honor?

**BECK:** That's recognizing my probabilistic background. Shinozuka was a very distinguished professor that had been at various universities. When he died, he was in his eighties, and he was Emeritus at Columbia University in New York. His whole area was probabilistic stuff. Not Bayesian; he was not an advocate of Bayesian stuff. He very early on did modeling of earthquake ground motions, spatial distributions, so-called stochastic fields. He had an enormous number of papers related to probabilistic aspects of engineering. When he passed away, some of his former students and colleagues thought that they should recognize him, and they proposed to ASCE a medal. ASCE says, "Have you got the money?" They don't endow these medals. You have to raise the money. They did, and I was a very early recipient. I don't think I was the first. He died relatively recently, and the medal was created relatively recently. Maybe 2017 or something, it was created. That recognizes the stochastic dynamics. That was his area.

As a matter of fact, that *Probabilistic Engineering Mechanics* Journal, there were co-editors, my officemate at Caltech, Pol Spanos, Greek guy, and Shinozuka. Shinozuka was the senior guy. Spanos did a really clever thing; he was buddy with a senior guy, and they created this journal, and the journal took off. They used to call him Shino. Everybody knew about Shino. He came to the U.S. from Japan to do his PhD and never went back.

**ZIERLER:** Jim, this has been a great discussion. In our next one I look forward to going all the way back to New Zealand, learning about your family. We'll get the story going right back up to the present.

[End of Recording]

**ZIERLER:** This is David Zierler, Director of the Caltech Heritage Project. It is Thursday, May 26th, 2022. I'm delighted to be back with Professor James L. Beck. Jim, it's great to be with you again. Thanks for joining me.

**BECK:** It's a pleasure to be back.

**ZIERLER:** Today what we're going to do, after our initial where we took a terrific tour of all of your contributions, your approach to the research—today I'd like to go all the way back to New Zealand, learn about your family background. Let's start first with your parents, but perhaps even before them, how many generations back does your family go in New Zealand?

**BECK:** On my mother's side, my great great grandfather came from England. On my father's side, my paternal grandfather was adopted, and we've not been able to go beyond that. This was 1880 or something. He came from a Scottish area in New Zealand, an area settled by the Scots down in the South Island, so very likely had Scottish blood.

**ZIERLER:** Tell me about your parents. Where did they grow up?

**BECK:** Both of them grew up in Taumarunui, which is where I was born. My dad was born in 1919, so he grew up during the Depression, basically. He was in a poor family, so he had to leave school at 12 to go working, so he never went to high school. My mother was born ten years later, 1929. Her father was a farmhand out in the boonies. It was just a very small farming community. There was a two-classroom elementary school. She stayed there until she was 14, did an extra year with a teacher, but never went to high school. Neither of my parents went to high school. They did very well in life, they were smart, but they just never had a formal education.

**ZIERLER:** What were your parents' professions?

**BECK:** My mother was a housewife. She did, when I was young, work on Friday evenings, which was a big thing in New Zealand, because all the stores used to close during the weekend, and on Friday, they were open until 9:00 p.m. I guess she used to work all day Friday, or maybe she went midday, but she wouldn't come home until after 9:00 p.m. My dad, when he left school, he started as a painter, but he was allergic to something in the paints, so in the end he switched over to become a butcher apprentice. Ultimately, he ended up managing the butcher shop in Taumarunui. I also should add that he went away as a young man to the Second World War. In December 1940, he went to North Africa and then to Greece. When Greece capitulated in April of 1941, my dad was captured, and he spent the rest of the war as a prisoner of war in Austria.

**ZIERLER:** Wow. Did he ever talk about his experiences? Did you ever get to hear stories?

**BECK:** It's interesting—and I think this is a common theme—he did not to me, but occasionally we would have a party at our place, and I would hear him discussing some things from the War, and I was hanging around listening. When my two boys got older, teenagers, they got very curious and they asked him, and he kind of opened up, so I heard some more about it. I heard some of his experiences. He lost four years of the prime time of his life, right? I think he was 21? Oh, actually, that's right—on his way to the War, the boat pulled into Sydney, and he had his birthday there, at 21. My mother grew up during the war years, of course, and out in the country, kind of isolated. They both—well, I wouldn't say they had to struggle. I don't know what to say about that. My dad came back from the War and was working in the butcher shop. He used to deliver meat on a bicycle with a basket on the front, sometimes. He was mostly working in the shop. He delivered meat to my grandparents, and there was this attractive young girl who at that stage was only 16. He had his eye on her, and when she turned 18, her father gave him permission to marry her, and then they did. I was born 14 months after they got married, so my mother was only 19.

**ZIERLER:** Did you grow up where your parents were?

**BECK:** Yes, until I was 15. In May of 1964, my parents moved to Auckland, basically to allow me to get a better education. There was nothing wrong with Taumarunui High School, but there were schools in Auckland that were more highly ranked and challenging, they felt, for me.

**ZIERLER:** How far away is Auckland?

**BECK:** It's 188 miles from Taumarunui. Yes, Taumarunui is a very isolated town. At the time I was growing up, it was a population of 6,000. It's in the middle of rugged country. The highways in and out, you have to wind around and so on. We moved to Auckland when I was 15 and a few months. I really thrived at the school I went to. It was called Mount Albert Grammar School. I was able to pick up the subjects pretty much that I was learning at Taumarunui High School. I had English and French, but mostly science—chemistry, physics. I dropped biology, to my pleasure [laughs] at that time. It wasn't very interesting. I had biology back at Taumarunui High School.

The interesting thing was that I had a class called Electricity and Magnetism, which you think, "Well, that's part of physics." But there was a national exam called the National School Certificate which had that as a subject. I loved it. I took this class. The academic year starts in February there and finishes December. I was up there in May, I think, so I was like three months into the term. I had to catch up. I had the textbook and everything. I loved that subject and got 96% in the National School Certificate exam in that subject. Before I give it back to you, I note that I just got contacted from a classmate—he is putting a group together from our class, about ten so far—because they're having their 100th year celebration, the Grammar school, and it's going to be in September. He's reaching out and finding people on the internet and so on. It was kind of appropriate, because it's happening right now while we're doing these interviews. I might go back for this centenary. We'll see what happens. I did very well at that school, so I owe it a lot. I might go back just to see these guys.

**ZIERLER:** When the family moved to Auckland, did you move to the suburbs, or were you in the city proper?

**BECK:** No, in the suburbs. What happened is my dad's war buddy that came from the same area in New Zealand and was with him when he was captured and in the prisoner of war camp, he had a butcher shop in a suburb of Auckland called New Lynn, and he had to get out of it. My dad swapped our house in Taumarunui for his butcher shop, basically. The reason this buddy of dad's had to leave Auckland was that his family owned a farm, and it was run by his two brothers, and his two brothers had a car accident and got killed, so he was the only one left to run the show, so he had go to back. That's how my father ended up with a butcher shop in Auckland.

**ZIERLER:** Moving to Auckland, either in your neighborhood or in the school, was there any diversity? Were there any people with heritage from Africa, from Asia, indigenous people? Did you see anybody who didn't look like you?

**BECK:** Yes, there were a sprinkling of Asians in the class. By the way, I should say it was only males. It has since gone coed. For the first 75 years or so, it was just males. I don't think that we had any Māori's in the class. It was different in Taumarunui—I should add that in Taumarunui, the European settlers only got there in the early 20th century. It is in what's called the King Country Province. There was a Māori king there early last century, so it was a Māori area. We did have at Taumarunui High School, a number of Māoris, but not at Mount Albert Grammar. My class, they streamed you and I was in the top academic class, focused on going to university. In fact, the school focused on making a good reputation by cultivating us to take a national university scholarship exam and hopefully to do very well so that the school got high rankings, which I did. There were certainly Māori boys on campus that I'd see. In fact, I had a couple in the rugby team. I played rugby, not for the school top team, but for a lower-down team. There were Māori boys there. I don't think there was any Asians playing rugby with me.

**ZIERLER:** Growing up, did you always gravitate towards science? Were you interested in nature and exploring and taking things apart?

**BECK:** Yes, my whole life was, "What's behind it?" I wanted to penetrate down, either when I was young by pulling everything apart, or later, getting into what's the theoretical basis, like we've talked about the probability. Math was the dominant thing, but certainly science, physics, and to some extent chemistry. I remember that my parents got me—and I think it came weekly; it came out of Great Britain—*Understanding Science*. It was this very colorful magazine illustrating different topics in science and engineering, for example how an internal combustion engine works or how a radio works, or about galaxies, and all this sort of stuff. I used to read those with interest. It went for a couple of years. I actually still have them; they're stored somewhere. I've got probably 100 of them or something. Science has moved on—that was many years ago—but still, a lot of the stuff is so basic, I think it would still be of interest to young people.

**ZIERLER:** What about the Space Race? Being so isolated in New Zealand, were you following that, the Soviet-American rivalry?

**BECK:** Oh, yes. When Sputnik went up in 1957, I was fascinated by it. I remember laying out on the lawn at my grandmother's place—she had a house up on a hill—tracking at night, watching the satellite go over. I don't know if that was the Sputnik, now. I can't remember if the trajectory covered New Zealand. Maybe the U.S. put up one that had a trajectory that went over New Zealand. Yes, I was of course interested in the Space Race. I was 20 years old when they put the man on the Moon, which was a great event. Didn't have television myself, but I watched it on somebody else's television.

**ZIERLER:** When did your family get a television set?

**BECK:** We didn't have it in Taumarunui because it was too isolated. They ultimately put in some repeater station, but after I had gone. We didn't have it when I first moved to Auckland. We rented a place for a year or two, and then my parents bought a house. I think it was at that stage that we got the television. I was probably 17, maybe. Oh, but I should add that my auntie, who lived in Auckland, had a television very early, and I used to go visit and stay at my auntie's. She would quietly let me stay up late so I could see *Bonanza* and these sorts of shows—there was that spooky one, something about the night, and all that. So, I did get to see TV before that, but it was not news or anything I was watching.

**ZIERLER:** Jim, when it was time to start thinking about college, was leaving New Zealand an option? Was that even conceivable at that point?

**BECK:** No, not for a bachelor's, because it would be way too expensive. At that time, New Zealand university educations were almost free. I think we paid $50 a term per subject or something. It was nominal. Of course, $50 was worth a lot more then. But I had never, ever thought of that, and I don't know anybody who went overseas for an undergraduate degree. It was quite common at the graduate level. The University of Auckland is the biggest and generally speaking the most highly ranked, although some other universities in other different subject areas are more highly ranked. Obviously, that was the best one to go to, because it was right in the same city. I bought myself a car for my first year of university, an old car. I lived at home, gave my parents some nominal rent to help them out. I was getting scholarships. I won scholarships, so I was getting some income.

**ZIERLER:** University in New Zealand, is it modeled after the British system where you declare a major right away?

**BECK:** Yes, definitely, and you don't have to do humanities and social science like at Caltech, which was [laughs] good for me, because I thrived more on the technical subjects. I went straight into a bachelor of science in mathematics and physics. I took physics for the first couple years, but really my major was viewed as mathematics. Although you didn't really declare the major; you declared you were doing a bachelor of science, and then you took what you wanted to do.

**ZIERLER:** Did you ever think about theory? Did you ever pursue that path at all, or was it always more on the experimentation side?

**BECK:** Oh, no, definitely theory. No, I was a mathematician. We had experimental classes, labs, things like that, in physics. Nothing in mathematics. No, I was basically a theoretician. I guess I had an aptitude for math and I loved it.

**ZIERLER:** Was it a dual major, then? Did you have both a math and a physics degree?

**BECK:** You could say that, yes. It just says a bachelor of science; it doesn't say bachelor of science in math. I think in my CV, I put math because I thought, well, I only took a couple of—maybe I took three classes—Physics 1, 2, 3—which is like first, second, third year, but that was it. But you could view it as like a double major.

**ZIERLER:** Being in college in the late 1960s in New Zealand, was there any political protest of any kind like you'd see in the United States and in Europe?

**BECK:** Oh, yes. The only time I've ever marched in a political protest was at that time because of the Vietnam War. I was at the age where if I had been in America, I'd be being called up. New Zealand had a professional army, volunteers, so they never did a callup, but they had a token contingent there, just because the U.S., Australia, and New Zealand had this pact to defend each other. If America got attacked, New Zealand would come to help. [laughs] They did send a rather small contingent. It wasn't the size of a battalion or anything. Most students in the university did not approve of New Zealand's participation in Vietnam because of what was happening, so there were lots of protests and speeches on campus. Then they organized a march up the main street of Auckland, Queen Street, and I participated. That's the only time I've ever politically protested. I felt strongly about it, and of course I was young. It was very relevant, because my peers, at least in America, my age group was being killed for a war that didn't seem just at the time, to me. That's it.

There was a student who was a year older than me that loved to get up on the soapbox in the square at the university and protest and so on. He wrote a book when he was about 21 called *Bullshit and Jellybeans*. I loved it. He ended up being mayor of a big city in New Zealand, or two cities, actually, one was right down at the bottom of the South Island. But mostly I kept my head down, because I was just busy working, enjoying what I was doing in my work. Of course, I had friends that I did things with.

**ZIERLER:** To foreshadow to graduate school, did you do any engineering work as an undergraduate?

**BECK:** No, no. That was an issue. I'm sort of jumping ahead, but I got interested in earthquake engineering and people said, "Oh, go to Caltech. It's the world leader in earthquake engineering." I remember going to talk to a professor and I said, "I'm a bit worried because I have no engineering background." He says, "Don't worry. It's more important to have a math background if you're in engineering at Caltech." I think he was right! Because I picked up a lot of the engineering in my—I had to take classes, of course, in the first year as a graduate student at Caltech. I took earthquake engineering and structural mechanics and things like that.

**ZIERLER:** What was the source of your interest in earthquakes? Does New Zealand have earthquakes? Did you experience them growing up?

**BECK:** I did. Yes, it's a seismically active country. It's on the edge of the Pacific Plate. In fact, the boundary between it and the Indian-Australian Plate, which is a huge tectonic plate—New Zealand is the boundary between that and the Pacific Plate. As you know, the San Andreas Fault is a boundary of the Pacific Plate and the North American Plate. You sort of go diagonally across this huge tectonic plate, the Pacific one, and you end up at a subduction zone off the east coast of New Zealand. New Zealand is being wracked around a bit, because in the South Island, the Indian-Australian Plate is being subducted under the Pacific Plate. That's on the west. On the east and the North Island, it's the other way around. New Zealand's got a big transform fault like the San Andreas. It's called the Alpine Fault because it's pushed up the Southern Alps. A lot of the earthquakes in New Zealand are big and deep, so they're not so destructive, but we do have damaging shallow ones there, too.

**ZIERLER:** What was the physics that you liked the most, as an undergraduate?

**BECK:** Hmm. I think basically electricity, magnetism, more than say the thermal side. Quantum mechanics was intriguing. I had such a good math background that I knew all about Hilbert spaces and all that. The math in quantum mechanics wasn't the problem. But what did it all mean? That, it turned out, no one really knew. [laughs] I wasn't the only one! I like to dig at the basics down to the bottom and figure everything out, and I didn't really have the time, because I was busy. I revisited that like three decades later. I can't say at the time quantum mechanics—well, it intrigued me, but yeah, I was more traditional I think, in these other topics. I guess gravity, there wasn't much to do with it, but I guess mechanics, and electricity and magnetism.

**ZIERLER:** When you expressed this interest in earthquake engineering, did you know yourself about the Seismo Lab in Caltech, or one of your professors alerted you?

**BECK:** One of my professors. I took a class in the Engineering School in Engineering Science, so it was quite mathematical, and I got to know the head of the department, Professor Cecil Segedin. He was a resource that I went to after I started working for the New Zealand government, to sort of figure out where to go for my graduate studies. He worked in fluid mechanics. At the time, I had two paths I could go, either fluid mechanics—and he suggested England-Cambridge; there was a famous group of Professor George Batchelor—or earthquake engineering. I was kind of—"Which way shall I go?" I was doing research in both areas at the lab I was in. He recommended going to Caltech if I'm going to do earthquake engineering. He mentioned a couple of guys that had gone through Caltech, one in engineering science and one from civil engineering at the University of Auckland. I actually visited them and talked to them about it, just to get a handle on it. Until that time, I hadn't heard of Caltech.

