It is an honor and a pleasure to be invited to participate in this conference. There can be little doubt of the great influence R.L. Moore had on mathematics and mathematicians over his long career. And that influence continues to this day. His influence outside the field of mathematics is less widely known and given my own career choices, I am quite glad of the topic of this conference.
I have pursued an academic career in mathematics from 1968 to 1979 achieving a tenured position as associate professor at the University of Oklahoma during that period. Due to personal considerations that need not concern us today, I decided to make a change at my career, first taking leave of absence at OU and three years later resigning as I worked for my PhD in Statistics at A&M. With that in hand, I continued an academic position at the University of Delaware while simultaneously doing consulting work with a variety of businesses and government agencies, including a year with DuPont Pharmaceuticals. Finally, I left the academic world entirely in 1989 to take a full time position in Statistics with DuPont in its non-pharmaceutical enterprises.
My first published article was “Concerning the Separation of Certain Plane-like Spaces by Compact Dendrons”, and appeared in the Duke Mathematics Journal. I still publish but the titles of my articles now are more on the lines of “Testicular Maturation in Pre-Pubertal New Zealand White Rabbits”, and appear in journals like Veterinary Pathologies and the Journal of the American Statistical Association. And, I say in the aftermath of this presentation and earlier in an interview with the late Ben Fitzpatrick, I attribute whatever measure of success I have had as an industrial statistician to the training and experience that I received working under RL Moore. And I hope to indicate the truth of this claim in this presentation.
So I want to talk a little bit about how it is that I went from Topology to Statistics and how Dr. Moore’s influence continues in this new career. There have certainly been other influences in my life, but what I gained from working with Dr. Moore has had a very profound influence on many of the decisions I have made and on how I conduct myself. I have identified eight areas of major influence that I think he has had on my career and I am sure in one way or another he has had similar influences on the careers of many people in this room. I am going to describe these eight areas in varying detail without implying that they are equally important, mutually exclusive or exhaustive. The first one I want to talk about is the obvious one and that is Clear Thinking.
I want to identify several aspects of clear thinking. The first one of which is thinking logically. Mathematical proofs are not arguments however persuasive. A proof is an irrefutable demonstration that something is true. One of the initial reasons I went into mathematics is that I saw this field as something that I could hold onto without fear of my accomplishments being swept away by changes in politics, social mores, emotions, obscure references and the like. In Dr. Moore’s classes there was no credit for trying, for appearances or for eloquence. We either had a proof or we didn’t. He honed whatever natural ability we had into as sharp an instrument of reasoning as we were capable of developing and that skill could be transferred into many areas. With a solid foundation, I was able to move in time to a less concrete field of work. But, the understanding of the rigors of mathematical proofs has been very much in my mind, when I can construct arguments to justify statistical conclusions.
An aspect of thinking logically that Dr. Moore stressed is visualizing the problem. He encouraged us to draw pictures to clarify ideas, both as a tool for presentation and for developing the ideas in the first place. A good picture can be very helpful in avoiding pitfalls in possible approaches to a problem. Or, it can help clarify the problem and suggest a fruitful line of inquiry. While the pictures I draw today are rather different from anything that we would have seen in any of Dr. Moore’s classes, the value is the same. And, I want to illustrate that with a recent major problem that I attacked. We were trying to develop a statistical model with the level of chemical absorbed by fish in a natural habitat. It was expected that larger fish would absorb not just more chemical but have a higher density of the chemical. I’m not going to go into the biology of why that might be true, but I did expect a monotone relationship between chemical concentration and fish size. But what relationship, and how do we measure the size of a fish? The obvious size measurements are length and weight. Should both of them be used in our model? Should they be used directly or after some transformation to a different scale? What is the mathematical relationship, if any, between chemical concentration and size?
To assess the first question, I plotted length against weight trying various simple transformations. This plot shows one of the results. Now a couple of things stand out here. One is that there is a very linear relationship between the logarithm of the length (that’s the vertical scale) and the logarithm of the weight. The other thing that stands out is that there are two populations here. These two populations are parallel to the eye and, in fact, formal mathematical modeling technique verifies that they are parallel. And, this uniform vertical distance between the two straight lines translates into a length to weight ratio of the upper population being two and a half times the length to weight ratio of the lower population. Well, two and a half is about the difference between centimeters and inches. And, what we were led to discover by looking at this plot is that over the twenty two years that data had been collected it was sometimes collected in inches, sometimes collected in centimeters. Had I not drawn this picture we could have had a lot of fun trying to come up with a correct mathematical model for this data.
