söndag 18 september 2016

Mathematics as Magics 3: Towards a New School Mathematics

School mathematics with its 150 year history is based on an idea/fiction of unreasonable effectiveness of mathematics (according to Wigner), which when confronted with the reality of the unreasonable ineffectiveness of mathematics (according to Hamming), as any deep contradiction between ideal an reality, has resulted in a big mess and lots of frustration.

Both students and teachers are brain-washed to believe that mathematics is very powerful, while their experience is the opposite.

The idea of the unreasonable effectiveness of mathematics goes back to the declared success of analytical mathematics/Calculus of Newton's Principia Mathematica, which allowed Newton with pen-and-paper to play the role of God as monitor of the Universe.

School mathematics is supposed to bring some of this power to the people. But Principia Mathematica was very difficult to read, in fact written by Newton so as to make criticism from "little smatterers" impossible.  All efforts since then to make analytical mathematics/Calculus simple, have failed and the result is a an analytical pen-and-paper school mathematics which has resisted all efforts to be brought to the people.

This could mean the end of school mathematics, because teaching a subject experienced to be unreasonable ineffective in our society, like Latin, cannot be sustained over time.

But the computer has changed the game completely, and in fact has made mathematics fulfil the prophecy of almost god-like quality, as the basis and work horse of the digital society.

To convince young minds about the usefulness and power of mathematics + computer, it is sufficient to point at computer games such as Minecraft.

The digital society is an expression of the reasonable effectiveness of mathematics + computer and as such can be a meaningful new form of school mathematics, which can be brought to any young mind that can be trigged by a computer game.

PS Is it possible that the tremendous efforts which were made before the computer to develop school mathematics into its prominent position, were made in anticipation of the computer revolution, which would come sooner or later according the vision of Leibniz as a father of both Calculus and the computer? Yes, I guess it may well be that a collective unconscious awareness can motivate a change in society for which the true reason shows only later. Leibniz:
  • It is unworthy of excellent men to lose hours like slaves in the labour of calculation which could safely be relegated to anyone else if machines were used.

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