Frasi di Richard Wesley Hamming

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Richard Wesley Hamming

Data di nascita: 11. Febbraio 1915
Data di morte: 7. Gennaio 1998

Richard Wesley Hamming è stato un matematico statunitense, famoso per l'ideazione del Codice di Hamming.

Dopo il dottorato conseguito all'Università dell'Illinois nel 1942, Hamming fu professore all'Università di Louisville fino all'inizio della Seconda guerra mondiale. Nel 1945 fece parte del Progetto Manhattan, programmando uno dei calcolatori digitali per calcolare le soluzioni delle equazioni fornite dai fisici del progetto.

Nel 1968 ricevette il Premio Turing.

Frasi Richard Wesley 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.“

—  Richard Hamming

The Art of Doing Science and Engineering: Learning to Learn (1991)
Contesto: 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

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

—  Richard Hamming

The Art of Doing Science and Engineering: Learning to Learn (1991)
Contesto: 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?

„No vision, not much of a future.“

—  Richard Hamming

The Art of Doing Science and Engineering: Learning to Learn (1991)
Contesto: 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.

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

—  Richard Hamming

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Contesto: 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.

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

—  Richard Hamming

The Unreasonable Effectiveness of Mathematics (1980)
Contesto: 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

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Contesto: 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.

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

—  Richard Hamming

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Contesto: 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 the same as an art course.“

—  Richard Hamming

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Contesto: 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.

„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

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Contesto: 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.

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

—  Richard Hamming

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Contesto: 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.

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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“

—  Richard Hamming

The Art of Doing Science and Engineering: Learning to Learn (1991)
Contesto: 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.

„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

The Art of Doing Science and Engineering: Learning to Learn (1991)
Contesto: 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

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

—  Richard Hamming

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Contesto: 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.

„Science is supposed to be cumulative, not almost endless duplication of the same kind of things.“

—  Richard Hamming

One Man's View of Computer Science (1969)
Contesto: 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.

„The idea that theorems follow from the postulates does not correspond to simple observation.“

—  Richard Hamming

The Unreasonable Effectiveness of Mathematics (1980)
Contesto: 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.

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

—  Richard Hamming

The Art of Doing Science and Engineering: Learning to Learn (1991)
Contesto: 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.

„They are not fixed for all eternity.“

—  Richard Hamming

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Contesto: 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.

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

—  Richard Hamming

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Contesto: 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.

„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.“

—  Richard Hamming

You and Your Research (1986)
Contesto: 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.

„The assumptions and definitions of mathematics and science come from our intuition“

—  Richard Hamming

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Contesto: 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.

„Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam egestas wisi a erat. Morbi imperdiet, mauris ac auctor dictum.“

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