The Art of Doing Science and Engineering ← We Can Solve This

I firmly believe in Pasteur's remark, "Luck favors the prepared mind." In this way I can illustrate how the individual's preparation before encountering the problem can often lead to recognition, formulation, and solution. Great results in science and engineering are "bunched" in the same person too often for success to be a matter of random luck.

As graduate students working toward a master's degree, they have the basics well in hand. That leaves me the task of adding "style" to their education, which in practice is usually the difference between an average person and a great one.

I have found that the personal story is far, far more effective than the impersonal one; hence there is necessarily an aura of "bragging" in the book that is unavoidable.

If you find the mathematics difficult, skip those early parts. Later sections will be understandable provided you are willing to forgo the deep insights mathematics gives into the weaknesses of our current beliefs. General results are always stated in words, so the content will still be there but in a slightly diluted form.

Your scientific training has emphasized the role of words, along with a strong belief in reductionism, hence to emphasize the possible limitations of language I shall take up the topic in several places in the book. I have already said "style" is such a topic.

Vicarious learning from the experiences of others saves making errors yourself, but I regard the study of successes as being basically more important than the study of failures.

there are so many ways of being wrong and so few of being right, studying successes is more efficient, and furthermore when your turn comes you will know how to succeed rather than how to fail!

You must also adapt your style to fit the future, since merely copying the past will not be enough if you aspire to future greatness—a

The technical knowledge involved in your life will quadruple in 34 years, and many of you will then be near the high point of your career. Pick your estimated years to retirement and then look in the left-hand column for the probable factor of increase over the present current knowledge when you finally quit!

How are you to recognize "fundamentals"? One test is they have lasted a long time. Another test is from the fundamentals all the rest of the field can be derived by using the standard methods in the field.

In science if you know what you are doing you should not be doing it. In engineering if you do not know what you are doing you should not be doing it.

Often it is not physical limitations which control but rather it is human made laws, habits, and organizational rules, regulations, personal egos, and inertia, which dominate the evolution to the future. You have not been trained along these lines as much as I believe you should have been, and hence I must be careful to include them whenever the topics arise.

Reading some historians you get the impression the past was determined by big trends, but you also have the feeling the future has great possibilities. You can handle this apparent contradiction in at least four ways: 1. You can simply ignore it. 2. You can admit it. 3. You can decide the past was a lot less determined than historians usually indicate and individual choices can make large differences at times.

It is probable the future will be more limited by the slow evolution of the human animal and the corresponding human laws, social institution, and organizations than it will be by the rapid evolution of technology.

the accuracy of the vision matters less than you might suppose, getting anywhere is better than drifting, there are potentially many paths to greatness for you, and just which path you go on, so long as it takes you to greatness, is none of my business. You must, as in the case of forging your personal style, find your vision of your future career, and then follow it as best you can.

In forming your plan for your future you need to distinguish three different questions: What is possible? What is likely to happen?

In forming your plan for your future you need to distinguish three different questions: What is possible? What is likely to happen? What is desirable to have happen?

in a sense, this is a religious course—I am preaching the message that, with apparently only one life to live on this earth, you ought to try to make significant contributions to humanity rather than just get along through life comfortably—that the life of trying to achieve excellence in some area is in itself a worthy goal for your life.

It has often been observed the true gain is in the struggle and not in the achievement—a life without a struggle on your part to make yourself excellent is hardly a life worth living. This, it must be observed, is an opinion and not a fact, but it is based on observing many people's lives and speculating on their total happiness rather than the moment to moment pleasures they enjoyed.

We should note here transmission through space (typically signaling)

We should note here transmission through space (typically signaling) is the same as transmission through time (storage).

In 1993, there were more people in Government (excluding the military), than there were in manufacturing! What will the situation be in 2020? As a guess I would say less than 25% of the people in the civilian work force will be handling things, the rest will be handling information in some form or other.

It has rarely proved practical to produce exactly the same product by machines as we produced by hand.

mechanization requires you produce an equivalent product, not identically the same one. Furthermore, in any design it is now essential to consider field maintenance since in the long run it often dominates all other costs.

Only when field maintenance is part of the original design can it be safely controlled; it is not wise to try to graft it on later. This applies to both mechanical things and to human organizations.

Somewhere in the mid-tolate 1950s in an address to the President and V.Ps of Bell Telephone Laboratories I said, "At present we are doing 1 out of 10 experiments on the computers and 9 in the labs, but before I leave it will be 9 out of 10 on the machines". They did not believe me then, as they were sure real observations were the key to experiments and I was just a wild theoretician from the mathematics department, but you all realize by now we do somewhere between 90 % to 99 % of our experiments on the machines and the rest in the labs. And this trend will go on!

But you were all taught about the evils of the Middle Age scholasticism—people deciding what would happen by reading in the books of Aristotle (384–322) rather than looking at Nature. This was Galileo's (1564–1642) great point which started the modern scientific revolution—look at Nature not in books! But what was I saying above? We are now looking more and more in books and less and less at Nature! There is clearly a risk we will go too far occasionally—and I expect this will happen frequently in the future. We must not forget, in all the enthusiasm for computer simulations, occasionally we must look at Nature as She is.

good design. In the past Engineering has been dominated to a great extent by "what can we do", but now "what do we want to do" looms greater since we now have the power to design almost anything we want. More than ever before, Engineering is a matter of choice and balance rather than just doing what can be done. And more and more it is the human factors which will determine good design—a topic which needs your serious attention at all times. 7. The effects on society are also large. The most obvious illustration is computers have given top management the power to micromanage their organization, and top management has shown little or no ability to resist using this power. You can regularly read in the papers some big corporation is decentralizing, but when you follow it for several years you see they merely intended to do so, but did not. Among other evils of micromanagement is lower management does not get the chance to make responsible decisions and learn from their mistakes, but rather because the older people finally retire then lower management finds itself as top management—without having had many real experiences in management! Furthermore, central planning has been repeatedly shown to give poor results (consider the Russian experiment for example or our own bureaucracy). The persons on the spot usually have better knowledge than can those at the top and hence can often (not always) make better decisions if things are not micromanaged. The people at the bottom

In the past Engineering has been dominated to a great extent by "what can we do", but now "what do we want to do" looms greater since we now have the power to design almost anything we want. More than ever before, Engineering is a matter of choice and balance rather than just doing what can be done. And more and more it is the human factors which will determine good design—a topic which needs your serious attention at all times.

You can regularly read in the papers some big corporation is decentralizing, but when you follow it for several years you see they merely intended to do so, but did not.

Furthermore, central planning has been repeatedly shown to give poor results (consider the Russian experiment for example or our own bureaucracy). The persons on the spot usually have better knowledge than can those at the top and hence can often (not always) make better decisions if things are not micromanaged. The people at the bottom do not have the larger, global view, but at the top they do not have the local view of all the details, many of which can often be very important, so either extreme gets poor results.

I believe you can expect to see much more of this loose association between small organizations as a defense against micromanagement from the top which occurs so often in big organizations.

It will be the same in business, much of what is now taught is based on the past, and has ignored the computer revolution and our responses to some of the evils the revolution has brought; the gains are generally clear to management, the evils are less so.

How much the trends, predicted in part 6 above, toward and away from micromanagement will apply widely and is again a topic best left to you—but you will be a fool if you do not give it your deep and constant attention.

I say the same to you—you must assume the responsibility for what you believe.

The growth of most, but by no means all, fields follow an "S" shaped curve. Things begin slowly, then rise rapidly, and later flatten off as they hit some natural limits.

It is evident Electrical Engineering in the future is going to be, to a large extent, a matter of: (1) selecting chips off the shelf or from a catalog, (2) putting the chips together in a suitable manner to get what you want, and (3) writing the corresponding programs. Awareness of the chips, and circuit boards which are currently available will be an essential part of Engineering, much as the Vacuum Tube Catalog was in the old days.

In one day there are 60× 60×24=86,400 seconds. In one year there are close to 3.15×107 seconds, and in 100 years, probably greater than your lifetime, there are about 3.15×109 seconds. Thus in 3 seconds a machine doing 109 floating point operations per second (flops) will do more operations than there are seconds in your whole lifetime, and almost certainly get them all correct!

From a chart drawn up long ago by Los Alamos (LANL) using the data of the fastest current computer on the market at a given time they found the equation for the number of operations per second was and it fitted the data fairly well.

The limiting asymptote is 3.576×109 for the von Neumann type computer with a single processor. Here, in the history of the growth of

The limiting asymptote is 3.576×109 for the von Neumann type computer with a single processor.

When I first got digital computing really going inside Bell Telephone Laboratories I began by renting computers outside for so many hours the head of the Mathematics department figured out for himself it would be cheaper to get me one inside—a deliberate plot on my part to avoid arguing with him as I thought it useless and would only produce more resistance on his part to digital computers.

Once a boss says "no!" it is very hard to get a different decision, so don't let them say "No!" to a proposal.

the machine processes bits of information according other bits, and as far as the machine is concerned there is no meaning to anything which happens—it is we who attach meaning to the bits.

FORTRAN, meaning FORmula TRANslation, was proposed by Backus and friends, and again was opposed by almost all programmers. First, it was said it could not be done. Second. if it could be done, it would be too wasteful of machine time and capacity. Third, even if it did work, no respectable programmer would use it—it was only for sissies!

