Das Kalenderblatt 100725

24/07/2010 - 17:44 von WM | Report spam
Attempts to create "pure" deductive-axiomatic mathematics have led to
the rejection of the scheme used in physics (observation - model -
investigation of the model - conclusions - testing by observations)
and its substitution by the scheme: definition - theorem - proof. It
is impossible to understand an unmotivated definition but this does
not stop the criminal algebraists-axiomatisators. {{Hier ist nicht von
Vertretern einer speziell für Kriminalisten entworfenen Algebra die
Rede.}} For example, they would readily define the product of natural
numbers by means of the long multiplication rule. With this the
commutativity of multiplication becomes difficult to prove but it is
still possible to deduce it as a theorem from the axioms. It is then
possible to force poor students to learn this theorem and its proof
(with the aim of raising the standing of both the science and the
persons teaching it). It is obvious that such definitions and such
proofs can only harm the teaching and practical work.

It is only possible to understand the commutativity of multiplication
by counting and re-counting soldiers by ranks and files or by
calculating the area of a rectangle in the two ways. Any attempt to do
without this interference by physics and reality into mathematics is
sectarianism and isolationism which destroy the image of mathematics
as a useful human activity in the eyes of all sensible people. {{Man
erinnere sich nur an das Urnenproblem aus KB100711 oder die leere
"Grenzmenge" mit einer unendlichen Anzahl von Elementen, die eíne
ebenso unendliche Summe bilden aus KB100723.}}

V.I. Arnold: "On teaching mathematics" (1997)
Translated by A.V. Goryunov

Gruß, WM

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#1 Alfred Flaßhaar
24/07/2010 - 18:12 | Warnen spam
WM wrote:


Der englischsprachige Text hàtte in Richtung "very BE" eine Überarbeitung
verdient. Dann wàre der deutssprachige Anteil überflüssig.

Freundliche Grüße, Alfred Flaßhaar

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