In October 2012 New Scientist Magazine published a special issue that was devoted to this burning question - "what is reality?".
Having published a video called "Imagining the 'Zeroth' Dimension" in late August, there were definitely some quotes from that issue that caught my eye:
"These are very difficult issues," says philosopher of science James Ladyman of the University of Bristol, UK, "but it might be less misleading to say that the universe is made of maths than to say it is made of matter."
Difficult indeed. What does it mean to say that the universe is "made of mathematics"? An obvious starting point is to ask what mathematics is made of. The late physicist John Wheeler said 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, and so on. Keep nesting the nothingness like invisible Russian dolls and eventually all of mathematics appears. Mathematician Ian Stewart of the University of Warwick, UK, calls this "the dreadful secret of mathematics: it's all based on nothing" (New Scientist, 19 November 2011, p 44). Reality may come down to mathematics, but mathematics comes down to nothing at all.
So a question that is often asked is how do we get "something" from the "nothing" of the unobserved quantum fabric?
According to prevailing wisdom, a quantum particle such as an electron or photon can only be properly described as a mathematical entity known as a wave function. Wave functions can exist as "superpositions" of many states at once. A photon, for instance, can circulate in two different directions around an optical fibre; or an electron can simultaneously spin clockwise and anticlockwise or be in two positions at once.
When any attempt is made to observe these simultaneous existences, however, something odd happens: we see only one. How do many possibilities become one physical reality?
This is the central question in quantum mechanics...
If reality is ultimately math, and math is ultimately derived from "nothing", or zero, then this quote from Jan Westerhoff can have a very interesting interpretation.
In our search for foundations, we have gone round in a circle, from the mind, via various components of matter, back to the mind - or, in the case of the Copenhagen interpretation, from the macroscopic to the microscopic, and then back to the macroscopic. But this just means that nothing is fundamental, in the same way there is no first or last stop on London Underground's Circle Line. The moral to draw from the reductionist scenario seems to be that either what is fundamental is not material, or that nothing at all is fundamental.
- from the article "Reality: Is Matter Real?", by Jan Westerhoff, a philosopher at the University of Durham and the University of London's School of Oriental and African Studies, both in the UK
Which takes us back to Imagining the "Zeroth" Dimension, and the lovely mind flip that Gevin Giorbran described for us - if everything is ultimately derived from an underlying symmetry state, and a universe such as ours is derived from a breaking of that symmetry, then that can lead us to a way of imagining how there is an underlying "nothing" of all possibilities in perfect balance, and zero becomes the biggest number of all. Please watch this video for more on this fascinating idea.
A direct link to the above video can be found at http://www.youtube.com/watch?v=emlcwyvnsg0