On 28/04/2013, at 3:31 AM, Craig Weinberg <whatsons...@gmail.com> wrote:

> 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> 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.

Can you conceive of a real number? I can't. It's like conceiving of infinity - 
you can say it but I don't think you can really do it. But that is beside the 
point: if you can conceive of something why should that mean that it is true 
or, even worse, that there is a little bit of that something in your brain?

> 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.

We can simulate any classical system with discrete arithmetic. If we could not 
then computers would be useless for many of the things they are actually used 

Stathis Papaioannou

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