Richard Hamming - Learning Quotes

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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
Besides the theory there are a lot of small technical details that must be learned so well that you can recall them almost instantaneously, such as the trigonometric identities... put one part of the identity on one side of a 3 x 5 card and the other part on the other side. Using these flash cards you can, in the odd moments of your daily life, learn the mechanical parts of the course.... for this kind of low-level material many short learning sessions are much more efficient than a few long, intense ones; but this is not necessarily true for larger ideas.... most students will not use such trivial devices as flash cards; it seems to be beneath their dignity. They suffer accordingly.

Richard Hamming
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
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
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?

Richard Hamming
Probability is the mathematics of uncertainty.... many modern theories have uncertainty built into their foundations. Thus learning to think in terms of probability is essential.

Richard Hamming
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
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