Richard Hamming Quotes

There are so many ways of being wrong and so few ways of being right that it is much more economical to study successes.

This is a book about thinking. One cannot talk about thinking in the abstract, at least not usefully. But one can talk about thinking about digital filters, and by studying how great scientists thought about digital filters, one learns, however gradually, to think like a great scientist.

We are mainly interested in the processes... not... in presenting mathematics in its most abstract form. ...we will often begin with concrete forms and then exhibit the process of abstraction.

Transmission through space (typically signaling) is the same as transmission through time (storage).

Apparently an "art"—which almost by definition cannot be put into words—is probably best communicated by approaching it from many sides and doing so repeatedly, hoping thereby students will finally master enough of the art, or if you wish, style, to significantly increase their future contributions to society.

When you are famous it is hard to work on small problems. [...] The great scientists often make this error. They fail to continue to plant the little acorns from which the mighty oak trees grow. They try to get the big thing right off. And that isn't the way things go. So that is another reason why you find that when you get early recognition it seems to sterilize you. [...] The Institute for Advanced Study in Princeton, in my opinion, has ruined more good scientists than any institution has created, judged by what they did before they came and judged by what they did after.

The Turing test is a popular approach, but it flies in the face of the standard scientific method, which starts with the easier problems before facing the harder ones. Thus I soon raised the question with myself, “What is the smallest or close to the smallest program I would believe could think?” Clearly, if the program were divided into two parts, then neither piece could think. I tried thinking about it each night as I put my head on the pillow to sleep, and after a year of considering the problem and getting nowhere I decided it was the wrong question! Perhaps “thinking” is not a yes/no thing, but maybe it is a matter of degree.

Since I was trying to teach "style" of thinking in science and engineering, and "style" is an art, I should therefore copy the methods of teaching used for the other arts—once the fundamentals have been learned. How to become a great painter cannot be taught in words... Art teachers usually let the advanced student paint, and then make suggestions... more or less as the points arise in the student's head—which is where learning is supposed to occur!

Probability is too important to be left to the experts. [...] The experts, by their very expert training and practice, often miss the obvious and distort reality seriously. [...] The desire of the experts to publish and gain credit in the eyes of their peers has distorted the development of probability theory from the needs of the average user. The comparatively late rise of the theory of probability shows how hard it is to grasp, and the many paradoxes show clearly that we, as humans, lack a well grounded intuition in the matter. Neither the intuition of the man in the street, nor the sophisticated results of the experts provides a safe basis for important actions in the world we live in.

an examination of history and of reports of those who have done great work, all seem to show that typically the pattern of creativity is as follows. 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.

As a practicing computer veteran, this reviewer has the habit of looking at the hypothesis of a theorem and asking:

Indeed, to generalize, almost all of our experiences in this world do not fall under the domain of science or mathematics. Furthermore, we know (at least we think we do) that from Godel's theorem there are definite limits to what pure logical manipulation of symbols can do, there are limits to the domain of mathematics. It has been an act of faith on the part of scientists that the world can be explained in the simple terms that mathematics handles. When you consider how much science has not answered then you see that our successes are not so impressive as they might otherwise appear.

The applications of knowledge, especially mathematics, reveal the unity of all knowledge. In a new situation almost anything and everything you ever learned might be applicable, and the artificial divisions seem to vanish.

The Art of Doing Science and Engineering is the full, beautiful expression of what “You and Your Research” sketched in outline.

To summarize, from simple counting using the God-given integers, we made various extensions of the ideas of numbers to include more things. Sometimes the extensions were made for what amounted to aesthetic reasons, and often we gave up some property of the earlier number system. Thus we came to a number system that is unreasonably effective even in mathematics itself; witness the way we have solved many number theory problems of the original highly discrete counting system by using a complex variable.