Almost all professionals are slow to use their own expertise for their own work. The situation is nicely summarized by the old saying, "The shoe maker's children go without shoes". Consider how in the future, when you are a great expert, you will avoid this typical error!

To see the obvious it often takes an outsider, or else someone like me who is thoughtful and wonders what he is doing and why it is all necessary.

Even when told, the old timers will persist in the ways they learned, probably out of pride for their past and an unwillingness to admit there are better ways than those they were using for so long.

This raises, as I wished to, the ugly point of when is something understood? Yes, they wrote one, and used it, but did they understand the generality of interpreters and compilers? I believe not.

"Almost everyone who opens up a new field does not really understand it the way the followers do".

The reason this happens so often is the creators have to fight through so many dark difficulties, and wade through so much misunderstanding and confusion, they cannot see the light as others can, now the door is open and the path made easy.

Please remember, the inventor often has a very limited view of what he invented, and some others (you?) can see much more. But also remember this when you are the author of some brilliant new thing; in time the same will probably be true of you.

you see how it is you can devise any language you want, provided you can uniquely define it in some definite manner. It goes on top of the machine's language, making the machine into any other machine you want. Of course this is exactly what Turing proved with his Universal Turing Machine, but as noted above, it was not clearly understood until we had done it a number of times.

What I wanted to know was how the job of communication can be efficiently accomplished when we have the power to design the language, and when only one end of the language is humans, with all their faults, and the other is a machine with high reliability to do what it is told to do, but nothing else. I wanted to know what redundancy I should have for such languages, the density of irregular and regular verbs, the ratio of synonyms to antonyms, why we have the number of them that we do, how to compress efficiently the communication channel and still leave usable human redundancy, etc. As I said, he could not hear the question concerning the engineering efficiency of languages, and I have not noticed many studies on it since.

The question arises, "Is programming closer to novel writing than it is to classical engineering?" I suggest yes! Given the problem of getting a man into outer space both the Russians and the Americans did it pretty much the same way, all things considered, and allowing for some espionage. They were both limited by the same firm laws of physics. But give two novelists the problem of writing on "the greatness and misery of man", and you will probably get two very different novels (without saying just how to measure this). Give the same complex problem to two modern programmers and you will, I claim, get two rather different programs.

There are many proposals on how to improve the productivity of the individual programmer as well as groups of programmers. I have already mentioned top-down and bottom-up; there are others such a head programmer, lead programmer, proving the program is correct in a mathematical sense, and the waterfall model of programming to name but a few. While each has some merit I have faith in only one which is almost never mentioned—think before you write the program, it might be called. Before you start, think carefully about the whole thing including what will be your acceptance test it is right, as well as how later field maintenance will be done. Getting it right the first time is much better than fixing it up later!

One trouble with much of programming is simply that often there is not a well defined job to be done, rather the programming process itself will gradually discover what the problem is!

Many studies have shown programmers differ in productivity, from worst to best, by much more than a factor of 10. From this I long ago concluded the best policy is to pay your good programmers very well but regularly fire the poorer ones—if you can get away with it!

One way is, of course, to hire them on contract rather than as regularly employed people, but that is increasingly against the law which seems to want to guarantee even the worst have some employment. In practice you may actually be better off to pay the worst to stay home and not get in the way of the more capable (and I am serious)!

I made the comparison of writing software with the act of literary writing; both seem to depend fundamentally on clear thinking. Can good programming be taught? If we look at the corresponding teaching of "creative writing" courses we find most students of such courses do not become great writers, and most great writers in the past did not take creative writing courses! Hence it is dubious that great programmers can be trained easily.

The habitual use of "governmentese" over the years probably seeps into their writing style and makes them worse. I suspect the same for programmers! Neither years of experience nor the number of languages used is any reason for thinking the programmer is getting better from these experiences.

An examination of books on programming suggests most of the authors are not good programmers!

By the 1950s I had found I was frightened when giving public talks to large audiences, this in spite of having taught classes in college for many years. On thinking this over very seriously, I came to the conclusion I could not afford to be crippled that way and still become a great scientist; the duty of a scientist is not only to find new things, but to communicate them successfully in at least three forms: writing papers and books prepared public talks impromptu talks Lacking any one of these would be a serious drag on my career.

How to learn to give public talks without being so afraid was my problem. The answer was obviously by practice, and while other things might help, practice was a necessary thing to do.

I immediately accepted the offer because here was a chance to practice giving talks as I had just told myself I must do. I soon decided I should give a talk which was so good I would be asked to give other talks and hence get more practice.

At first I thought I would give a talk on a topic dear to my heart, but I soon realized if I wanted to be invited back I had best give a talk the audience wanted to hear, which is often a very, very different thing.

What would they want to hear, especially as I did not know exactly the course they were taking and hence the abilities of people? I hit on the general interest topic, The History of Computing to the Year 2000—this at around 1960. Even I was interested in the topic, and wondered what I would say! Furthermore, and this is important, in preparing the talk I would be preparing myself for the future.

I began, at any lecture I attended anywhere, to pay attention not only to what was said, but to the style in which it was said, and whether it was an effective or a noneffective talk.

Yes, we did some of the hardest problems on the most primitive equipment—it was necessary to do this in order to prove machines could do things which could not be done otherwise. Then, and only then, could we turn to the economical solutions of problems which could be done only laboriously by hand! And to do this we needed to develop the basic theories of numerical analysis and practical computing suitable for machines rather than for hand calculations.

This is typical of many situations. It is first necessary to prove beyond any doubt the new thing, device, method, or whatever it is, can cope with heroic tasks before it can get into the system to do the more routine, and in the long run, more useful tasks.

Any innovation is always against such a barrier, so do not get discouraged when you find your new idea is stoutly, and perhaps foolishly, resisted. By realizing the magnitude of the actual task you can then decide if it is worth your efforts to continue, or if you should go do something else you can accomplish and not fritter away your efforts needlessly against the forces of inertia and stupidity.

In such a rapidly changing field as computer software if the payoff is not in the near future then it is doubtful it will ever pay off.

we got the machine in under one pretext, but its presence in the long run changed both the problem and what the computer was actually used for. When you successfully use a computer you usually do an equivalent job, not the same old one. Again you see the presence of the computer, in the long run, changed the nature of many of the experiments we did.

You must struggle with your own beliefs if you are to make any progress in understanding the possibilities and limitations of computers in the intellectual area.

how sure are you, you are not just a collection of molecules in a radiant energy field and hence the whole world is merely molecule bouncing against molecule? If you believe in other (unnamed, mysterious) forces how do they affect the motion of the molecules, and if they cannot affect the motion then how can they affect the real world? Is physics complete in its description of the universe,

Thus in a sense, computers are the ultimate in music. Except for the trivial details (of sampling rate and number of levels of quantization, which could be increased if you wanted to pay the price), the composers now have available any sound which can exist, at any rates, in any combinations, tempos, and intensities they please. Indeed, at present the "highest quality recording of music" is digital.

There can be no future significant technical improvements. It is now clearly a matter of what sounds are worth producing, not what can be done.

Before this, the composer had often to wait years and years until fame reached out and the music composed earlier was first heard in real life rather than only in the imagination.

In a very real sense, machines can best do routine jobs thus freeing humans for more humane jobs.

Unfortunately, many humans at present are not equipped to compete with machines—they are unable to do much more than routine jobs.

Computers have both displaced so many people from jobs, and also made so many new jobs it is hopeless to try to answer which is the larger number. But it is clear that on the average it is the lower level jobs which are disappearing and the higher level jobs which are appearing.

one would like to believe most people can be trained in the future to the higher level jobs—but that is a hope without any real evidence.

There have long been on the market self-diagnosis kits for some diseases. That is nothing new. It is merely the going farther and prescribing the treatment that bothers people.

One major trouble is, among others, the legal problem. With human doctors so long as they show "due prudence" (in the legal language), then if they make a mistake the law forgives them—they are after all only human (to err is human). But with a machine error whom do you sue? The machine? The programmer? The experts who were used to get the rules?

Often the legal problems of new applications are the main difficulty, not the engineering!

A routine response to nonroutine situations can spell disaster.

