The Art of Doing Science and Engineering: Learning to Learn

by Richard Hamming

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

Are you so much better in doing a simulation that you can be trusted not to find what you want to find? Self-delusion is a very common trait of humans.

One of the recurring themes in this book is that 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. If you do not get a firm grasp on these aspects, then as a practicing seer of what is going to happen in your area of specialization you will make a lot of false predictions you will have to explain as best you can when they turn out to be wrong.

Regularly I read or hear that I am supposed to believe that the new gimmick, typically these days the computer, will make a significant difference, in spite of all past promises which have apparently failed miserably. Beware of the power of wishful thinking on your part—you would like it to be true, so you assume it is true!

There is another important factor, known as the Hawthorne effect, that it is necessary to explain.

What you learn from others you can use to follow; What you learn for yourself you can use to lead.

Mathematics is nothing but clear thinking.

Mathematics is the language of clear thinking.

Thus Platonic mathematicians will say they “discovered” a result, not that they “created” it. I “discovered” error-correcting codes, rather than “creating” them, if I am a Platonist. The results were always there, waiting to be discovered; they were always possible.

All the music critics to the contrary, what music communicates cannot (apparently) be put into words.

Similarly, the three things of Classical Greece, truth, beauty, and justice, though you all think you know what they mean, cannot (apparently) be put into words. From the time of Hammurabi, the attempt to put justice into words has produced the law, and often the law is not your conception of justice. There is the famous question in the Bible, “What is truth?” And who but a beauty judge would dare to judge “beauty”?

We now have to face the fact that light apparently comes in quanta, and the quanta appear to be both particles and waves. Almost every professor when teaching qm is forced, one way or the other, to say, “I cannot explain this duality. You will just have to get used to it!”

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.

Creativity, originality, novelty, and other such words are regarded as “good things,” and we often fail to distinguish between them—indeed, we find them hard to define.

This is also true in many large organizations today: the elders are sure they know how the future should be handled and the younger members of the tribe, when they do things differently, are not appreciated.

I hope the above has disentangled some of the confusion between creativity, novelty, and originality, but 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!

Then comes the moment of “insight,” creativity, or whatever you want to call it—you see the solution.

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 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.

An expert is one who knows everything about nothing; a generalist knows nothing about everything.

Of course geologists now claim they had always sort of believed in it (the textbooks they used to the contrary), and it was only necessary to exhibit the actual mechanism in detail before they would accept the continental drift theory, which is now “the truth.” This is the typical pattern of a change in the paradigm of a field. It

One of my favorite ones was that you cannot lift water more than 33 feet.

All impossibility proofs must rest on a number of assumptions which may or may not apply in the particular situation.

If an expert says something can be done he is probably correct, but if he says it is impossible then consider getting another opinion.

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!

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

Consider the case of Einstein, who gave qm such a start with his photoelectric paper, and was in his turn a plain drag on qm when he so aggressively opposed the theory of qm as it developed. 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 that once again the person who opened up the field did not understand what he had done, and is best ignored at a later date!

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

90% of the time, the next independent measurement will fall outside the previous 90% confidence limits!

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

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 you optimize the components, you will probably ruin the system performance.

Part of systems engineering design is to prepare for changes so they can be gracefully made and still not degrade the other parts.

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

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.

The rating system in its earlier stages may tend to remove exactly those you want at a later stage.

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

That measure of software productivity, which is widely used, is one of the reasons why we have such bloated software systems these days.

You get what you measure.

Why do I believe this talk is important? It is important because 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. Thus in a real sense I am preaching the messages that (1) it is worth trying to accomplish the goals you set yourself and (2) it is worth setting yourself high goals.

There is an old saying: “A prophet is without honor in his own country.” Mohammed fled from his own city to a nearby one, and there got his first real recognition!

“Why are you not working on and thinking about the important problems in your area?”

“It ain’t what you do, it’s the way that you do it.”

I must come to the topic of “selling” new ideas. You must master three things to do this (Chapter 5): Giving formal presentations, Producing written reports, and Mastering the art of informal presentations as they happen to occur.

Change does not mean progress, but progress requires change.

The unexamined life is not worth living.