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The nature of engineering, the science of humanities, and Godel's theorem

Ubiquity, Volume 2000 Issue September, September 1 - September 30, 2000 | BY William A. Wulf 


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William A. Wulf was the first person to receive a computer science Ph.D. (1968) from the University of Virginia. His distinguished career includes serving as assistant director of the National Science Foundation and chair and chief executive officer of Tartan Laboratories Inc. Currently on leave as the AT&T Professor of Engineering and Applied Sciences at the University of Virginia, Wulf is president of the National Academy of Engineering and vice chair of the National Research Council. His specialties are architecture, computer security, and hardware-software codesign.

UBIQUITY: Tell us about the National Academy of Engineering, and about national academies in general.

WILLIAM A. WULF: There are academies of science and academies of engineering all around the world, and they generally follow one of two basic models. In the former Soviet Union and its client states, the academy is part of the government and runs the national research laboratories, generally along the lines of what the Department of Energy does in this country. In most of the rest of the world the academies are not part of the government and are purely honorific societies. So, for example, being elected to the Royal Society in London is a very high honor and recognition of a lifetime's contributions to science.

UBIQUITY: How did the idea of national academies get transferred to America?

WULF: In 1863, a bunch of scientists in this country decided that we ought to have one of those honorific academies, too, and they incorporated a not-for-profit corporation in Washington. If you remember your civics, in Washington in 1863, there was no city government -- the federal government acted as the city administration. So the charter for the corporation came from the U.S. Congress. We now make a big deal of the fact that we operate under a congressional charter, but in fact, it was absolutely standard practice when they incorporated. What was nonstandard was that somebody inserted some language into the otherwise boiler-plate charter, saying that the academy would provide advice to the federal government on any issue of science and technology, do so whenever asked, and do it without compensation (which has been interpreted to mean not-for-profit.)

UBIQUITY: Then the Academy is much more than just an honorific society?

WULFE: That's right, we have two roles. We are both honorific and a very special, close adviser to the federal government. In addition to the charter, there have been a series of presidential executive orders and, most recently, a modification to the Federal Advisory Committee Act, that allows us to simultaneously have a privileged position with respect to the government, and yet be extremely independent. Independence is very important to our role; we have to be able to tell the government what they don't wan to hear -- and, in fact, we regularly kick the government in the shins on issues. There is a phrase kicking around the Academies that I am very fond of: "telling truth to power." That's what we do.

UBIQUITY: What's a good example of that?

WULF: Oh, I'm sure you remember the Clipper chip controversy a few years ago. Congress asked us to look into the question of what the national policy should be with respect to cryptography -- not just Clipper. We began our report saying that we had all of the clearances necessary to look at the classified information and that there was nothing in the classified environment that would negate what we're going to say in the unclassified report. That way we got around the argument that you frequently heard in those days -- "if you knew what I know then you'd be in favor of Clipper too." Second, we said that "under no circumstances should there be any imposition of restrictions on the use of cryptography within the borders of the United States." We also made recommendations about the export of cryptographic products, and a number of other things that were contrary to administration policy.

UBIQUITY: What kinds of people were involved in the writing of your report?

WULF: On that committee we had a retired four-star army general whose career was in military intelligence; a former attorney general; a former deputy director of NSA; and a number of techies like Marty Hellman who really understand cryptogography. People of that caliber made it very hard for the administration to ignore.

UBIQUITY: So then the report was well received?

WULF: No. It made the administration very unhappy. But, essentially all of its recommendations have now been adopted as US policy.

UBIQUITY: What's the process the National Academy of Engineering uses to develop one of its reports?

WULF: Typically, when the Feds ask us for advice we will put together a committee of 10 to 20 people, who spend anywhere from three months to three years, depending on the subject, analyzing the problem. And then they write what I think of as a Ph.D. dissertation; that is, it's a book that's 300 pages long and it's got 500 references in it, and it's very tightly reasoned, with no opinion unsupported by fact. NAE reports are also about as accessible as Ph.D. dissertations -- that is, they are written for people who already have a general understanding of what the problem is, and are simply wanting to know what it is in the research literature that applies to whatever the particular policy decision is.

UBIQUITY: How many of these "Ph.D. dissertations" does the NAE produce?

WULF: We produce between 200 and 250 a year -- that's one of those 300-page books about every working day. About 30 of those are in response to congressional requests, and most of the rest are in response to executive branch agencies. We also get a few requests from the judicial branch.

UBIQUITY: Do you post the reports on the Web?

WULF: Everything that's been done in the last 10 years, I think, is on the Web, and we're working our way backward from there. Things now go up on the Web the day they're released. Check out "" (it's NAP for National Academy Press).