The second question was the relationship between the chemical concentration and fish size and looking at this picture it is clear there is no need to look at both length and weight, because whatever you know about weight is already picked up by length as a simple linear relationship here. So I concentrated on looking at length since that was more traditional in this particular field, aquatic toxicology, and wanted to look at the relationship between chemical concentration and length. Now the data was collected at a number of different locations, 18 locations as is indicated here on this plot, and I expected that the chemical concentration might vary from location to location. This was a pollution problem after all, and pollution wouldn’t be the same in all areas in this locale. I am going to be really careful not to tell you what the locale is, otherwise I violate company interests here. So I plotted for each location, the log of chemical concentration against the log of length and I found that at most of these locations there was again a roughly linear relationship between these two and that led me to develop a fairly simple mathematical or statistical model. There is this principle called “parsimony” in science when you look for the simplest possible explanation for the information that you’ve got and if that linear relationship here does it, than that’s what we’ll use.
The next aspect of thinking clearly is thinking creatively. Proving a difficult theorem or constructing a difficult example without help from other students or without mathematical literature requires great leaps of imagination. This activity is not restricted to mathematics. The work I do now often requires working with messy data where there is no clear cut method of analysis. It is necessary to adapt methodology from unexpected sources or to develop new methods. Contrary to my expectations as a young man, my work in industry has been every bit as intellectually challenging and creative as what I did in topology. It is quite different, to be sure. Along with creativity of mathematics, I found my sense of humor, my social ease, and understanding of the world around me growing along with my mathematical skills.
One of the keys to the success of the Moore method of teaching is, I think, going from strength to strength. That is, we develop an extraordinary depth of understanding in a relatively small area of mathematics. The strength this gave us can later be used as a stepping-stone to building strength in other areas. Many of Dr. Moore’s most successful mathematic students went on to make significant contributions in subjects in which they had no formal training. This is the hallmark of a great education. The value of the Moore method goes far beyond the material that we covered. All students of the method understand this. I will make this point in various ways throughout this talk. I came across a quote in an otherwise meaningless bit of science fiction drivel that I read recently. And, that is, “The point you see is not the answers themselves, but the mental development we enjoy through striving for those answers.”
Another aspect of clear thinking is thinking independently. Certainly, one of the hallmarks of the Moore method is the necessity of working independently. Dr. Moore and his students were fiercely independent. Each successful student was someone determined to be the first to discover and present the proof or counter example. Failing that, we were determined to find any flaw in the work claiming to have the solution ahead of us. Going to the board with work never previously discussed with anyone requires the ability to work independently and builds self-reliance. A topic that I will come back to in a moment. Not having a text or external resource of any kind to work with requires an independence of thought that those who have not experienced may find difficult to fully appreciate. This experience is a wonderful character builder for those who survive. And I will illustrate the value of independent thinking in the context of my next point, which is self-reliance.
The Moore method is not for the faint hearted. Having said that I would also point out that I was excruciatingly shy as a boy and as a young man. I would never volunteer to go in front of class, had a horror of presenting to an audience, and rarely spoke out in groups of more than three people. Dr. Moore did not ask for volunteers. Indeed, he ignored volunteers; he called on whomever he wanted. Had it been otherwise, I wouldn’t have survived in his class. In my own case, I started out with the summer measure theory and geometry classes. Dr. Moore called on me the second day of class in Measure Theory. I presented what I thought was a proof; no one challenged me, even after Dr. Moore asked the class if there were any questions. He had me go through the proof again. And again, no one had a question. He had me go through the proof a third time. Still no one had a question. I was so clueless, I’m sure you’re not, but I was so clueless at the time as to why he wanted me to repeat the proof. Finally, he pointed out the obvious flaw in my argument. He did this in a way that did not seem to flaw me as a person, or reflect on my character, but merely to deal with the issue of logic. I decided that day that I could survive and never again feared presenting in his class. That’s not to say I overcame my shyness overnight or that even today I am the most outgoing person you’ll ever meet. But, I have made so many presentations in the last thirty some odd years, that I’ve lost count.
We learn from this example, and many like it, to listen critically to arguments. To question whatever was not clear. To challenge. Some people, of course, carry this to the point of challenging even when the argument appears sound to them, to find out whether the presenter really understood what he or she was saying. This self-reliance that was developed and continually strengthened in Dr. Moore’s classes has proved invaluable in my industrial career. I will point out some of the reasons for that claim.