**ZIERLER:** You stayed on for the master's at Auckland?

**BECK:** Yes. I went straight on for that. Then after the year of that, where I had to do six classes, very intensive, of pure and applied math, I had had enough of just learning passively, and so I put off my PhD, and went and worked for the New Zealand Government in a research lab.

**ZIERLER:** What kind of lab work was it?

**BECK:** I should back up a little bit and say that the first summer that I was at university—remember in New Zealand, that's 1967-1968; we finish in December and go back in February at the university. That summer, I went and worked in Wellington for the Physics and Engineering Lab of the Department of Scientific and Industrial Research. That was a government department that doesn't exist anymore, headed by the Minister of Science. I got a taste of the research there and liked it. I actually worked in the Optics Section at that time. Then when I went back the following summer, I worked in the Heat Transfer Section. They were interested in geothermal areas for power production and how long the geothermal fields could be maintained, how much steam could be pumped out, and all that sort of stuff. I stayed there the following summer, so I did three summers, and got a couple of papers, one from working in optics, and one from working in the heat transfer section. Then when I started full time at PEL, I went back to the heat transfer section, and so I started working in that area for a couple years and got involved in a couple of different areas.

Just because of my math background, people would come to me. I'm the young guy with all the math, and so on. They would say, "I'm working on this intriguing problem, would you be interested in looking at it?" I got involved in a couple of things. One was an anisotropic theory of growth stresses in trees, which is very intriguing. When you cut the tree for timber, it releases these stresses and warps the timber, especially in hardwoods. I looked at an analysis of that using anisotropic elasticity theory. That should have been a paper but I finished it just before I was leaving, in August of 1974, to go to graduate school at Caltech, so it's forever a technical report of the lab. The lab no longer exists, but I put the report on my website so people can get at it. Then I got into this other area—the Engineering Seismology Section Head came to see me. He said, "We've got a really interesting proposed design by the chief engineer of the New Zealand Railways, and they're not sure how to analyze it. I've got this idea that I think it'll work, but it's completely novel. There's nothing like it in the world. Would you be interested in seeing it, analyzing its earthquake response?" We needed a dynamic model. We needed strong earthquake motions that had been recorded for input to the model. That got me interested in that side of things.

**ZIERLER:** When you went to work for the government, did you always intend to go to graduate school, that this would be a gap for a couple of years?

**BECK:** I did, and the people at the Lab, the management, they pointed out that I should apply for a National Research Council Fellowship, to go overseas anywhere. It was very generous. It was competitive. They said that after working there a few years, I should go for it, and they would throw their weight behind it. This Council picked people from across New Zealand each year, and I got the fellowship, which was very generous. I was married by then, and I also had two little kids, so it was needed. I actually won a Fulbright Fellowship too, but the National Research Council wouldn't let you have both. The Fulbright really just paid my expenses to get to America. Then I'd have to rely on getting a GRA or a GTA or something. Clearly the National Research Council Fellowship was the best option. By the way, it was very generous, and it wasn't taxed by the U.S. government or the New Zealand government. It was the only time in my life I had no taxes to pay on my income! I don't think that's the case now.

**ZIERLER:** Did you look anywhere besides Caltech?

**BECK:** I did. For the earthquake engineering, I looked at a couple of other places. Actually, I can't remember whether I did Stanford or Berkeley. I was focused on Caltech. I do remember one was Purdue, and Purdue sent my acceptance by ordinary mail—in those days, that took a month or something to get to New Zealand—instead of sending it my airmail. Everything goes airmail now, I think. I had already been accepted by Caltech by the time the Purdue acceptance came. I didn't apply for Cambridge for the fluid mechanics because I had decided that I'd go the earthquake engineering route. I must say that part of that was California seemed a very desirable place compared with foggy, wet England. That had some influence. Because for both of them, I was interested intellectually in working in the areas, fluid dynamics and basically structural dynamics and earthquake loads. That sort of settled the deal, and off I went to Caltech.

**ZIERLER:** It's such a far way away, and you don't know what the future holds, but did you have a sense that when you left for Caltech, that you'd be moving to the United States, making a life for yourself here?

**BECK:** No, not at all. I planned to go back to New Zealand, work again for the DSIR and just settle down. There were a lot of good guys, my colleagues, good people and good technically. I was happy there before I went to America. When I came back, though, no internet in those days, 18-hour flight from Los Angeles, I felt isolated down there, even though there was a community of researchers. It was like I'd left the main action. I couldn't settle down. I let my advisor, Paul Jennings, who later became Provost at Caltech, know that I'd be interested in coming back—not necessarily to Caltech, because at that stage they didn't have a position open, but I'd be interested in other possibilities. It turned out that they did open a position at Caltech, and I applied for it.

Also UC Irvine, there was a New Zealander who was the head of the civil engineering department there. When he knew from Paul, because Paul was a friend of his, that I was interested in coming back—they also had a position open—he contacted me, phoned me and said, "Apply for our position, too. If you don't get the Caltech, here's a possibility. We'd love to have you." I came over and interviewed for both of those positions and got offers for both of them. I said to my wife, "I think I'm going to have to choose between prestige and money." UC Irvine quickly offered me a pretty good salary for those days, and I didn't think Caltech would match it, but I told them what UCI had offered me, and they matched it, and I never had to face that tradeoff.

**ZIERLER:** Back in 1974, what were your impressions when you first arrived at Caltech?

**BECK:** I was impressed at how my classmates could speak up. Generally, I had the feeling that the students there, the Americans, were confident in public speaking. That was a big thing for me; I was as nervous as anything to do seminars and so on, when I first arrived. I attributed that to the different cultures in New Zealand. Basically, in New Zealand, children were to be seen but not heard, whereas here, you had these sessions where people got up and—it's like a show-and-tell or something, and you speak about things. They're encouraged to speak out in class and so on. I remember that sort of sticking out. I could see that the quality of the classes was exceptional. I liked that. I rose to the occasion. I thrived on that. I felt that it was much easier than in the New Zealand system at university, because at Caltech we had exams every quarter, and you're only tested on that quarter's subjects. In New Zealand, you had exams at the end of the year, so you were tested on the whole year. You had to study all of it. To me, it was a piece of cake; I only had to study for the last quarter, 10 weeks or something. That was another thing.

**ZIERLER:** Your initial interest in earthquake engineering, what program did that lead you to? Were you at the Seismo Lab? Where were you?

**BECK:** No, no. Caltech had an earthquake engineering program. They had an Earthquake Engineering Research Lab. I think it nominally still exists, but there's only one, I think, person doing earthquake engineering now, Professor Domniki Asimaki. But this was a very strong program. There were excellent technical reports being published by the EERL, as it was called. They cooperated with the Seismo Lab. We had this joint Earthquake Research Affiliates program to raise money from industry for research. That was basically George Housner and Bob Sharp in geology. He was a contemporary of George's. We used to have these annual Earthquake Research Affiliates conferences where we'd get up and talk about our research. We cooperated with Seismo Lab, but we were the engineering side, and they were the seismology side.

There was a big difference in the data being utilized, too, because they had seismographs, very sensitive instruments, that go off scale when strong shaking occurs that is of interest from the engineering point of view, and we had these accelerographs, which Caltech, particularly Professor Donald Hudson, had sort of encouraged or consulted with a company to build in Pasadena. These accelerographs were distributed around in taller buildings because of an LA City bylaw that primarily was due to Professor George Housner. He got the City Council to say, "We need to understand how these high-rise buildings react in earthquakes, and the way to do that is to put instruments in it that will record the building's motions when an earthquake comes." They're not running all the time; they've got batteries and they trigger when there's an earthquake. That bylaw was passed sometime in the late 1960s, and in 1971, the San Fernando earthquake occurred—I think it was February 9th—and something like 50 buildings had recorded motions. All of a sudden, all this data was available to tell us how buildings respond in earthquakes. None of the instrumented buildings were badly damaged. Well, there was one, the Holiday Inn in Van Nuys, that suffered pretty seriously. Luckily, it didn't collapse. The rest of them, it got them going, but it didn't really stress them where we would be worried.

**ZIERLER:** Academically or administratively, was there much cross-pollination with the Seismo Lab?

**BECK:** Not a lot. Paul Jennings and Hiroo Kanamori, both eminent in earthquake engineering and seismology respectively, cooperated on some research that was interesting, that was sort of a common thing between them. There was some joint activity going on. But it wasn't until 1995 that we were approached by Ed Stolper, who later became Provost at Caltech, about the possibility of opening up a joint appointment in the two groups, and the person that ended up filling that was Tom Heaton, who at that time worked for the USGS in Pasadena. He was a joint appointment. In fact, his title was Professor—well, it's Emeritus now—but anyway, I think he still is Professor of Engineering Seismology. It was the idea of putting engineering and seismology together. That led to more cooperation between the two groups. Interestingly enough, if you look at Tom's graduate students, PhD students, the large majority are actually civil engineers, so it's quite interesting.

**ZIERLER:** What was the process for you choosing a graduate advisor?

**BECK:** I was going there in earthquake engineering, and the two leading figures there were Housner, who was about to retire, and Jennings. Jennings had been a graduate student supervised by George Housner. When I got there and talked to Professor Housner, he suggested that I could work with Paul Jennings.

**ZIERLER:** Because he was not taking graduate students at that stage?

**BECK:** That's right. Yes, he was on his last graduate student.

**ZIERLER:** What was Housner like when you interacted with him?

**BECK:** He was a real gentleman. He never pushed his own self forward. He was a much more subtle motivator—a very astute sort of guy, smart, had a sense of humor. When I was a professor, I'd get little cartoons or something from him that he'd cut out of magazines or newspapers, made copies of and distributed that were funny, something related to earthquakes or something. A very interesting guy to talk to, because he had such a broad understanding, a very deep understanding of things. He published textbooks on statics and dynamics for undergraduates and published a lot of seminal papers. Yes, just a great human being. He devoted his life to earthquake engineering at Caltech. He never married. He was there from a graduate student in the 1930s until 90. He kept coming in. Then he got macular degeneration and couldn't drive, so he stopped coming in. He died at 98.

**ZIERLER:** What was Jennings working on when you connected with him?

**BECK:** He hadn't had a lot of PhD students at that stage. There was one guy, a Greek guy, but that was a contemporary, where he was looking at rocking structures, which is something Housner got everyone intrigued in—rocking in earthquakes. One of the students just before me, he's now a structural engineer in Seattle. He's in his mid-seventies but he's still active. I was trying to think what his thesis was on, and I cannot think at the moment what he did.

Paul didn't have many students, and he was a guy that gave you great freedom. He did steer me a bit. He said, "We've got all these earthquake records from structures in the San Fernando earthquake in 1971 and really people have been dabbling in looking at them but no one has really done it systematically." I started getting into that, and found that, oh, there's this whole area of system identification that should be used, wasn't used in earthquake engineering, just a systematic way of trying to determine models from data, or improve or update models. Of course, I didn't have the Bayesian updating in those days. I got into that.

I looked at some fundamental issues in theory. Identifiability. If you've got just a few records—these were expensive instruments, over $1,000, so there were only a few in each structure. In fact, you had to put one in the basement under the bylaw, and one on the roof, and if it was beyond six stories, I think, you had to put one in mid-height. They were triaxial, so they recorded two horizontal components and a vertical one of acceleration. So, we didn't have much data at all, so you had to take that—the issue of identifiability, what can you uniquely determine about a model? Suppose you postulate some sort of mathematical form for the model, then how much can you learn about that model? Can you estimate all the parameters, make unique estimates, for example, if you've got some sort of optimality criterion? That was theoretical work.

Then I worked on what algorithms can we use that will work better than what this trial and error and playing around with it had done so far with this data. I had one that was *really* beautiful mathematically. Then it didn't work very well when I went to real data. Worked great with simulated data where you know the answers and you generate response as if it was an earthquake response. You take a calculated earthquake response and add some noise. It worked well. But when it came to real data, it didn't. Then I worked on another method that wasn't so mathematically elegant but more straightforward, and it worked very well, and that's what I pushed further in my thesis.

**ZIERLER:** When you talk about working with real data, what does that look like? What's the experiment?

**BECK:** When these instruments trigger, they are measuring accelerations. They can't be measuring displacements of the building. A displacement relative to what? To the ground? There's no way it has a reference. It's actually an inertial system, so it's a measuring acceleration. To get displacements at the points in the building, you would have to so-called double-integrate the time histories of acceleration. First get velocity with one integration, then another integration to get displacement. The problem with that is noise in the records. Low-frequency noise completely messes things up, so your displacements don't look good. That's a whole other story. But, they are time histories. They are acceleration time histories. You've missed the very beginning, because it has to be triggered, so it's got to be shaking about 1% of gravitational acceleration, g. In the San Fernando earthquake, some of the buildings recorded up to 50% g, half a g. If you had been standing in those buildings, you'd have half of your body weight horizontally, sort of slamming you about. You'd certainly have to be holding on to something.

Yes, so they're just time histories of accelerations. That's the raw data. They had been processed—because they were on films, so they had to digitize it, 70-millimeter film. Caltech had developed a whole digitizer system to do that. They actually did that for the earthquake research community, at that stage, because there was no CA State program until I think the late 1970s that was recording the motions and digitizing them and so on.

**ZIERLER:** When did you know you had enough to defend? What was the sense of completion you had with your thesis?

**BECK:** I felt I had a good dose of the theory, this identifiability, non-uniqueness, that was sort of mathematical and gave some good results, good practical results. That you shouldn't try to identify the so-called stiffness and damping matrices of a linear structural model. You should go and just identify the modal parameters. That's much less information but that's all you can determine reliably. That's the theory. Then I had these two methods, the elegant mathematical one—Richard Bellman, a famous guy in math and electrical engineering at USC, had come up with it—called invariant embedding filter but that didn't work so well in practice, because of modeling errors with the real data. Then I developed this other thing which I called modal minimization, later MODE-ID, to identify the modal properties. Then I applied it to two sets of building records from the 1971 San Fernando Earthquake to demonstrate how it works, what you can gain from it.

There was the 42-story Union Bank building in Downtown L.A. which sits next to the freeway down there, and the nine-story—both of these were steel-frame buildings—and the nine-story Building 180 at JPL, which had been instrumented. I had the theory, then I had the algorithms, the methods for getting out these parameters that I proved were what the data should give you uniquely, and then I applied these methods to these real earthquake records from two steel-frame buildings. That sort of seemed like, "Okay, that's good. I've got the theory, I've got the data, I've got some results from the data." That seemed to be enough. I'm sure I talked to Paul Jennings and he said, "That's enough." [laughs]

**ZIERLER:** How far out into the real world did you see this research? Did you see obvious applications, or was that not yet on your radar?

**BECK:** No, I was aware right from the start that this would be useful information. For a start, in those days, when they were designing against earthquakes, they were using dynamic modeling, but they were linear models. A question was, how good is that, when you've got strong shaking, and possibly damaging shaking, and we know steel yields and all that. When do these linear models break down? There was this assessing of linear structural models, but on top of that, these linear models, you have damping in the system. Damping, energy dissipation, in structures is a very complicated thing. It's hysteretic, it's deteriorating damping, and so on. But in linear dynamic models, we use a viscous damping model, which it really isn't, but how adequate was that? We have the idea of equivalent viscous damping. What are the appropriate values to use in design? Because you can't do any theory. It's the wrong theory. It's not viscous damping in reality—we know that—so it's not like you can have a theoretical model and predict what the damping should be. That was purely empirical, and initially people just took a guess, basically. There were some accepted standards of what damping could be used, but no real data for it at earthquake levels. I was able to get that damping for the modes of vibration, what it exhibited for the equivalent viscous damping. Assessing the models, and finding these parameters, particularly the damping parameters, was useful background information for structural design.

Or even determining the natural frequencies. Because you'd have a theoretical model, a finite element model, say, and you'd predict what these frequencies would be, and they'd turn out to be wrong. They were never what I actually got out of my method, out of the strong motion records. In many cases, they were perhaps within about 10% or something of the actual observed frequencies that I extracted from the data. Yes, the industry was interested in that. I remember I got involved with my computer program MODE-ID to look at an offshore platform off the coast of Santa Barbara. It was a Chevron platform, and they were very interested in, what is the damping in the structure at earthquake levels? They had got strong motion records on the platform during some earthquake, so I was able to analyze these data with my technique and get out the equivalent viscous damping ratios. They previously had used a huge boat where they tied a gigantic cable between the platform and the boat—it was like a tugboat—and they pulled the platform and then released the cable, so that it oscillated, to try to get the damping out of the response data. But of course, once there were earthquake records from the platform, that was much more relevant.

