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

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