Quentin Anciaux writes: > In all of these discussion, it is really this point that annoy me... What is > the calculation ? Is it a physical process ? Obviously a calculation need > time... what is the difference between an abstract calculation (ie: one which > is done on a sheet of paper or just in your head) with an "effective" > calculation ? What is the meaning of "instantiating" in a block universe > view ?
I am generally of the school that considers that calculations can be treated as abstract or formal objects, that they can exist without a physical computer existing to run them. The goal is to model the universe (among other things) as such a calculation. If we demand that a calculation exists in a universe, and a universe is also a calculation, then we have an infinite regression. One might postulate a God who is infinite himself and is the endpoint of the regression, but absent such supernatural entities, the model otherwise doesn't work. Why model the universe as a calculation? Well, for one reason, because it seems to work. It appears that physical law is essentially mathematical, implying that it should be feasible in principle to construct a program which could simulate the entire universe to any degree of accuracy. It would seem odd, given that the universe can be a calculation, if it weren't a calculation. If it seems objectionable to have a calculation without a calculator, perhaps simpler examples can support the intuition. You can imagine a triangle without a triangulator. You can imagine a number without someone who counts. Perhaps you can even imagine a mathematical proof without a prover. Mathematical objects may have virtually unlimited complexity and internal structure, and can be said to exist independently of anyone who thinks about them or discovers them. Computations seem to fit very comfortably into this framework. If we allow ourselves to imagine calculations as having mathematical reality, and further to imagine that our universe is such a calculation, then we have unified mathematical and physical reality. There is no longer a difference. Things which are physically real are merely a subset of the things which are mathematically real. If we don't take this step, we have two kinds of reality, mathematical and physical, which makes for a more awkward (IMO) philosophical position. However I certainly understand that all these arguments are only persuasive and indicative and certainly do not amount to a proof. Nevertheless it is my hope that by pursuing these ideas we can construct testable propositions which, if verified, will add weight to the possibility that this is the nature of reality. Hal Finney