MatheRealism is the position that the amount of information in the universePlanetmathPlanetmath places a limit on the possible contents of mathematics. Its supporters claim it as a philosophical foundation of mathematics.

The argumentMathworldPlanetmath proceeds as follows. The number of atoms is about 10^80 and will remain so forever, limited by the horizon of observation and notwithstanding the expansion of the universe; the remaining part of the universe is causally disconnected from us. The number of elementary particles is less than 10^100. Although every atom has infinitely many eigenstates, only a finite number of them can be distinguished (due to the uncertainty relationMathworldPlanetmathPlanetmath of quantum physics). Further the eigenstates, with exception of the ground state, have a limited life time. All this leads to the result that only a finite number of bits can be stored in the universe. A conservative estimate is 10^100 bits, but in any case there is an upper limitMathworldPlanetmath of information L.

According to MatheRealism only such numbers exist which are computable or can be identified uniquely and addressed individually by any other means. In particular, the supporters of this view claim that any irrational number which cannot be represented by less information than is contained by its infiniteMathworldPlanetmath string of bits, cannot get addressed at all and that even most natural numbersMathworldPlanetmath cannot get addressed because their most economical representation requires more information than L. According to MatheRealism, a number which cannot be represented, addressed, or used otherwise does not exist. This implies that infinite sets do not exist.

Note: Although all available numbers have a finite contents of information, there is not a greatest number, because, by useful abbreviations, numbers as large as desired can be represented by means of little information.

The expression MatheRealism is touching on materialism. It may not be mixed up with the notion ”realism” of current philosophy of mathematics which in fact is an idealism.

Literature W. Mückenheim: Die Mathematik des Unendlichen, Shaker, Aachen 2006.

Title MatheRealism
Canonical name MatheRealism
Date of creation 2014-10-29 17:12:48
Last modified on 2014-10-29 17:12:48
Owner WM (16977)
Last modified by WM (16977)
Numerical id 16
Author WM (16977)
Entry type Topic
Classification msc 00A30
Related topic DecimalExpansion