To begin with, in my interview with DuPont, Don Marquardt, the manager of the group at that time, and at that time President of the American Statistical Association told me that if I wanted or needed direction or guidance, then I would not be happy in that position. I was to be an independent agent who carried his own weight and paid his own way. The company provided me with an office and some equipment, a small support staff and a library, and I was required to pay for it all through charges to internal and external customers. As a consultant within this large corporation, I had an assigned group of businesses to support. But, it was up to me to develop and maintain contacts and work up the work requests. The businesses were not required to use my services and had to pay directly for them. They could go outside of the company for statistical help if they chose. During the first five or six years with DuPont I was one of a group of about 35 statisticians who supported DuPont around the world. We could talk to one another and get occasional help provided that we pay for the time referred. During the next seven years, I transferred out of that group to become the sole statistical support for DuPont’s Toxicology Group. As such, I supported about 150 scientists and technicians and dealt with lab management, business managers, regulatory statisticians, and statisticians of other companies on joint projects. None of these people were required to do anything that I recommended. It was up to me to convince them to do so. There is no one or thing that I can consult since there is no one else with any knowledge of this field and my abilities. So self-reliance is critical in this position. I’ll indicate some of the issues that I deal with in some more detail. It would probably be appropriate to point out that about 18 months ago I did finally persuade the lab management to hire another statistician at the Masters Level to take some of the workload from me. I have also had the services of contract computer and statistical support from interns for varying lengths of times on special projects. So under the heading of self-reliance I want to talk about the need to withstand serious business pressures.
Our toxicology lab is a product safety assessment center for the company. DuPont makes many chemicals that we use in agriculture and a large variety of other businesses. It is our job to determine whether these chemicals are safe for use, safe for manufacture, and under what conditions they are safe. There are many regulations governing this type of work and we deal with regulatory communities or agencies from countries all over the world. There are ample opportunities for conflict. I like to describe our lab as the Middle East of industry. The land of Israel, by this map, and I am sure you are familiar, is a little tiny sliver of land at the juxtaposition of three continents. It is a land that is very rich in cultures coming into contact, rich in ideas and of course rich in conflict. Whenever you have many contrasting cultures coming into contact with one another, the potential for conflict is very real. I would like to re-label this map and put Haskell Laboratory here in this little narrow area in between three large competing forces. There are DuPont businesses that are out to make money selling product, there are regulatory agencies whose charge is to protect the public, and there are science, health and environmental issues about how best do we measure safety. Quite frequently there are three distinct points of view and our laboratory is right there in the middle trying to make everybody happy, failing that, trying to make everybody believe what we say. If we think a chemical is not safe for use, we have to convince the affected business to abandon millions of dollars in development costs and perhaps hundreds of millions of dollars in lost sales. This is not an idle claim. We did recently kill two important new products that were valued in the hundreds of millions of dollars in annual sales. Certainly, statistics was not the only factor in making those decisions. But, it was the earlier indicator. It took a while for the biologists to catch up with what I had been telling them. I am sure they have a different perspective on that. On the other hand, if we think a chemical is safe, and one of the regulatory communities challenges us on it, then we have to come up with the convincing evidence to refute their claims and support our own. My statistical arguments have been credited with saving three important products valued in the hundreds of millions of dollars in annual sales. Finally, if statistical conclusions are seemingly at odds with biological judgment, then the statistics group, essentially that means me, has to defend the methodology and results that I advocate against strong opposition from people who believe their own judgments over mine.
A case in point involved a change in methodology that I championed at the laboratory. After a thorough search of the relevant literature, and analysis of many experiments, I began to advocate a very different way to analyze their data. A few scientists, with whom I work, accepted these changes. Many others are very vocal in opposition. Business managers were warned that there might be adverse affects on the business since my methods might find compounds unsafe at lower levels of exposure than was the case with the old methods. There were literally billions of dollars at stake and the issue inflamed our laboratory for about two years. There were meetings in which I was attacked relentlessly, both professionally, and personally. Friends dropped away. Even the nicer folks made me feel a little bit like this fellow on the Dilbert cartoon. I did manage to get support from a key manager and gradually won over all the management of our laboratory. Many of the opposition side have left the company and I am now pleased to report that the methods I advocated are lab standards and I’m working with some success to change the world regulatory community to adopt these methods as well. A less self-reliant person could not have withstood the pressures I was under at this time. I give a good deal of credit to the Moore experience inside and outside of the classroom. There’s much to the credit of our management and the key scientists that they could see past the immediate impact on business to the long-term health of the company and the public on safety standards. I talk to statisticians in other companies on occasion and often hear how impossible it is to improve methodology in a heavily regulated industry. My experience shows that it can be done.
Another aspect of self-reliance is withstanding regulatory pressure. Part of the campaign to change methods in our lab was to get these methods accepted by the regulatory community. There was a well-respected NIEHS statistician, National Institute for Environmental Health Sciences, who was a strong advocate of the older methods. He made claims about methods that I recommended that I knew to be false. And, it took a long time, a yearlong computer simulation to compare his methods to mine. At the conclusion then, I carefully documented both the theoretical framework and the simulation results and sent him a summary. He was sufficiently impressed to adopt my methods for his own work. A few years ago, I led five-company technical response to a challenge from EPA regarding a class of chemicals they regarded as unsafe. Our response involved a serious and detailed criticism of the methodology by which EPA had arrived at the different conclusions. So convincing was our response that the EPA statistician was discredited and the opposition to these products was dropped. Now, we don’t win all of our arguments with the deregulators, but when we do it its usually because we have good science on our side and we are willing to fight for it. I also serve on two international statistics-working groups that are charged with reviewing regulatory requirements and recommending changes. My point of view on one of these communities is distinctly in the minority at this point, but I am working to change that. One of my critics at the laboratory during this change in methodology a few years ago told me that if I wanted to change the way statistics was done in our laboratory, I should change the world. Well, I don’t know that she meant it that way, but I have taken that as a serious challenge and we will see.
