On Saturday, April 27, 2013 5:40:18 AM UTC-4, stathisp wrote:
>
> On Tue, Apr 23, 2013 at 3:14 AM, Craig Weinberg 
> <whats...@gmail.com<javascript:>> 
> wrote: 
> > A quote from someone on Facebook. Any comments? 
> > 
> >> "Computers can only do computations for rational numbers, not for real 
> >> numbers. Every number in a computer is represented as rational. No 
> computer 
> >> can represent pi or any other real number... So even when consciousness 
> can 
> >> be explained by computations, no computer can actually simulate it." 
>
> If it is true that you need real numbers to simulate a brain then 
> since real numbers are not computable the brain is not computable, and 
> hence consciousness is not necessarily computable (although it may 
> still be contingently computable). But what evidence is there that 
> real numbers are needed to simulate the brain? 
>

Since we ourselves can easily conceive of real numbers without converting 
them from floating point decimals in our conscious mind, and since we are 
talking as if the mind supervenes on the brain locally, then we would have 
to explain where this faculty comes from. Whether it is the brain or the 
mind which we are talking about emulating with Comp, the final result must 
include a capacity to conceive of real numbers directly, which we have no 
reason to assume will ever be possible with a Turing based digital machine.

Besides that, it should be pretty clear that the world of classical physics 
is quite enamored with real-number type relations rather than decimal. Even 
at the microcosmic levels, where we find discrete states rather than 
continuous, it is not at all clear that this is a true reflection of nature 
or a local reflection of our instrumental approach. The digital approach is 
always an amputation and an approximation. Not a bad thing when we are 
talking about sending videos and text across the world, but not necessarily 
a good thing for building a working brain from scratch.

Craig
 

>
>
> -- 
> Stathis Papaioannou 
>

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