UBIQUITY: How is the National Academy of Engineering related to the National Academy of Sciences?

WULF: The original corporation was The National Academy of Sciences, but that has now evolved into four organizations that all operate under the Congressional charter. Three are the honorific entities: The National Academy of Sciences, The National Academy of Engineering, and the Institute of Medicine. (Don't ask why it's not called The National Academy of Medicine. It should be.) The fourth organization is the National Research Council, which is the operating arm of the honorific entities, and that's where most of these studies are done.

UBIQUITY: How many members are there in the various organizations?

WULF: About 2,000 in the NAS, about 2,000 members in the NAE, and about 1,200 members of the IOM. But at any given point in time there will be on the order of 500 committees working on questions posed by the Feds and those committees will have the active participation of anywhere from 6,000 to 10,000 unpaid individuals, only about 10 or 15 percent of whom are actually Academy members.

UBIQUITY: Why so many who are not members of one of the Academies?

WULF: When we put together a committee to address one of these problems, we try to find the very best people in the country on that subject, and many of those experts may not yet be Academy members. Most people elected to the Academy are in their 50s, just because it usually takes that long to accumulate the track record that gets one elected.

UBIQUITY: Let's talk for a moment about the nature of engineering. Grade school, students tend to be taught that "engineering is applied science" -- that science is theory and engineering is applied theory. What do you think of that approach?

WULF: You're going to quote my answer?

UBIQUITY: Apparently not. Let's find a work-around. What's your own definition of engineering?

WULF: My favorite operational definition of what an engineer does -- which is not quite the same thing as what engineering is -- is "design under constraint." Engineers design solutions for human problems, but not any old solutions will work, because there is a long list of constraints that the solution must satisfy.

UBIQUITY: Identify some of those constraints for us.

WULF: There are the obvious ones like size, weight, power-consumption, heat-dissipation and so on. But there's also safety, reliability, maintainability and manufacturability, ergonomic factors, environmental impact, and on and on. I've never built the whole list, but there must be 50 to 100 different of constraints that an engineer consider in a various designs.

UBIQUITY: Do the various constraints all get equal billing?

WULF: Sorry for the weasel-answer, but it depends! However, the reason I reacted negatively to your question about engineering being "applied science" is that nature is almost never the hardest constraint to satisfy. Thus science, our understanding of nature, is seldom the "long pole in the tent" of a design, at least in my experience. So engineering is not "just applied science"!

UBIQUITY: What is the generally perceived position now of computer science, among all the science and engineering disciplines?

WULF: One of the wonderful things about this discipline we call computer science -- and I call it computer science only because everyone else does -- is that it spans an enormous intellectual distance, going all the way from very theoretical and abstract mathematics to very crafty application programming. The fact that we have all of that stuff under the same umbrella is a great strength. I think that people who talk about splitting software engineering away from computer science are profoundly wrong.

UBIQUITY: What is the root of their mistake?

WULF: Putting on blinders. Consider an analogy -- there is only one nature: there isn't a physics nature and a chemistry nature and a biology nature and an entomology nature, there is just one single nature. Academic divisions into disciplines and subdisciplines are purely human constructs, and they do not help in understanding nature. All they ultimately do is create barriers to both understanding and communication, by building communities that have different vocabularies, different methodologies, and even different funding agencies. The fact that we separated other sciences and engineering is not something that we should be proud of, or emulate in computer science. Rather, I think we ought to work very hard to have it remain a single field within which lots of different people with generally similar interests can gather and interact.

UBIQUITY: If the sociologists looked now at the standing of computer science within all the science and engineering disciplines, what would they find?

WULF: When I got my Ph.D. in computer science in '68, there probably weren't more than a few dozen of us holding a degree with that title. And at that point in time the discipline was very defensive. Whether it was true or not, people in the field felt like other disciplines were looking down their noses on this upstart which was, in their view, organized around an "instrument"! "How can you have a science organized around an instrument? We don't have a science of telescopes. We have a science of astronomy!" Well, now we have a science of computers, and it's well accepted.

UBIQUITY: What is most responsible for that development?

WULF: Clearly, the economic impact of computing and telecommunications has had something to do with it, but probably even more important has been the development of really a sound corpus of knowledge. There are deep intellectual concepts in computer science now. So I don't believe that other fields look down on it anymore in the way that I was describing, although I still see computer scientists sometimes behaving as though they did.

UBIQUITY: What's happening at the student level?