Some of these experiences remind me of a story that I heard at the University of Texas. I believe it was from Dr. Moore, though it might have been from one of his students possibly John Henrichsen. It concerned another of Dr. Moore’s students, whose name I cannot recall. He was describing the Moore method to a sole faculty member who expressed concerned that students of this method suffered from not learning from the experience or knowledge of others. He replied that Dr. Moore’s students learned at them, not from them. While a few of us really claim we cannot or should not learn from others, or that we should not be aware of the work of others, the notion that they aren’t the experts, we are, is critical to understanding what I call life as an activity, as opposed to a spectator sport. That is also a key to the kind of self-reliance that we developed under Dr. Moore’s tutelage.
Next under this heading of self-reliance, I’ll put fighting for a cause. I won’t belabor this point since I have already illustrated it in this methodology change, so I’ll limit myself to one simple example from Dr. Moore’s life that I had a small role in. As an undergraduate student I took some 15 hours of graduate coursework from Dr. Moore, not a terribly unusual thing to do, and I had a total of over 60 hours of mathematics coursework, far more than required for a degree in mathematics. I had heard that it was possible to reserve graduate work taken as an undergraduate for graduate credit. So, I traipsed over to the graduate dean’s office to request that these 15 hours be so reserved. The Dean’s Office informed me that it was not possible and that in fact, I must drop the graduate course that I was currently enrolled in. I went back and told Dr. Moore what I had been told at the Dean’s Office. He went over to the Dean’s Office and vehemently insisted that the Dean not interfere with his judgment about who should take his classes. The Dean’s position was that the university received greater support from the state for graduate students, than for undergraduate students, so undergraduates taking graduate courses cost the university money. Dr. Moore was not impressed by that argument. And he continued to insist that the office not interfere. The final exchange had the Assistant Dean saying that if they allowed this, the Board of Regents wouldn’t like it. Dr. Moore’s reply was that if they did not allow it, Dr. Moore wouldn’t like it. It was allowed. Only after the matter was resolved did Dr. Moore call me into his office and ask very kindly that in the future I come to him first. I will only add that this standing up for what one wants or believes is the key to success in business, in many professions and, in fact, in life itself.
We tell such things to our children when they tell us, “Everyone does X or Y,” when we know it is not wise. We often admire people we see fighting the good fight especially when they succeed against the odds. The story of David and Goliath certainly comes to mind. I think the training we received from Dr. Moore and the example that he provided by his own conduct strengthened us in our resolve to overcome obstacles and reach personal and professional goals. This naturally leads to a discussion of persistence.
We learned that Dr. Moore was never going to tell us how to prove a theorem or construct a counter example. If we didn’t do it, it wouldn’t be done. Some people hear about the Moore method and see only the problems. A small amount of material is possible to cover in this way, the lack of exposure to some important idea. They don’t understand the value of the method. I’m trying to bring this out in several ways. One is the notion of persistence. Given that he would never tell us the way, we were persistent working on a problem until it was cracked. To be sure, sometimes it was necessary to put it down for a while and deal with some other problems. But, it was always there and we would go back to it time and again until finally it would yield. This is a valuable lesson in many endeavors.
At times my wife has thought I am crazy as a result. But, it works for me. Two days before my interview with DuPont, the heat was not working in our house. It was about 20 degrees outside (this is Delaware, not Texas). I wrapped up in a blanket, had a small space heater and worked away at the computer putting together a talk. The last night before my interview, I was having great difficulty getting the software I was using to work. There was something I just did not understand about it. About midnight before the interview I had yet to complete a single slide. My wife told me to prepare hand written slides. While this was quite common in academic presentations, I didn’t think it would go over very well in a corporate presentation. So I continued to work away and finally figured out what the problem was, finishing my presentation about 5:00AM. Since I was hired, it obviously paid off. But, beyond the obvious, part of the payoff was my sense of accomplishment in defeating another obstacle. The good feeling helped carry me through a great interview. I suspect the experience would have been markedly different if I had gone in having given up on this problem.
While not exactly a testimonial, I will relay another story of persistence, perhaps carried too far. One Thanksgiving day, my wife, and I point out that it was a different wife in those days, told me that she had failed to get sweet potatoes for our Thanksgiving day and wanted me to go out and find some that day, Thanksgiving day. I went out in search of them. Before I was done I had visited about 15 stores located over a wide area. I finally got the potatoes, only to discover that dinner was ruined by the time I got home. My wife was more careful with what she asked me to do after that. Now I used this story in my interview with DuPont in answer to a question to describe any weaknesses that I had, and it has come in handy on several occasions since then.