**ZIERLER:** Besides Jennings, who else was on your thesis committee?

**BECK:** Bill Iwan, Professor Wilfred Iwan, who just passed away a couple of years ago. Professor Hiroo Kanamori, a Caltech seismologist. I had taken a seismology class from him—it was a wonderful class—in the first year. It was introduction to seismology, basically. It covered a very broad area of seismology. I had him on the committee. I had Professor Tom Caughey, who was very eminent. He was in applied mechanics and mechanical engineering at Caltech. He was very interested in non-linear dynamics and stochastic dynamics. He and I would often have chats. That was the nice thing about Caltech; we had a coffee room in our building. I'd go in for coffee, and maybe Tom would be there on his own. He would say, "How's your thesis research going? Sit down and talk to me about it" that kind of thing, and I would. He was great to talk to. Then of course I went back on the faculty and he was a colleague, and I enjoyed interacting with him then. He was the remaining one, I think. Actually, there were five faculty. Professor Chuck Babcock was on it too. Jennings, Iwan, Kanamori, Babcock and Caughey, I think.

**ZIERLER:** To go back to that question about your assumptions and ambitions arriving at Caltech, thinking you would go back to New Zealand, was that the game plan? Did you want to go back? Did you promise your family that you were going to go back after you defended?

**BECK:** I did. And not only that, I had a contract [laughs]. One of the things about this National Research Council Fellowship that I got was that you had a contractual obligation—for every year they paid you the Fellowship, you had to go back and work for a year for the New Zealand government, anywhere in the New Zealand government, doing research. What happened is that when I went back, I had been almost four years doing my PhD at Caltech, so I had basically four years that I had to work in New Zealand. Of course, I had no worries about that, no concerns about that initially, but by the time I had *done* the four years and went back, as I've told you, I got restless. I kind of missed the action. Caltech was where everyone used to come, some of the most well-known people in earthquake engineering coming through and giving talks.

I managed to [laughs] last three years there, and then this offer came up and all that, so I went to the management at the Lab and negotiated that I would pay back the one quarter, the one year out of the four that I hadn't done. I'd pay back a quarter of what they'd paid me, and we set up a payment schedule and so on, and then off I went, and I started paying back the New Zealand government. Fortunately for me, the New Zealand dollar started going down and down and down. I had set it up in U.S. dollars, and it was getting more and more New Zealand dollars, and I paid it off in like three years instead of five years or something. Yes, originally my intention was to go back, settle down, and work for the government. Then when I didn't, I had to buy my way out of it, extract myself from the situation. I didn't want to wait another year, the fourth year.

**ZIERLER:** Why extract yourself? Was it just not intellectually compelling to you?

**BECK:** No, I can't say that, because I was with some really good people, and we did some really interesting stuff before I went to the U.S., very novel earthquake engineering designs. But Caltech—well, it wasn't even Caltech, really, because I was just looking to go back to the U.S. I kind of just got hooked on California, you know? I just liked the lifestyle, the weather. It rains a lot in New Zealand. I liked the fact that you were right where most of the action was. New Zealand is isolated. It's way down there in the Pacific. As I said before, no internet, 18-hour flights to get to L.A. It was just isolated, and I felt it. Even though there was a good community in New Zealand, it was just the way I felt, as a young man, and I kind of felt that New Zealand somehow was too small for me now. I wanted to get back in the Big Apple, kind of.

**ZIERLER:** On what terms did you leave Caltech? Was there any discussion about if you want to come back, maybe there will be a faculty position for you? Did you stay in touch with Caltech when you went back home?

**BECK:** I did. Paul Jennings, when I left, said, "It's not out of the question you could end up coming back here." There was no promise because they didn't have any faculty positions open or anything, but it was clear that the people in the earthquake engineering program would like to have me come back if there was an opportunity, if they were able to create a faculty position, which they did some years later. They had to put up a case for the earthquake engineering program, so that's what they did. I don't know now how many others they interviewed for it, but I got the offer. When I was looking to come back, I wasn't counting on Caltech. That was a possibility, but I wasn't counting on it. I just was looking at what other opportunities I could have coming back there, in academia.

**ZIERLER:** Did they open up a position? Was this a new position that expanded the program? What were the circumstances of you applying?

**BECK:** They had lost an assistant professor who didn't get tenure, so there really was a reduction in the number of professors. At Caltech, if someone retires or goes somewhere or doesn't get tenure, you don't automatically get a position to open up in your group. No, you have to make the case from scratch again. Not only was there one less young faculty; George Housner retired, I think, 1979 or 1980 or something. I left in 1978. I took the last class from him that he taught. He was stepping down as active faculty, becoming a Professor Emeritus, still very active in many respects but not teaching or having a research group, so they needed to boost their ranks a bit. There was an age gap between me and Paul Jennings. When I look back, it wasn't that big, but I think he's 11 or 12 years older or something. There was no one in the intermediate age range.

In fact, across Mechanical Engineering, that was so, too. There was a lot of older faculty, and they just hadn't kept the young ones coming in, or if any came in, they didn't keep them. In fact, after I was appointed, they had a postdoc from Berkeley, John Hall, and they were impressed with him, so not long after I became a professor there, I think 1983 they opened up a new position and John got it, so John was a colleague of mine. I arrived in 1981, and he was already there as a postdoc and became faculty earthquake engineering in 1983.

**ZIERLER:** When you were back in New Zealand for the government, were you engaged at all academically? Were you publishing? Were you staying current in the literature?

**BECK:** Yes, I was, but not very active. I worked on getting a paper out of my thesis, but there were pressures on the group. The Engineering Seismology group ran the National Strong Motion Network, so I was the chief guy for the analysis of the data we were getting. I got involved in software for digitizing accelerograph film records and so on. There's a couple of technical reports on it listed in my CV. I didn't really get into some meaty research, I don't think, after I went back, that led to papers. I was involved in various activities, but they didn't lead to papers while I was there. I had a couple of good papers from there, before I left for graduate school, but when I got back, I didn't really get going there. I'm trying to think now what we were working on. My boss was very interested in these dampers, lead rubber dampers. We were doing tests on those, and so on, but no technical publications on that.

**ZIERLER:** Having been at Caltech and just in the United States generally, how modern were the New Zealand facilities? Were you working with good instrumentation?

**BECK:** Yes. It turned out that my boss in the Engineering Seismology Section, Ivan Skinner, was very creative. He actually was an electrical engineer by training. He had a bachelor's degree in electrical engineering. He never did a PhD because he went off to the Second World War near the end of it. He had designed strong motion accelerographs independently of the American one in Pasadena. There was a company that was making them using his design, and they were being installed in the Strong Motion Network in New Zealand. Our group was very innovative, and we were on the leading edge. This whole thing of base isolation, which you may have heard of, which is big internationally, and there's buildings in the United States and so on, we were the first.

Ivan had the idea of putting the buildings on lead rubber bearings, a sandwich of rubber and lead, that were used, at that time, for accommodating thermal expansion and contraction of bridges. The idea was to make low-rise buildings, up to, say, six or maybe even ten stories, put them on this flexible base, so that it kind of shifts their spectrum down to low frequencies where typically there's less energy in earthquakes, although not so for really huge earthquakes. We had I think the first base-isolated building in the world in New Zealand. It was built in 1976 while I was over at Caltech. It was built next to the Wellington Fault, which goes through the center of Wellington. It was the headquarters of the Ministry of Works and Development of the New Zealand Government. That was due to Ivan Skinner and our paper showing the viability of it, which was published in 1975, I think, in the *International Journal of Earthquake Engineering and Structural Dynamics*.

We were on the leading edge, I felt. As a matter of fact, when I came to graduate school, I should mention that I was thinking I would continue in this exciting area of base isolation. It seemed like it should take off. There was nothing going on in the States, here. Oh! No, there was a professor at Berkeley who had done a sabbatical leave with us in New Zealand and gone back all fired up about it. At Berkeley, he had a large shake table he could access, to test things. I remember talking to Housner about base isolation and he said, "That sounds too specialized." That sort of discouraged me. I don't think he bought into the idea. Maybe Jennings didn't either. But it took off in the U.S. This guy, Jim Kelly, a Scotsman at Berkeley, was I think later considered "Mr. Base Isolation" in the United States. Many people don't know that he came and spent a sabbatical before I went to graduate school with Ivan Skinner, and I went back with the idea. He was actually not an earthquake engineer himself. He was in materials science, I think.

**ZIERLER:** To go back to a question from when you were in graduate school thinking about real-world applications, what aspects of your thesis research were relevant back in government service in New Zealand, and what was just simply new science, a different ballgame for you?

**BECK:** I've mentioned the fact that I got damping ratios and looked at linear models and so on. This all was helpful in the building code, the seismic design code. In fact, it's issued by what was called then the Standards Association of New Zealand. Ivan was on this committee—I'm not sure if he was chair—something like the seismic design committee, and there were national guidelines or requirements, in many cases, when you design structures, for wind and for earthquakes. Some of my stuff was sort of relevant in a general way. As I said, design offices in those days and even today use linear models, and how good are they for predicting earthquake response? What sort of damping levels should we be using? These sort of issues. I had, in a general way—although I cannot point to the fact that this influenced a particular seismic design code provision. The Lab did a lot of fundamental research, but because it was funded by New Zealand taxpayers' money, it was always directed towards a goal of something practical. You had to justify it. Like my convection in a box of porous material, a paper, by the way, that has been cited over 300 times.

**ZIERLER:** Is that your most cited paper?

**BECK:** No, I have one that has been cited over 2,000 times, and that is to do with system reliability, calculating failure probabilities for dynamic systems under any excitation. It's very general, but we were motivated by earthquake excitation. That was a completely new idea. Remember we talked about Monte Carlo simulation? Our method uses a more sophisticated version that goes by the acronym MCMC—Markov Chain Monte Carlo simulation. It used some tricks which were very novel, and the community in system reliability was interested in that, kind of latched onto it, and it spread. It spread out from earthquake engineering. People use it in financial stuff, chemical kinetics stuff, and all that. Whenever you're interested in a system and you're worried about it failing and you don't have certainty—which you never do; you've always got uncertainty—this is an efficient tool for calculating failure probabilities, much more efficient than plain old Monte Carlo.

**ZIERLER:** How much interface did you have with academia in New Zealand when you were there after graduate school?

**BECK:** Very little in the way of collaboration and research, but I used to visit a couple of my former professors that were working in areas close to mine. One wrote a book on flow in porous media and had the figure from my convection paper and all that. I used to enjoy talking to him, Professor Nield at the University of Auckland I would call in—because my parents lived in Auckland—I would often call in to have a talk with these guys that were former professors of mine. Not often, but occasionally. I kept that contact, but I never had any collaboration with anybody in the New Zealand universities. It's interesting looking back—our Engineering Seismology group was quite advanced. The people in universities would be looking to my boss Ivan in some respects, I think, in terms of being a leader in earthquake engineering in New Zealand. There were more novel ideas coming out of our lab at the DSIR than out of the universities. I think it's fair to say that.

**ZIERLER:** On the personal side, your family being back in New Zealand, was that a tough sell, when the opportunity to return to Caltech came up?

**BECK:** Yes, but my parents were very supportive. They always were, and they realized this is just a wonderful opportunity for me. It was sad. They tried to come over as often as they could. Up until 1998, they were coming over. My dad was 79 on the last trip. He came for my daughter's wedding. They came. But yes. In the early days, phone calls were incredibly expensive, like $5 a minute or something to call New Zealand, so we were writing letters, back and forth. I still have some of the letters. My dad rarely wrote—it was mainly my mother—but sometimes my dad would add a sentence or two at the end.

**ZIERLER:** How old were your kids when you moved back?

**BECK:** They were I think 12, 9, and 3. The third one was a bit of an afterthought, so he was six years younger than his brother.

**ZIERLER:** He wouldn't have remembered the transition.

**BECK:** No, no, he's a real American. He was born here. He was born just a couple of months before we went back.

**ZIERLER:** Wow.

**BECK:** Yeah, so he's American. He has both New Zealand and U.S. citizenship.

**ZIERLER:** Last question for today, and I think it's a great narrative point to pick up for next time when you join the faculty. At this point, joining the faculty at Caltech—it's a great honor—what do you see as your areas of expertise, where you can make the kinds of contributions to the field that one would expect of Caltech faculty?

**BECK:** I came back thinking earthquake engineering is my domain, and I'm going to be working in that area. I had done these couple of innovative things, not my idea but I worked on the technical aspects, back in New Zealand with the stepping, or rocking, railway bridge and the base isolation of buildings. Base isolation was quite hot; I thought I'd get involved in that. One of the realities, though, as a professor, is you've got to get funded to have a research group. Not long after I got on the faculty, NSF decided to have an earthquake engineering research center. The funding was multiple millions. This is a long story, but Caltech submitted a joint proposal with Berkeley, Stanford, USC, UCLA and UC Irvine—there were six universities—for this research center. We agreed it would be centered at Berkeley, but we'd all share in the research, and Berkeley had this big testing facility. Buffalo, New York—SUNY Buffalo—won the competition. New York, for earthquakes? There were some interesting things going on. In fact, the National Research Council later issued a book about some of the problems in research funding in the U.S. and one of them was this case.

Anyway, what happened is that we didn't get it, so it took us a while to get our act together, but we got a state program going, and PG&E threw in some money. It was mainly the guys up at Berkeley that were working on it. We ultimately created a center ourselves, and I got funding from that, but it took four or five years to set it up, I think. In the meantime, there was this dearth of funding for earthquake engineering research. Up until then, NSF had a natural hazard mitigation program, and it was funding earthquake engineering quite well. Of course, I was a new guy on the block, so I didn't have the prestige of Housner and Jennings. Jennings was on the original NSF proposal, I think, and we had the Berkeley people and all that. I tried on my own too, of course, to get some funding. So, I struggled a bit there. It took a while.

**ZIERLER:** What about the USGS? Was that a resource?

**BECK:** I didn't look at it as so, but I think I probably should have. Later, some colleagues, a younger guy that's no longer in the group, got some funding through them. But he did a good thing. He went and did a postdoc there. He got a PhD at Caltech in earthquake engineering and then went and did a postdoc over in seismology, so it gave him I think more credibility on the seismo side. They were interested in what he was doing. What did they call it? Rupture-to-rafters. You want to model everything from the earthquake shaking at the source—the rupture—all the way through propagation of seismic waves into your structure, and then you model the structural response. He was able to span the whole range with his computer simulations. There was funding there, but I don't know if it was in my days, and I never tried. Maybe I should have. I kind of just did the traditional thing that we were doing in our EERL group, so I didn't break out until later. You can see in the 1980s my record is thin, and it wasn't until in the 1990s things started to get going. Then the last couple of decades before I retired, I was publishing a lot and doing a lot. But it took me a while to get going.

**ZIERLER:** It's inspirational for graduate students to know that even for assistant professors, things can be a little shaky at the beginning.

**BECK:** [laughs] That's right. Actually, to tell you the truth, if I was starting now and I did that, I don't think I would get tenure. It's so much tougher now. I feel for these young guys. There's a lot of pressure on them, a lot of expectations, much more than I feel there was in my days.

**ZIERLER:** That's great place to pick up for next time, particularly on the topic of the culture at Caltech where the impetus is to give junior faculty the tools they need to succeed. I think that's a really important point, and let's pick up on that for next time.

[End of Recording]

**ZIERLER:** This is David Zierler, Director of the Caltech Heritage Project. It is Wednesday, June 8th, 2022. I'm delighted to be back with Professor James L. Beck. Jim, once again, it's a great pleasure to be with you. Thanks for joining me.

**BECK:** Good morning, David.

**ZIERLER:** Today what we're going to do is pick up in the late 1980s and the early 1990s, a new opportunity for you, a bit of a career shift. As you got more involved in issues relating to geophysics and seismology, what did you feel like your particular area of expertise was that you could contribute in significant ways in these fields?

