On 27 Apr 2013, at 17:10, John Mikes wrote:
Dear Stathis and Bruno,
Stathis' reply is commendable, with one excessive word:
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.
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.
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).
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.
My remark to Bruno: in my (agnostic?) mind 'machine' means a
functioning contraption composed of finite parts,
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).
an ascertainable inventory, while 'universal machine' - as I
understand(?) the term includes lots of infinite connotations
(references).
That's right, but they are themselves composed of a finite number of
finite parts.
So I would be happy to name them something different from 'machine'.
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.
I accept 'computation' as not restricted to numerical (math?)
calculations although our (embryonic, binary) Touring machine is
based on such.
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.
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.
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.
I know you like Robert Rosen, who asserted that Church Turing thesis
is false, but he has not convinced me at all on this.
The Universal Computer (Loeb?)
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.
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.
requires better descriptions as to it's qualia to include domains
beyond our present knowledge and the infinities. (Maybe humanmind?
which is also unidentified).
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.
Bruno
JohnM
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?
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?
--
Stathis Papaioannou
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