My experience in industry is that people generally don’t ask for something unless they want it. When that is not the case, people get in trouble. And, I’ll give you one example among several. I got a request one day at 5:00PM for comments on a proposed new OECD deregulation, that is the European equivalent of EPA. Any comments I had would be forwarded to Europe, the next morning, at 10:00AM. This regulation dealt with something that I had worked on extensively on which I had strong views. The person making the request was well aware of that and was perhaps trying to keep influence on the subject to himself as a way of making himself more important. He copied about twelve people when making the request, to give the appearance that he was seeking my input. Now, whatever it may sound like today, my ego is not overly large, but I don’t care to be ignored either. I worked all night and delivered 35 pages of comments the next day at 9:30AM. I also copied everybody on his distribution list with a plain statement about how unreasonable the request was. There were several repercussions to this exchange. I’m happy to report that we now have a mostly cordial and productive relationship, and he and everybody else understands that I will produce when called on. In my view and I believe it is consistent with the training we received from Dr. Moore, there is great value in sticking with a problem until it is solved. In my present work, if I can’t solve a problem, it doesn’t get solved. And since not solving it isn’t acceptable in that environment, the kind of persistence that I am talking about is quite valuable. There was a Dilbert cartoon that came out about the same time playing up to this unreasonable request and I posted it on my door for weeks after this in hope that this fellow would come by. The next of the eight points that I want to bring up is what I call the intimidation factor.
One benefit of working with Dr. Moore is learning how to work with this factor. First, there is the man himself. Dr. Moore was a very imposing figure. He dominated his environment. We were all in awe of him on many levels. One simple story to illustrate this – several students were talking in the hall near his office, and I think several of them are here today, when Dr. Moore walked up and spoke to him briefly. Everyone noticed that his pants were unzipped, but no one pointed it out to him. After he had entered his office, one of the students reached down and unzipped his own pants and said with great conviction, “I don’t know what it is but there has to be a reason.”
My first point under this heading is that having worked under the great RL Moore, no one else can intimidate me. Department chairmen, deans, business managers, eminent scientist, political leaders, physicians don’t overly impress me. Now, with that I don’t mean to imply contempt for them, or that I don’t appreciate or need their expertise. Rather I have a healthy view that they are good people like me. In other words, they aren’t Dr. Moore. This is not just some sort of hero worship. Dr. Moore was truly extraordinary. All the rest are just folks.
Another aspect of this idea concerns the written word. We spent time in some classes tearing apart written and verbal statements. The reaction he sought was to make us understand that the written word had no sacred value. It was no better than it’s meaning. Just as we criticized bad proofs, not stupid people, in his classes, we valued good thoughts not because of their context in a book, or who said them, but for their meaning. This carries over into many areas. Anyone who has lived through the sixties and seventies understands the concept of questioning authority. While Dr. Moore was no radical in the wild eyed political sense, we certainly were encouraged to judge things on their merit, not on their trappings. In this vein I would also mention another area in presenting proofs to the class and dealing with many people trying vigorously to find fault with what you’re saying. Learning to defend my arguments with calm assurance, logic and even humor have been extremely helpful in my career. Some of the examples I have already mentioned illustrate this point. I would like to talk a little more about humor.
This is an important part of Dr. Moore’s classes. He had a keen sense of humor and shared it with his classes. He encouraged us to laugh at mistakes. But, did so in a way that even the person making the mistake did not feel he or she was being laughed at, just the mistake. Everyone was treated with respect and dignity, but statements and ideas could be laughed at, torn apart, discarded. In my current position, I find humor to be a valuable tool. Often tensions can be dispelled or prevented from developing by a few choice comments, puns or plays on words. In business, we are all under pressure and must work cooperatively with one another. I’m rarely in a situation where there is a clear leader and everyone has to do what that leader says. Rather, we have loose teams working toward a common goal, each member having responsibilities that are mutually agreed on. A little humor makes the working relationships go much smoother than otherwise.
One of the reasons the Dilbert cartoon strip is so popular in industry is the pleasure we get from laughing at the ridiculous things that go on. It is a rare office that does not have a Dilbert strip posted somewhere. We have taken our work seriously; we try not to take ourselves too seriously. In this vain, I will mention something that WT Reid said to me when we both were faculty members at the University of Oklahoma. The Dean had issued a ruling that our department found objectionable. During the discussion of what actions we should take in response, I proposed something, not entirely seriously, that was rather radical and confrontational. WT suggested to me that in dealing with the Dean, it was unacceptable to call him an SOB. It would be much better to say that we had seen his mother run out from under the steps barking.
