# Re: Rationals vs Reals in Comp

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On 27 Apr 2013, at 17:10, John Mikes wrote:```
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```Dear Stathis and Bruno,
Stathis' reply is commendable, with one excessive word:
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" r e a l ". I asked Bruno several times to 'identify' the term 'number' in common-sense language. So far I did not understand such (my mistake?) I still hold 'numbers' as the product of human thinking which cannot be retrospect to the basis of brain-function. (Unless we consider BRAIN as the tissue-organ in our skull, executing technical steps for our "mentality" - whatever that may be.
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Well, we usually consider the brain to be the tissue-organ, and in the comp theory, we assume his function can be replaced by a suitable universal machine, that is computer.
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I am not sure what it is that you don't understand in the notion of number. Usually it means "natural numbers", but mathematicians have thousand of generalization of that concept (integer, rational numbers, real nubers, complex numbers, quaternion, octonions, and many others).
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In common sense language, natural numbers are related to the words "zero", "one", "two", "three", etc. I am not sure what problem you have with them.
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My remark to Bruno: in my (agnostic?) mind 'machine' means a functioning contraption composed of finite parts,
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OK. And we can be neutral at the start if those part are physically realized or not. The machine I talk about have been defined precisely in math, and can be assumed to be approximated in the physical world (primitive or not).
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an ascertainable inventory, while 'universal machine' - as I understand(?) the term includes lots of infinite connotations (references).
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That's right, but they are themselves composed of a finite number of finite parts.
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```So I would be happy to name them something different from 'machine'.
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On the contrary, the alluring fact about universal machine is that they are machine. They are finite. General purpose computers and programming language interpreters are example of such (physical, virtual) universal machines.
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I accept 'computation' as not restricted to numerical (math?) calculations although our (embryonic, binary) Touring machine is based on such.
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With the Church Turing thesis, all computers are equivalent for the computations they can execute. They will differ in the unboundable range of provability, knowability, observability and sensibility though.
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I am still at a loss to see in extended practice a 'quantum', or a 'molecularly based' computer so often referred to in fictional lit.
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Yes, we will see, but we already believe (with respect to all current facts and theories of course) that they do not violate the Church Turing thesis. It is a theorem that a quantum computer does not compute more functions than a Turing machine, or than Babbage machine.
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I know you like Robert Rosen, who asserted that Church Turing thesis is false, but he has not convinced me at all on this.
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```The "Universal Computer" (Loeb?)
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It is Turing who discovered it explicitly, but Babbage, Post, Church and others made equivalent discoveries. Gödel and Löb's discoveries concerns notion like truth and provability, which quite typically have no corresponding Church thesis, and there is no notion of universality related to them.
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On the contrary, we know that provability is constructively NOT universal. We can build a machine contradicting any attempt to find a universal provability predicate. Some machines (the Löbian one) can prove that about themselves.
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requires better descriptions as to it's qualia to include domains beyond our present knowledge and the infinities. (Maybe "human"mind? which is also unidentified).
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That can depend on the theory that you will assume. With comp, our brain are equivalent to Turing machine, with respect to computations, but not with respect of provability, knowability, sensibility, etc.
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Bruno

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```JohnM

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On Sat, Apr 27, 2013 at 5:40 AM, Stathis Papaioannou <stath...@gmail.com > wrote: On Tue, Apr 23, 2013 at 3:14 AM, Craig Weinberg <whatsons...@gmail.com> wrote:
```> A quote from someone on Facebook. Any comments?
>
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>> "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."
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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?

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Stathis Papaioannou

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