Do not be fooled into thinking that psychological novelty is trivial. Once the postulates, definitions, and the logic are given, then all the rest of mathematics is merely psychologically novel—at that level there is in all of mathematics technically no logical novelty! There is a common belief, if we appeal to a random source of making decisions then we escape the vicious circle of molecule banging against molecule, but from whence comes this external random source except the material world of molecules? There is also the standard claim a truly random source contains all knowledge. This is based on a variant of the monkeys and the typewriters story. Ideally you have a group of monkeys sitting at typewriters and at random times they hit random keys. It is claimed in time one of them will type all the books in the British Museum in the order in which they are on the shelves! This is based on the argument that sooner or later a monkey will hit the right first key; indeed in infinite time this will happen infinitely often. Among these infinite number of times there will be some (an infinite number) in which the next key is hit correctly. And so it goes; in the fullness of infinite time the exact sequence of key strokes will occur. This is the basis for the claim, all of knowledge resides in a truly random source, and you can get it easily if you can write a program to recognize "information". For example, sooner or later the next theory of physics will occur in the random stream of noise, and if you can recognize it you will have filtered it out of the stream of random numbers! The logic of the situation is inescapable—the reality is hardly believable! The times to wait are simply too long, and in truth you cannot always recognize "'information" even when you see it. There is an old claim, "free will" is a myth, in a given circumstance you being you as you are at the moment you can only do as you do. The argument sounds cogent, though it flies in the face of your belief you have free will. To settle the question, What experiment would you do? There seems to be no satisfactory experiment which can be done. The truth is we constantly alternate between the two positions in our behavior. A teacher has to believe if only the right words were said then the student would have to understand. And you behave similarly when raising a child. Yet the feeling of having free will is deep in us and we are reluctant to give it up for ourselves—but we are often willing to deny it to others! As another example of the tacit belief in the lack of free will in others, consider when there is a high rate of crime in some neighborhood of a city many people believe the way to cure it is to change the environment—hence the people will have to change and the crime rate will go down! These are merely more examples to get you involved with the question of, "Can machines think?" Finally, perhaps thinking should be measured not by what you do but how you do it. When I watch a child learning how to multiply two, say three digit, numbers, then I have the feeling the child is thinking; when I do the same multiplication I feel I am more doing "conditioned responses"; when a computer does the same multiplication I do not feel the machine is thinking at all. In the words of the old song, "It ain't what you do, it's the way that you do it". In the area of thinking maybe we have confused what is done with the way it is done, and this may be the source of much of our confusion in AI.

There is a common belief, if we appeal to a random source of making decisions then we escape the vicious circle of molecule banging against molecule, but from whence comes this external random source except the material world of molecules?

The truth is we constantly alternate between the two positions in our behavior. A teacher has to believe if only the right words were said then the student would have to understand. And you behave similarly when raising a child. Yet the feeling of having free will is deep in us and we are reluctant to give it up for ourselves—but we are often willing to deny it to others!

In two previous chapters I closed with estimates of the limits of both hardware and software, but in these two chapters on AI I can do very little. We simply do not know what we are talking about; the very words are not defined, nor do they seem definable in the near future.

AI requires your careful thought and should not be dismissed lightly just because many experts make obviously false claims.

Just because computers have not yet been programmed to think does not mean they cannot think; it may mean programmers are stupid!

Whatever your opinion is, what evidence would you accept you are wrong?

It is hard to get people to aggressively think about how things in their own area might be done differently. I have some times wondered whether it might be better if I asked people to apply computers to other areas of application than their own narrow speciality; perhaps they would be less inhibited there!

the purpose, as stated above, is to get the reader to think more carefully on the awkward topics of machines "thinking" and their vision of their personal future, you the reader should take your own opinions and try first to express them clearly, and then examine them with counter arguments, back and forth, until you are fairly clear as to what you believe and why you believe it.

if you want airplanes to hit each other, you assemble them near an airport, put them in two dimensional levels of flight, or send them in a group;

For spheres of unit radius this means the volume of the sphere approaches 0 as n increases.

As we say, the volume is almost all on the surface.

This has importance in design; it means almost surely the optimal design will be on the surface and will not be inside as you might think from taking the calculus and doing optimizations in that course.

Therefore, for large n the diagonal is almost perpendicular to every coordinate axis!

I have found it very valuable in important situations to review all the basic derivations involved so I have a firm feeling for what is going on.]

In linear algebra and other courses you learned to find the set of perpendicular axes and then represent everything in terms of these coordinates, but you see in n-dimensions there are, after you find the n mutually perpendicular coordinate directions, 2n other directions which are almost perpendicular to those you have found! The theory and practice of linear algebra are quite different!

to further convince you your intuitions about high dimensional spaces are not very good,

Examine this carefully! Are you sure of it? If not, why not? Where will you object to the reasoning? Once satisfied it is correct we apply it to the case of n=10 dimensions. You have for the radius of the inner sphere and in 10 dimensions the inner sphere reaches outside the surrounding cube! Yes, the sphere is convex, yes it touches each of the 1024 packed spheres on the inside, yet it reaches outside the cube!

So much for your raw intuition about n-dimensional space, but remember the n-dimensional space is where the design of complex objects generally takes place. You had better get an improved feeling for n-dimensional space by thinking about the things just presented, until you begin to see how they can be true, indeed why they must be true. Else you will be in trouble the next time you get into a complex design problem.

To simplify the problem of the representation of information we will, at present, examine only the problem of the transmission of information from here to there. This is exactly the same as transmission from now to then, storage. Transmission through time or through space are the same problem.

Other forms can be similarly handled, but the generality is not worth the extra notation.

We have learned to "tune" the words we use to fit the person on the receiving end; we, to some extent, select according to what we think is the channel noise, though clearly this does not match the model I am using above since there is significant noise in the decoding process, shall we say.

This inability of the receiver to "hear what is said" by a person in a higher management position but to hear only what they expect to hear, is, of course, a serious problem in every large organization, and is something you should be keenly aware of as you rise towards the top of the organization.

When you think about the man-machine interface one of the things you would like is to have the human make comparatively few key strokes—Huffman encoding in a disguise! Evidently, given the probabilites of you making the various branches in the program menus, you can design a way of minimizing your total key strokes if you wish.

It is true at that time I was already very interested in the process of discovery, believing in many cases the method of discovery is more important than what is discovered.

I knew enough not to think about the process when doing research, just as athletes do not think about style when the engage in sports, but they practice the style until it is more or less automatic.

I would deliver them the answers on Tuesday. Well, one weekend, just after we left on a Friday night, the machine failed completely and I got essentially nothing on Monday. I had to apologize to my friends and promised them the answers on the next Tues. Alas! The same thing happened again! I was angry to say the least, and said, "If the machine can locate there is an error, why can it not locate where it is, and then fix it by simply changing the bit to the opposite state?" (The actual language used was perhaps a bit stronger!). Notice first this essential step happened only because there was a great deal of emotional stress on me at the moment, and this is characteristic of most great discoveries.

Working calmly will let you elaborate and extend things, but the break throughs generally come only after great frustration and emotional involvement. The calm, cool, uninvolved researcher seldom makes really great, new steps.

Notice familiarity with the binary system, which was not common then, (1947–1948), repeatedly played a prominent role in my thinking. It pays to know more than just what is needed at the moment!

Thus finding an error correcting code is the same as finding a set of code points in the n-dimensional space which has the required minimum distance between legal messages

I wanted to be honest with you and show you how easy, if you will follow Pasteur's rule, "Luck favors the prepared mind.", to succeed by merely preparing yourself to succeed. Yes, there were elements of luck in the discovery; but there were many other people in much the same situation, and they did not do it! Why me? Luck, to be sure, but also I was preparing myself by trying to understand what was going on—more than the other people around who were merely reacting to things as they happened, and not thinking deeply as to what was behind the surface phenomena.

Does anyone dare to say they, in my position, could not have done it? Yes, you are just as capable as I was to have done it—if you had been there and you had prepared yourself as well!

Of course as you go through life you do not know what you are preparing yourself for—only you want to do significant things and not spend the whole of your life being a "janitor of science" or whatever your profession is. Of course luck plays a prominent role. But so far as I can see, life presents you with many, many opportunities for doing great things (define them as you will) and the prepared person usually hits one or more successes, and the unprepared person will miss almost every time.

You establish in yourself the style of doing great things, and then when opportunity comes you almost automatically respond with greatness in your actions. You have trained yourself to think and act in the proper ways.

a random walk of random decisions will not get you anywhere near as far as those taken with your own vision of what your future should be.

Let us pause and examine what has happened so far. First, we have not defined "information", we merely gave a formula for measuring the amount. Second, the measure depends on surprise, and while it does match, to a reasonable degree, the situation with machines, say the telephone system, radio, television, computers, and such, it simply does not represent the normal human attitude towards information.

The name "entropy" is used because the same mathematical form arises in thermodynamics and in statistical mechanics, and hence the word "entropy" gives an aura of importance which is not justified in the long run. The same mathematical form does not imply the same interpretation of the symbols!

enlarged sphere about the received signal it is almost certain the original sent signal lies in it. Thus the error correction of an arbitrarily large number of errors, nQ, with arbitrarily close to no errors after decoding is not surprising.

We now abstract what we have learned. We have seen all initial definitions, to a larger or smaller extent, should get the essence of our prior beliefs, but they always have some degree of distortion and hence non-applicability to things as we thought they were. It is traditional to accept, in the long run, the definition we use actually defines the thing defined; but of course it only tells us how to handle things, and in no way actually tells us any meaning. The postulational approach, so strongly favored in mathematical circles, leaves much to be desired in practice.

I then observed we both knew the telephone company was going to total digital transmission about as fast as they could, and this time we would leave behind a very much larger number of disgruntled engineers. Hence, I concluded, we should do something now about the situation, such as get adequate elementary books and other training devices to ease more of them into the future and leave fewer behind. He looked me square in the eye and said, Yes Hamming, you should." and walked off! Furthermore, he went on encouraging me, via John Tukey with whom he often spoke, so I knew he was watching my efforts.

What to do? In the first place I thought I knew very little about digital filters, and, furthermore, I was not really interested in them. But does one wisely ignore one's V.P. plus the cogency of ones own observations? No! The implied social waste was too high for me to contemplate comfortably.