So, I talked a little about communication skills. I don’t recall Dr. Moore ever using the word communicate, or talking directly to the concept of communicating ideas. He, nonetheless, taught us a lot about the importance and the art of communication. In the early classes we spent hours learning how to say what we meant, and to mean what we say. Mathematics was a spoken language and an imprecise statement was the subject of laughter. We learned what it meant to deny a statement, what it meant to back-up a claim, how to ask questions, how to respond to questions, what to say, what to write down, what pictures to draw and when to be quiet. We certainly received a lot of practice at making presentations and in questioning presenters. All of this is directly applicable in an industrial position, such as I now hold. I am frequently called on to speak to groups of people, different kinds of people, scientists, other statisticians, regulators, managers, and adversaries. It is necessary to tailor these presentations to the audience. The statisticians want the mathematical underpinnings, scientists want to know how it affects their work and how they can use it, management wants to know the effect on the bottom line, regulators want to know how it will affect their ability to judge product safety, and adversaries want to find out if I know what I’m talking about. It is important, for all these audiences, to deliver a coherent message. To cut through the B.S.
Dr. Moore once quoted someone as saying, “That idea is best, when once stated, is obvious to everyone.” He had no fear of being understood. This is something that I strive for as well. I want people to understand what I am saying. I have no interest in dazzling people with obscurity, with snappy quotes from Goethe, or snazzy presentation graphics. When I speak there is some point to be made, and the idea is central, not the presentation. That is not to say that presentation style is completely irrelevant or unimportant. But, the focus is on the idea. Clear exposition is required. That means I must understand what I am trying to say. First of all, it means that I must have something to say. Next, I must express it in a way that the listener or reader can understand what I am trying to say and finally I try to present sufficient evidence to convince the listener that I am right or at least understand what it is that I am trying to do. We have all probably sat through technical presentations that clearly the presenter did not expect us to understand or else the presenter never even thought about the need to be understood. I have no value for that sort of thing and it would never have been allowed in our classes.
Now in my present line of work, I don’t prove theorems. I do document what I say through a mix of careful presentation of concept, literature citations, appropriate scientific backing, use of respected researchers in the field, contacts in other companies, contacts with regulators, computer simulations, demonstrations with our own data. Somewhat to my surprise I learned early on at my laboratory that the vocal opponents of my methodology were not impressed by ideas coming from other disciplines. For example, they dismissed statistical papers from the pharmaceutical literature as irrelevant to toxicology. While this struck me as highly unscientific, I adapted by diligently searching out statistical papers in toxicology. When they countered with other literature that sided with a different approach, I brought in the author of that approach to tell them that it did not apply to our data. When a few of them sided with scientists from a different company to claim things were run differently there, I contacted statisticians at twenty-one other companies to give clear and compelling evidence of what they actually did. When the competitor at a different company claimed that his approach worked, I searched out convincing counter examples based on real laboratory data. The point is to understand the game these people are playing and make it work for me. To communicate in terms that they understand.
Dr. Moore spent a great deal of time and energy making sure that his audience, that is, his students and selected faculty, understood the Moore method. It was not just a matter of his giving us a list of theorems to prove and examples to find, he wanted us to appreciate what we were doing and why. He wanted us to want to follow his approach, and to do that we had to understand it. He also was an active participant in campus affairs, known for arguing before the faculty on issues of importance to him. He didn’t use mathematical arguments in these cases. He was known as a persuasive and eloquent speaker.
I have heard once, most likely not in one of his classes, that it is not enough to be right. To be right and fail is not the mark of genius. It is necessary to get your idea across and win over the opposition. I quote George C. Scott in the movie Patton, “Wars are not won by dying for your country. Wars are won by making some other poor dumb SOB die for his country.” So while he may not have used the word communicate, he understood how to communicate and developed our ability to do the same. The next heading I want to bring up is the love of learning. Or it could also be titled the love of meeting a challenge.
I first learned of Dr. Moore from an acquaintance. He was mathematics major. At the time I was majoring in Physics and taking courses from the second floor group. He told me of Dr. Moore’s fierce reputation, how difficult it was to succeed in his classes, and indirectly belittled what I was doing and implied that I couldn’t make it in Dr. Moore’s classes. Now it is not true that he actually said or meant that, but that is how I took it, and it became a challenge impossible for me to turn down. I needed to find out if I had what it takes. I’ve taken this attitude of rising to a challenge throughout my professional life. As an industrial statistician, I am constantly learning or developing new methodology, new applications, and new computer languages. A new problem comes in and I wonder if I’ll be able to solve this one. At first, it may appear to be beyond my abilities, but I jump in, learn what I need to learn and come up with a solution. Failure is not an option. The successes I had in Dr. Moore’s classes, the fact that I succeeded as one of his students gave me the courage to keep tackling new challenges.
