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.”

it is only illustrative material. Style of thinking is the center of the course. I am concerned with educating and not training you.

department, as well as many parts of the whole Laboratories. We privately called ourselves “the four young Turks,” and many years later I found top management had called us the same!

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

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. I need to discuss science vs. engineering. Put glibly: 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

In spite of the difficulty of predicting the future and that unforeseen technological inventions can completely upset the most careful predictions,

left or right with n independent random steps will, on the average, end up about steps from the origin. But if there is a pretty girl in one direction, then his steps will tend to go in that direction and he will go a distance proportional to n. 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

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?

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

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.

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.

You may want to explore models which do not have a hard upper saturation limit but rather finally grow logarithmically; they are sometimes more appropriate.

Once a boss says “no!” it is very hard to get a different decision, so don’t let them say “no!” to a proposal. I found in my early years I was doubling the number of computations per year about every 15 months.

Thus 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.

Digital computers are now being used extensively to simulate neural nets, and similar devices are creeping into the computing field. Neural nets, in case you are unfamiliar with them, can learn to get results when you give them a series of inputs and acceptable outputs, without ever saying how to produce the results.

then slightly altered one (or more) of these parameters. Then he made one formula play, say, ten games against the other, and the formula which won the most games was clearly (actually only probably) the better program. The machine went on perturbing the same parameters until it came to a local optimum, whereupon it shifted to other parameters. Thus it went around and around, repeatedly using the same parameters, gradually emerging with a significantly better checkers-playing program—certainly much better than was Samuel himself. The program even beat a Connecticut state checkers champion! Is it not fair to say, “The program

But when you take a course in Euclidean geometry, is not the teacher putting a similar learning program into you? Poorly, to be sure, but is that not, in a real sense, what a course in geometry is all about? You enter the course and cannot do problems; the teacher puts into you a program and at the end of the course you can solve such problems. Think it over carefully. If

But let us note some things carefully. From large organizations new effects can arise. For example, we believe there is no friction between molecules, but most large structures show this effect—it is an effect which arises from the organization of smaller parts which do not show the effect.

it seems to be more a problem of writing the program than it is building a machine, unless you believe, as with friction, that enough small parts will produce a new effect—thinking from non-thinking parts. Perhaps that is all thinking really is! Perhaps it is not a separate thing, it is just an artifact of largeness. One cannot flatly deny this, as we have to admit we do not know what thinking really is.

A careful examination of people’s reports on their great discoveries often shows they were led by past experiences to finding the result they did. Circumstances led them to success; psychological but not logical novelty.

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.