After some pressure he agreed to write the book, so I was saved, so I thought. But monitoring what he was doing revealed he was writing nothing. To rescue my plan I offered, if he would educate me over lunches in the restaurant (you get more time to think there than in the cafeteria), to help write the book jointly (mainly the first part), and we could call it Kaiser and Hamming. Agreed! As time went on I was getting a good education from him, and I got my first part of the book going but he was still writing nothing. So one day I said, "If you don't write more we will end up calling it Hamming and Kaiser."—and he agreed. Still later when I had about completed all the writing and he had still written nothing, I said I could thank him in the preface, but it should be called Hamming, and he agreed—and we are still good friends! That is how the book on Digital Filters I wrote came to be, and I saw it ultimately through three editions, always with good advice from Kaiser.

Doing what needed to be done, though I did not want to do it, paid off handsomely in the long run.

Learning a new subject is something you will have to do many times in your career if you are to be a leader and not be left behind as a follower by newer developments.

If you sample a nonbandlimited function, then the higher frequencies are "aliased" into lower ones, a word devised by Tukey to describe the fact that a single high frequency will appear later as a single low frequency in the Nyquist band. The same is not true for any other set of functions, say powers of t. Under equal spaced sampling and reconstruction a single high power of t will go into a polynomial (many terms) of lower powers of t.

Lo, and behold, the famous transfer function is exactly the eigenvalues of the corresponding eigenfunctions! Upon asking various Electrical Engineers what the transfer function was no one has ever told me that! Yes, when pointed out to them it is the same idea they have to agree, but the fact it is the same idea never seemed to have crossed their minds! The same, simple idea, in two or more different disguises in their minds, and they knew of no connection between them! Get down to the basics every time!

I needed only a firm understanding of the aliasing effects due to sampling. It is another example of why you need to know the fundamentals very well; the fancy parts then follow easily and you can do things that they never told you about.

When digital filters first arose they were viewed merely as a variant of the classical analog filters; people did not see them as essentially new and different. This is exactly the same mistake which was made endlessly by people in the early days of computers.

This is a common, endlessly made, mistake; people always want to think that something new is just like the past—they like to be comfortable in their minds as well as their bodies—and hence they prevent themselves from making any significant contribution to the new field being created under their noses. Not everything which is said to be new really is new, and it is hard to decide in some cases when something is new, yet the all too common reaction of, "If s nothing new." is stupid. When something is claimed to be new, do not be too hasty to think it is just the past slightly improved—it may be a great opportunity for you to do significant things. But again it may be nothing new.

Many people had the opportunity to discover (really rediscover) the Gibbs' phenomena, and it was Gibbs who made the effort. It is another example of what I maintain, there are opportunities all around and few people reach for them.

I used to tease John Tukey you are famous only when your name was spelled with a lower case letter such as watt, ampere, volt, fourier (sometimes), and such.

It must be your friends, in some sense, who make you famous by quoting and citing you, and it pays, so I claim, to be helpful to others as they try to do their work. They may in time give you credit for the work, which is better than trying to claim it yourself.

In any case the fun of working with good people on important problems is more pleasure than the resulting fame.

Teamwork implies a very careful consideration for others and their contributions, and they may see their contributions in a different light than you do!

If N is too big you stop and reconsider your design.

He plotted the results and approximated the functions. I asked him how he got the exponent 0.4. He replied he tried 0.5 and it was too large, and 0.4, being the next natural choice, seemed to fit very well.

the Fast Fourier Transform (FFT) has emerged requiring about N log N operations. This reduction in computing effort has greatly transformed whole areas of science and engineering—what was once impossible in both time and cost is now routinely done.

I had at that time an IBM Card Programmed Calculator (CPC), and the "butterfly" operation meant it was completely impracticable to do with the equipment I had. Some years later I had an internally programmed IBM 650 and he remarked on it again. All I remembered was it was one of Tukey's few bad ideas; I completely forgot why it was bad—namely because of the equipment I had at time. So I did not do the FFT, though a book I had already published (1961) shows I knew all the facts necessary, and could have done it easily!

Moral: when you know something cannot be done, also remember the essential reason why, so later, when the circumstances have changed, you will not say, "It can't be done". Think of my error! How much more stupid can anyone be?

When you decide something is not possible, don't say at a later date it is still impossible without first reviewing all the details of why you originally were right in saying it couldn't be done.

Let us analyse carefully what we do and its implications, because

Let us analyse carefully what we do and its implications, because what we do to a great extent controls what we can see.

Once again a wide spread misinterpretation of a result because of a lack of understanding of the basics behind the mathematical tool, and only knowing the tool itself. A little knowledge is a dangerous thing—especially if you lack the fundamentals!

We will set aside this observation, noting only often these days we record the signal on a tape or other media, and later process it in the lab—and therefore we have the future available now.

If you will only ask yourself, "Is what I am being told really true?" it is amazing how much you can find is, or borders on, being false, even in a well developed field!

The experts were told something in class when they were students first learning things, and at the time they did not question it. It becomes an accepted fact, which they repeat and never really examine to see if what they are saying is true or not, especially in their current situation.

The more I thought about her casual remark the more I felt he needed real guidance—meaning me! I looked him up in the Bell Telephone Laboratories phone book and explained my interest and how I got it. He immediately wanted to come up to my office, but I was obdurate and insisted on meeting in his laboratory. He tried using his office, and I stuck to the lab. Why? Because I wanted to size up his abilities and decide if I thought his problem was worth my time and effort, since it promised to be a tough nut to crack.

Furthermore, I was soon convinced, although I knew little about the details, his experiment was important to physics as well as to Bell Telephone Laboratories. So I took on the problem. Moral: To the extent you can choose, then work on problems you think will be important.

Obviously it was a smoothing problem, and Kaiser was just teaching me the facts, so what better to do than take the experimentalist to Kaiser and get Kaiser to design the appropriate differentiating filter?

Kaiser had always thought of a signal as a function of time, and the square of the area under the curve as the energy, but here the energy was the independent variable! I had repeated trouble with Kaiser over this point until I bluntly said, "All right, his energy is time and the measurements, the counts, is the voltage". Only then could Kaiser do it. The curse of the expert with their limited view of what they can do.

Kaiser is a very able man, yet his expertise, as so often happens to the expert, limited his view. Will you in your turn do better? I am hoping such stories as this

Kaiser is a very able man, yet his expertise, as so often happens to the expert, limited his view. Will you in your turn do better? I am hoping such stories as this one will help you avoid that pitfall.

My contribution? Mainly, first identifying the problem, next getting the right people together, then monitoring Kaiser to keep him straight on the fact filtering need not have exclusively to do with time signals, and finally, reminding them of what they knew from statistics (or should have known and probably did not).

In closing, if you do not, now and then, doubt accepted rules it is unlikely you will be a leader into new areas; if you doubt too much you will be paralyzed and will do nothing. When to doubt, when to examine the basics, when to think for yourself, and when to go on and accept things as they are, is a matter of style, and I can give no simple formula on how to decide. You must learn from your own study of life. Big advances usually come from significant changes in the underlying beliefs of a field.

when you are young then serendipity has probably a long time to pay off, but when you are old it has little time and you should concentrate more on what is at hand.

when a situation is constantly recurring and the lab testing equipment is in constant use. But let lab equipment lie idle for some time, and suddenly it will not work properly! This is called "shelf life", but it is some times the "shelf life" of the skills in using it rather than the "shelf life" of the equipment itself! I have seen it all too often in my direct experience. Intellectual shelf life is often more insidious than is physical shelf life.

I am suspicious, to this day, of getting too many solutions and not doing enough very careful thinking about what you have seen.

Volume output seems to me to be a poor substitute for acquiring an intimate feeling for the situation being simulated.

another belief of mine—doing simple simulations at the early stages lets you get insights into the whole system which would be disguised in any full scale simulation. I strongly advise, when possible, to start with the simple simulation and evolve it to a more complete, more accurate, simulation later so the insights can arise early.

Why tell the story? Because it illustrates another point I want to make—an active mind can contribute to a simulation even when you are dealing with experts in a field where you are a strict amateur.

One major step you must do, and I want to emphasize this, is to make the effort to master their jargon. Every field seems to have its special jargon, one which tends to obscure what is going on from the outsider-and also, at times, from the insiders! Beware of jargon—learn to recognize it for what it is, a special language to facilitate communication over a restricted area of things or events.

But it also blocks thinking outside the original area for which is was designed to cover. Jargon is both a necessity and a curse.

The thieves' argot, group slang, husband and wife's private language of words, gestures, and even a lift of an eyebrow, are all examples of this common use of a private language to exclude the outsider. Hence this instinctive use of jargon when an outsider comes around should be consciously resisted at all times—we now work in much larger units than those of cave man and we must try continually to overwrite this earlier design feature in us.

That is why, to this day, I insist a person with the intimate understanding of what is to be simulated must be involved in the detailed programming. If this is not done then you may face similar situations where both the proposer and the programmer know exactly what is meant, but their interpretations can be significantly different, giving rise to quite different results!

In practice you have to be very careful when simulating an unstable situations—though I will tell you in Chapter 20 about an extreme case I had to solve because it was important to the Laboratories, and that meant, at least to me, I had to get the solution, no matter what excuses I gave myself it could not be done.

