MatheRealism

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

The argument proceeds as follows. The number of atoms is about10^80 and will remain so forever, limited by the horizon ofobservation and notwithstanding the expansion of the universe; theremaining part of the universe is causally disconnected from us. Thenumber of elementary particles is less than 10^100. Although everyatom has infinitely many eigenstates, only a finite number of them canbe distinguished (due to the uncertainty relation of quantumphysics). 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 bitscan be stored in the universe. A conservative estimate is 10^100bits, but in any case there is an upper limit 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 ofthis view claim that any irrational number which cannot berepresented by less information than is contained by its infinitestring of bits, cannot get addressed at all and that even most naturalnumbers cannot get addressed because their most economicalrepresentation requires more information than L. According toMatheRealism, a number which cannot be represented, addressed, or usedotherwise 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.

单词	MatheRealism
释义	MatheRealism MatheRealism is the position that the amount of information inthe universe places a limit on the possible contents of mathematics.Its supporters claim it as a philosophical foundation of mathematics. The argument proceeds as follows. The number of atoms is about10^80 and will remain so forever, limited by the horizon ofobservation and notwithstanding the expansion of the universe; theremaining part of the universe is causally disconnected from us. Thenumber of elementary particles is less than 10^100. Although everyatom has infinitely many eigenstates, only a finite number of them canbe distinguished (due to the uncertainty relation of quantumphysics). 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 bitscan be stored in the universe. A conservative estimate is 10^100bits, but in any case there is an upper limit 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 ofthis view claim that any irrational number which cannot berepresented by less information than is contained by its infinitestring of bits, cannot get addressed at all and that even most naturalnumbers cannot get addressed because their most economicalrepresentation requires more information than L. According toMatheRealism, a number which cannot be represented, addressed, or usedotherwise 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.
随便看	KdistanceSet K-distance set Keepflipchange keep-flip-change KeithNumber Keith number KempeChain Kempe chain KempnerSeries Kempner series KenosymplirosticNumbers Kenosymplirostic numbers Kernel kernel kernel Kernel1 KernelOfAHomomorphismBetweenAlgebraicSystems kernel of a homomorphism between algebraic systems KernelOfAHomomorphismIsACongruence kernel of a homomorphism is a congruence KernelOfALinearMapping kernel of a linear mapping ker⁡L={0} if and only if L is injective Key key