**BECK:** It depends whether I'm looking earlier in my career or back—whether we're talking about the 1990s. Earlier in my career, I was actually following a mentor in New Zealand that had some good ideas, and I was the young guy with the math that worked on them. We were looking at very innovative designs. I think that we talked about this earlier, but one was we were the first in the world to propose base isolation of buildings, where you put buildings on pads that are sandwiches of rubber and steel, horizontal plates. We proposed this to the Ministry of Works and Development in New Zealand, and they actually built a building right near the Wellington Fault, which is a huge fault that runs through the center of Wellington City. That was built while I was a graduate student at Caltech. That was one example where I did some real earthquake engineering, and it started a whole new area. The idea was my boss's, I must say.

But what happened was—New Zealand was a bit of a backwater, isolated. There was a professor at Berkeley who somehow—oh, he was interested in some energy-absorbing stuff we were doing. He was actually in materials science. He came down on a sabbatical with our group in New Zealand—this was a government research lab—and got interested in the base isolation. He went back—he was at Berkeley—he had a shake table, he had graduate students—and did some really good work, and it sort of blossomed, and I think people would think of him as the sort of pioneer in base isolation. But people in Japan, for example, I think recognize my boss, Ivan Skinner.

Another thing that I got interested in there—and I know I'm going backwards, but it's very interesting—the New Zealand Railways came up with a new design for a railway viaduct that went over a big canyon. The existing one was old and made of steel so to avoid rusting, they had to keep painting. They decided they wanted reinforced concrete, more durable, but it turns out to be difficult to design a tall viaduct in reinforced concrete in earthquake country. They had this really novel idea, and they came to us and said, "Hey, how do we analyze this?" The novel idea was that the piers would not be tied down at the bottom. They would be guided. But in a big earthquake, the whole viaduct would move side to side, and the piers would lift, like you were rocking your body side to side, lifting a leg up backwards and forwards. It turns out, of course, that this limits the stresses in the legs at the expense of deforming the deck. But the deck, you can design to withstand much larger forces, with reinforcing steel. We analyzed that.

Not a lot of attention was paid to it, but in recent years, there has been this interest in rocking structures that has grown. There's a professor, a Greek professor in Southern Methodist University, that has been sort of pushing it, and he wrote a nice review paper, and put my stuff in there. Now, I'm told by a former postdoc in a structural design office, that this is kind of a growing area of interest, where you actually allow structures to rock. Those things had a big impact. Well, the base isolation had a huge impact. The stepping viaduct bridge was something that was sort of unique and then there's more interest recently, of even allowing buildings, maybe, to do this, which would be tricky. That was real earthquake engineering.

Around the period we're talking about now, I had always been interested in system identification of structures using seismic response records, motions recorded in the structure during an earthquake. I was looking at how to handle model uncertainty there. I was working on probability, as I've mentioned before, how to interpret it, the Bayesian probability. Around this time—1989 was my first paper—I started to publish on this Bayesian approach. I kind of stuck my neck out there, because in engineering, no one was using a Bayesian approach and it was frowned upon. It's sort of like, "Oh, that's just all very subjective." I persevered. I published another paper with a graduate student in 1991. Then if you look in the 1990s, you'll see that there's lots of papers popping up that say "probabilistic system identification," "probabilistic structural health monitoring." This area was growing, and it became the one that I'm probably most known for—basically bringing engineering, certainly civil engineering, structural engineering, this whole idea of Bayesian probability to handle modeling uncertainty.

Parallel to that, some of the stuff that I did in my thesis, where I developed a program to identify the modes of vibration in seismic response records, that was going along too. I was getting consulting jobs. People would come to me and say—for example, Chevron came, and they said, "Look, we've got an offshore platform in Santa Barbara Channel, and we recorded the"—what earthquake was that? Oh, it was the Northridge, earthquake, I think? No, an earlier earthquake, the 1987 Whittier Narrows Earthquake. Anyway, they said, "We've got these seismic response records from the offshore platform. We'd love to know what damping is being exhibited in the modes of vibration." This is not something you can calculate theoretically. I did some work with some people at Chevron Research Lab on this. Then there was a bridge. Then there were some buildings. People came to me with these seismic response records. So, running parallel to this was work coming out of my thesis, which had no probability, because I didn't subscribe to Bayesian probability when I did my thesis. But at the same time, I'm publishing this more theoretical stuff, so like there was a dual track there, going forward.

**ZIERLER:** In the early 1990s, just being at Caltech, what was relevant in terms of these new interests for you?

**BECK:** You mean the environment at Caltech?

**ZIERLER:** Yeah, I'm thinking specifically there's the Seismo Lab. You had that visiting professorship at the University of Southern California, the regional connections there. Tell me about that.

**BECK:** Yes. We always had some links with the Seismology Lab, but they were scientists interested in earthquakes for the sake of earthquakes. We were engineers wanting to protect our infrastructure. That's not to say they weren't interested too, but that wasn't their main focus, although Hiroo Kanamori, who you would know, a very famous seismologist at Caltech, always had an interest in it—it's earthquake engineering where the rubber hits the road. At USC, when I did my first sabbatical, that was in the Civil Engineering Department, and my host actually did a PhD in the 1960s at Caltech and was interested in earthquakes and active control and things like that. I don't even think I visited any of the seismologists down there. I might have. But that center that they ended up with—what was it called? SCEC, Southern California Earthquake Center—I don't think that was formed when I was on sabbatical. I might be wrong. The sabbatical, what was it? 1989, 1990, I think?

**ZIERLER:** That's right.

**BECK:** I did later go to SCEC meetings, because I was interested, but they were interested in the seismological aspects, not the engineering aspects. They were interested in the science aspects, so there wasn't a lot of cross-fertilization. I always was involved with—I was on committees that were looking at data from the running of the seismic network, and how we could benefit companies, industry, from this data. This of course was motivated by the ultimate goal of having early warning. No, that wasn't until the 2000s that I started actually doing some research on it. Tom Heaton, as you know, was taking the lead there. He had this vision of early warning systems. So, there wasn't a lot of interaction with seismology. I might have mentioned that when I was a graduate student, I took a very good course from Hiroo Kanamori, which was basically an introduction to seismology, so I always wanted to know the science, because it's important—what sort of ground motions can we expect, and so on. I was interested in that, but I cannot say that we did any collaborative work at that time.

**ZIERLER:** Tell me about some of your work in what is known as control and response prediction.

**BECK:** Control systems have been around for years and years. I think there's a paper in the 1970s, where the guy was saying, "We should be introducing structural control systems into structures to reduce their response in an earthquake." That turned out to be, as you might imagine, very challenging, because these are large structures, lots of inertia, huge forces involved in an earthquake, and so to create systems like hydraulic actuators, for example, that could be utilized, is difficult. There was a lot of theoretical work but it never really led to anything practical. Then people sort of got into the idea, "Well, what about passive damping?" And what about what's called semi-active, where you tune the passive damper depending on what's happening in the response. That got very interesting. It's a highly non-linear control system. We got interested in control because of that excitement. My argument was, "Look, modern robust control is looking at model uncertainties but not in a probabilistic way, not in a Bayesian probabilistic way. I talked to John Doyle at Caltech, who was in control and dynamical systems, over in CMS. I had a student—we didn't jointly supervise him, but John allowed the student to come into his lab and use the test structure that was there, because John had a student interested in that. We got into the area of robust control from a Bayesian probability point of view. We did some work in that, during the 1990s, and then maybe a little bit into the 2000s, and then I sort of left that area. I wanted to make the point that robust control should be done from a probabilistic point of view rather than a hard bounds point of view. That is, they would say parameters are in this range, for sure, and can we have a control system that will work well even when we aren't certain of the parameters for the model of the dynamical system. Can we have that it performs well regardless? But they put bounds on it. Whenever you put a boundary on something, it makes you a little nervous. How do you know the parameter value shouldn't be—that the most appropriate value—shouldn't be outside that interval? If you make the interval too big, then you degrade the control system performance in a sense, because you have to allow for such a large range of parameters it's not so effective. I had a philosophical point to make in that control stuff, and I sort of made it and moved on. A couple of my students continued to work in that area. One is at Notre Dame, and the other is at University of Michigan. Actually, he was a postdoc, the one at University of Michigan, Caltech graduate. I don't think they're doing much in that area nowadays either. The shift has come more to—there was this big buzzword, "smart structures," and it meant control, active control or semi-active control, and structural health monitoring. I was doing both, but then I sort of went over to the structural health monitoring. I felt that might be more interesting and more effective way to spend my time.

**ZIERLER:** I wonder if you can explain a little about how you take data from a specific earthquake. For example, building records from the 1989 Loma Prieta event, how do you take that data and put it into something that can be actionable for building control, for building plans?

**BECK:** Several different ways. One is nowadays it's standard practice to run a finite element program, you make a model of the structure and how it responds, and you put in earthquake records and simulate its response. The question is, how good is the model? You have to have real data to assess that. Typically, they were linear models in the early days. Now, they're doing some non-linear stuff. But the question was, how good is a linear model for an earthquake? An earthquake shakes a building quite a lot. Is a linear model adequate? Surprisingly, from my work—system identification—I found that a linear model is appropriate until you're getting significant damage in the structure, but it's not the linear model that's appropriate at very small amplitudes, or so-called ambient vibrations, where we can look at the modes of vibrations and so on. Buildings shake all the time, in ambient conditions. It's quite different. The frequencies, the natural frequencies, drop a lot, and the damping changes a lot. We were able to comment on the suitability of the linear models. The other point is that these finite element models predict periods, natural periods, natural frequencies, for the modes of vibration, and how good are they? We found that okay, the theoretical ones differed a lot from the ambient vibration modal frequencies that we were seeing, but they were quite close to the earthquake ones. Typically, like 10% to 15% different is what I found. Then there's an issue of damping. Damping in structures is very complicated. There's a simple model, because it's linear; it's called viscous damping. That's more appropriate for like your shock absorbers in your car. People had used this for years, but the question was, what's the appropriate level of viscous damping to take? It's not really viscous damping. We can't do anything theoretical, so what should we do? People would take a stab at it. There were sort of standard ways. We were able to show them what was being exhibited in real structures, even up to the onset of damage, because there were some records obtained on structures that were damaged. One in particular almost collapsed. It was a hotel out at Van Nuys in the 1971 San Fernando Earthquake, where it was lucky it didn't collapse. It had shear failures. You could see light through the columns in the fourth floor. [laughs] It was that bad. But it stood up! Then they repaired it, and it's still there! [laughs] We were able to look at that. There was enormous changes in the natural frequencies from the beginning of the earthquake until the time where it started to get damaged.

Another thing I could do was take time windows and just take the data from that time window: the input, the shaking at the base; and the output, shaking at the floors, that were measured, and just take a few-second window and look at what's going on, what are the equivalent frequencies, equivalent damping values in the modes of vibration in those windows, and you could see this enormous change going on. The real model should be non-linear. We revisited that building many years later and did a non-linear model using Bayesian techniques and got remarkable agreement with the data. That's kind of like playing with the parameters to fit the data, but still, you would not be able to fit the data with a linear model over the whole time, 40 seconds or whatever, of shaking, but we could with the nonlinear model. I'm commenting on the capabilities of the models that they use in the design office, the finite element models. You're providing them with damping values that they will need to just sort of stick in. They basically used to do a modal analysis, get the modes of vibration and then put in damping in the modes. Each mode is described by a simple equation. It's just like a single degree of freedom oscillator. If you have a mass on a spring with a dashpot and you pull it aside and let it go and it sways, and its equation of motion basically describes each mode—it's quite interesting—if it's linear dynamics.

**ZIERLER:** What was some of your work in the 1990s when you were looking at stochastic characterization of ground motion, and specifically thinking about applying that to structural response?

**BECK:** Every earthquake record is completely different, even if it's at the same site, and even if it's an aftershock of the main shock. Of course, it would be smaller, but completely different characteristics. You wonder about just taking recorded motions and running them through the model of a structural design to see what happens and altering the design to improve the performance. We were advocating, and people before me too, that it really should be a stochastic model, a probabilistic model, that describes the time history. The time history is a function, and you've got a probability distribution over these functions, if you like, so it's kind of a generalization of looking at the probability distribution on a single variable, which is just a constant, but you're uncertain about it. Now you've got a whole function in time—it's the ground shaking—plus you have three components at one point. You've got a vertical and two horizontal components. But how do you come up with a reasonable stochastic ground motion? Of course, you go to real data, and you try to construct it from that. That had a long history. In fact, we've talked about George Housner and his graduate student at the time, Paul Jennings. They developed, using their judgment, stochastic ground motion models, and picked some to be used in design, because no records that strong at that time had been recorded. All the seismological instruments go off scale in a big shaking. It's only when the engineers in the 1960s started to put out the strong motion accelerographs that they started to record these things, but we didn't have one close to a fault from a magnitude eight, or even magnitude seven. They did this stochastic modeling and picked some samples. We got interested in that, and we did work on that. I did that with several students. Then that fed later into the work I did on reliability, which is just what's the probability that you'll get the performance you want during an earthquake. Well, you don't know what's going to hit the structure in the future, so you have these probability stochastic ground motion models that you use for that. That's why we got into it and we played around in that area for a while.

**ZIERLER:** Tell me about cyclic plasticity, some of your work in that field, in the mid 1990s.

**BECK:** This was sort of an offshoot, because—well, I mentioned it with linear models, that the real problem is non-linear. But what? Non-linear just says "not linear." It doesn't say anything about the model. There's an infinite set of possible non-linear models. But it was *clear* that what you want is a model that involves plasticity. That is, steel will yield. The reinforcing will yield in a concrete member or a steel member itself. If you put enough force in there and strain it enough, it will yield. That is, its stress will no longer increase linearly with the strain. The strain will keep going, and the stress will hardly increase. That's yielding. Of course, in an earthquake, it doesn't all go in one direction. It keeps shaking backwards and forwards. If you imagine you're pulling it over and you can plot stress versus strain, and it's going over on this curve—but when you come back, it doesn't come back down the curve. If it did, that would be called an elastic system. It actually has hysteresis; it comes down differently. If you keep cycling it, backwards and forwards—that's where the "cyclic" comes from—you find that you get these fat hysteresis loops, and it turns out that the area of them, in the stress-strain plot, is a measure of the energy being dissipated as heat, so your mechanical energy is dissipated as heat. It would get too hot to touch, if it was a big enough response. We wanted to use such models in system identification, so we said they had to be parsimonious. We couldn't have models that had a huge number of parameters. It would be hopeless trying to identify them.

I was interested in parsimonious models of plasticity. I proposed this to a graduate student, and away we went, and we ended up getting into theoretical models for plasticity, this sort of work also being done by some of my colleagues in aeronautics or mechanical engineering. We had some good contributions there. I did that, and then left that field, but my latest paper [laughs]—I've come all the way back. I had a woman professor that visited on sabbatical leave, and she was interested in this sort of stuff. It took us a few years, but we finally wrote a paper that goes back to our original plasticity model, the hysteretic model. As a matter of fact, my first student worked on that one, and we showed recently what a lot of interesting properties it has and how it connects up with other hysteretic models that have been proposed, and how you can efficiently simulate it, because it's kind of tricky when you have these sharp corners in the hysteresis loops when the velocity reverses, because it doesn't come back down. It comes back differently, and you can overshoot. Anyway, there's certain numerical problems, so we showed how to handle them. That was nice, because that student who originally worked on that graduated in 1987 with a PhD, so it was like a 35-year loop, maybe. [laughs] That was very satisfying, late in my career, to get back to that, and I think it's a nice paper. Other than that, in between, I didn't—oh, no, that's not true. I was going to say I didn't do anything in the 2000s, and maybe we'll get to this later, but I revisited this whole problem of using plasticity models with a student. An issue is that these models are not identifiable. If you just do kind of least squares fitting to the data, you find there's multiple solutions. You can just throw up your hands and say, "Which one do I take? Can you use prior information to choose one?" But it turns out in the Bayesian framework, there's a very rigorous approach to it. Basically, you have to consider all the models that are highly probable based on the data and use them to make predictions. It's all theoretically sound. It relies on the so-called Theorem of Total Probability. But it's computationally very difficult to do. I had this student work on this and we used so-called Markov chain Monte Carlo simulation to tackle the problem, MCMC, so I revisited it. He graduated in 2006, so we have some papers around that time, on that. Off and on, I've been doing these plasticity models, looking at them from the point of view of modeling structural response.