There are always answers of some sort f or important problems if you are determined to get them. They may not be perfect, but in desperation something is better than nothing—provided it is reliable!

Faulty simulations have caused people to abandon good ideas, and these occur all too often!

I would put the problem slightly differently: Why should anyone believe the simulation is relevant? Do not begin any simulation until you have given this question a great deal of thought and found appropriate answers.

The relevant accuracy and reliability of simulations are a serious problem. There is, unfortunately, no silver bullet, no magic incantation you can perform, no panacea for this problem. All you have is yourself.

Remember this fact, older minds have more trouble adjusting to new ideas than do younger minds since you will be showing new ideas, and even making formal presentations to, older people throughout much of your career. That your children could understand what you are showing is of little relevance to whether or not the audience to whom you are running the exhibition can.

Old people are not very quick to grasp new ideas—it is not they are dumb, stupid, or anything else like that, it is simply older minds are usually slow to adjust to radically new ideas.

in midcourse corrections you get the vehicle pointed in exactly the right direction and then fire the retro or other rockets to get the corrections, and during such times you do not allow the people to move around in the vehicle as that can produce rotations and hence spoil the careful directing of the rockets.

when I was occasionally asked to do some ecological simulation I quietly asked for the mathematically expressed rules for every possible interaction, for example given the amount of rain what growth of the trees would occur, what exactly were the constants, and also where I could get some real live data to compare some test runs. They soon got the idea and went elsewhere to get someone more willing to run very questionable simulations which would give the results they wanted and could use for their propaganda.

I suggest you keep your integrity and do not allow yourself to be used for other people's propaganda; you need to be wary when agreeing to do a simulation!

In the insurance business the company is betting you will live a long time and you are betting you will die young.

beware of any simulation of a situation which allows the human to use the output to alter their behavior patterns for their own benefit, since they will do so whenever they can.

My main idea, besides the ease and accuracy, was to keep their minds focused on what they were best able to do—chemistry—and not have them fussing with the machine with which they were not experts. They were, moreover, in charge of the actual computing. I made it easy to do the book-keeping and the mechanics of the computer, but I refused to relieve them

the reliability of a simulation, of which you will see many in your career since it is becoming increasingly common, is of vital importance. It is not something you can take for granted just because a big machine gives out nicely printed sheets, or displays nice, colorful pictures. You are responsible for your decisions, and cannot blame them on those who do the simulations, much as you wish you could. Reliability is a central question with no easy answers.

In practice most signals have a fairly sharp cutoff in the frequency band; with no cutoff there would be infinite energy in the signal!

Alas, we know far too little of what the pilot "feels" (senses). Does the pilot feel only the Fourier real frequencies, or maybe they also feel the decaying Laplace complex frequencies (or should we use wavelets?). Do different pilots feel the same kinds of things?

I had little to do except to keep the girl on the desk calculator honest and on the job. My real contribution was: (1) the realization we could simulate what had happened, which is now routine in all accidents but was novel then, and (2) the recognition there was a convergent direction field so the initial conditions need not be known accurately.

My reason for telling you the story is to show you GIGO need not be right.

We see almost all the uncertainty is in the one resistor of size 1/10, and the gain of the amplifier, (–10–9), need not be accurate. Thus the feedback of H.S.Black allows us to accurately build things out of mostly inaccurate parts.

Good minds are still needed in spite of all the computing tools we have developed. But the best mind will be the one who gets the principle into the design methods taught so it will be automatically available for lesser minds!

All the analysis I, or my friends, could produce was inadequate. So I went to the proposers and first objected to the condition at infinity, but it turned out the distance was being measured in molecular layers, and (in those days) any realistic transistor would have effectively an infinity number of layers. I objected then to the equation itself; how could it represent reality? They won again, so I had to retreat to my office and think.

It was an important problem in the design and understanding of the transistors then being developed. I had always claimed if the problem was important and properly posed then I could get some kind of a solution. Therefore, I must find the solution; I had no escape if I were to hold on to my pride.

This is a sad commentary on your education. You are lovingly taught how one theory was displaced by another, but you are seldom taught to replace a nice theory with nothing but randomness! And this is what was needed; the ability to say the theory you just read is no good and there was no definite pattern in the data, only randomness.

Now I suggest to you quite seriously, many simulations are nothing more than Rorschach tests.

How is the outsider to distinguish this from a Rorschach test? Did he merely find what he wanted to find, or did he get at "reality"?

The doctors wanting to be honest found they could not be! Are you so much better in doing a simulation you can be trusted not to find what you want to find? Self-delusion is a very common trait of humans.

Experience has taught me generally a decisive boss is better than a waffling one—you know where you stand and can get on with the work which needs to be done!

Long before this, once I had decided to stay at the Labs and realized my poverty in the knowledge of practical electronics, I bought a couple of Heathkits and assembled them just for the experience, though the resulting objects were also useful.

if for the transmission of information via solitons wins out over the current pulse signaling method then this should produce basically new methods of signal analysis in the future, and you had best keep abreast of it if it happens,

we now (1993) often interconnect the larger units of a computer with fiber optics. It seems only a matter of time before major parts of internal wiring will go optical. Cannot one make, in time, "mother boards" by which the integrated circuit chips are interconnected, using fiber optics? It does not seem to be unreasonable in this day of the material sciences. How soon will fiber optic techniques get down to the chips? After all, the bandwidth of optics means, inferentially, higher pulse rates! Can we not in time make optical chips, and have a general light source falling on a photocell on the chip (like some hand held calculators) to power the chip and avoid all the wiring of power distribution to the chips?

If a major drop in switching costs came about, how would you design a computer? Would the von Neumann basic design survive at all? What would be the appropriate computer designs with this new cost structure? You can try, as I indicated above, to keep reasonably abreast by actively anticipating the way things and ideas might go, and then seeing what actually happens. Your anticipation means you are far, far better prepared to absorb the new things when they arise than if you sit passively by and merely follow progress.

You cannot lead everywhere in this highly technological society, but you need not be left behind by every new development—as many people are in practice.

Once a fiber optic wire is installed then potentially you have available almost all the information you could possibly want, including TV and radio, and possibly newspaper articles selected according to your interest profile (you pay the printing bill which occurs in your own house).

But will this happen? It is necessary to examine political, economic, and social conditions before saying what is technologically possible will in fact happen. Is it likely the government will want to have so much information distribution in the hands of a single company? Would the present cable companies be willing to share with the telephone company and possibly lose some profit thereby, and certainly come under more government regulation? Indeed, do we as a society want it to happen?

One of the recurring themes in this book is frequently what is technologically feasible, and is even economically better, is restrained by legal, social, and economic conditions. Just because it can be done economically does not mean it should be done.

One claim made was the student was advanced about 10% along the education path over those who did not use the system. When I inquired as to whether this meant it was the same 10% shift all through the educational system, or whether he meant 10% on each course, compound interest as it were, he did not know!

Another terrible fact is carefully watching the students to see what happens in practice has shown a good student often picks what they know is the wrong answer simply out of either boredom or amusement to see what the book will say. Hence it does not always work out as it was thought it would; the better students do not necessarily progress significantly faster than the poorer ones!

But a lot of evidence on what enabled people to make big contributions points to the conclusion a famous prof was a terrible lecturer and the students had to work hard to learn it for themselves! I again suggest a rule: What you learn from others you can use to follow; What you learn for yourself you can use to lead.

Another argument I had with this same dean was his belief the students should be allowed to take the extension courses which were under his wing at their own pace; I argued the speed in learning was a significant matter to organizations—rapid learners were much more valuable than were slow learners (other things being the same); it was part of our job to increase the speed of learning and mark for society those who were the better ones.

"Why," said I, "did you not respond with that in the dean's class last hour?" The fact is, what they knew in one class at one hour with one professor did not transfer to the another hour in a room across the hall with another professor.

This is not to say Mathematics is perfect—not at all—but nothing better seems to be available. You have only to look at the legal system and the income tax people, and their use of the natural language to express what they mean, to see how inadequate the English language is for clear thinking. This simple statement, "I am lying." contradicts itself!

I should note some philosophers have doubted even their communication system, let alone any details of it, would resemble ours in any way at all. But people who have their heads in the clouds all the time can imagine anything at all and are very seldom close to correct

There are, I am told, some 467 theorems in Euclid, but not one of these theorems turned out to be false after Hilbert's added his postulates! Yet, every theorem which needed one of these new postulates could not have been rigorously "proved" by Euclid! Every theorem which followed, and rested on such a theorem, was also not "proved" by Euclid. Yet the results in the improved system were still the same as those Euclid regarded as being true. How could this be? How could it be Euclid, though he had not actually proved the bulk of his theorems, never made a mistake? Luck? Hardly!

It soon became evident to me one of the reasons no theorem was false was that Hilbert "knew" the Euclidean theorems were "correct", and he had picked his added postulates so this would be true. But then I soon realized Euclid had been in the same position; Euclid knew the "truth" of the Pythagorean theorem, and many other theorems, and had to find a system of postulates which would let him get the results he knew in advance. Euclid did not lay down postulates and make deductions as it is commonly taught; he felt his way back from "known" results to the postulates he needed!

one of Hilbert's claims, "When rigor enters, meaning departs."

if you want my position, I am partly an intuitionist. The above example about Cauchy's theorem illustrates my attitudeMathematics shall do what I want it to do.

