On Saturday, April 27, 2013 2:20:20 PM UTC-4, stathisp wrote:
> On 28/04/2013, at 3:31 AM, Craig Weinberg <whats...@gmail.com<javascript:>> 
> 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. 

Sure I can. It's easy because I'm not trying to conceive of it literally 
like a computer, but figuratively as an idea. Pi, as the ratio of the 
circumference of a circle to its radius, can be understood in radians or 
just geometrically by visual feel. Pi falls out of the aesthetics of 
circularity itself, and it need not be enumerated abstractly. 

> 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?

You can either say that it is in your brain or that it isn't, but either 
way, the thing that Comp claims to be able to emulate does something which 
Comp cannot do now, and which gives us no reason to expect that it will 
ever do.

> 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 for.

Inspecting a classical system from some arbitrary level of substitution is 
different than being a proprietary system which is by definition unique. 
The very kinds of things which machines fail at are the things which are 
most essential to consciousness.


> --
> Stathis Papaioannou

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