**ZIERLER:** Do you have a memory of when computational tools really began to be useful in thinking about optimal design and lessening risk in buildings?

**BECK:** The finite elements was developed in the late 1960s by structural engineering professors. In the 1970s, there were lots of research in universities developing these finite element codes to broaden them into general solid mechanics and fluid mechanics. What was your original question?

**ZIERLER:** I'm thinking more in the mid 1990s, just as computers are becoming a little more powerful, some of the computational tools, so that when you're thinking about optimal design, minimizing risk in building applications, what simulations or software was available at that time that really advanced the field?

**BECK:** I wanted to start on the theoretical side of things, but the computational power wasn't there in the design office, because you had to have a mainframe computer to do the calculations. Then of course came the microcomputers, and they grew in power in the 1980s. They got more and more powerful, so that you could do things on a desktop machine that you would need a mainframe to do ten years before. Not only did the computing power get faster and more memory and everything, software appeared that was very convenient to program quickly. I'm thinking specifically of MATLAB. I remember in the early 1990s, I think it was, I remember John Doyle was using MATLAB and talking about it. It was a new software. I got my students involved, and by the mid to late 1990s, everyone was programming in MATLAB, no longer using Fortran, which I used to use. They were all using MATLAB. We had microcomputers that were running C, because if you've heard of—what is it?—Linux operating system—I had a graduate student that was a computer whiz, so in 1994, we were running the beta version of Linux on our microcomputers. All of a sudden, I was freed up of all this cost of paying for big computer systems that were in a special building at Caltech. I had them in my own lab, and they were doing these powerful calculations. This eventually happened in the design office, of course. Now everybody has got powerful computers on their desk. They run this software. A lot of software that was developed coming out of Berkeley. A professor at Berkeley started a company and marketed software for design of structures against earthquakes, finite element stuff. That, I guess, was happening in the 1990s. It's commonplace now.

**ZIERLER:** You've alluded to this before, but thinking about non-linear random vibration problems, just how difficult that is, what are some solutions, or at least approximate solutions, for these problems?

**BECK:** There was a lot of work done on what's called—okay, so if it's linear dynamics, there's some mathematics that you can use that's relatively simple. What about when they are non-linear systems? A couple of professors at Caltech actually had a number of students in the 1960s and 1970s and so on where they looked at equivalent linearization of systems, how you find a linear system that somehow has a similar response to so-called stationary excitations. So it's not really earthquakes, because earthquakes don't last forever. A stationary distribution means probabilistically it sort of goes on forever and it's the same. The excitation is very erratic but if you describe it probabilistically, it stays the same with time. Of course, that's not so appropriate for earthquakes. This equivalent linearization was a very common method. But then that activity all stopped, sometime in the 1990s, because of these powerful computers and everything. Why do that when you can actually run Monte Carlo simulations? You actually take a sample from your probability distribution for your input. You run that input—it's a time history—through your dynamic model, and you get an output, of whatever you're interested in. Then you do several more, and several more, and you build up a set of samples for your output, as a representation of the probability distribution for the output. The research on analytical approximations really pretty much died out. Sometimes it can be useful to have a sort of quick and dirty solution to a problem. I think we've done that occasionally in the past. But mostly people don't do that now; they just compute Monte Carlo simulations.

**ZIERLER:** I'm familiar with the term "asymptotic" as it relates to particle physics, but in your field, talking about asymptotic expansion, or asymptotic approximation, what does that word mean?

**BECK:** For example, suppose that you have an integral that depends on a parameter that can be larger; you can take any value, if you want to. What happens if that parameter gets very large. Asymptotically, that integral may approach an approximation that gets better and better, as the parameter gets bigger and bigger. In particular, in our work, we use what's called Laplace's asymptotic approximation. Laplace came up with this in 1800 or something. The parameter that is viewed as getting larger and larger is the amount of data points you have in your Bayesian analysis. We're talking about collecting records from structures, and these are digitized maybe at a hundredth of a second, or two hundredths of a second. You have a lot of data points, if you have ten seconds of data, for example. We were using that approximation to understand what these integrals in the Bayesian analysis were telling us. You write down the integral, but since you cannot write an analytical solution for the integration, you don't know what it's telling you. We got into this Laplace asymptotic approximation. That lasted about ten years or so. I actually came up with that in like 1988 or something. It turned out that in statistics, a guy had published a paper—I think it was 1986—on that, but we independently came up with it. That guided our Bayesian work for ten years or so, until the late 1990s. It was nice, because it actually provided a justification for what people were doing when they just did non-linear least squares to estimate the parameters. You could do a whole Bayesian thing, and ask, what is the most probable model, and as you get more and more data, what's the asymptotic approximation for that? You find it's doing what they were doing before, just doing the best fit to the data in a least squares sense. The problem is, of course, that that optimization might give a non-unique estimate. Now what do you do? We've talked about that. That's our question of identifiability in system identification. This Laplace approximation can still work if you have a finite number of optimal estimates. It gets very difficult if you have a continuum of them, a whole region of parameters which all give optimal solutions, and this can happen. We were getting stuck there in the late 1990s on this issue. Then serendipitously we discovered Markov chain Monte Carlo simulation. That allows you to tackle the Bayesian integrals without any asymptotic approximation. It gives you samples from the probability distribution that you're trying to get that's an integral over all the model parameters. With that advent, our Laplace asymptotic approximation research sort of stopped. But it was very helpful for us for ten years, because what it allowed us to do was to show that the Bayesian analysis, you can do things with it, and you can find out things using this asymptotic approximation. Everybody used to throw up their hands and say, "Well, the Bayesian stuff, not only is it subjective, but it's kind of hopeless, because you've got these high dimensional integrals that you cannot do analytically." We tackled that problem, first with the Laplace asymptotic approximation, then with MCMC. Which, by the way, was discovered or put forward in a statistics paper about 1994 as a way to do Bayesian updating, as we found out later. We discovered MCMC simulation in 1998, although it had been invented many years before, working on another problem in reliability. I said to the student, "Hey, we could use this for Bayesian updating" and so we did.

**ZIERLER:** In applying Bayesian probabilistic approaches in structural health monitoring, was the field sufficiently mature enough where you had to do some level of evangelizing that this was a solid approach?

**BECK:** Yes, mainly because I was saying the way to handle this is you've got to use Bayesian probability. That was the tough part. Because everybody was struggling in that area, because of some fundamental problems, and they didn't know how to tackle them. I came along and said, "Use Bayesian probability." But of course, I had to convince people that Bayesian probability was rigorous. That took a while. Now, everybody is doing it, but in those days, no one was doing it.

**ZIERLER:** What were some of the assumptions or biases that would suggest that it was not a rigorous approach?

**BECK:** Before?

**ZIERLER:** Yes.

**BECK:** You mean why Bayesian probability wasn't widely accepted? Well, it all comes down to this. In Bayes' Theorem you've got two parts. One is the prediction of the data. If you have some data, given a model, you have a probabilistic description of what it predicts. If you plug in the data, that's called the likelihood function. You have a probabilistic model, for predicting something, an output, and it depends on model parameters. Then you plug in the data that you've actually got for the output, and then it becomes the likelihood function. It's a function only of the model parameters. That's one factor in Bayes' Theorem. It gets multiplied by another factor called the prior, and the prior is a probability distribution of the model parameters. That's where everybody got stuck in the early days. They thought, "What is this thing?" The other one, the likelihood, they thought, "Well, that's dealing with the real world." They could take the relative frequency of repeatable events and use that frequentist interpretation for the probability. But for the prior distribution over the model parameters, what does that mean? A model parameter is not a repeatable event. You can't look at its relative frequency in the long term, in the way probability is interpreted in the frequentist approach. I was saying, "No, what it is, this is a measure of how *plausible* you think it is, each model." Because every time you choose a value of the parameter vector, you're choosing a model from some class of models. Think of the whole set of models, and the prior probability distribution is over that set, and it's telling you how probable each model is in that set.

Now, clearly, that's just up to you, so it's subjective, and people wanted everything to be objective. But that's not how life is. You do not have enough data or information to be completely objective. Whenever you make decisions, for example, you always have uncertainty. If you want to try to quantify things, you have to express that uncertainty that you had prior to the data, and that's what the prior does. That's where everybody got hung up on this Bayesian stuff. I remember I loved probability and statistics at university. I did those courses. In fact, the first year, I did the second-year statistics and got A++, which [laughs] looking back, I must have been about 99% right or something in the examinations. I loved it. But it was meaningless to me when I did my thesis, because it just didn't seem to apply. For a one-off earthquake record in a building, how can I talk about the long-term relative frequency of events for the model parameters? I knew about Bayesian stuff, and they talked about degree of belief in the prior, and I thought, "That's subjective" and so on. I kind of dismissed it just like everybody else. But once I found the rigorous basis for it, which was actually in a paper in 1946 by a physicist, I realized, "Oh, that's what it is. It's a generalized logic for quantitative plausible reasoning." That changed my whole attitude. That took quite a few years in the 1980s. That's how I ended up using it, but I had to convince people. I published papers, and they were kind of ignored for a while, but then eventually I get the chance to convince my students [laughs] because I get to talk to them all the time, and then they go out and they're proponents of it, and their students are proponents of it, and then it spread.

**ZIERLER:** Is this process of convincing colleagues in the field that this is rigorous taking place purely in a theoretical context, or are there real-life applications where it really bears out?

**BECK:** I think that it's in the sense there's real-life applications. People were faced with these problems in system identification, structural health monitoring, non-uniqueness of parameters, that is, their optimal estimates. They didn't know what to do with them. They didn't know how to handle them. Then we showed them, "Hey, if you take this approach, this is how you do it." It's rigorous. Everybody agrees on the probability axioms. Everybody agrees, no matter which interpretation. I'm just saying, "Hey, take this interpretation. Use the same probability axioms. Now you can talk about handling non-unique optimal estimates." And properly handle modeling uncertainty. That was the key. No one could handle modeling uncertainty with a frequentist interpretation of probability. They would say the data has got noise. No, the noise is negligible, measurement noise, with modern instrumentation. The problem is your model isn't good enough to give you a good fit. It's not that there's noise in the data; it's your modeling error, and how do you handle that probabilistically. That was the way I approached it—"Look, if we do system ID this way, here's the problem. What about if we do it with this Bayesian approach? You can solve all these problems." I also did it for structural health monitoring. That's the way I approached it to convince people.

**ZIERLER:** In the late 1990s, what were some of your contributions in the broader effort to create what was known as a performance-based optimal structural design?

**BECK:** That was very interesting. PG&E and the State of CA funded a big earthquake engineering research center, called the PEER Center. I think it was 1998 when it went online. Multimillion dollars for research. It was headquartered at Berkeley, but six universities were involved on the West Coast, and we were one. Their whole theme was seismic performance-based design. It came out of the engineering profession's dissatisfaction with the building codes. The building codes are there to protect the public. They're not there to protect the owner's investment. Let's say the owner wants to go above code, wants a safer building, or a building that is more likely to be functional after an earthquake so that he doesn't lose income. Well, you could say, "If you spend this more money, and we put this much steel in, and it costs you this much, the probability of collapse or the probability of losing functionality we would calculate as this." But to an investor, that's meaningless, because, "Okay, I'm paying money upfront. I'm buying this probability increase. But how do I connect these up? That's not an apples and apples comparison."

We said, "Okay, what you've got to do is look at the lifetime costs from earthquake damage and discount them to the present." Now you can say, "Okay, if you invest this much, you'll decrease your expected lifetime costs from earthquake damage, let's say over 50 years, by this amount, and it's much bigger." Or something. Then they can look at this and make a tradeoff as an investor. As you can imagine, looking at lifetime costs from earthquake damage is a horrendous problem, because [laughs] there are so many uncertainties involved. But we just broke it all down into the pieces. We made probability models for each piece. It involved things like fragility functions, the probability that certain components will be damaged given certain strains or whatever on that component. We looked at repair costs and probability distributions on not only how much it costs if that part got broken, but how long, because he wanted to look at downtime for repairs. We did a whole analysis that involved damage and loss, and then you sort of integrate it all, and you have to include models of how frequently earthquakes come along, and what they'll do when they come depending on how big they are, and so on and so on, so it's quite complicated. But then we get a final number.

For example, you could look at, "If I buy a building, should I insure it, or should I retrofit it? I'll still probably insure it, but maybe I could have less insurance if I retrofit it." That's the sort of upfront costs when looking at expected costs in the long run over a lifetime. You can make the lifetime whatever you like. You can make it ten years, if you like. You discount back to the present. By the time we were finished, you could do those cost-benefit analyses. I had a postdoc from Stanford who worked with me in the early 2000's. He was interested in practical stuff like wood-frame homes. Should you insure them? Residential property. We had a paper on how you could do the analysis. That was of interest to the California Earthquake Authority, the people you can get earthquake insurance from in California. Yes, so that performance-based design was basically the idea, "Let's allow the owner of the building being constructed to decide what level of earthquake resistance they want, above a building code minimum."

I don't know if that's happening, nowadays, in the rigorous way that we did it but it certainly had a lot of interest in the profession. They even created booklets on how to do this and so on, out of the Applied Technology Council in California. They got a contract to do that. I think FEMA funded them. Anyway, there were other good people working in the PEER Center that were looking at aspects of this too. We published a nice paper in 2007 that laid it all out in the *Earthquake Engineering and Structural Dynamics* journal, and it was coauthored with a professor at Stanford and one of his students, and a professor at UCLA and one of his students, and me with one of my students, so we have this nice paper that lays it all out, after almost ten years of working in that area.

**ZIERLER:** We talked about structural health monitoring. What was the value in the late 1990s of looking specifically at what you called ambient vibrations?

**BECK:** There was a long interest in that, because as I said, structures vibrate all the time. You don't feel them, usually, but if you have sensitive instruments, you can record it. This gave us an opportunity to look at the dynamics of structures in an experimental way by just putting sensors in the building and recording their motions that happen all the time. Of course, it's very low-amplitude motions, and I thought, "Well, good, that means it should be governed by linear dynamics, so let's see what we can do with appropriate system ID methods—do we see some of the modes of vibration and what are their damping values, and so on?" It's a challenging problem when you ask those questions, because you don't know the input. The input is wind. It's microtremors. It's traffic going by shaking the building through ground vibrations, so it's not as straightforward, perhaps, as in the earthquake problem where we've got instruments in the base, and we know that the motion from the earthquake gets into the structure through the base. That's the only thing attached to the Earth. If we *record* enough degrees of freedom in the base, we would capture the input, but in ambient vibrations, we don't know where it is. It's wind on the sides, it's microtremors at the base, and all that, so it's challenging. The one advantage is you can collect a lot of data. You can go for minutes, or hours if you want to, whereas an earthquake is all over in typically a minute or less. You have a lot of data that you can crunch on.

We showed a way of doing this analysis of ambient vibration, which amazingly converts it into a problem of basically free vibrations of the structure, that is, it's like you gave the structure an impulsive kick and then let it sway. Mathematically, it's equivalent to the free vibration solutions of the structure, but it's actually coming from these ambient vibrations where it's being excited. The theory is based on a stochastic model for the ground motion, and you look at cross-correlations of the response at different points. Perhaps you know the concept, you have a time lag between the records, and you multiply them together. It turns out that if you look at these cross-correlations as a function of the time lag, mathematically you can show that it's like a free vibration solution, where the time lag is like a real time, a pseudo time, of the free vibrations. Once we massage the data, do all the cross-correlations, then we just applied my computer program MODE-ID that I developed in my thesis to extract the modal parameters in this case, the simplest case of free vibrations. That told us something about the dynamics, but it's limited because it's not damaging motions or anything.