Computer scientists, excluding the AI people, tend to belong to the constructivist school, if they think about the matter at all.

There is a group of people in software who believes we should "prove programs are correct" much as we prove theorems in Mathematics are correct. The two fallacies they commit are: (1) we do not actually "prove" theorems! (2) many important programming problems cannot be defined sharply enough so a proof can be given, rather the program which emerges defines the problem! This does not mean there is nothing of value to their approach of proving programs are correct, only, as so often happens, their claims are much inflated.

many of our tastes since they exclude too much that we find valuable

As you know from your courses in Mathematics, what you are actually doing, when viewed at the philosophical level, is almost never mentioned. The professors are too busy doing the details of Mathematics to ever discuss what they are actually doing—a typical technician's behavior!

Again I stop and remark to you the obvious lessons to learn from this wave-particle duality. With almost 70 years, and no decent explanation of the duality, one has to ask, "Is it possible this is one of those things we cannot think?" Or possibly it is only it cannot be put into words.

There are smells you can not smell, wave lengths of light you cannot see, sounds you cannot hear, all based on the limits of your sense organs, so why do you object to the observation given the wiring of the brain you have then there can be thoughts you cannot think?

Von Neumann in his classic work on QM proved there were no hidden variables, meaning there was no lower structure and Nature was essentially probabilistic—a point Einstein never would accept. But the proof was found to be fallacious, new proofs found, and in their turn found to be fallacious—the current situation being a toss up as to what you want to believe.

Man is not a rational animal, he is a rationalizing animal. Hence you will find that often what you believe is what you want to believe rather than being the result of careful thinking.

The Aspect experiments apparently force you to accept non-local effects—what happens at one place is affected by remote things and the effect which is transmitted does not, in any real sense, pass through the local areas in between but gets there immediately. But apparently you cannot use the effect for useful signaling.

Bell sharpened this up into the famous "Bell inequalities" on the relationships of apparently independent probability measurements, and this result in now widely accepted. Non-local effects seem to mean something can happen instantaneously without requiring time to get from cause to effect—similar to the states of polarization of the two particles of the Aspect experiments.

It is important to notice, while I have indicated maybe we can never understand QM in the classical sense of "understand", we have never-the-less created a formal Mathematical structure which we can use very effectively. Thus, as we go into the future and perhaps meet many more things we cannot "understand", still we may be able to create formal Mathematical structures which will enable us to cope with the fields. Unsatisfactory? Yes! But it is amazing how you get used to QM after you work with it long enough.

Evidently "not done before" is hardly enough to make anything important or original. "Originality" seems to be more than not having been done before.

The Art world, especially painting, has had a great deal of trouble with the distinction between creativity and originality for most of this century. Modern artists, and Museum Directors, offer to the public things which are certainly novel and new, but which many of the potential paying public often does not like. For many people the shock value of various forms of art has finally worn off, and the average person no longer responds to the current "modern art".

We also have the fact many of the current highly valued works of Art were not appreciated during the artist's lifetime—indeed the phenomenon is so common as to be discouraging. By a kind of inverted logic it does allow many people to believe because they are unappreciated therefore they must be a great artist!

I am not able to say just what this word "creativity", which we value so much in our society, actually means. In women's fashions it seems to mean "different", but not "too different"!

I once applied the well known method of least squares to a problem in magnetics. The other person wrote it up, with me as joint author, and sent it to me for my signature (for release for publication). I went to a shrewd physicist friend and said I could not publish a paper which merely applied least squares. He observed to me his most requested reprint was for a paper in solid state physics which applied standard circuit analysis to the problem; and since the paper awaiting my signature was new in the area I should sign and let it be published.

Creativity seems, among other things, to be "usefully" putting together things which were not perceived to be related before, and it may be the initial psychological distance between the things which counts most.

It appears to be the "set of the mind" at the creative moment enables creativity to be done. Can we do anything to increase creativity?

I think creativity in an individual can probably be improved. Indeed, it has been a topic in much of the course, though I have often called it "style".

I have no real suggestions (I can put into concrete words) on how to make you, magically, more creative in your careers. The topic is too important to ignore, even if I do not understand the creative act very well. Better I should try to do it, a person you know who has experienced it many times, than you get it from some people who themselves have never done a significant creative act.

I often suspect creativity is like sex; a young lad can read all the books you have on the topic, but without direct experience he will have little chance of understanding what sex is—but even with experience he may still not understand what is going on! So we must continue, even if we are not at all sure we know what we are talking about.

Introspection, and an examination of history and of reports of those who have done great work, all seem to show typically the pattern of creativity is as follows.

There is first the recognition of the problem in some dim sense.

This is followed by a longer or shorter period of refinement of the problem. Do not be too hasty at this stage, as you are likely to put the problem in the conventional form and find only the conventional solution. This stage, more over, requires your emotional involvement, your commitment to finding a solution since without a deep emotional involvement you are not likely to find a really fundamental, novel solution.

A long gestation period of intense thinking about the problem may result in a solution, or else the temporary abandonment of the problem. This temporary abandonment is a common feature of many great creative acts. The monomaniacal pursuit often does not work; the temporary dropping of the idea sometimes seems to be essential to let the subconscious find a new approach.

Then comes the moment of "insight", creativity, or what ever you want to call it—you see the solution. Of course it often happens that you are wrong; a closer examination of the problem shows the solution is faulty, but might be saved by some suitable revision. But maybe the problem needs to be altered to fit the solution! That has happened! More usually it is back to the drawing board, as they say, more mulling things over.

The false starts and false solutions often sharpen the next approach you try. You now know how not to do it!

When stuck I often ask myself, "If I had a solution, what would it look like?" This tends to sharpen up the approach, and may reveal new ways of looking at the problem you had subconsciously ignored but you now see should not be excluded. What must the solution involve? Are there conservation laws which must apply? Is there some symmetry? How does each assumption enter into the solution, and is each one really necessary? Have you recognized all the relevant factors?

If the solution does come from the subconscious, what can we do to manage our subconscious? My method, and it is implied above, is to saturate the subconscious with the problem, try to not think seriously about anything else for hours, days, or even weeks, and thus the subconscious which, so far as we know, depends heavily upon live experiences to form its dreams, etc. is then left with only the problem to mull over.

We simply deprive it of all else as best we can!

Probably the most important tool in creativity is the use of an analogy.

Something seems like something else which we knew in the past.

Wide acquaintance with various fields of knowledge is thus a help—provided you have the knowledge filed away so it is available when needed, rather than to be found only when led directly to it. This flexible access to pieces of knowledge seems to come from looking at knowledge while you are acquiring it from many different angles, turning over any new idea to see its many sides before filing it away. This implies effort on your part not to take the easy, immediately useful "memorizing the material" path, but prepare your mind for the future.

What is fundamental partly depends on the individual and their mental makeup. It is obvious you need many "hooks" on the knowledge if you are to use it in new situations.

We reason mainly by analogy. But it is curious a valuable analogy need not be close—it need only be suggestive of what to do next.

Many a poor analogy has proved useful in the hands of experts.

We find the analogies when something reminds us of something else—is it only a matter of the "hooks" we have in our minds?

Over the years of watching and working with John Tukey I found many times he recalled the relevant information and I did not, until he pointed it out to me. Clearly his information retrieval system had many more "hooks" than mine did. At least more useful ones! How could this be? Probably because he was more in the habit than I was of turning over new information again and again so his "hooks" for retrieval were more numerous and significantly better than mine were.

Hence wishing I could similarly do what he did, I started to mull over new ideas, trying to make significant "hooks" to relevant information so when later I went fishing for an idea I had a better chance of finding an analogy. I can only advise you to do what I tried to do—when you learn something new think of other applications of it—ones which have not arisen in your past but which might in your future.

I often suspect, as I will later discuss more fully, what the individual regards as ideal conditions for creativity is not what is needed, but rather the constant impinging of reality is often a great help.

In the past I have deliberately managed myself in this matter by promising a result by a given date, and then, like a cornered rat, having at the last minute to find something! I have been surprised at how often this simple trick of managing myself has worked for me. Of course it depends on having a great deal of pride and self-confidence. Without self-confidence you are not likely to create great, new things. There is a thin line between having enough self-confidence and being over-confident. I suppose the difference is whether you succeed or fail; when you win you are strong willed, and when you lose you are stubborn!

I believe it can be taught. It cannot be done with simple tricks and easy methods; what must be done is you must change yourself to be more creative.

In planning to change yourself clearly the old Greek saying applies, "Know thyself." and do not try heroic reformations which are almost certain to fail. Practice on small ones until you gradually build up your ability to change yourself in the larger things.

It is most likely to happen to the very creative people; their previous successes convince them they can solve any problem; but there are other reasons besides over-confidence why, in many fields, sterility sets in with advancing age.

Managing a creative career is not an easy task, or else it would often be done. In mathematics, theoretical physics and astrophysics, age seems to be a handicap (all characterized by high, raw creativity) while in music composition, literature, and statesmanship, age and experience seem to be an asset.

