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Richard Hamming

Geburtstag: 11. Februar 1915
Todesdatum: 7. Januar 1998

Richard Wesley Hamming war ein amerikanischer Mathematiker, dessen Arbeit großen Einfluss auf die Informatik und Telekommunikation hatte.

Zitate Richard Hamming

„Education is what, when, and why to do things. Training is how to do it. Either one without the other is not of much use.“

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— Richard Hamming
The Art of Doing Science and Engineering: Learning to Learn (1991), Context: I am concerned with educating and not training you.... Education is what, when, and why to do things. Training is how to do it. Either one without the other is not of much use. You might think education should precede training, but the kind of educating I am trying to do must be based on your past experiences and technical knowledge.<!-- Preface

„It is the same as an art course.“

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— Richard Hamming
Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985), 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.

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

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— Richard Hamming
Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985), 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.

„When a theory is sufficiently general to cover many fields of application, it acquires some "truth" from each of them.“

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— Richard Hamming
Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985), Context: When a theory is sufficiently general to cover many fields of application, it acquires some "truth" from each of them. Thus... a positive value for generalization in mathematics.

„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“

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— Richard Hamming
Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985), 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.

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

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— Richard Hamming
The Unreasonable Effectiveness of Mathematics (1980), 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.

„No vision, not much of a future.“

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— Richard Hamming
The Art of Doing Science and Engineering: Learning to Learn (1991), Context: 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 √n.... the accuracy of the vision matters less than you suppose, getting anywhere is better than drifting, there are potentially many paths to greatness for you... No vision, not much of a future.

„They are learned by the constant use of the language and cannot be taught in any other fashion.“

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— Richard Hamming
Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985), Context: Mathematics, being very different from the natural languages, has its corresponding patterns of thought. Learning these patterns is much more important than any particular result... They are learned by the constant use of the language and cannot be taught in any other fashion.

„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“

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— Richard Hamming
The Art of Doing Science and Engineering: Learning to Learn (1991), Context: 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 idea that theorems follow from the postulates does not correspond to simple observation.“

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„Only when field maintenance is part of the original design can it be safely controlled“

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— Richard Hamming
The Art of Doing Science and Engineering: Learning to Learn (1991), Context: The more complex the designed system the more field maintenance must be central to the final design. Only when field maintenance is part of the original design can it be safely controlled... This applies to both mechanical things and to human organizations.

„Are you sure you are not merely "programmed" in life by what by chance events happens to you?“

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— Richard Hamming
The Art of Doing Science and Engineering: Learning to Learn (1991), Context: When you take a course in Euclidean geometry is not the teacher putting a... learning program into you?... 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.... Are you sure you are not merely "programmed" in life by what by chance events happens to you?

„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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— Richard Hamming
The Art of Doing Science and Engineering: Learning to Learn (1991), 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.

„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“

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— Richard Hamming
Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985), 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.

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

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— Richard Hamming
Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985), 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.

„Great scientists tolerate ambiguity very well.“

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— Richard Hamming
You and Your Research (1986), 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.