[ExI] Meaningless Symbols.
stathisp at gmail.com
Tue Jan 12 13:44:07 UTC 2010
2010/1/12 Ben Zaiboc <bbenzai at yahoo.com>:
> Stathis Papaioannou <stathisp at gmail.com> wrote:
>> Of course, there
>> remains ... the possibility,
>> however unlikely, that the brain is not computable.
> I'm at a loss to understand this. On the face of it, it seems to be a claim that brains do not and cannot exist, but that can't be what you mean.
> Everything that exists has been 'computed' Everything is made of fundamental units that have been combined according to a set of rules.
> When we talk about making simulations we are just talking about moving this process to a different kind of fundamental unit, and discovering then applying the relevant set of rules. Thus we create models of things and processes, re-creating them on a different level of reality.
> If any aspect of a thing or process is not captured in the model, it means the model is not fine-grained enough, not extensive enough, or uses the wrong rules. All these things are fixable, at least in principle.
> So what does it mean to say that something is 'not computable', if not that it's impossible?
Computable means computable by a Turing machine. Not all numbers and
functions are computable, but it is not clear how this is relevant to
True randomness is not computable (except by a trick involving
observers in branching virtual worlds) but there is no evidence that
pseudo-randomness, which is computable, won't do as well. Real numbers
are not computable, but even if it turns out that some physical
parameters are continuous rather than discrete there is no reason to
suppose that infinite precision arithmetic will be required to
simulate the brain, since thermal motion effects would make precision
beyond a certain number of decimal places useless. Finally, there may
be new physics, such as a theory of quantum gravity, which is not
computable. Roger Penrose thinks that this is the case, and that the
brain utilises this exotic physics to do things that no Turing machine
ever could, such as have certain mathematical insights. However, few
believe that Penrose is right, and almost all agree that his main
argument from Godel's theorem is wrong. On balance, it seems that the
brain works using plain old fashioned chemistry, which no-one claims
is not computable.
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