Simulation independence

I recently came across Nick Boström's article about the simulation argument, which goes that there is a non-zero chance that we are actually simulated individuals, and not actually made of carbon at all. It was spun out of The Matrix series of movies, though is a recurring theme right from Descartes and the Brain in a Vat.

Key to this idea is the argument of substrate independence, that is, carbon-based cells are not the only possible way of conjuring consciousness. Surely it isn't the carbon-based molecules per se that cause consciousness, but rather their configuration, and the kinds of computation (if that's the right word) being performed. Surely any "computer program" that reproduces the workings of the brain sufficiently well would suffice, since its operation and outputs would be essentially identical to the biological brain.

The simulation argument goes that we are not all that far from achieving that level of computation, so therefore there may well exist simulated minds in the near future. The problem is, how would you tell if you are real or not? The short answer is that you can't, as Descartes argued.

It occurs to me that there are two forms of simulation argument:

• One where your brain is simulated, for purposes unknown. I'll call the first one brain simulation.
  
• One where your entire universe is simulated (again for unknown purposes), and the cells in your brain are created within that simulation. Maybe this universe was allowed to evolve from a Big Bang. I'll call this one physics simulation.
  

Clearly it would take a whole load more computing horsepower to acheive the second, in fact, the second may only exist as a thought experiment, or in some higher-order universe where computations of our own universe would be much more straightforward. For example, we could simulate small "universes" in Conway's Game of Life, the principle is the same but the scale is different.

One of my pet theories is simulation independence, which I will explain.

1. A simulation is a model obeying mathematical rules.
2. The result of a simulation is a mathematical structure.
   
3. Mathematical structures exist independently of physical existence, or whether they are created or perceived by man. This is the Platonic world of ideals.
   
4. Therefore, simulations exist independently of observation, a phenomenon I call simulation independence.

This may seem like semantics, but I think it has some profound consequences:

• When people run a simulation, they are discovering something that's already there. They are observing something that has already happened, and would have happened irrespective of whether they had run the simulation.
• There is no theoretical limit to the size or complexity of simulations. Simulations exist in a Platonic world, that are bounded by the axioms of mathematics, not the physical limitations of computability in the universe you are in.
• When you switch off a simulation, the simulation (in the Platonic world) keeps on running.
  
• It makes no sense to ask whether you are part of a simulation, because the inhabitants of the simulation are in the Platonic world. You don't have to worry.
  
• Anything that can exist, does exist, provided it makes coherent sense from a mathematical model.
• There does not need to be a Modeller.
• Everything that will happen, in a sense has already happened in the Platonic world. Time is an illusion.
  
• Parallel universes exist (provided that they are mathematically valid).
  
• We are very likely living in a mathematical structure conjured by the Platonic world of ideals.
  

The question of whether the mathematical world exists independently of the physical world is fundamental, but I don't think it can be denied. Our current understanding of the universe is that it is governed by mathematical laws, and mathematics describes pretty much everything. Therefore, this mathematics must have been applicable in the early universe before humans or any kind of consciousness arose. We also notice the unnerving consistency of mathematics, where calculations are reproducible. This is spooky, and in my mind, proof of the independent status of mathematics.

Plato's world of ideals wasn't really talking about mathematics, but was talking about the higher level concepts such as horses. Nevertheless, the concept of existence beyond the human mind, and beyond the physical world, was introduced.

Although there is no Modeller, where does the Platonic world of mathematics come from?

I wrote a short story exploring the idea of simulation independence. Be warned: its quality is on a par with Nick Boströms poetry.