The Art of Doing Science and Engineering: Learning to Learn

by Richard Hamming

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!

The above is the standard conflict between the mathematician’s and the engineer’s approaches. Each has a different aim in solving the differential equations (and in many other problems), and hence they get different results out of their calculations. If you are involved in a simulation, then you see there can be highly concealed matters which are important in practice but which the mathematicians are unaware of, and they will deny the effects matter.

With, at last, time to think for long periods, I found the answer.

Yes, having some pride in your ability to deliver what is needed is a great help in getting important results under difficult conditions.

Now I suggest to you quite seriously that 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”? Regrettably, many, many simulations have a large element of this, adjusting things to get what is wanted. It is so easy a path to follow.

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. “Luck favors the prepared mind.”

Long ago Landé suggested in the two-slit experiment that the probability distribution belonged to the apparatus, not the photon or the electron. This makes much of the mysticism, including Feynman’s assertion that the wave-particle duality is fundamentally a paradox, seem to disappear. Landé has been almost uniformly ignored, but experiments now planned, or already done, may revive his opinion.

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, moreover, 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 whatever you want to call it—you see the solution. Of course, it often happens that you are wrong;

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!

You prepare your mind for success “by thinking on it constantly” (Newton), and occasionally you are lucky.

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.

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 that when later I went fishing for an idea I had a better chance of finding an analogy.

There is much talk about having the right surrounding atmosphere—as if that mattered much! I have seen the creative act done under the most trying circumstances. Indeed, I often suspect, as I will later discuss more fully, that 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!

Without self-confidence you are not likely to create great new things. There is a thin line between having enough self-confidence and being overconfident. I suppose the difference is whether you succeed or fail; when you win you are strong-willed, and when you lose you are stubborn!

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.

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.

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.

This is a problem in all time series. 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 people below the poverty level to continue the projects they manage!

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.

Newton observed that 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.

Brains are nice to have, but many people who seem not to have great iqs have done great things.

Having disposed of the psychological objections of luck and the lack of high-iq-type brains, let us go on to how to do great things.

Among the important properties to have is the belief you can do important things. If you do not work on important problems, how can you expect to do important work?

“If what you are working on is not important and not likely to lead to important things, then why are you working on it?” After that I was not welcome and had to shift to eating with the engineers! That was in the spring, and in the fall one of the chemists stopped me in the hall and said, “What you said caused me to think for the whole summer about what the important problems are in my field, and while I have not changed my research it was well worth the effort.” I thanked him and went on—and noticed in a few months he was made head of the group. About ten years ago I saw he became a member of the National Academy of Engineering.

Confidence in yourself, then, is an essential property. Or, if you want to, you can call it “courage.”

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 scared of nothing.” I learned to repeat it to myself when stuck, and at times it has enabled me to go on to a success.

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.

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. Another reason is that 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.

Reasons that great work in math/physics tends to be done early in a person's career.

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

working with one’s door closed lets you get more work done per year than if you had an open door, but I have observed repeatedly that later those with the closed doors, while working just as hard as others, seem to work on slightly the wrong problems, while those who have let their door stay open get less work done but tend to work on the right problems!

After quite a few weeks of wondering what to do

When stuck, often inverting the problem and realizing the new formulation is better represents a significant step forward.

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 thought about the remark for some weeks and decided that 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:

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.

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.

Huge fraction of time dedicated to "thinking great thoughts" and not being productive on low-level things.

I strongly recommend taking the time, on a regular basis, to ask the larger questions, and not stay immersed in the sea of detail where almost everyone 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 that there is much room for improvement! You can sort of see why this is a necessary trait. If you believe too much, you will not likely see the chances for significant improvements; if you do not believe enough, you will be filled with doubts and get very little done, chances are only the 2%, 5%, and 10% improvements.

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.

Be willing to drop small things to work on big things.

A problem is important partly because there is a possible attack on it and not just because of its inherent importance.

Look over what you have done, and recast it in a proper form. I do not mean give it false importance, nor propagandize for it, nor pretend it is not what it is, but I do say that by presenting it in its basic, fundamental form, it may have a larger range of application than was first thought possible.

I am sorry to have to point this out; many scientists and others think good ideas will win out automatically and need not be carefully presented. They are wrong; many a good idea has had to be rediscovered because it was not well presented the first time, years before!

To master the presentation of ideas, while books on the topic may be partly useful, I strongly suggest you adopt the habit of privately critiquing all presentations you attend and also asking the opinions of others.

You are likely to be saying to yourself you have not the freedom to work on what you believe you should when you want to. I did not either for many 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.

I have a massive and rare opportunity and must not squander it.

Finally, I must address the topic of whether the effort required for excellence worth it. I believe it is—the chief gain is in the effort to change yourself, in the struggle with yourself, and it is less in the winning than you might expect.