The Art of Doing Science and Engineering: Learning to Learn

by Richard Hamming

Without a vision of what kind of education will be appropriate at that time, how are we to evaluate proposed cai projects? Just because something can be done, especially using computers, does not mean it should be done. We must create a vision of what the educated person will be in the future society, and only then can we confidently approach the problems which arise in cai.

23 Mathematics

As you live your life your attention is generally on the foreground things, and the background is usually taken for granted. We take for granted, most of the time, air, water, and many other things, such as language and mathematics. When you have worked in an organization for a long time its st...

By now it should become clear that symbols mean what we choose them to mean. You are all familiar with different natural languages where different words (labels) are apparently assigned to the same idea. Coming back to Plato: What is a chair? Is it always the same idea, or does it depend on context? At a picnic a rock can be a chair, but you do not expect the use of a rock in someone’s living room as a chair. You also realize any dictionary must be circular; the first word you look up must be defined in terms of other words—there can be no first definition which does not use words.

24 Quantum mechanics

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.

25 Creativity

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. How

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! Hence one day we have the solution, either as we awake, or it pops into our mind without any preparation on our part, or as we pick up the problem again there the solution is! In a way, I am repeating Pasteur, “Luck favors the prepared mind.” You prepare your mind for success “by thinking on it constantly” (Newton), and occasionally you are lucky.

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 to prepare your mind for the future. It is for this reason I have urged you in many of the chapters to get down to the fundamentals of a field, since it implies you must examine things many ways before you can decide what is fundamental and what is frills. In fact, for one person they may be in one order, and for another in the opposite order. 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.

Back to the topic of whether we can teach creativity or not. From the above you should get the idea that 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. As I have thought about it in the past, I realize how often I have tried to change myself so I was more as I wished I were and less as I had been. (Often I did not succeed!) Changing oneself is not easy, as anyone who has gone on a diet to lose weight can testify; but that you can indeed change yourself is also evident from the few who do succeed in dieting, quitting smoking, and other changes in habits. We are, in a very real sense, the sum total of our habits, and nothing more; hence by changing our habits, once we understand which ones we should change and in what directions, and understand our limitations in changing ourselves, then we are on the path along which we want to go.

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. You must learn to walk before you run in this matter of being creative, but I believe it can be done.

I have not yet discussed the delicate topic of dropping a problem. If you cannot drop a wrong problem, then the first time you meet one you will be stuck with it for the rest of your career.

Of course, I do not know your field of expertise to say what effect age will have, but I suspect really great things will be realized fairly young, though it may take years to get them into practice. 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!

In closing I want to remind you yet again of Pasteur’s remark, “Luck favors the prepared mind.” 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.

26 Ex...

As remarked in an earlier chapter, as our knowledge grows exponentially we cope with the growth mainly by specialization. It is increasingly true: An expert is one who knows everything about nothing; a generalist knows nothing about everything. In an argument between a specialist and a generalist, the expert usually wins by simply (1) using unintelligible jargon, and (2) citing their specialist results, which are often completely irrelevant to the discussion. The expert is, therefore, a potent factor to be reckoned with in our society. Since experts both are 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.

potentially disagreee with this. A generalist is often seen as someone with surface level understanding, but true value comes from a generalist who has the minimal viable knowledge of a given area and then can flex and combine with other areas of knowledge

It is not just for the pleasure of poking fun at the experts I bring this up. There are at least four other reasons for doing so. First, as you go on you will have to deal with experts many times, and you should understand their characteristics. Second, 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. Third, it appears to me that the rate of progress, the rate of innovation and change of the dominant paradigm, is increasing, and hence you will have to endure more changes than I did. Fourth, if only I knew the right things to say to you, then when a paradigm change occurs fewer of you would be left behind in your careers than usually happens to the experts.

It appears that most of the great innovations come from outside the field, and not from the insiders.

Those experts who do look for the possible innovative crackpot are likely to spend their lives in the futile pursuit of the elusive, rare crackpot with the right idea, the only idea which really matters in the long run. Obviously the strategy for you to adopt depends on how much you are willing to be merely one of those who served to advance things, vs. the desire to be one of the few who in the long run really matter. I cannot tell you which you should choose; that is your choice. But I do say you should be conscious of making the choice as you pursue your career. Do not just drift along; think of what you want to be and how to get there. 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! But also, you cannot afford to pursue every “crackpot” idea you hear about. I have been talking about paradigms of science, but so far as I know the same applies to most fields of human thought, though I have not investigated them closely. And it probably happens for about the same reasons; the insiders are too sure of themselves, have too much invested in the accepted approaches, and are plain mentally lazy. Think of the history of modern technology you know!

I have covered the two main problems of dealing with the experts. They are: (1) the expert is certain they are right, and (2) they do not consider the basis for their beliefs and the extent to which they apply to new situations.

the 2nd point is a great point

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.

What you did to become successful is likely to be counterproductive when applied at a later date.