What might seem tangential to this topic, I think my next illustration probably fits in here. There are no heroes in my life now. Indeed I had to go through a period of anger towards Dr. Moore, to stop working on the problems that he gave us and start working on what became my dissertation. The one time I told him what I was doing, he discouraged me from doing it. As angry as I was at the time, I ignored that advise. If anything, it encouraged me to continue in order to demonstrate to him that I had the insight that he might not credit. Whether this was deliberate on his part, I can’t say, I do know that he was aware, and beyond the initial cause of anger, he never provoked me. I think he knew that any additional provocation might have pushed me right out of the program. By the time my dissertation was finished, I was over my anger, and while I have not named anger as a tool by Dr. Moore, it is a tool that can be put to good ends. I used it then, perhaps unconsciously; I used it in dealing with the conversion of the lab to the new methodology. The people who were opposed to me made idiotic claims that infuriated me. Getting into a shouting match was doomed to fail. After the arguments are over, I still have to work with them. And, I can’t compel them to do what I want. I must persuade them. I channeled my anger into productive action that ultimately led to success.
Dr. Moore did not suffer fools, and I do not claim to develop my negotiation skills such as they are completely based on his example. Whether Dr. Moore deliberately made me angry at the time of my dissertation I don’t know. I am sure he did not take a simple approach to teaching. He looked for and used many tools to develop students. He did not employ the same approach with everyone. One message I take from observing and from thinking about him is that we need to use what works and to work with the tools that we have. In my case, anger and a love of a challenge are great motivators, and yet I must have a cooperative working relationship with many people who have different ideas.
I am locked currently in a fierce battle with a rival statistician in another company over the proper methodology to use in analyzing toxicology data. My first introduction to him was an insulting letter he wrote to one of my colleagues about a position paper I had authored. I responded with a strongly worded, well-documented and lengthy defense of my work and the critique of his. We have been going at it now for several years and while we are now personally cordial, competition is still strong, and in fact I am meeting with him next week to continue the fight. In Dr. Moore’s classes we learned the joy of solving tough problems, in competing intellectually with other strong contributors. The lessons we learned from this activity have been instrumental throughout my career and I am sure that is true of others. There is nothing more satisfying than finally solving a tough problem that has consumed my energy for hours, days, and weeks. The next idea I want to talk about is working within a framework.
Now in Dr. Moore’s classes we worked within a set of Axioms. This was the framework within which we were to operate. Our proof ultimately rested on those axioms. What could be derived from the axioms were proofs, and what could not be derived either were counter examples or remained conjectures. A implies B or it doesn’t. We couldn’t drag in some other set of axioms that would allow proof. That’s not to say we couldn’t alter the framework. We did have more than one set of axioms in which to work, but it was always clear with which system we were working. That’s a useful concept that applies to my present job. I’m given certain tasks to accomplish and I have a set of tools available to achieve those tasks. I’m free to challenge the adequacy of the tools, for example, by asking for more people, better software, better hardware, more time, but once the ground rules have been set I have to work within those rules to reach the goal.
To illustrate, several years ago as part of the controversy over methods, I was challenged to provide software that would carry out my methodology. None existed at the time. There was no way to fully implement my ideas without some way to automate most of it; the volume of work was simply too great. I told management that I would have to have more resources to develop programs for the lab. They didn’t authorize any additional support. Not providing the software would prevent me from succeeding in changing the methodology. I was able to hire graduate student interns for a few months at a time, a few interns in a larger statistics group in the engineering department on a part time basis, and the services of one part time programmer working out of her home some 1500 miles away, and for a short time I could use one of the engineering consultants and a succession of contractors. Those were the tools that I had, plus an expert knowledge of the software in which the work was to be done, and a thorough understanding of what it was I wanted to do. While it took longer than I wanted with these tools, I did manage to deliver a set of user-friendly programs for lab wide use. I could have abandoned the project on grounds of inadequate support. I could have waited until the magic moment when help would have arrived. Had I been looking for excuses for failure rather than ways to succeed, I would have stopped. But my training under Dr. Moore prompted me to try to solve the problem within the constraints imposed. In fact, it did work, and by delivering the product, the issue of whether to use my methods was brought to a head. At that point I could point out the enormous investment in time and effort to deliver this product, and that became one of the arguments in favor of using it, and therefore using my own methods. My last point has to do with mathematics and life as action.
It should be clear that Dr. Moore’s influence upon his students was not restricted to the subject matter of his classes. It was an entire way of life. It permeated everything that we do. My first experience with him was when I approached him about taking his summer Geometry class. It was necessary to get his approval to take that class. As I learned, this was no simple thing. He asked many questions of me. It was clear that it was important to him to have the right students in his class. People willing to work, people with a real interest in mathematics, people of no previous background in the particular course. I was also impressed by the respect with which he treated me, even on this first encounter. He addressed me consistently as Mr. Green. No other teacher had ever done that. They had either called me by my first name, or not used my name at all or not even paid any attention to me.