Yes, in my areas the really great things are generally done while the person is young, much as in athletics, and in old age you can turn to coaching (teaching) as I have done.

My advice is if you want to do significant things, now is the time to start thinking (if you have not already done so) and not wait until it is the proper moment—which may never arrive!

Yes it is a matter of luck just what you do, it is much less luck you will do something if you prepare yourself to succeed. "Creativity" is just another name for the great successes which make a difference in history.

Since experts are both necessary, and also at times do great harm in blocking significant progress, they need to be examined closely.

All too often the expert misunderstands the problem at hand, but the generalist cannot carry though their side to completion. The person who thinks they understand the problem and does not is usually more of a curse (blockage) than the person who knows they do not understand the problem.

The record of the experts saying something is impossible just before it is done is amazing.

Experts in looking at something new always bring their expertise with them as well as their particular way of looking at things. Whatever does not fit into their frame of reference is dismissed, not seen, or forced to fit into their beliefs. Thus really new ideas seldom arise from the experts in the field.

There is an old statement which covers this aspect of the expert. It goes as follows: "If an expert says something can be done he is probably correct, but if he says it is impossible then consider getting another opinion."

as you go on you will have to deal with experts many times, and you should understand their characteristics.

in time many of you will be experts, and I am hoping to at least modify the behavior of some of you so that you will, in your turn, not be such a block on progress as many experts have been in the past.

the expert faces the following dilemma. Outside the field there are a large number of genuine crackpots with their crazy ideas, but among them may also be the crackpot with the new, innovative idea which is going to triumph. What is a rational strategy for the expert to adopt? Most decide they will ignore, as best they can, all crackpots, thus ensuring they will not be part of the new paradigm, if and when it comes.

Do not automatically reject every crazy idea, the moment you hear of it, especially when it comes from outside the official circle of the insiders—it may be the great new approach which will change the paradigm of the field!

The experts live in their closed world of theory, certain they are right and are intolerant of other opinions. In some respects the expert is the curse of our society with their assurance they know everything, and without the decent humility to consider they might be wrong. Where the question looms so important I suggested to you long ago to use in an argument, "What would you accept as evidence you are wrong?" Ask yourself regularly, "Why do I believe whatever I do". Especially in the areas where you are so sure you know; the area of the paradigms of your field.

About all I can do is to beg you to watch and see for yourself how often the above descriptions occur in your career, and hope thereby you will not be the drag on progress the expert so often is. In my own case, I vowed when I rose to near the top I would be careful, and as a result I have refused to take part in any decision processes involving current choices of computers. I will give my opinion when asked, but I do not want to be the kind of drag on the next generation I had to put up with from the past generation. Modesty? No, pride!

If my claim progress has not stopped miraculously at present, but rather there is probably an accelerating rate of progress, then it will be even more true when you are in charge that: What you did to become successful is likely to be counterproductive when applied at a later date.

Physicists are polite about this point as they hate to admit their tin god Einstein could be so definitely wrong; they excuse him this way and that, but under pressure they have to admit once again the person who opened up the field did not understand what he had done, and is best ignored at a later date!

While living in California I have met and talked with a number of ex-Navy officers of the rank Captain, and the stories they tell often reveal a degree of distaste in their careers. How could it be otherwise? If you are passed over for an important (to you) promotion in an organization, then it will tend to affect all the relevant memories of a great career and taint them darker. It is this social, as well as the economic, consequence I care about and why I am preaching this lesson—you must keep up or else things will overtake you and may spoil the memories of your career.

one day one of the higher ups in the project showed me the test equipment in the attic. Being me, after a time I asked, "Why do you believe the test equipment is as reliable as what is being tested?"

I had long ago argued at Bell Telephone Laboratories we should form a life testing department whose job is to prepare for the testing of the next device which is going to be invented, and not just test after the need arises. I got nowhere, though I made a few, fairly weak, suggestions about how to start. There was not time in the area of life testing to do basic research—they were under too much pressure to get the needed results tomorrow. As the saying goes, "There is never time to do the job right, but there is always time to fix it later." especially in computer software!

a friend of mine at Bell Telephone Laboratories, who was a very good statistician, felt some data he was analyzing was not accurate. Arguments with the department head they should be measured again got exactly nowhere since the department head was sure his people were reliable and furthermore the instruments had brass labels on them saying they were that accurate. Well, my friend came in one Monday morning and said he had left his brief case on the railroad train going home the previous Friday and had lost everything. There was nothing else the department head could do but call for remeasurements, whereupon my friend produced the original records and showed how far off they were! It did not make him popular, but did expose the inaccuracy of the measurements which were going to play a vital role at a later stage.

From that experience I learned never to process any data until I had first examined it carefully for errors. There have been complaints that I would take too long, but almost always I found errors and when I showed the errors to them they had to admit I was wise in taking the precautions I did. No matter how sacred the data and urgent the answer, I have learned to pretest it for consistency and outliers at a minimum.

I offer you Hamming's rule: 90% of the time the next independent measurement will fall outside the previous 90% confidence limits!

The definition of what is being measured is constantly changing. For perhaps the best example, consider poverty. We are constantly upgrading the level of poverty, hence it is a losing game trying to remove it—they will simply change the definition until there are enough of people below the poverty level to continue the projects they manage!

What is now called "poverty" is in many respects better than what the Kings of England had not too long ago!

Most of our institutions (and people) are slow to react to changes such as the shift to service from manufacturing, and even slower to ask themselves how what they were doing yesterday should be altered to fit tomorrow.

What can the Government Economists use for their basic data other than much of this inaccurate, systematically biased data? Yes, they may to a lesser or greater extent be aware of the biases, but they have no way of knowing how much the data is in error. So it should not surprise you many economic predictions are seriously wrong. There is little else they can do, hence you should not put too much faith in their predictions.

In my experience most Economists are simply unwilling to discuss the basic inaccuracy in the economic data they use, and hence I have little faith in them as Scientists. But who said Economic Science is a Science? Only the Economists!

If Scientific and Engineering data are not at all as accurate as they are said to be, by factors of 5 or more at times, and economic data can be worse, how do you suppose Social Science data fares? I have no comparable study of the whole field, but my little, limited experience does suggests it is not very good. Again, there may be nothing better available, but that does not mean what data is available is safe to use.

It took them a long while before they listened, but they finally came to realize the truth of: Small samples carefully taken are better than large samples poorly done. Better, both in lower cost and in greater accuracy.

As earlier remarked, the average adult has one breast and one testicle, but that does not represent the average person in our society.

A favorite pastime of mine, when I read or hear about some data, is to ask myself how people could have gathered it—how their conclusions could be justified? For example, years ago when I was remarking on this point at a dinner party, a lovely widow said she could not see why data could not be gathered on any topic. After some moments of thought I replied, "How would you measure the amount of adultery per year on the Monterey Peninsula?"

There is a clever proposed method whose effectiveness I do not know in practice. Suppose you want to measure the amount of murder which escapes detection. You interview people and tell them to toss a coin without anyone but themselves seeing the outcome, and then if it is heads they should claim they have committed a murder, while if tails they should tell the truth. In the arrangement there is no way anyone except themselves can know the outcome of the toss, hence no way they can be accused of murder if they say so. From a large sample the slight excess of murders above one half gives the measure you want. But that supposes the people asked, and given protection, will in fact respond accurately. Variations on this method have been discussed widely, but a serious study to find the effectiveness is still missing, so far as I know.

The obligations in each case were of: (1) immediate importance, (2) longer range importance, and (3) very long term importance. I also realized under (2) and (3) one of my functions in the research department was not so much to solve the existing problems as to develop the methods for solving problems, to expand the range of what could be done, and to educate others in what I had found so they could continue, extend, and improve my earlier efforts.

The first rule of systems engineering is: If you optimize the components you will probably ruin the system performance.

During my last two undergraduate college years when I was the University of Chicago, the rule was at the end you had to pass a single exam based on 9 courses in your major field, and another exam based on 6 in your minor field, and these were mainly what mattered, not what grades you got along the way. I, for the first time, came to understand what the system approach to education means. While taking any one course, it was not a matter of passing it, pleasing the professor, or anything like that, it was learning it so at a later date, maybe two years later, I would still know the things which should be in the course.

All the proposed reformations of the standard calculus course I have examined, and there are many, never begin by asking, "What is the total Mathematical education and what therefore should be in the calculus course?"

The question, as in so many situations, "What is the total problem in which this part is to fit?" is simply regarded as too big, and hence the sub-optimization of the courses goes on. Few people who set out to reform any system try first to find out the total system problem, but rather attack the first symptom they see. And, of course, what emerges is what ever it is, and is not what is needed.

I suspect it was the telephone company which first had to really face the problems of systems engineering. If decent service was to be supplied then all the parts had to interconnect, and work at a very high reliability per part. From the first the company provided a service, not just equipment. That is a big difference. If you merely construct something and leave it to others to keep it running it is one thing; if you are also going to operate it as a service then it is another thing entirely!

I cited earlier the half-life time of engineering details as being 15 years—half of the details you learn now will probably be useless to you in 15 years. Rule 3:

cited earlier the half-life time of engineering details as being 15 years—half of the details you learn now will probably be useless to you in 15 years.

The closer you meet specifications the worse the performance will be when overloaded.