Then the idea became, "Well, look, when an earthquake comes along, you get non-linear response and you can get damage, what if you go back now and measure the ambient vibrations afterwards? Maybe you can figure something out from that." Well, yes, the modal parameters may have changed permanently. The frequencies may have shifted permanently. What does that imply about damage in the structure? It now feeds into structural health monitoring. That's a really challenging problem, too, but we showed how to do that with this Bayesian analysis. Many papers—you'll start to see them popping up as you go through my CV. I think the first one was in 1991, where we said something like "probabilistic structural health monitoring." Later, it was called "Bayesian structural health monitoring." We used ambient vibrations to get the modal parameters while it's in a healthy state. You have an earthquake, look at the ambient vibrations afterwards and extract the modal parameters. The changes in the modal parameters imply something about changes in the structure, and it's basically updating a finite element model of the structure using this data, the estimated modal parameters before and after the earthquake. It's basically damage detection and location using changes in the modal parameters. That's what we did. We continued along these lines.

What has gotten better over the years is what prior information we put in, which is needed because it's a hopelessly ill-conditioned inverse problem. You cannot do it by optimization, the old way of doing things. You'll get multiple solutions. The more prior information you put in, the better conditioned it becomes. Never completely; it's never perfect. We've tried to improve our probabilistic analyses of the building response data by getting more prior information in. That's another whole story that we came up with a decade ago, where we realized that you can use sparsity; that damage doesn't occur everywhere, it only occurs in a few locations, barring collapse of the whole structure. We can impose that constraint in a very nice way in a Bayesian analysis. It's called sparse Bayesian learning. We didn't invent that, but we realized you can use it with structural health monitoring, and so we did.

**ZIERLER:** In the early 2000s, as you got involved in thinking about optimizing strategy for recovery after earthquakes—obviously this is a very multidisciplinary effort; politicians, taxation, very different kinds of areas of research that are involved here. What did you feel like your area of expertise was that contributed to the field of recovery after earthquakes?

**BECK:** It comes to this performance-based design thing. We developed how to do the economics of the earthquake recovery for structures. In recovery—firstly, we were able to look at probabilistic analysis. How long is it going to take you to recover? How long before functionality? The models of all of this—damage analysis and loss analysis and all that—allowed this. You could try various strategies for recovery, and you could analyze the economic consequences for the future. That's our area in looking at recovery, what should you do? Maybe you should just demolish a damaged building. Or maybe you should fix it. If you're going to fix it, what level should you fix it to? Give it more earthquake resistance than it used to have? These questions can be answered using these expected lifetime costs. I should say that it goes beyond expected; that's a mean value. You can get into decision analysis, and you can get into things called utility functions, preference functions. We got into decision theory, learned all about decision theory. We have a couple of papers on that in *Earthquake Spectra*, which is a journal for earthquake professionals, not just earthquake engineers.

**ZIERLER:** When you look at structural health monitoring, how do you define what a benchmark problem is?

**BECK:** It's kind of like universally what a benchmark is. I don't know if the original meaning is they actually built something on a bench or something? I don't know how the term came about. But anyway, in our case, a benchmark is a well-defined problem that everybody can work on, and that everyone can use their favorite method to analyze it and see how it goes, because we know the answers. I formed a task group in 1999—in Engineering Mechanics of ASCE—to address benchmarks for structural health monitoring because I saw that people were doing theoretical things which were, to be frank, useless, because they made assumptions that would never be satisfied in real life. I wanted to steer things in a way that, "Hey, let's try to do this for real problems." We started off with some theoretical finite element modeling of a structure, kind of virtually damaged it. You can generate artificial data from the undamaged case, and then the student would change part of the model, like reduce its stiffness in some areas or remove a structural connection or something, and damage it that way, simulate damage.

We also did some experimental work. Of course, you can't go out and damage real structures, but there were people, for example a guy at the University of British Columbia in Vancouver, that had a large structure on a shake table, and we could go in and unbolt pieces of it. It was a steel frame structure. We could take a brace out, or loosen a connection, and so on. We then collected vibration data from it. So, in addition to the simulated data benchmarks, there were experimental data benchmarks that people can study. They're well-defined problems. I've noticed that the simulated data is much more popular to analyze, and over the years, many people have gone to that data and said, "Okay, let's see how well we can do with our method." There was a special issue published on it in the *Journal of Engineering Mechanics* in 2004 where a number of people that had worked in the task group published the results of their methods. Here we are, more than 20 years after this task group was formed, and people are still using these benchmarks, so it has served a good purpose. Actually, people went on to also create benchmarks in structural control, examining how well the seismic response can be reduced. There's a number of benchmarks out there now, all related to so-called smart structures.

**ZIERLER:** It's outside of your field, but I wonder if you took an interest in how the World Trade Center towers collapsed after they were flown into by terrorists with planes on September 11th.

**BECK:** I'm not a real structural engineer, so I kind of stayed clear of commenting or doing an analysis, but several colleagues at different universities, one at MIT and one at Tufts University, for example, were really intrigued and got into analyzing what happened. As I remember the story—and I think there's agreement—there was another guy at Northwestern that also did an analysis, and I'm sure there were papers that followed up, but these guys, within a week, they sent out to their friends and colleagues an analysis of what happened. The planes went in and the buildings at first withstood the enormous impact. What happened was the planes were full of fuel, of course, and that fuel caught on fire—it was burning so hot that the temperatures got to thousands of degrees Celsius, and the heat started to soften the steel. You can melt steel if you raise it to a few thousand degrees Celsius, or something like that, as you know. Molten steel, right? What happened is those stories got softened to the extent that they didn't have the strength to support the floors above, so those floors started coming down. You've got a huge mass, huge weight, dropping down. It hit the floor below. That just buckled everything at that level, and so it collapsed down to the next floor, so it was pancaking—bang, bang, bang, bang, bang, bang, bang—just collapsing floor-by-floor going down. But it withstood something like—one was over an hour, and one was close to an hour, I think, before that happened, so the towers stood there for a long time, but eventually the fire did them in. So, it wasn't the impact; it was the subsequent fire. I don't know how you would protect against that. Well, now the new world towers have some sort of shell frame around the outside, so the planes would hit that and it would reduce their impacts. I don't know; I haven't seen an analysis of what they expect. However, if you've got that sort of intense fire in a building, there's nothing you can do. The steel is going to melt.

**ZIERLER:** Did you do any consulting work with regard to analyzing property investment and risk as it relates to infrastructure and earthquakes?

**BECK:** No, I didn't. We laid out how to do it, and I spoke at a few conferences. I remember once I was in New Zealand on sabbatical leave and I went to a conference and talked about how you could do it to structural design engineers. But I don't think anyone ever contacted me and said, "Hey, we're using your approach." Even though we laid it out all, it's still complex and you need the right software and everything. There's a postdoc of mine who is now a professor at the University of Colorado in Boulder who continued and did consulting in this area. He might know of cases, but I haven't seen him for quite a few years. We've lost contact a bit. So, no, I don't know if anyone used it.

**ZIERLER:** What were some of the big takeaways in the early 2000s when you looked at wood-frame buildings?

**BECK:** This postdoc who stayed on for some years and became a research scientist at Caltech was the guy that was heading basically this effort, with the wood frame buildings, along with a former colleague of his at a structural engineering consulting company. I was, of course, on the project but the details are now a bit hazy. I think things like, should we do this for wood-frame buildings? Should we, for example, tie them down—that's a no-brainer—at the base? That's older buildings. Should we put certain types of steel brackets at connections of the wood frame? You can provide some sort of ductility, that way, plasticity, things like that. It costs you money, and then you say, "Well, what does that buy us?" We looked at this expected lifetime cost.

I remember this postdoc and I talking; we were kind of interested in, "Should you insure?" I forget all the details, but I went away from it thinking, "Nah." In practice there's a large deductible, and at least in my case, I decided not to do earthquake insurance for my private residence. That's about as far as I can go on that. More intellectually, I was very engaged to work out how you could do this performance-based design, how do you estimate the probability distribution of the costs over a lifetime, and so on, and how you make decisions. Once I had sorted all that out, I was not so intellectually engaged. I was happy to have people in my group who wanted to work on it, and there was a student who got a PhD in that area in 2007, but I wasn't so intellectually engaged, and that may be why I can't remember the [laughs] details of it.

**ZIERLER:** We talked about Bayesian solutions for structural health monitoring. Two-stage Bayesian structural health monitoring. What does that mean, two-stage?

**BECK:** Instead of going directly from your sensor data, vibration data, accelerometers and so on, to updating the model, it's like I said before: you extract the modal parameters for the modes of vibration. You can only get the low-frequency modes. You might be lucky if you—in a high-rise, you might get ten modes of vibrations, including swaying in both directions and torsional modes. You extract the modal parameters. That's the first stage. Then what I said before—the earthquake comes, you collect the modal parameters data afterwards, and you look at changes. The first stage is extracting the modal parameters from the data. For example, in the benchmark problem, you've got time histories, which are pseudo or real accelerometer data. You use that to estimate the modal parameters, and you look at before and after the damage. The second stage is, you update the finite element model to assess the location and severity of any damage. This second stage is much more difficult.

By the way, I showed in my thesis, the first stage, finding modal parameters from the response data, it's an identifiable problem, that is, there's uniqueness when determining the parameters. The problem is that going to the second stage, where you take the changes in modal parameters and look at the changes in the structure, as implied by changes in the structural model, that is very challenging, because there's so many things that could be changed in the structure. That's a highly ill-conditioned inverse problem, non-unique, as I said. People were stuck on that. The Bayesian approach allows you to tackle it, and the more prior information you can put in, the better, such as the sparsity of structural damage. That's the two-stage approach. First stage, determine the modal parameters from the actual accelerometer data. Second stage, use the changes in modal parameters from before and after to find out where the damage is and how severe it is.

I should say that you have to calibrate some model of the structure using data before any damage, such as a finite element model. We use pre-earthquake data to update it. We call it a calibrated model. Then for the possibility of damage, you estimate the modal parameters, and you now update your calibrated model and see where it changes its stiffness, to be consistent with the data. If it reduces stiffness in one story, for example, you say, "Aha, that's damage there. That's why there's a reduction in stiffness." Because if something breaks, you lose stiffness, as you might imagine. That's the idea.

**ZIERLER:** The phrase "instrumented buildings" in the context of looking at real-time loss estimation—what does that mean, "instrumented buildings"?

**BECK:** Buildings that have sensors distributed throughout them to measure—you can't measure displacements in a building, because displacement relative to what? So you have these inertial devices—accelerometers. You're actually measuring accelerations in the building. Nowadays, as Tom Heaton will tell you, you can buy these little cheap solid-state things and sprinkle them all over the building, and they'll all talk through the internet, and you can collect masses of data in an earthquake. Prior to that, in the older days, it was expensive. A good accelerograph was about $1,000, so you couldn't afford to put too many out there. But a building which had them we called an "instrumented building." It had the accelerographs sitting in there waiting for an earthquake to come, and then they would trigger. Of course, now, the dynamic range is so high on these solid-state accelerometers that you don't have to trigger them. You can continuously measure everything. You get the ambient vibrations. You get the earthquake motions when it comes. You capture everything. They don't go off-scale. They've got a huge dynamic range, maybe up to a g or 2 g's or something. But you can go down to milli-g's, thousandths of a g. It has all changed.

**ZIERLER:** What have you learned about property values over the life of a given building, when you're looking specifically at the effect of seismic risk?

**BECK:** It's not done regularly but it should be, these analyses I talked about in the performance-based design, lifetime cost, because the value of a structure should be set by not only its income you're expecting from rents or whatever, but also losses that can come from earthquakes or any other sources. Income can vary depending on the economy and all that, so you've got to model all that, but that was all done. That's all standard stuff for people, investors, like looking at the stock market, what it's going to do.

What was ignored was looking at the earthquake risk, and how you'd bring that into an investment analysis, an income and expenses kind of analysis over the lifetime. Two structures alongside each other may have similar income, but one has a far better earthquake resistance. In other words, its lifetime economic losses are expected to be much less. You should know that and be willing to pay more for that structure than the other one, even though the income streams look the same. Again, it gets back to a question you asked me before. I don't know if anyone is actually doing that, but they should. They should. Again, intellectually, I wanted to show them how to do it, but then I'm not going to be out there trying to wave the flag and get people to do that. That's not my interest. I moved on to other things that I wanted to solve.

**ZIERLER:** This is a field I was interested to see that you were involved in—artificial neural networks. What's the connection there?

**BECK:** This is standard stuff. A lot of people in CMS do it, for example—this is AI, Artificial Intelligence. We have physics-based models, finite element models, using Newton's Second Law and all that. But let's say you just said, "Okay, I've got this input. I've measured these base motions in an earthquake. I've got this output throughout the structure. Can I develop a neural network from this data that could predict, if I put another earthquake into the base, what the response will do?" We played around with that for a while. The neural networks—and this was prior to deep neural networks with many layers—they have a huge number of parameters to estimate, and you've got to find values for them, and sometimes it works well, and sometimes it works extremely poorly. For a while, we were interested in this challenge. I wanted to explore Bayesian methods and see how well they could do but eventually I sort of lost interest. Now these deep neural networks are being used, as you know, for automating driving and all sorts of things. Google's search engine uses them. I don't know if it should be revisited, but I haven't looked at it in the modern generation of neural networks.

**ZIERLER:** Does AI or neural networks get us ever closer to instantaneous loss estimation for instrumented buildings? Is it true real time?

**BECK:** It could be, yes. The thing is, to be able to get it to reliably determine a neural network model, you have to train it, and it's not easy in our field. In many of the fields, you've got billions of pieces of data coming in, like Google's search engine, but in our case, how do you train the neural network to learn the dynamics of the structure? It's no good using ambient vibrations, because in an earthquake it's going to look different. The structural dynamic characteristics are going to look different. In principle, what you said could be done. If it could learn it quickly, maybe it could learn and predict very quickly. But you need lots of training data for a neural network to train it, for it to learn, and we don't have that, other than the ambient vibration stuff, but that's not going to help you for predicting damage. That's the challenge of it.

**ZIERLER:** What was happening in the field of seismic early warning, where you saw an opportunity to get involved?

**BECK:** Again, I looked at it and thought—I was interested in the intellectual problem of how could you utilize these early warnings in an engineering way, rather than just "Everybody, get your head down—get under the desk, there's an earthquake coming." You can think of things like elevators, and an earthquake is coming so automatically take them to the nearest floor, stop there and open the doors. Or shut down a nuclear power plant; there's a big earthquake coming in. Or surgeons are doing surgery, a lot of them now with robotics, and stopping it, or in some other way you have to do something. You don't want blood flowing everywhere. How do you handle situations like that? You've got to look at costs and benefits. How do you quantify that? How can you do it quickly?

It gets back into decision theory again and making estimates of the benefits and the costs. It's kind of tied in with what we had done with the performance-based seismic design. I had one PhD student working on it, and Tom Heaton had another, who were doing civil engineering research. We had some joint papers with them. Then with the student I had working on early warning systems, we did some stuff on our own. But that was the idea. Firstly, what engineering applications could you conceive of, and then how would you automate the decision making? You've only got a few seconds. You can't have a human come in and say, "Oh yeah, maybe I should do—" No, it has to automatically do it, so you've got to be very careful. You really want a rigorous framework to handle the uncertainties and the cost-benefit analysis before you make the decision of shutting down or not. In a nuclear power plant, the consequences of shutting down and it was a false alarm would be enormous, right? It could be millions of dollars, would be millions. You have to look at the cost-benefit analysis. You can have false alarms, for example. The system is not perfect, so you have to look at it. There's always the risk you'll do something wrong, but you have to do what's rational and what looks most probable.

**ZIERLER:** What are some of the unique challenges of looking at non-linear control of offshore platforms?

**BECK:** Well, did I do something on that? [laughs]

**ZIERLER:** Yeah.

**BECK:** Non-linear control of offshore platforms. I think it's no different in terms of non-linear control conceptually and even theoretically, than against earthquakes, but offshore platforms—well, earthquakes can occur, too, if they're like out in the Santa Barbara Channel, but mainly you're worried about wave actions. It's really tricky, because storms are unpredictable. You have these rogue waves that get generated, just very infrequently. It has all the essence of looking at the structural control stuff that we did for buildings. I don't think we explicitly considered offshore platforms, but conceptually it's the same sort of thing.

I don't think any offshore platform that I know about has active control. They have passive control. Passive control is like putting in big hydraulic dampers, viscous dampers or something, or coulomb friction plates that slide when things deform, so you get friction, you get this type of energy dissipation. Actually, Caltech has a building which has got that frictional type of damping. Which one is it? I think it's Broad that has braces that give damping, at a certain shaking level they allow frictional yield and slide, and you'll get damping within this brace. That's called passive damping.