WULF: In the last two or three years the surge of undergraduate students in computer science has been tremendous, and that causes strains of several varieties. There is a little bit of unhappiness on the part of other engineering disciplines as they see students who might otherwise have been electrical engineers or mechanical engineers now going into computer science. And, at the same time, the computer science departments are not able to grow their faculties anywhere quickly enough to respond to the growth in the numbers of undergraduate majors. So I'm seeing faculties that are more strained than I have seen for many years.

UBIQUITY: Do you see those tensions as resolving in our lifetimes? Is this situation going to get worse or will there be a happy ending?

WULF: It probably will be a function of what happens to the economy. The particular short-term phenomenon of a large number of students opting for computer science or computer engineering is a reflection of the belief that that's where a lot of our future economic growth will be. I agree with that, by the way! I also think you're going to see exactly the same thing with bioengineering departments in the near future.

UBIQUITY: I hadn't thought of that. Is there any sign of that yet?

WULF: I haven't seen the bulge in the students that we have seen in computer science and computer engineering right now, but I believe it's right around the corner.

UBIQUITY: Continuing on the big tent theme: I noticed in your CV that one of your interests was an effort to assist humanities scholars to exploit information technology. How do you see the humanities fitting in nowadays in both education and research?

WULF: Oh, let me warn you that you're going to get a long answer. First of all, two things: Every time that computer scientists have approached a new problem domain, we've discovered new things about computers. I think there's a tremendous opportunity for computer science to look at humanistic scholarship as a problem domain that will open up whole new classes of fascinating challenges.

UBIQUITY: And the second thing?

WULF: I think that computing and telecommunications will have both a larger and a more profound effect on scholarship in the humanities than they had on scholarship in the sciences.

UBIQUITY: Can you give us an example?

WULF: Let me give you my favorite example, and this will speak to the issues of both of scholarship and education. My daughter is a historian at American University, and so I know a little bit about historiography, the methodology of historical scholarship. Historiography has been changing for the last three or four decades, as my daughter says, away from a focus on the kings and the generals, to a focus on what common people were doing at interesting historical times. . . . I also got tangled up with a fine historian at UVa by the name of Ed Ayres. Ed is a civil war historian, and his current project is to collect really detailed information on about 10,000 individuals. Half of them lived in Stanton, Virginia, and half in Chambersburg, Pennsylvania. These are two ends of the Shenandoah Valley. They are demographically almost identical. The agriculture and industry was almost identical. Everything's the same except that they're on opposite sides of the Mason-Dixon Line. Each of the towns happened to field a regiment, and the two regiments happened to fight each other.

UBIQUITY: How did he gather data on the people?

WULF: Ed's got all the newspapers from both towns for about thirty years surrounding the war. He's got all the birth-death records. He's got the military records. He has tax records, which include maps that tell you where individuals lived. He has letters and diaries from several library collections. In fact, he's got letters and diaries that would have been inaccessible to scholars in previous times. We loaded our scanner in a car and drove over to the towns, after having put an ad in the newspaper saying: Please bring your records, and we'll scan them in. We got a lot of people who would bring in old Uncle Zeke's letters from when he was in the army. They never would have given those letters to a library, but they were just delighted to have them become part of this archive.

UBIQUITY: Where is it archived?

WULF: Well, all of this stuff is online. Increasingly, it's becoming hyper-linked, so you can be reading a newspaper and see a name and click on the tax records and find out where the individual lived and who his next-door neighbor was. Then you can wander through it in an uncontrollable way, which I'll come back to later. It really says something about education.

UBIQUITY: What are the implications for research scholarship?

WULF: There is an impact on both the substance and the sociology of the scholarship. It lets historians ask questions that there was no way to answer before. But I think the impact on the sociology of the scholarship is the most interesting thing. For example, until we started putting this stuff online, scholarship in the humanities was always an individual activity. Unlike the scientists, there were never teams of researchers going after something. People would work individually. Second, most of the scholarship was done during the summer because you had to travel to the place where the records were. You'd go to UVa to see their collection of Civil War letters. You couldn't take them away with you. Then you would go up to the University of Pennsylvania and get their Civil War records, and so on. All of a sudden there are groups of historians who find that they have common interests in being able to use these records. They can work all year round.

UBIQUITY: OK, now talk about the implications for education.

