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Calculus systematically evades a great deal of numerical calculation.
Richard Hamming
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Just as there are odors that dogs can smell and we cannot, as well as sounds that dogs can hear and we cannot, so too there are wavelengths of light we cannot see and flavors we cannot taste. Why then, given our brains wired the way they are, does the remark, "Perhaps there are thoughts we cannot think," surprise you?
Richard Hamming
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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.
Richard Hamming
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This text is organized in the "spiral" for learning. A topic... is returned to again and again, each time higher up in the spiral. The first time around you may not be completely sure of what is going on, but on the repeated returns to the topic it should gradually become clear. This is necessary when the ideas are not simple but require a depth of understanding...
Richard Hamming
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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.
Richard Hamming
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The past is... much more uncertain—or even falsely reported—than is usually recognized.
Richard Hamming
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Statistics should be taught early so that the concepts are absorbed by the student's flexible, adaptable mind before it is too late.
Richard Hamming
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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.
Richard Hamming
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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.
Richard Hamming
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What you learn from others you can use to follow.
What you learn for yourself you can use to lead.
Richard Hamming
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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.
Richard Hamming
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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.
Richard Hamming
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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.
Richard Hamming
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The Buddha told his disciples, "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense". I say the same to you—you must assume the responsibility for what you believe.
Richard Hamming
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The methods of mathematics are the main topic of the course, not a long list of finished mathematical results with such highly polished proofs that the poor student can only marvel at the results, with no hope of understanding how mathematics is actually created by practicing mathematicians.
Richard Hamming
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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.
Richard Hamming
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A central problem in teaching mathematics is to communicate a reasonable sense of taste—meaning often when to, or not to, generalize, abstract, or extend something you have just done.
Richard Hamming
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Either you will be a leader, or a follower, and my goal is for you to be a leader.
Richard Hamming
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The feeling of having free will is deep in us and we are reluctant to give it up for ourselves—but we are often willing to deny it to others!
Richard Hamming
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An idea which arises in the field, based on the direct experience of the people doing the job, cannot get going in a centrally controlled system... The not invented here (NIH) syndrome is one of the major curses of our society...
Richard Hamming
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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 the pure state.
Richard Hamming
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There is no agreed upon definition of mathematics, but there is widespread agreement that the essence of mathematics is extension, generalization, and abstraction... [which] often bring increased confidence in the results of a specific application, as well as new viewpoints.
Richard Hamming
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The standard process of organizing knowledge into departments, and subderpartments, and further breaking it up into separate courses, tends to conceal the homogeneity of knowledge, and at the same time to omit much which falls between the courses.
Richard Hamming
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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.
Richard Hamming
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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.
Richard Hamming
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Quote of the day
Now if the harvest is over, And the world cold, Give me the bonus of laughter, As I lose hold.
John Betjeman
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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