In preparation for writing this chapter I reread once more an unpublished set of essays on: One Man's Systems Engineering, by H.R.Westerman (1975), then of Bell Telephone Laboratories.

In preparation for writing this chapter I reread once more an unpublished set of essays on: One Man's Systems Engineering, by H.R.Westerman (1975), then of Bell Telephone Laboratories. They are the only deeply philosophical discussion I know of the "what, how, and why" of systems engineering.

He believes specialists brought together to make a team are the basis of systems engineering, and between jobs they must go back to their specialties to maintain their expertise. Using the group too often to fight fires is detrimental in the long run since then the individuals do not keep their skills honed up in their areas.

while running the computing center in the early days I came to the belief small problems were relatively more important than large ones; regulardependable service was a desirable thing. So I instituted a 1 hour period in each morning and each afternoon during which only 3 minute (or less) problems were to be run (mainly program testing) and if you ran over 5 minutes you got off the machines no matter how much you had claimed you were practically finished. Well, people with 10 minute problems broke them up into three small pieces with different people for each piece and ran them under the rules-thus increasing the load in the input/output facilities. My solution's very presence alters the system's response. The optimal strategy for the individual was clearly opposed to the optimal strategy for the whole of the laboratories, and it is one of the functions of the systems engineer to block most of the local optimization of the individuals of the system and reach for the global optimization for the system.

Westerman believes, as I do, while the client has some knowledge of his symptoms, he may not understand the real causes of them, and it is foolish to try to cure the symptoms only.

Let me close with the observation I have seen many, many solutions offered which solved the wrong problem correctly. In a sense systems engineering is trying to solve the right problem, perhaps a little wrongly, but with the realization the solution is only temporary and later on during the next round of design these accepted faults can be caught provided insight has been obtained.

a solution which does not provide greater insight than you had when you began is a poor solution indeed, but it may be all that you can do given the time constraints of the situation.

We began to realize the answer is all targets should be equally expensive to the enemy—there should be no under-defended or over-defended target, each should be defended in proportion to the damage that could be done by the enemy. Thus we began to see the Nike missile is merely a device to make the enemy pay a price for the damage he can inflict, with no "cheap" targets available.

The current popular example of this effect is the use of the bottom

The instrument you use clearly affects what you see. The current popular example of this effect is the use of the bottom line of the profit and loss statement every quarter to estimate how well a company is doing, which produces a company interested mainly in short term profits and has little regard to long term profits.

If in a rating system every one starts out at 95% then there is clearly little a person can do to raise their rating but much which will lower the rating; hence the obvious strategy of the personnel is to play things safe, and thus eventually rise to the top. At the higher levels, much as you might want to promote for risk taking, the class of people from whom you may select them is mainly conservative! The rating system in its earlier stages may tend to remove exactly those you want at a later stage. Were you to start with a rating system in which the average person rates around 50% then it would be more balanced; and if you wanted to emphasize risk taking then you might start at the initial rating of 20% or less, thus encouraging people to try to increase their ratings by taking chances since there would be so little to lose if they failed and so much to gain if they succeeded. For risk taking in an organization you must encourage a reasonable degree of risk taking at the early stages, together with promotion, so finally some risk takers can emerge at the top. Of

Accuracy of measurement tends to get confused with relevance of measurement, much more than most people believe.

If you regard giving grades in a course as a communication channel then, as just noted, the equally frequency use of all the grades will communicate the maximum amount of information—whilst the typical use in Graduate Schools of mainly the two highest grades, A and B, greatly reduces the amount of information sent. I understand the Naval Academy uses rank in class, and in some sense this is the only defense against "grade inflation" and the failure to use the whole dynamic range of the scale uniformly, thus communicating the maximum amount of information, given a fixed alphabet for grades. The main fault with using rank as the grade is by chance there may be all very good people in a particular class, but some one of them will have to be at the bottom!

Some systems of measurement clearly have bad features, but tradition, and other niceties, keep them going.

All organizations have this problem. You are now at the lower levels in your organization and you can see for yourself how things are reported and how the reports differ from reality—it will still be the same unless you, when you are in charge, change things drastically.

If you will but look around in your organization you will find lots of strange things which really should not happen, but are regarded as customary practice by the personnel.

Thus in a real sense I am preaching the message: (1) it is worth trying to accomplish the goals you set yourself, and (2) it is worth setting yourself high goals. Again, to be convincing to you I will talk

Thus in a real sense I am preaching the message: (1) it is worth trying to accomplish the goals you set yourself, and (2) it is worth setting yourself high goals.

as far as I know each of you has but one life to lead, and it seems to me it is better to do significant things than to just get along through life to its end. Certainly near the end it is nice to look back at a life of accomplishments rather than a life where you have merely survived and amused yourself.

I want to get you to the state where you will say to yourself, "Yes, I would like to do first class work. If Hamming could, then why not me?" Our society frowns on those who say this too loudly, but I only ask you say it to yourself! What you consider first class work is up to you; you must pick your goals, but make them high! I will start psychologically rather than

Newton observed if others would think as hard as he did then they would be able to do the same things. Edison said genius was 99% perspiration and 1% inspiration. It is hard work, applied for long years, which leads to the creative act, and it is rarely just handed to you without any serious effort on your part. Yes, sometimes it just happens, and then it is pure luck. It seems to me to be folly for you to depend solely on luck for the outcome of this one life you have to lead.

Courage, or confidence, is a property to develop in yourself. Look at your successes, and pay less attention to failures than you are usually advised to do in the expression, "Learn from your mistakes".

While playing chess Shannon would often advance his queen boldly into the fray and say, "I ain't scaird of nothing". I learned to repeat it to myself when stuck, and at times it has enabled me to go on to a success. I deliberately copied a part of the style of a great scientist. The courage to continue is essential since great research often has long periods with no success and many discouragements.

The desire for excellence is an essential feature for doing great work.

the difference between having a vision and not having a vision, is almost everything, and doing excellent work provides a goal which is steady in this world of constant change.

One reason for this is fame in Science is a curse to quality productivity, though it tends to supply all the tools and freedom you want to do great things.

most famous people, sooner or later, tend to think they can only work on important problems—hence they fail to plant the little acorns which grow into the mighty oak trees.

Not that you should merely work on random things—but on small things which seem to you to have the possibility of future growth.

I changed the problem from just getting answers to the realization I was demonstrating clearly for the first time the superiority of digital computers over the current analog computers, thus making a significant contribution to the science behind the activity of computing answers.

I had worked with John Tukey for some years before I found he was essentially my age, so I went to our mutual boss and asked him, "How can anyone my age know as much as John Tukey does?" He leaned back, grinned, and said, "You would be surprised how much you would know if you had worked as hard as he has for as many years".

I thought about the remark for some weeks and decided, while I could never work as hard as John did, I could do a lot better than I had been doing.

In a sense my boss was saying intellectual investment is like compound interest, the more you do the more you learn how to do, so the more you can do, etc. I do not know what compound interest rate to assign, but it must be well over 6%—one extra hour per day over a lifetime will much more than double the total output. The steady application of a bit more effort has a great total accumulation.

At the urging of others, for some years I set aside Friday afternoons for "great thoughts". Of course I would answer the telephone, sign a letter, and such trivia, but essentially, once lunch started, I would only think great thoughts—what was the nature of computing, how would it affect the development of science, what was the natural role of computers in Bell Telephone Laboratories, what effect will computers have on AT&T, on Science generally? I found it was well worth the 10% of my time to do this careful examination of where computing was heading so I would know where we were going and hence could go in the right direction. I was not the drunken sailor staggering around and canceling many of my steps by random other steps, but could progress in a more or less straight line. I could also keep a sharp eye on the important problems and see that my

I strongly recommend this taking the time, on a regular basis, to ask the larger questions and not stay immersed in the sea of detail where almost every one stays almost all of the time.

Great people can tolerate ambiguity, they can both believe and disbelieve at the same time. You must be able to believe your organization and field of research is the best there is, but also there is much room for improvement!

Most great people also have 10 to 20 problems they regard as basic and of great importance, and which they currently do not know how to solve.

Most great people also have 10 to 20 problems they regard as basic and of great importance, and which they currently do not know how to solve. They keep them in their mind, hoping to get a clue as to how to solve them. When a clue does appear they generally drop other things and get to work immediately on the important problem.

Again, you should do your job in such a fashion others can build on top of it. Do not in the process try to make yourself indispensable; if you do then you cannot be promoted because you will be the only one who can do what you are now doing!

I have long held the attitude of telling every one freely of my ideas, and in my long career I have had only one important idea "stolen" by another person.

I have found people are remarkably honest if you are in your turn.

essential—you must learn to sell your ideas, not by propaganda, but by force of clear presentation.

years—I had to establish the reputation on my own time that I could do important work, and only then was I given the time to do it.

It is part of the job of those who are going to rise to the top. Along the way you will generally have superiors who are less able than you are, so do not complain since how else could it be if you are going to end up at the top and they are not?

A plan for the future, I believe, is essential for success, otherwise you will drift like the drunken sailor through life and accomplish much less than you could otherwise have done.

Most of the things I have been saying were not said to me; I had to discover them for myself. I have now told you in some detail how to succeed, hence you have no excuse for not doing better than I did. Good Luck!