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[Dec. 23rd, 2010|11:54 am] |
That the mathematics is precise enough to be interpreted automatically allows active exploration to be extended to the mathematics. The requirement that the computer be able to interpret any expression provides strict and immediate feedback as
to whether the expression is correctly formulated. Experience demonstrates that interaction with the computer in this way uncovers and corrects many deficiencies in understanding.
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When we started we expected that using this approach to formulate mechanics would be easy. We quickly learned though that there were many things we thought we understood that we did not in fact understand. Our requirement that our mathematical notations be explicit and precise enough so that they can be interpreted automatically, as by a computer, is very effective in uncovering puns and flaws in reasoning.
-- Structure and Interpretation of Classical Mechanics
You think you know when you learn, are more sure when you can write, even more when you can teach, but certain when you can program.
-- Alan Perlis |
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