Consider this with you will probably become an expert later in your career, where you will be less likely to consider novel ideas/approaches

Please remember this when you have risen to the top and are in charge; do as I have tried to do and let the next generation have a cleaner chance at success than you were granted by your management while you were rising to the top.

the old expert is all too often wrong and a block to progress.

There is the final, and overwhelming, reason for telling you these things. I have observed again and again that most experts are left behind as their field progresses and new paradigms come in.

If you do not keep up in your field, that is almost certainly what will happen to you.

It is this social as well as 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.

We are all human, but that does not prevent us from trying to modify our instincts, which were evolved over the long span of history. Civilization is merely a thin veneer we have put on top of our anciently derived instincts, but the veneer is what makes it possible for modern society to operate. Being civilized means, among other things, stopping your immediate response to a situation, and thinking whether it is or is not the appropriate thing to do. I am merely trying to make you more self-aware so you will be more “civilized” in your responses, and hence probably, but not certainly, be more successful in attaining the things you want.

27 Unreliable data

If you want to be certain, then you are apt to be obsolete.

There is never time to do the job right, but there is always time to fix it later,

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.

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. Institutions and people prefer to go along smoothly, and hence lag far behind, than to make the effort to be reasonably abreast of the times. Institutions, like people, tend to move only when forced to.

If the data is usually bad, and you find that you have to gather some data, what can you do to do a better job? First, recognize what I have repeatedly said to you: the human animal was not designed to be reliable; it cannot count accurately, it can do little or nothing repetitive with great accuracy. As an example, consider the game of bowling. All the bowler needs to do is throw the ball down the lane reliably every time. How seldom does the greatest expert roll a perfect game!

Second, you cannot gather a really large amount of data accurately. It is a known fact which is constantly ignored. It is always a matter of limited resources and limited time. The management will usually want a 100% survey when a small one consisting of a good deal less, say 1% or even 0.1%, will yield more accurate results! It is known, I say, but ignored.

they finally came to realize the truth that small samples carefully taken are better than large samples poorly done—better both in lower cost and in greater accuracy.

Third, much social data is obtained via questionnaires. But it is a well-documented fact that the way the questions are phrased, the way they are ordered in sequence, the people who ask them or come along and wait for them to be filled out, all have serious effects on the answers.

I recently filled out a long, important questionnaire (important in the consequent management actions which might follow). I filled it out as honestly as I could, but realized I was not a typical respondent.

Fourth, there is another aspect I urge you to pay attention to. I have said repeatedly that the presence of a high-ranking officer of an organization will change what is happening in the organization at that place and at that time, so while you are still low enough to have a chance, please observe for yourself how questionnaires are filled in. I had a clear demonstration of this effect when I was on the board of directors of a computer company. I saw underlings did what they thought would please me, but in fact angered me a good deal, though I could say nothing to them about it. Those under you will often do what they think you want, and often it is not at all what you want!

28 Systems engineering

Parables are often more effective than is a straight statement, so let me begin with a parable. A man was examining the construction of a cathedral. He asked a stonemason what he was doing chipping the stones, and the mason replied, “I am making stones.” He asked a stone carver what he was doing; “I am carving a gargoyle.” And so it went; each person said in detail what they were doing. Finally he came to an old woman who was sweeping the ground. She said, “I am helping build a cathedral.”

If, on the average campus, you asked a sample of professors what they were going to do in the next class hour, you would hear they were going to “teach partial fractions,” “show how to find the moments of a normal distribution,” “explain Young’s modulus and how to measure it,” etc. I doubt you would often hear a professor say, “I am going to educate the students and prepare them for their future careers.” You may claim in both cases the larger aim was so well understood there was no need to mention it, but I doubt you really believe it. Most of the time each person is immersed in the details of one special part of the whole and does not think of how what they are doing relates to the larger picture. It is characteristic of most people to keep a myopic view of their work and seldom, if ever, connect it with the larger aims...

Systems engineering is the attempt to keep at all times the larger goals in mind and to translate local actions into global results. ...

In systems engineering it is easy to say the right words, and many people have learned to say them when asked about systems engineering, but as in many sports such as tennis, golf, and swimming, it is hard to do the necessary things as a whole. Hence systems engineers are to be judged not by what they say but by what they produce. There are many people who can talk a good game but are not able to play one.

The first rule of systems engineering is: If you optimize the components, you will probably ruin the system performance. This is a very difficult point to get across. It seems so reasonable: if you make an isolated component better, then the whole system will be better—but this is not true; rather, the system performance will probably degrade!

Cramming is clearly a waste of time. You really know it is, but the behavior of most of you is a flat denial of this truth. So, as I said above, words mean little in judging a systems engineering job; it is what is produced that matters.

enthusiasms. 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 suboptimization 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 whatever it is, and is not what is needed.

Things change so fast that part of the system design problem is that the system will be constantly upgraded in ways you do not now know in any detail! Flexibility must be part of the modern design of things and processes. Flexibility built into the design means not only will you be better able to handle the changes which will come after installation, but it also contributes to your own work as the small changes which inevitably arise both in the later stages of design and in the field installation of the system.