Ричард Хэмминг цитаты

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Ричард Хэмминг

Дата рождения: 11. Февраль 1915
Дата смерти: 7. Январь 1998

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Ричард Уэсли Хэмминг — американский математик, работы которого в сфере теории информации оказали существенное влияние на компьютерные науки и телекоммуникации. Основной вклад — т. н. код Хэмминга, а также расстояние Хэмминга.

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русский и украинский философ, поэт, педагог
Годфри Харолд Харди фото
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Цитаты Ричард Хэмминг

„We do not always know what we are talking about.“

—  Richard Hamming
Context: We do not always know what we are talking about.... Troubles... can be made to arise whenever what is being said includes itself—a self-referral situation.

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„They are not fixed for all eternity.“

—  Richard Hamming
Context: The assumptions and definitions of mathematics and science come from our intuition, which is based ultimately on experience. They then get shaped by further experience in using them and are occasionally revised. They are not fixed for all eternity.

„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.“

—  Richard Hamming
Context: 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. Of course, you seldom, if ever, see either pure state.<!-- (1997), p. 5

„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
Context: 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.

„Without continuous mathematics, the study of discrete mathematics soon becomes trivial and very limited. ...The two topics“

—  Richard Hamming
Context: Increasingly... the application of mathematics to the real world involves discrete mathematics... the nature of the discrete is often most clearly revealed through the continuous models of both calculus and probability. Without continuous mathematics, the study of discrete mathematics soon becomes trivial and very limited.... The two topics, discrete and continuous mathematics, are both ill served by being rigidly separated.

„There is no unique, correct answer in most cases. It is a matter of taste“

—  Richard Hamming
Context: There is no unique, correct answer in most cases. It is a matter of taste, depending on the circumstances... and the particular age you live in.... Gradually, you will develop your own taste, and along the way you may occasionally recognize that your taste may be the best one! It is the same as an art course.

„Great scientists tolerate ambiguity very well.“

—  Richard Hamming
Context: Most people like to believe something is or is not true. Great scientists tolerate ambiguity very well. They believe the theory enough to go ahead; they doubt it enough to notice the errors and faults so they can step forward and create the new replacement theory. If you believe too much you'll never notice the flaws; if you doubt too much you won't get started. It requires a lovely balance.

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„It is the same as an art course.“

—  Richard Hamming
Context: There is no unique, correct answer in most cases. It is a matter of taste, depending on the circumstances... and the particular age you live in.... Gradually, you will develop your own taste, and along the way you may occasionally recognize that your taste may be the best one! It is the same as an art course.

„There is simply too much known to continue the older approach of giving detailed results.“

—  Richard Hamming
Context: 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.

„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“

—  Richard Hamming
Context: 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.

„Until we understand languages of communication involving humans as they are then it is unlikely many of our software problems will vanish.“

—  Richard Hamming
Context: The fundamentals of language are not understood to this day.... Until we understand languages of communication involving humans as they are then it is unlikely many of our software problems will vanish.

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„The newer aspects of many fields start with the admission of uncertainty.“

—  Richard Hamming
Context: Probability plays a central role in many fields, from quantum mechanics to information theory, and even older fields use probability now that the presence of "noise" is officially admitted. The newer aspects of many fields start with the admission of uncertainty.

„Euclid's postulates came from the Pythagorean theorem, not the other way around.“

—  Richard Hamming
Context: 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.

„In the face of almost infinite useful knowledge, we have adopted the strategy of "information regeneration rather than information retrieval." ...most importantly, you should be able to generate the result you need even if no one has ever done it before you“

—  Richard Hamming
Context: In the face of almost infinite useful knowledge, we have adopted the strategy of "information regeneration rather than information retrieval."... most importantly, you should be able to generate the result you need even if no one has ever done it before you—you will not be dependent on the past to have done everything you will ever need in mathematics.

„He who works with the door open gets all kinds of interruptions, but he also occasionally gets clues as to what the world is and what might be important.“

—  Richard Hamming
Context: I noticed the following facts about people who work with the door open or the door closed. I notice that if you have the door to your office closed, you get more work done today and tomorrow, and you are more productive than most. But 10 years later somehow you don't quite know what problems are worth working on; all the hard work you do is sort of tangential in importance. He who works with the door open gets all kinds of interruptions, but he also occasionally gets clues as to what the world is and what might be important.

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