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We are beginning to find not only is intelligence not adequately defined so arguments can be settled scientifically, but a lot of other associated words like, computer, learning, information, ideas, decisions, expert behavior—all are a bit fuzzy...
Richard Hamming
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Faced with almost an infinity of details you cannot afford to deal constantly with the specific; you must learn to embrace more and more detail under the cover of generality.
Richard Hamming
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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.
Richard Hamming
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Any unwillingness to learn mathematics today can greatly restrict your possibilities tomorrow.
Richard Hamming
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Great results in science and engineering are "bunched" in the same person too often for success to be a matter of random luck.
Richard Hamming
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It is obvious: The past was once the future and the future will become the past.
Richard Hamming
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Indeed, one of my major complaints about the computer field is that whereas Newton could say, "If I have seen a little farther than others, it is because I have stood on the shoulders of giants," I am forced to say, "Today we stand on each other's feet." Perhaps the central problem we face in all of computer science is how we are to get to the situation where we build on top of the work of others rather than redoing so much of it in a trivially different way. Science is supposed to be cumulative, not almost endless duplication of the same kind of things.
Richard Hamming
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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.
Richard Hamming
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Transmission through space (typically signaling) is the same as transmission through time (storage).
Richard Hamming
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It is easy to measure your mastery of the results via a conventional examination; it is less easy to measure your mastery of doing mathematics, of creating new (to you) results, and of your ability to surmount the almost infinite details to see the general situation.
Richard Hamming
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Science and mathematics... have added little to our understanding of such things as Truth, Beauty, and Justice. There may be definite limits to the applicability of the scientific method.
Richard Hamming
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Much of present science rests on engineering tools, and as time goes on, engineering seems to involve more and more of the science part.... the two fields are growing together!... and now there is not enough time to allow us the leisure which comes from separating the two fields.
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Somewhere in the mid-to-late 1950s in an address to the President and V. Ps of Bell Laboratories I said, "At present we are doing 1 out of 10 experiments on the computers and 9 in the labs, but before I leave it will be 9 out of 10 on the machines". They did not believe me... by now we do somewhere between 90% to 99% on the machines... And this trend will go on!
Richard Hamming
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It may be said "In research, if you know what you are doing, then you shouldn't be doing it." In a sense, if the answer turns out to be exactly what you expected, then you have learned nothing new, although you may have had your confidence increased somewhat.
Richard Hamming
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The beauty of mathematics often makes the subject matter much more attractive and easier to master.
Richard Hamming
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We intend to teach the doing of mathematics. The applications of these methods produce the results of mathematics (which usually is only what is taught)... There is also a deliberate policy to force you to think abstractly... it is only through abstraction that any reasonable amount of useful mathematics can be covered. There is simply too much known to continue the older approach of giving detailed results.
Richard Hamming
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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!
Richard Hamming
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The calculus is probably the most useful single branch of mathematics.... I have found the ability to do simple calculus, easily and reliably, was the most valuable part of mathematics I ever learned.
Richard Hamming
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When you yourself are responsible for some new application in mathematics... then your reputation... and possibly even human lives, may depend on the results you predict. It is then the need for mathematical rigor will become painfully obvious to you.... Mathematical rigor is the clarification of the reasoning used in mathematics.... a closer examination of the numerous "hidden assumptions" is made.... Over the years there has been a gradually rising standard of rigor; proofs that satisfied the best mathematicians of one generation have been found inadequate by the next generation. Rigor is not a yes-no property of a proof... it is a vague standard of careful treatment that is currently acceptable to a particular group.
Richard Hamming
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If you expect to continue learning all your life, you will be teaching yourself much of the time. You must learn to learn, especially the difficult topic of mathematics.
Richard Hamming
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The idea that theorems follow from the postulates does not correspond to simple observation. If the Pythagorean theorem were found to not follow from the postulates, we would again search for a way to alter the postulates until it was true. Euclid's postulates came from the Pythagorean theorem, not the other way around.
Richard Hamming
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We must not forget, in all the enthusiasm for computer simulations, occasionally we must look at Nature as She is.
Richard Hamming
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Unfortunately... the ADA language was designed by experts, and it shows all the non-humane features you can expect from them. It is... a typical Computer Science hacking job—do not try and understand what you are doing, just get it running. As a result of this poor psychological design... although a government contract may specify the programming be in ADA, probably over 90% will be done in FORTRAN, debugged, tested, and then painfully, by hand, be converted to a poor ADA program, with a high probability of errors!
Richard Hamming
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Often it is not physical limitations... but rather it is human made laws, habits, and organizational rules, regulations, personal egos, and inertia, which dominate the evolution of the future.
Richard Hamming
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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... The second is Engineering.. The third is ethics, morals, or... value judgements.... you will probably have an idea of how to alter things to make the more desirable future occur... having a vision is what tends to separate the leaders from the followers.
Richard Hamming
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Be a sinner and sin strongly, but more strongly have faith and rejoice in Christ.
Martin Luther
Richard Hamming
Wikipedia
Born:
February 11, 1915
Died:
January 7, 1998
(aged 82)
Bio:
Richard Wesley Hamming was an American mathematician whose work had many implications for computer engineering and telecommunications.
Known for:
Introduction To Applied Numerical Analysis (1971)
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