**ZIERLER:** Another nomenclature question—"constructed facilities." When you're looking at system identification of constructed facilities, what does that mean?

**BECK:** It's not infrastructure; it's a subset of infrastructure. It's where you have buildings or bridges. Structural—it's basically building structures, I would say.

**ZIERLER:** Your work simulating enormous earthquakes, the possibility of something like the 7.9 San Andreas Fault from 1857, obviously this is before high-rises and skyscrapers. What were some of the things that you learned about the potential impacts if, heaven forbid, the Los Angeles area would experience that magnitude earthquake?

**BECK:** It's not that I did analysis of that. My colleague, John Hall, along with Tom Heaton, did do that. The scary thing about these big earthquakes is they have a lot of energy at low frequencies, compared with smaller earthquakes. The high-rise buildings have low natural frequencies, fundamental frequencies. The lowest one for a 50-story building might be a five-second period. That's 1/5 hertz in frequency.

**ZIERLER:** Meaning what? What happens in those five seconds?

**BECK:** It means that if you pluck the building over from the top and let it go, it would sway over and sway back and take five seconds to do one cycle. There's a lot of energy in the spectrum of a big earthquake around five second period, and so it could pump energy into the building—let me first say that buildings basically see earthquakes through filters around their natural frequencies. This is a linear thing, and they do change their natural frequencies, as I told you, when it comes non-linear motion. But they see the earthquake through, for example, the fundamental mode of vibration, which attracts the most energy into the building, which will just be seeing the earthquake through a narrow band filter, really, around its fundamental frequency. A relatively small earthquake won't have much energy at those frequencies, so the building won't even notice the earthquake, but a big earthquake will have a lot of energy there and can cause very strong shaking.

There are other complications, too. There's a near-source effect if you're right next to the fault. But if the San Andreas ruptures, as you say, giving an earthquake magnitude of eight, for example, it will have a lot of energy at longer periods, and the worry is that the high-rise buildings have never been tested in this way, because we've not had big earthquakes right next to modern high-rise buildings. We don't have that experience. It's all theoretically predicted. Depending on how you look at it, it could be a bit scary. I think really this is an area where academics are absolutely important, because if you're in the profession, it's very difficult to come out and to do this in a frank way. You get into the territory where people will say, "Well, there's lots of uncertainties," and there are, so you cannot make deterministic predictions, but it does look like for big earthquakes, with high-rise buildings near the faults, you're going to get a very strong shaking response.

**ZIERLER:** In 2011, did you get involved in the crisis with the Fukushima disaster?

**BECK:** No, it wasn't really structural. No, I didn't. I did get involved in a number of different projects in Japan coming out of the Kobe earthquake, which was very damaging, and where an earthquake fault basically ruptured through the city of Kobe. It led to some very interesting research projects in Japan. There's nothing like a destructive earthquake to loosen up research funds in earthquake engineering. I got involved in some things there, but no, not Fukushima. That was totally awesome, that tsunami, the power of that tsunami, just amazing, in the videos. You saw them, I'm sure.

**ZIERLER:** Yeah. We talked about Bayesian neural networks. How did you apply this to looking at the integrity of bridges?

**BECK:** I think that was the work with—

**ZIERLER:** Arangio.

**BECK:** Yes. She was a visiting student from a university in Rome, La Sapienza. She came to work with me and she was interested in doing this with neural networks. I guess her advisor said, "Oh, you should do a Bayesian approach" and approached me—could she come over and work with me? I think this was again trying to look at the neural networks as a way of having a model that could simulate the dynamics without having to spend a huge effort in developing a finite element model. For something like a bridge, it can take months, maybe, to develop it.

As it turned out, the main thing I think with her was how you can look at the different levels in a Bayesian approach. You don't just take a model class and look within that for the best model based on data. You can take different model classes, such as different structures, architectures, for the neural networks, and look at the probability of the model class, the whole model class, the whole set of models, as you vary the parameters. Each neural network with a different structure is a different model class. Within that model class, you can take different values for the weights in the neural networks so there's also parameters to be estimated. There's a whole lot of them. By looking at the next level up in Bayes' Theorem where you go from within a model class to across different model classes, you can apply Bayes' Theorem there too. That was, as I recall, the key thing in her stuff, is that she could look at structure in the neural networks and propose which is the most probable one to use.

**ZIERLER:** Tell me about the development of ePAD, earthquake probability-based automated decision-making.

**BECK:** That was one of my graduate students who is from Hong Kong and is now a professor in Tokyo, working in statistical science. He did his PhD in civil engineering. He wanted to come up with a name, and it was kind of like iPad, right? ePAD. But that was the probabilistic formulation I was talking about, to automate decision-making when you have earthquake early warning. That's what he called his framework.

**ZIERLER:** We've all heard of Occam's razor, of course. How did you apply that in one of your presentations on Bayesian system identification?

**BECK:** That's a really interesting thing that comes out of the Bayesian approach, and it relates to what I just said about the research with Arangio, with looking at the higher level in modeling, say different architectures for your neural networks, different model classes. You can do that in anything. Let's say I have some sort of non-linear model and a linear model and we have parameters that we're uncertain about, and I get some data. Can I compare these two models? Well, it's not easy. You can't do it just on the basis of how well they fit the data, because maybe one of them has a whole lot of parameters, and you estimated those parameters from the data, so it would be really biased to do that. It turns out that the Bayesian analysis, when you go and do Bayes' Theorem at the model class level rather than *within* a model class where you estimate parameters, you're now at a kind of higher level and you're looking at different model classes based on the same data, it applies an Occam's razor. It's actually a beautiful result. We proved theoretically what's going on, although people had realized earlier that it *was* going on and had some hand-waving arguments. In about 2005, we showed rigorously what was going on.

What did Occam say? He said don't multiply entities unnecessarily, or basically, don't make it more complex than you need to, if it can explain the data. If you have two models of equal fits to the data, take the simpler one, was that kind of philosophy. But what do you mean by "fits to the data"? How do you quantify that? And what do you mean, "simpler"? How do you quantify that? People thought, "Well, it's the number of parameters," but that's not a good way. It turns out that the real answer is, and you look at Bayes' Theorem at the model class level to get this, you find that you must look at the equivalent of the likelihood, which appears in Bayes' Theorem within a model class—the equivalent is what we call the evidence, also called the marginal likelihood. It's the probability of getting the data, given the whole model class. Not any particular model within the model class; the whole *set* of models. It involves an integral over all of the parameter values and so on. It's complex and challenging, but when you look at that evidence, there's this beautiful result.

If you take the log of the evidence, you can show mathematically, it's a difference between two terms. One is the average of the log likelihood. Now, it's well-known in statistics that the log likelihood is a good measure of fit to the data. For example, if you take Gaussian errors, it becomes just the sum of the squares of the errors, in other words least-squares fitting, if you want to minimize it. So you have one term in the log evidence, the log likelihood, but you have to subtract a term, which is technically called the relative entropy, sometimes cross entropy, in the sense of Shannon's Information Theory. It gets us into Information Theory. It's the relative entropy of the posterior to the prior. What is it actually telling us? It's a measure of how much information your model class extracts from the data to learn about the parameters. So it's this beautiful result. The complexity is really how much information is this model class extracting from your data? It's this technical term—relative entropy of the posterior to the prior. Of course if you have more parameters, typically you extract more information from the data, and it gets penalized by that, the data fit.

The second term is subtracted. There were some well-known decision criteria called Akaike's Information Criteria, after a Japanese statistician. There was also Bayesian Information Criterion. So, AIC and BIC. What we showed is, hey, they are just an asymptotic approximation to the correct expression for the log evidence for the model class that we talked about, and it is the log evidence that controls the *probability* of each model class. So that is a measure of how plausible that model class is based on the data, and also given a set of candidate model classes, so it's conditional on that. This log evidence term is difficult to compute, but it's very fundamental. We spent a lot of effort on developing and testing algorithms to compute it, and there still could be more research done on that. It implements Occam's razor. You take the most plausible, the most probable, model class among all these sets of candidate model classes based on the same data, and you turn out to be implementing a form of Occam's razor. You have a data fit term, you want that to be as high as possible, and you have information extracted from the data. You want that to be as low as possible. But there's a tradeoff. The more parameters, the better fit, that kind of thing. That's the Occam razor at work. It's a tradeoff of the fit to the data and the simplicity of the model class. But it's not simplicity in the sense of it looks mathematically simple. It's actually more subtle than that, as I said.

**ZIERLER:** We talked about some of the possibilities with AI and neural networks. What about the idea of a virtual inspector, right before or after a major earthquake event?

**BECK:** It took a while for us to get the paper on the Virtual Inspector done. It came from when the student that graduated in 2007 was working on this performance-based design, and I had said, "Hey, we could look at a virtual inspector" What is it? It's a computer program that does what a building inspector does. What inspector? The guys that go around after an earthquake and they red-tag or green-tag, or sometimes yellow-tag, a building. If it's red-tagged, it says they went in and they looked at it and said, "Oh, this building is in a dangerous state. I can see this damage." Yellow tag means it's got to be looked at a bit further. Green tags mean no damage was observed and the public, people, can come back into it. We thought, "Why can't we do that virtually? We can ahead of time say, if you had this earthquake—again, looking over a lifetime if we wanted, with all the probabilistic aspects—what is the probability of getting a red tag or a green tag?" This student and I were thinking about this, and I said, "This is a virtual inspector." She liked that term so that's what we called it. That's what it does. Instead of looking at the probability for losses from earthquake damage, it looks at the probability that your building has damage that will be red-tagged after the event, which is a very practical thing.

**ZIERLER:** In 2017, your publication rate was really as robust as it ever was. I wonder if one of the reasons for retiring at that point was that you could actually do more of the work?

**BECK:** No, because you lose your research group, so you lose that leverage you have when you have a lot of smart people working around you. Plus, at my age, I don't program. [laughs] I'm not going to be writing MATLAB programs. No, it just comes a time when I felt it would be nice just to do my own research, not have to worry about funding a research group. I had two years scholarly leave, so I think I taught for 34 or 35 years. Not that I didn't like teaching, but been there, done that, it was time to—I was ready to retire. And I was excited about my quantum mechanics research, which is completely different, and I wouldn't corrupt a civil engineering student to work on a thesis in quantum mechanics.

**ZIERLER:** [laughs]

**BECK:** They wouldn't get a job anywhere.

**ZIERLER:** What are the areas in quantum mechanics that you always wanted to investigate but really couldn't during your professional career?

**BECK:** I had this idea, once I figured out what probability is, to apply it to quantum mechanics since it is probabilistic mechanics, all to do with probabilities. It's not deterministic. There were these things like Bell's Inequality and Quantum Entanglement and all that. They're all probabilistic things, actually, and they're all thinking of probability in terms of a frequentist approach for its interpretation. I started to think about how you would look at it from a Bayesian point of view, and then things change. I wrote one paper that I published since I retired that I had been thinking about for a long time. It has been totally ignored. I think there's one guy who cited it. But basically saying [laughs], "John Bell's definition of locality"—which he gives as a probabilistic definition—"is incorrect." I prove it mathematically, that it's incorrect, so it collapses all that framework underneath Bell's Inequality, which is huge, but no one has paid any attention to it. I actually submitted it to a mainstream journal and the guys didn't understand what I was doing, and they didn't have the necessary probability background and thought I was wrong. One reviewer gave a counter argument which was simply wrong. I ended up publishing it in a journal which was more open to being on the fringe [laughs]. Actually, one of my CMS colleagues had pointed it out because he published a paper in there, the *International Journal of Quantum Foundations*.

The other thing that I got intrigued about is what is spin of a fundamental particle. I've always wondered about what spin is, and people say, "Oh, you can't give it a classical interpretation. You've got to go into quantum mechanics. You've got to go into relativistic quantum mechanics to fully understand it" and so on, because it pops out of Dirac's equation in wave mechanics, quantum mechanics. But I came across a paper which gave a sort of classical interpretation, and I picked up on that. It was written by a professor of physics in Spain. He wrote a book, actually, about 20 years ago. I picked up that, and then I showed that that model he was looking at is actually mathematically equivalent to a quite different looking model that was published by another physics professor at the University of Colorado in Boulder. I think that my work gives really good results, and I've actually put it up on arXiv.org last year in August but I haven't submitted it to a journal yet. It has kind of sat there, because I got interested in one aspect in it. A Russian professor contacted me and pointed to his papers, which were a different way of looking at this aspect, and when I looked at his papers, I thought, "Where did he get *that* term from?" I went and looked at my stuff, and I saw, "Oh, it's in there. It's to do with the electric dipole of an electron." I worked on that, and then unfortunately, I've been involved in other things more in my personal life and it has been sitting there. I haven't submitted it to a journal, and I should. Most physicists nowadays are not looking at these foundational questions in quantum mechanics, so it's a bit of a hard slog, I think, but we'll see. We'll see. I'll try to get it published.

**ZIERLER:** Do you think they should be looking at these foundational questions, given all of the ongoing mysteries in quantum mechanics?

**BECK:** I do! This is the frustrating part. But if you're a professional physicist, you're told—I'm told this, by physicists, not to try—that you'll waste your life if you try to get at the foundations of quantum mechanics. People have been looking at it for more than 80 years, and they still haven't sorted it out properly. Richard Feynman himself said, "I don't think anybody truly understands quantum mechanics." Now, if he doesn't [laughs], what hope have you got? But actually, it turns out it's very, very interesting, this spin. If I can just encapsulate it in in one short description, it's that what we think of as electrons going along a path, a straight path if it is a free electron, is actually not that simple. They move inherently in a helix. They're inherently going in a helix motion. It's just something that they do. It turns out that there's no—if you know about mechanics—you don't need centripetal forces or anything, because Newton's Second Law describes the center of this helix motion, not the helix motion itself. The spin, because it's an electron and it's spinning—if you move with it, it's just going to be stationary except for going around in a circle at extremely high frequency, 10 to the power of 21 hertz. It turns out that if you look at it, that generates a magnetic moment. You've got an electron going around very fast; it's like an electric current and it generates a magnetic moment, and that's what electrons exhibit. But this also generates an electric dipole, so it has a magnetic dipole and an electric dipole. The electric dipole frequency is at 10 to 21 hertz so it's very difficult to detect it, because that frequency is beyond most detections. But the magnetic dipole can be stationary, so it's easy to detect and it's well-known. It's a property of electrons known since the 1920s. The theory explains a lot. I also derived Dirac's wave equation from this basic mechanical model of the spinning electron, so it seems like it's got a lot to offer for it. We'll see what happens.

**ZIERLER:** To flip that question around, when you talk to seismologists, they insist that earthquakes are essentially classical systems. Do you see any opportunity to challenge any orthodoxies in that regard? Are there quantum mechanical aspects to seismology that they should be looking at?

**BECK:** I don't think there would be. Who knows, but I don't see that. I think it's a very complex phenomenon, slip between two interfaces in the Earth. I doubt whether quantum mechanics plays a role, that it's essential to understanding slip. Of course, what's slip at the fundamental level? It's molecule moving against molecule. What is the resistance? It's interatomic forces. So on some level, yeah, it's quantum mechanics, but I don't think quantum mechanics per se, the theory and that, will play a role. I would say that you should be able to, in principle, understand earthquakes without going into quantum mechanics. You can stay with classical mechanics. It's exceedingly challenging, because we don't know what's going on kilometers down in the Earth. We don't know the exact state of stress and strain and what the strength of the rocks and all that are. There's all sorts of puzzles, like the rupture pulse that seems to travel along the fault with healing behind it, so slip stops there. They used to think the whole thing just slipped and kept slipping until the end of the earthquake. It seems like—and Tom Heaton proposed this—there's a pulse running along, and it heals behind it. These are intriguing things, because it means friction is changing with velocity somehow. The expert I think in that now, at Caltech, is Nadia Lapusta. She's a professor in both Mechanical Engineering and Geophysics. I don't think she'll need to use quantum mechanics. I think she did training in physics, so she's probably good in quantum mechanics, but she won't need it, I think.

