By Alexandre V. Borovik
It truly is an strange publication which casts new and paradoxical mild at the nature of arithmetic. The e-book can be attention-grabbing -- probably for various purposes -- to varsity lecturers of arithmetic and maths majors at universities, to graduate scholars in arithmetic and machine technological know-how, to analyze mathematicians and desktop scientists, to philosophers and historians of arithmetic, to psychologists and neurophysiologists.
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Extra info for Mathematics under the Microscope
Notice that construction of the icosahedron is the same thing as construction of the finite reflection group H3 ; this can be done by means of linear algebra—which leads to rather nasty calculations, or by means of representation theory—which requires some knowledge of representation theory. It also can be done by quaternions—which is nice and beautiful, but requires knowledge of quaternions. The graphical construction is the simplest; using computer jargon, it is a WYSIWYG (“What You See Is What You Get”) mode of doing mathematics, which deserves to be used at every opportunity.
10 works as a proof because it is produced by “inverse vision”. To draw it, you have to run, in your head, the procedure for the construction of the icosahedron. 10. 34 2 What You See is What You Get Fig. 9. A symbolic human and a naturalistic bull. 17000 BC / Caves of Lascaux, Dordogne, France. Source: Wikipedia Commons. Public domain. anisms of perception of motion which glue, in our minds, cinema’s 24 frames per second into continuous motion. 10 deserves to be treated as a mathematical statement.
It is a popular misconception that It is a popular misconception that mathemathematics is a dull repetitive acmatics is a dull repetitive activity. tivity. Actually, mathematicians are easily bored by repetition. Perhaps this could create some difficulty in neurological studies of mathematics. Certain techniques for study of patterns of activation of the brain are easier to implement when the subject is engaged in an activity which is relatively simple and can be repeated again and again, so that the data can be averaged and errors of measurements suppressed.