The Fire in the Equations

I just had an interesting philosophical thought.

In my opinion, reductionism reduces the physical universe to a set of simple mathematical rules.

This cannot be all though; these mathematical rules also have reality. Let me explain:

There is a stationary particle with mass 10kg along a line which we shall take to be an x axis. A force of 10N is applied to it.

The behaviour, that is to say, the 'reality' of the particle can now be comprehensively stated thus:

x = 1/2t^2

Where t is time elapsed in seconds and x the displacement in meters.

Above is a universe that I have just created. I have described absolutely everything about it in reductionist terms with mathematics. However, it is not real.

That essence that would make it real is what I have once heard metaphorically described as 'The Fire in the Equations' of reductionism.

My insight was this:

If a Turing machine were to emulate this universe, we could argue that this would make it as real as ours (I am essentially assuming functionalism).

However, we must bear in mind that this Turing machine must also be real. We could physically reduce it to even more (more complex) equations, and then act this algorithm out upon another Turing machine, in order to breathe this sacred 'fire' into its equations.

Hence in order to make my universe real we would have to have an infinite chain of Turing machines which seems paradoxical. So what is the source of the fire?

Interesting to note are the similarities with the cosmological paradox.

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If a Turing machine were to emulate this universe, we could argue that this would make it as real as ours (I am essentially assuming functionalism).

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Functionalism is dead, it died.

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Hence in order to make my universe real we would have to have an infinite chain of Turing machines which seems paradoxical. So what is the source of the fire?

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If you restrict yourself to set theory then maybe, however I'm pretty sure you can reduce the universe to a finite set of equations using category theory.

The other problem of using a Turing machine is that it will miss Godel's undecidables conjuctures. You still have to get the correct axioms, which is a big problem. For example, if the universe didn't go by the axiom or theorem of the continuum hypothesis, then once you assume it something about the universe you emulate will be different too the real universe.

A better idear would be to try and get some mathematical results about existence, then maybe using that too find the theory of everything, then trying to run that on a computer.

Functionalism died? Do you mean formalism?

I am referring to functionalism, which says that if an algorithm acts something out, that thing which is being acted out is just as real as its real world counterpart. It is mainly used in reference to consciousness, and the idea that if you emulated the brain on, say, a computer, it would be just as conscious as us. I find it very hard to argue with this principle, because the converse is essentially asserting that sodium ions and plasma membranes etc. are somehow necessary for consciousness.