I was further struck by his interest in me a few days later when my differential equations teacher, Doug Stocks, called me at home to ask whether I had recently spoken with Dr. Moore. When I affirmed that, he said that Dr. Moore had forgotten my name and did not have a phone number for me but remembered that I had told him I was taking Mr. Stocks’s class. I was very much impressed that Dr. Moore had gone to the trouble of seeking me out in this way. Mr. Stocks did not know exactly what Dr. Moore wanted of me but told me I had made a favorable impression on him. Mr. Stocks went on to question me himself to satisfy him that I was serious and impressed on me that I was not to trifle with Dr. Moore when I went back to talk to him. It turned out that Dr. Moore had continued to think about our first conversation and had decided that it may be more appropriate for me to take his summer Measure Theory course instead of Geometry. In fact, I wound up taking both of them that summer.
What made a big impression on me was that he had taken such an interest in my future. This is characteristic of his approach to teaching. He did take a very keen interest in who took his classes, what they got out of them, how best to develop them, what to develop in them. He told us early on that he had no use for the university guidelines stating that we should expect three hours of outside class work for each hour in the classroom. He said he wanted us to think about his class all day, every day, to go to bed thinking about it, to wake up in the night thinking about it, to get up the next morning thinking about it, to think about it walking to class, to think about it while we were eating. If we weren’t prepared to do that, he didn’t want us in his class. It was also quickly evident that he meant exactly what he said. I remember walking across campus one day during the first year I was taking his classes, lost deeply in thought about some problem that he had posed. I’d be walking rapidly then slow down as something occurred to me and at one point I happened to become aware of my surroundings and I saw Dr. Moore a few feet away looking at me with a big smile beaming on his face. I realized that he knew I was taking his sentiment to heart and he obviously was very pleased about it. He never said a word, nor was there any need to.
He approached the teaching of mathematics with his entire being. He conveyed a deep love of the subject in all aspects. He saw mathematics as an activity. A way of life. Not just a subject to be put down at the end of the day before turning on the television. While I was a serious student in high school, and took pleasure in solving mathematical problems then, I truly experienced the love of learning under Dr. Moore’s influence. He took me to another level of happiness that I had not experienced before, and I have carried with me ever since. Dr. Moore seemed to have a real zest for his life. Clearly, he had great value for teaching, for developing students to become contributors. Teaching was not just a job. Showing me how much pleasure and satisfaction are possible from this totally involved approach to mathematics and teaching has been an inspiration to me.
I am blessed with a job that gives me a similar high level of satisfaction. It is very demanding intellectually, allowing much room for continual learning and development. It gives me more freedom than many think is possible in industry, and has the added incentive of immediate impact. People immediately use what I do. I would like to tie this into my earlier remarks about clear thinking. I have been offered numerous opportunities to move into a management role with DuPont, or with a couple of its competitors. I’ve made it clear to all of my managers that I have zero interest in such a position. Now I don’t mean to disparage management by this statement. I am glad someone does this sort of thing; I just don’t want it to be me. My skill, talent, interest, pleasure lie in solving difficult problems. My inter-personal and negotiating skills are much more modest. I understand that and choose to stay in work for which I am suited, which gives me deep satisfaction. One of my colleagues recently took a management role that I had turned down. He is miserable. The money is good. But, life is about more than money. I think Dr. Moore understood that very well. He never went after a Dean position or moved to a more elite school that might have given him more money or prestige. Instead he helped make the University of Texas a school of distinction in mathematics. Simply, he knew what was the right environment for him. We should all be so wise.
I hope this presentation makes clear that Dr. Moore did not teach us only in the classroom through subject matter. He demonstrated in many ways what it means to succeed in life. These lessons carry over into my present industrial job and into many other areas of my life. One reason that I really enjoy my current position is that I am constantly learning, developing, and meeting intellectual challenges. There is a good variety in the mix of the problems that I face. My position involves not just statistics, but mathematics, computer science, biology and a host of what we term influence activities. This is somewhat analogous to Dr. Moore using ideas from psychology, neurology, and philosophy to help him understand how to teach. How to reach and develop his students. He did not restrict himself to the field of mathematics or perhaps he saw that subject more broadly than most of us. Even in his eighties, when I was working with him, he was still taking a keen interest in what he was doing and looking for ways to improve his teaching. The example of his total emersion in and devotion to his life’s work is one of Dr. Moore’s great gifts to me. Early in my time with him, he came into class and told us a story about debating with himself the previous night about whether he was dreaming. Once he was convinced that he was dreaming, he went ahead and did something that he would not otherwise have done. Now I have no idea what that might have been. At the time I was horrified about being so cerebral as to debate with oneself about such a thing as being awake. Later, after I had learned from him to be really alive mentally this seemed an altogether natural thing to do. In some very real ways I think he woke me up to a real life, a life of the mind that I could only have dreamed of before meeting him.
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