What does it mean to say that the universe is made of mathematics? What is mathematics made of?
The late physicist John Wheeler says that the basis of all mathematics is 0=0.
All mathematical structures can be derived from something called ‘the empty set’, the set that contains no elements.
Say this set corresponds to zero you can then define the number 1 as the set that contains only the empty set; 2 as the set containing the sets corresponding to 0 and 1. Keep nesting the nothingness like invisible Russian dolls and eventually all of mathematics appears.
Mathematician Ian Stewart of the University of Warwick, U.K, calls this ‘the dreadful secret of mathematics: it’s all based on nothing.’
That may be the ultimate clue to existence- after all a universe made of nothing doesn’t require an explanation, indeed, mathematical structures don’t seem to require a physical origin at all.
“A dodecahedron was never created” says Max Tegmark of the Massechusetts Institute of Technology.
“To be created, something first has to exist in space or time and then exist. A dodecahedron doesn’t exist in space or time at all, he says- it exists independently of them.
‘Space and time are themselves contained within larger mathematical structures,’ he adds, these structures just exist, they can’t be created or destroyed.’
Amanda Gefter. New Scientist September 2012. P39
The following are works in progress: