The Art of Doing Science and Engineering: Learning to Learn

by Richard Hamming

Teachers should prepare the student for the student’s future, not for the teacher’s past. Most teachers rarely discuss the important topic of the future of their field, and when this is pointed out they usually reply: “No one can know the future.”

Education is what, when, and why to do things. Training is how to do it.

One answer is you must concentrate on fundamentals, at least what you think at the time are fundamentals, and also develop the ability to learn new fields of knowledge when they arise so you will not be left behind, as so many good engineers are in the long run.

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.

First principles

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.

In a lifetime of many, many independent choices, small and large, a career with a vision will get you a distance proportional to n, while no vision will get you only the distance . In a sense, the main difference between those who go far and those who do not is some people have a vision and the others do not and therefore can only react to the current events as they happen.

One of the main tasks of this course is to start you on the path of creating in some detail your vision of your future. If I fail in this I fail in the whole course.

You will probably object that if you try to get a vision now it is likely to be wrong—and my reply is that from observation I have seen 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...

No vision, not much of...

For many years I devoted about 10% of my time (Friday afternoons) to trying to understand what would happen in the future of computing, both as a scientific tool and as a shaper of the social world of work and play.

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 the first is science—what is possible. The second is engineering—what are the human factors which choose the one future that does happen from the ensemble of all possible futures. The third is ethics, morals, o...

Again, you can see why having a vision is what tends to separate the leaders from the followers.

Lastly, 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.

Words to live by

I suggest you must rethink everything you ever learned on the subject, question every successful doctrine from the past, and finally decide for yourself its future applicability. The Buddha told his disciples, “Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense.” I say the same to you—you must assume the responsibility for what you believe.

The purpose of computing is insight, not numbers. A good friend of mine revised it to: The purpose of computing numbers is not yet in sight.

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.

Mathematics is what is done by mathematicians, and mathematicians are those who do mathematics.

Mathematics is the language of clear thinking.

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

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

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. I observed to you some lectures ago that a friend behind my back remarked he doubted Hamming understood error-correcting codes—and I admitted he was probably right! I do believe in what I am telling you; the old expert is all too often wrong and a block to progress. 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!

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 they will admit, when pressed hard, are the true goals of the system.

The first rule of systems engineering is: 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.

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. The deeper, long-term understanding of the nature of the problem must be the goal of the systems engineer, whereas the client always wants prompt relief from the symptoms of his current problem.

If in a rating system everyone 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!

School

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

I began by asking what the important problems were in chemistry, then later what important problems they were working on, and finally one day said, “If what you are working on is not important and not likely to lead to important things, then why are you working on it?”

Thus what you consider to be good working conditions may not be good for you! There are many illustrations of this point. For example, 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!

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