WULF: I should have known this when my daughter became a historian, but I've come to learn that historians are control freaks. Their scholarship always appears in a book, and the book is a linear story. It is an argument about causality, and it uses historical facts to buttress the linear argument. Well, guess what? That's the way they teach too. They tell their students a story about what happened during the Civil War and what the causes were for various events. And they buttress that story with historical facts. Well, one day Ed came to me with a strange look on his face. I'm not sure whether it was horror or what, but he had just realized that he had lost control of his undergraduate Civil War course because he was trying to tell this linear story, and the students were bouncing all over his archives. They were asking what about X, or what about Y, or why didn't you incorporate this information into what you were saying? Or, doesn't this fact contradict what you were just saying? And so, in fact, Ed's course has changed from being a course about the Civil War per se, to being a course about historiography that uses the archives to let the students do, in effect, original research. And he estimates now that his second-year undergraduates are doing what at least would have been master's level dissertations -- not so much in the volume that is written, but in the kinds of questions that are being explored. And he is really excited about this.

UBIQUITY: Let me ask you to think about whether that same pedagogical tack would make sense in computer science, or not?

WULF: Well, let me broaden it to engineering. I think there are a lot of things that one can speculate that could be changed in the engineering curriculum. One that almost everybody agrees on is that there should be much more design experience. Engineering is about designing, but we tend to give a lot of courses that are more analytic than design in nature.

UBIQUITY: Why are the design courses limited?

WULF: One of the reasons that we limit the design experience is that it's not very valuable, unless you can actually fabricate the thing that you've designed and see whether in fact it behaves in the way that you intend it when you designed it.

UBIQUITY: What can be done to increase the mount of design opportunities?

WULF: There's a tremendous opportunity to use computers. We have wonderful physical models of the world now, and so I can't see any reason why we can't substitute simulation for fabrication and thereby cut out the amount of time, as well as the cost, of fabricating designs, consequently allowing for a design experience throughout the entire curriculum. In computer science, we pretty much have done that. That is, we give people programming courses, and then we give them programming exercises in a lot of courses. We did this at Virginia, and it was enormously successful.

UBIQUITY: Describe the format of the classes.

WULF: Most of the traditional programming exercises given to students are what are referred to as "open laboratory" experiments, or assignments. That is, you tell somebody to write a short routine and determine its performance by running a number of tests. I think there's a tremendous opportunity to change to a "closed laboratory" environment, which is rather more like a chemistry lab or a physics lab, where an entire class meets at a single time and there's an assigned experiment that is conducted in a couple of hours. The experiment is typically done by a team of students rather than a single student. The only thing that's done outside of class, perhaps, is to write up the results of the experiment. That format, aside from the fact that it encourages teamwork -- which I think is very important -- allows you to do experiments that you couldn't do in the open laboratory format.

In both the humanities example and the closed laboratory example, the point is that you try to move in the direction of using the information technology to provide a context in which students can explore. So-called "discovery-based" learning is a very hot topic these days, and there is some substantial evidence that students learn much better if they actually discover the information as opposed to simply being told the information.

UBIQUITY: You made some interesting remarks about how historians, for example, can now do communal research, more in the scientific mold. What are the prospects of involving undergraduate humanities students in joint enterprises with the sciences? Is there some way of involving all students -- humanity students and computer scientists and engineers and what have you -- in a new way of learning?

WULF: If I weren't doing this job at the NAE, the thing that I was going to do next at the University was to try to create a course for liberal arts students on the fundamentals of computing and telecommunications. It may sound a little esoteric to say it this way, but I think almost everybody in our culture knows that the speed of light is a constant. That's a fundamental limit. You can't go faster than that. Unless we learn something new in the physical domain, you're not likely to actually send space ships to other stars as a consequence. That fact is just a part of the culture that a large percentage of the population understands.

It seems to me that Godel's Theorem imposes a similar, hard constraint on what is knowable. But almost nobody has ever heard of Godel's Theorem. It's not part of the culture.

UBIQUITY: Give a brief explanation of Godel's Theorem, for those who have forgotten their lessons.

WULF: Basically what it says is that in any logic that's strong enough to state this theorem, there are true statements which cannot be proved. In the sense that we think of science and mathematics as a way of knowing things, as a way of validating the truth of a phenomenon or assertion, there are true things that we're not going to be able to prove. That's a pretty profound statement. Now, nobody needs to know how to prove Godel's theorem. Most people don't know how Einstein got to E-equals-mc-squared, although they certainly have seen that equation lots of places.

UBIQUITY: But what do you see is the consequence of their not knowing it?

WULF: The consequence of not knowing Godel's Theorem is perhaps not so obvious, but there are a large number of contemporary public policy issues that people read about in the newspaper everyday, where the deep underlying issue is never discussed. And it's not discussed because neither the journalist nor the audience have the context to be able to do it. The example that I'm thinking of is not a good one perhaps, but just recently there's been all of this discussion about Napster.

UBIQUITY: What does the general public not understand about Napster?