**ZIERLER:** Since going Emeritus, over the last five years, what are the areas that have been most important to you, without the research group, that are just intellectually stimulating, that you've wanted to remain involved in?

**BECK:** By far, the quantum mechanics. I wanted to keep involved while I can, in let's say my mainstream activities, so I've pursued things that I was doing with people that I was working with. I even picked up a new guy, but he was Tom Heaton's student, a Greek guy that came and approached me about getting involved with a paper he was writing. Actually, at that stage, he was writing a paper on his PhD thesis, and he asked me to get involved, and I ended up being coauthor. Mostly it's people that I worked with before, and we've continued to work. The new stuff is this quantum mechanics. I was really excited about that. One of the problems I see getting older is maintaining your interest. You just change. I used to love traveling. I went to many countries and professionally traveled all over the world. Now, it's a bit of a hassle and I'm not so interested. What has changed [laughs] with me? I was always thinking about problems and making notes and that, and I find that here I am at 73, and I'm no longer doing that as much. Maybe it's just things in my personal life going on, and so on, that may be distracting. I've got grandchildren, a couple of them with health problems and things like that. Maybe that's it. I still feel intellectually *capable*, but I'm not *motivated* like I used to be. To tell you the truth, all my colleagues, brilliant colleagues, as they got older, they just faded out in their research. None of them continued research until—the ones that have gone lived to a ripe old age, but they didn't keep working until the end. That's just something you face as you get older.

**ZIERLER:** In going emeritus, was it an opportunity to relocate away from Southern California as well?

**BECK:** It did free me up on that, although I've just recently, as I told you, moved up to Portland a few months ago. I originally thought of going back to New Zealand. In fact, I had a place down there, just a block back from a beach that I just rented out and never lived in it, with the intention of going there when I became Emeritus. But I've got three children. I've got three grandchildren. New Zealand is a long way away. In the end, that didn't eventuate, and a couple of years ago, I sold the place in New Zealand. Now, my family is kind of getting distributed around the United States, but at least we're all within the U.S.

**ZIERLER:** Now that we've worked right up to the present, for the last part of this excellent series of interview questions, I'd like to ask some broad retrospective questions, and then we'll end looking to the future. First, what do you see in terms of that career shift that you had right around the time that you achieved tenure? What are some of the takeaways there? What are some of the items of advice that you might give young scholars in the field as they're looking to chart their course?

**BECK:** I felt like we were the center of the earthquake engineering research at Caltech in the 1960s, 1970s, and into the 1980s, but it was maturing. Many of our students were in universities with their research groups. There's a lot of activity. In mainstream earthquake engineering, I feel that for a place like Caltech, there was sort of diminishing returns working in that. Fortunately, I had a very strong math background. I have a bachelor's in math and physics, master's in math, so I was able to get into the Bayesian probability, into more mathematical aspects. Research in smart structures I felt was the way to go, around that time. It was a hot area. Structural control, health monitoring, these are aspects of smart structures. I saw this as the future for my students, more than mainstream earthquake engineering, what was mainstream then. Research in smart structures offered some opportunities, because there were lots of intellectual challenges. That has proven to be the case, and now, in most research universities, the dominant research area in structural engineering is in smart structures. That's the shift. I didn't do any mainstream earthquake engineering going into the 1990s. I continued looking at earthquake records based on what I had done before, and that was mainly consulting work, but in terms of my intellectual energies, they were going into how to tackle system ID and non-uniqueness in estimation and structural health monitoring, that sort of thing, and structural control, so more in the smart structures. My general advice to young scholars in academia is to do research that you are passionate about, even if you have to do other research to get funding.

**ZIERLER:** What do you see as your most important contributions on the theoretical side?

**BECK:** There's a couple of things that stand out that I think were novel. A lot of things were the Bayesian stuff that I brought into structural engineering, like MCMC methods and so on, but some stand on their own. They didn't come in from other people's research in other areas. In my work on Bayesian updating, one contribution that stands out relates to the Occam razor. People realized that Bayes' Theorem at the model class level implements an Occam razor, a quantitative Occam razor, but they didn't have the mathematically rigorous expression which shows what you need to take as your data fit term and its tradeoff—subtract this as I've told you—the information extracted from the data by the whole model class. That's a very important thing. You need to not only know Bayesian probability, you also have to understand information theory to derive this.

I'm the sort of guy that—like in the 1980s, I got interested in Shannon's Information Theory, so I read up on it and studied it and thought about it, and so on. I had that background to make the connection. Because it's just mathematics, but unless you know what you're trying to do you are not going to derive it. Many people could look at the integral that is the amount of information extracted from the data, but that's not going to come to mind. That's something that's deep, to get to that. It's just a mathematical integral. It's a relative entropy. People know that and how to compute it and so on, but they don't understand what's behind it. It is the number of bits of information that are extracted from the data, if you use the logarithm to base two that is involved in the integral. That I think it is very important because it ties in with this idea of Occam's razor in a quantitative way and it showed rigorously what the meaning was. We also showed how some of the expressions that were used before are approximations to it that can be simply derived but they're not very good, and we gave a better approximation. That's one important contribution.

The other novel idea that I really liked was what I first introduced in 1992 at a conference when I made a presentation. I didn't have it written in my conference paper. I was talking about how do you decide where to put sensors on a structure? Say you have N sensors, and you want to put them in the structure, and you want to learn the most about the model for the structure for structural health monitoring or whatever. How do you decide where to put them? How can you do this in an optimal way? I had this idea, again from information theory, that you should put the sensors in such a way that you gain the most information about your model, for example, about its modal parameters, from the data that you're going to collect from the sensors. Of course, you haven't collected it yet, so you have to have a probabilistic description of what the data might be, so again, it's kind of a decision theory thing. That idea floated around, and then I finally had the right guy to work on it, and we published the first papers in 1998. Those were conference papers. Then we published a journal paper in 2000. That was a really novel idea.

This guy has actually gone on and looked at also applying it for an underground water distribution system. If your sensors are for pressure and water flow, and you want to find where the leaks are, where should you put your sensors? You've got N sensors under some budget; so where should you put them in the distribution network system? That's very similar to the structural problem: where should you put your accelerometers to learn the most about the structural damage, for example, where it's losing local stiffness? That turned out to use information theory. It was quite satisfying to have my second-to-last PhD student to work on that problem again, and we basically showed a way to do the optimization much more efficiently. It's a very challenging optimization as you may imagine, because if you have N sensors and you have M locations you can put them in, and M is a lot bigger than N, then there's a huge number of combinations. You can't look at every case. It's ten to the power of 20 number of cases, or something huge like that. You have to have a smarter way to optimize to find the optimal sensor distribution. Those are two theoretical ideas that I think are really very satisfying, and they're intellectually mine. Then there's the novel designs way back earlier in my career. I didn't have the idea, the insights, but I worked on it, and I'm proud of that. I was of course young, just out of university, before I did my PhD. I look back with pride on those things. I mentioned to you the stepping structure idea for the rocking bridge, and then the seismic base isolation idea, which we were pioneers in. Those are the novel earthquake resistant designs that stand out.

**ZIERLER:** What about in terms of applications, where we see the translation of the ideas that you've contributed to actually helping society out in the real world?

**BECK:** Certainly, that's true with the base isolation. I think a lot of our work that we did helped inform the building codes, or the code committees anyway. But I'm not someone who views his mission as getting out and convincing people to do something like this in the real world. What I tend to be is, "How do you do it properly? How do you do it rigorously?" Once I've intellectually worked all that out and published it, I kind of let it stand. Sometimes I've had a graduate student that might pick it up. On the base isolation, one of the graduate students of the Berkeley professor that came on sabbatical leave to our lab in New Zealand then went back and started research on it, that student was like a salesman. He started a company, and he gave talks. Actually, there was another New Zealander that did that too, over here in the States. He formed a company. Those guys had a mission to go out and they gave talks on base isolation at conferences. I have not been pushing my stuff right into the application stage. I stop and say, "Is this how you should do it?" Then I want to go on to another intellectual challenge. It's just the way I am.

**ZIERLER:** Where have you gained the most satisfaction in successfully moving some of the orthodoxies in the field to get to where we are today?

**BECK:** I get satisfaction out of seeing all the papers being done on Bayesian stuff in engineering. People are still discovering my work. I've been retired five years, I've had a few papers each year, but this year, I'm on target for my citations to be at least 20% or 25% more than they were last year. I'm actually increasing my citations. People are referencing my journal papers more than ever. I've got a Google Scholar account—in fact, I looked at it this morning—and it tells me I've got 22,600 citations to my papers, and I'm on track to get at least 2,200 citations this year. Last year, I got six under 2,000. My h-index is 72, which is pretty good. It means I've got 72 journal papers which have been cited 72 times or more, so that gives you an idea of the breadth of my impact, at least in terms of research activity. It doesn't say anything about what's happening in the real world with it, but at least people that do research like what I'm doing. There's a lot of them that cite my research.

I get a lot of satisfaction to see that, given my frustrations in the early days where I got resistance against it and had some difficulty, a little bit, on getting published—that's why I used conference papers, which are easier to get published—but now everybody is there, just about. One skeptic that I used to have interesting discussions with was an Austrian professor. He worked in reliability theory and loved the work that we were doing there but he had nothing to do with Bayes. I used to talk to him about it. He was a good friend and we had interesting conversations about Bayesian stuff but I didn't think I was convincing him. Then sometime in 2008, in an email to me, he said, "Oh, I've got a smart young woman student that would like to work on Bayes Theorem. Would you be willing to supervise her for a visit?" She came, and I thought, "Great! This is someone who I greatly respect, who was not enthusiastic about the Bayesian approach; now, he's actually going to get a graduate student to work on it, so he's going to learn a little bit about it." Sadly to say, three years later he died of melanoma at a reasonably young age of 67. But that student was really smart and I would have loved to have kept her as a postdoc, but she was going to get married in Austria, so she wanted to go back.

**ZIERLER:** What are some of the ongoing mysteries in the field? In other words, for young people starting out, charting the future of their career, what are some of the most fruitful areas to work on that haven't yet been resolved?

**BECK:** That's a good question. I've been thinking about this sort of thing for five years. I tend to then think about what I was doing and how it could be extended more. In my thinking, it's algorithmic. It's improving the algorithms so that we can have more challenging models that currently stretch our resources. Another thing that's interesting—and some of my students have done this—is how you include prior information. The more prior information you can build in, that is, the more you know about the problem that you're trying to solve, such as induced structural damage and detecting it, the better. How can you cleverly put some more prior information in?

That's another area, by the way, that I'm proud of. I had a student working with me, and we were doing sparse Bayesian learning for another reason, and I thought, "Damage is sparse. How would we build that into our Bayesian analysis?", that is, into the prior distribution for Bayes Theorem. I challenged him, and we had an idea, and we worked on it, and we finally figured it all out. It took us a while and a few papers, but we got better and better at it. That's something I'm also very pleased about. I think people should work on how to include more prior information into Bayesian analysis. For example, one thing we weren't able to do is to say that it should never stiffen up. It's very unlikely you'd damage a structure and locally it gets stiffer, and yet the way our analyses worked, it was very difficult to sort of truncate the parameter values, that is, to say, "No, it can't get stiffer; it only can get less stiff if it's damaged." That's enormous prior information and not easy to build in in a rigorous way, but I think ultimately, someone will do it.

**ZIERLER:** What do you see as some of the big surprises in your research career, things you didn't see coming?

**BECK:** Sometimes serendipity is at work. Just when we were getting stuck and pushing the Laplace asymptotic approach for Bayesian updating into unidentifiable cases—that is, when you have, from a classical estimation sense, a whole set, a continuum of optimal estimates, which can happen. We were stuck, and we were trying to push the asymptotic method, which involves manifolds of optimal estimates, not just discrete values, in the parameter space in this case, but if there were more than three dimensions for the manifold, we couldn't do anything numerically, and we were stuck.

Then I had this student working on reliability calculations using Monte Carlo simulation and so on, and he found this Markov chain Monte Carlo simulation method, which had been, by the way, around since the Second World War, but people didn't think of using it for Bayesian stuff. We weren't but we were using it for reliability. Then I said to this guy, "This could be used in Bayesian updating." So we published a paper on that, and then it took off. So, just when we were stuck, I had a student working on a different problem, he finds this MCMC method, and I suddenly think "Ah, that's just what we need to push our Bayesian analysis, so now we can handle unidentifiable models!" And we have. That was a big surprise, if you like, because I thought, "Where am I going to go with this stuff?" It's very challenging to evaluate these high-dimensional integrals over the model parameters that are involved in the Bayesian analysis.

By the way, in reliability, the integrals are in an even higher dimension, because you have to integrate over the stochastic input, which is a function, and you discretize it, say, so it's in very high dimensions. There are ways of tackling that, and one way that we found was this MCMC approach and then we brought it over to Bayesian updating. I think in terms of surprises, that was definitely not anticipated at all. The other stuff pretty much went where I could see it going when I got interested in it. It was just a matter of working on it and plugging away, because there were challenges.

**ZIERLER:** Do you think the field is in a place now where your strong background as an undergraduate in mathematics—is that still the best intellectual path to getting to these questions?

**BECK:** Yes, definitely. If you just have a typical engineering background, that's fine for going out to a design office and designing buildings and so on, but if you're going into academia and you want to get into research, I think nowadays that having a strong mathematical background is very, very useful. I was lucky; I was in civil engineering, and I found students that were really good at math. I have to say, some countries are better at educating their undergraduates in mathematics and engineering than others. France and Greece, for example, are very good. Yes, this whole area of smart structures—conceptual breakthroughs are important, getting ideas of how you might do it, but *analyzing* it properly is going to involve mathematics—non-linear control or these inverse estimation problems that are ill-conditioned.

I always felt lucky that I had gone into mathematics and then came to engineering. I had to learn engineering when I came to Caltech as a graduate student for my PhD, but that was a whole lot easier than having to learn mathematics if you never had it. To me, mathematics, I just had a natural bent for it. I think it's important. When I went back more to my mathematical roots, around the time after my tenure, that's when my research really blossomed. My early work was interesting. It was more engineering, and while I was doing programming and analysis, because they were non-linear systems, I was just numerically simulating the structural response with recorded earthquake motions as input and so on, but nothing with fancy math until later.

**ZIERLER:** Last question, looking to the future: Particularly with your interest in quantum mechanics, best case scenario, what mark do you hope to leave?

**BECK:** I had high hopes, but experience shows me that it's very difficult. Physicists in research, they're working in areas that—as I said, that discourages young physicists to work on the foundations. However, there are some that do. I've had some contact with a few of them. For my arXiv paper on electron spin, I got a guy from Spain, a guy from India, and a guy from Russia, all physics professors, that emailed me, so they at least paid attention to that work. I think there's some really interesting stuff there. I was discouraged a bit about the probability stuff with quantum entanglement because it seems to me that the Bayesian approach gives it a totally different perspective. The conditioning in probability is all about information. It's all about what you know implies *this*. Or probabilistically, it's that if you know this information or that, you have different probabilities. But people view the probability conditioning as causal. They say, "If you measure this, it causes this entanglement." But no, "If you measure this, you *know* this entanglement," is kind of the difference in interpretations. It's subtle and it requires a Bayesian approach to probability.

Hardly anyone in physics has a Bayesian perspective. Which is interesting because [laughs] the foundations of this whole Bayesian probability logic—probability as a logic for plausible reasoning—were established by physicists! There's a seminal paper, a beautiful paper in 1946, by a physicist Richard Cox at Johns Hopkins, and then there's Edwin Jaynes, who published a lot of very interesting papers and a beautiful book, *Probability Theory: The Logic of Science*—these are physicists! But they were kind of ignored within physics. Even though now, Jaynes is all over the internet, because there are many people referencing him, including people that have been following me because I picked up on him—I found his papers in 1980. I felt that if people could look at quantum entanglement from a Bayesian perspective, using probability as a logic, things would change, and I wanted to try to set that in motion, but I don't think I'm going to have the time, because I'm getting older, and it requires a concentrated effort to keep at it. One paper is not going to do it. You have to keep publishing in an area before they pay attention.

**ZIERLER:** I hope that happens however long you want to stay at it. It has been a great pleasure spending this time with you. I'm so glad we were able to do this. I'd like to thank you so much.

**BECK:** Thank you, David.

[END]