## Mathematical Realism

How does mathematics and reality relate to each other? Some mathematicians believe that mathematical entities are “real”, and this view can be characterized as a version of Platonic philosophy. Quine and Putnam developed an argument in support of mathematical realism, which starts with the observation that mathematics is indispensable for almost every other science. Here […]

## Ordinals, Cardinals, Representation of Numbers in Language.

Quoted from:  Pi in the Sky, by John Barrow. Oxford University Press, 1992. p. 37-38 “English: one/first ; two/second ; three/third ; four/fourth French: un/premier ; deux/second or deuxième ; trois/troisième ; quatre/quatrième German: ein/erste ; zwei/ander or zweite ; drei/dritter ; vier/vierte Italian: uno/primo ; due/secondo ; tre/terzo ; quattro/quarto In each of these […]

## Mathematical Infinity

“There are two approaches to mathematical infinity. It can be seen as defining limiting cases that can never be realized or as existing in some philosophical sense. These mathematical approaches parallel approaches to meaning and value that I call absolutist and evolutionary. The absolutist sees ultimate meaning as something that exists most commonly in the form of an all powerful infinite God. The evolutionary sees life and all of a creation as an ever expanding journey with no ultimate or final goal. There is only the journey. There is no destination. This video argues for an evolutionary view in our sense of meaning and values and in our mathematical understanding. There is a deep connection between the two with profound implications for the evolution of consciousness and human destiny.” (Paul Budnik)

## 0 to 6 dimensions and back – simple rotation.

This is a simple computer-simulated rotation from a point, which has 0 dimensions, to a line (1 dimension), a square (2), a cube (3), all the way up to 6 dimensions, and then down. Multi-dimensional objects are much more complex than we can imagine.   Related posts: Tesseracts: from 3 to 4 Dimensions. Klein Bottle […]