WULF: In the case of Napster, the underlying issue is that the notion of making a copy was a fine way to enforce intellectual property rights in a world of atoms. That notion is not the way to enforce intellectual property rights in a world of bits. I can put a copyright on a piece of e-mail and send it to you. That's perfectly legitimate and it is actually a copyright "document," quote and unquote. But there have been a dozen computers between you and me that have made copies of that thing without my permission. Are they subject to copyright violation? I think technically the answer is yes. As a practical matter, that's foolish. The root problem arises because, in a world of atoms, making a copy is a manifestation of wanting the information content of whatever you're copying. In a world of bytes, that's only one of the ways in which copy is used. Unless you know a little bit about the way computers are constructed, I can't talk about the fact that every time you run a program, you're making a copy of that program.

UBIQUITY: I don't want to belabor this, but I was wondering when you said, they ought to know something about Godel's Theorem. I know that you weren't saying: oh, they won't be able to order a bologna sandwich if they don't know something about Godel's Theorem.

WULF: Right. I was using that just as an example. I guess I wasn't trying to say that everybody needs to know Godel's Theorem. I was trying to draw a contrast between something that almost everybody knows and something that almost nobody knows that are nevertheless the same kind of fundamental limitations.

UBIQUITY: A survey was done last year in Britain of what English high school students, or prep students know. Hardly any of them had ever heard of Winston Churchill.

WULF: Well, about half of the people in this country know that the earth goes around the sun. If I'm remembering right, the number was 56 percent. In fact, that means there's 44 percent of the people that think that the sun goes around the earth. That's pretty scary.

UBIQUITY: Now, when you were thinking about this course at Virginia for liberal arts students, I was wondering what would you think about the idea of designing a curriculum that included liberal arts and sciences and engineering students in a different way than they're sort of segregated now?

WULF: Because of where I sit at the Academy of Engineering, I've thought a lot about some of that. And I have written that I think we've got to stop thinking of the baccalaureate as the first professional degree in engineering. As our body of knowledge continues to expand, we have crowded out more and more of the humanities. If you listen to the CEOs of major engineering and technology-based companies, they uniformly say: Engineering students need more communication skills; they need to know something about the business world. And there's just no room for that as long as you insist that the baccalaureate degree is a professional degree. The only way that I see any hope of doing the sort of thing that you're talking about is to recognize that that's no longer an achievable goal. That we have to start treating the master's as the professional degree, at which point we could perhaps reduce the number of hours that we require of our bachelor's students. If we do that, then there is a lot more room for the kind of integration you are talking about´┐Ż.I also think, by the way, that we should be teaching engineering as a humanistic activity to liberal arts students. The extensive and purposeful use of tools to modify our environment is as close as I can come to a definition of what distinguishes humans from lower animals -- so engineering is a quintessential humanistic activity! An understanding of that activity ought to be part of every educated person's background!

UBIQUITY: What is the current trend in levels of enrollment in engineering?

WULF: The number of students enrolling in engineering reached a high point in the middle '80s, and has been declining ever since. You can speculate on lots of reasons why that's true, but certainly one of them is that the engineering curriculum is both difficult and lengthy. Almost half of our students take more than four years to finish.

UBIQUITY: I know you're interested in diversity. Say something about that.

WULF: There are lots of reasons why one can be concerned about diversity in the engineering work force. You can make an argument on pure equity grounds. You can make an argument on the size of the work force, the fact that increasingly white males are becoming a minority in the population. If we only draw from that pool, the number of engineers will continue to drop. I think those are both valid arguments, but the one that I really believe in most strongly, is a little bit more elliptic, but much more profoundly important. I happen to think that engineering is an incredibly creative profession. I said what engineers do is "design under constraint", and doing those designs is a very creative activity. Now, that's not what the stereotype of engineers is, but it's true. In many ways, a good engineer has more in common with people in the fine arts than they do with people in the sciences. What makes them a good engineer is their creativity.

UBIQUITY: How do you define creativity?

WULF: Now, I actually consulted the literature on this. What makes someone creative? The short, Joe-Six-Pack answer is that creativity comes from applying what you already know, or experiences that you've already had, in unexpected contexts. What that says is that one's creativity is circumscribed by one's life experiences. And the extent that you've had a homogeneous, say, white male, engineering team, that limits the set of life experiences, and hence the creativity that will be applied to a problem. The degree to which you can involve different life experiences -- i.e., a diverse set of people, and that can mean diversity by gender, by ethnicity, by age, by any one of a number of things -- anything that enriches your pool of life experiences, you will have the potential to get a better design. That's why I think diversity in the engineering work force is, if not mandatory, at least highly desirable. It makes good sense from a business point of view. You want to get good solutions? Then put together a team that has diverse backgrounds.


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