On 22 Aug 2012, at 12:17, benjayk wrote:
Bruno Marchal wrote:
On 22 Aug 2012, at 00:26, benjayk wrote:
meekerdb wrote:
On 8/21/2012 2:52 PM, benjayk wrote:
meekerdb wrote:
On 8/21/2012 2:24 PM, benjayk wrote:
meekerdb wrote:
"This sentence cannot be confirmed to be true by a human
being."
The Computer
He might be right in saying that (See my response to Saibal).
But it can't confirm it as well (how could it, since we as
humans can't
confirm it and what he knows about us derives from what we
program into
it?). So still, it is less capable than a human.
I know it by simple logic - in which I have observed humans to be
relatively slow and
error prone.
regards, The Computer
Well, that is you imagining to be a computer. But program an
actual
computer that concludes this without it being hard-coded into it.
All it
could do is repeat the opinion you feed it, or disagree with you,
depending
on how you program it.
There is nothing computational that suggest that the statement is
true or
false. Or if it you believe it is, please attempt to show how.
In fact there is a better formulation of the problem: 'The truth-
value of
this statement is not computable.'.
It is true, but this can't be computed, so obviously no computer
can
reach
this conclusion without it being fed to it via input (which is
something
external to the computer). Yet we can see that it is true.
Not really. You're equivocating on "computable" as "what can be
computed"
and "what a
computer does". You're supposing that a computer cannot have the
reflexive inference
capability to "see" that the statement is true.
No, I don't supppose that it does. It results from the fact that we
get a
contradiction if the computer could see that the statement is true
(since it
had to compute it, which is all it can do).
A computer can do much more than computing. It can do proving,
defining, inductive inference (guessing), and many other things. You
might say that all this is, at some lower level, still computation,
Sorry, but the opposite is the case. To say that computers do proving,
defining, guessing is a confusion of level, since these are
interpretation
of computations, or are represented using computations, not the
computations
itself. If we encode a proof using numbers, then this is not the proof
itself, but its representation in numbers. Just as "Gödel's proof"
is not
Gödel's proof just because I say it represents Gödel's proof.
Or just as I say computers the word computers don't compute anything.
That is why when I say that a computer dreams, or that a number
dreams, it is a shorthand for a computer having an activity supporting
a dream, or a number involved in an arithmetical realization of a dream.
This makes sense in the comp theory.
In arithmetic too we already make the distinction between a number
representing a proof and the proof itself, which is the sequence of
distinct formula verifying some conditions.
Computers do that distinction.
PA use numbers as language like German use the German language, but
both the Germans and PA will distinguish what they talk about and the
syntactical terms used to denote them.
Imagine a computer without an output. Now, if we look at what the
computer
is doing, we can not infer what it is actually doing in terms of
high-level
activity, because this is just defined at the output/input. For
example, no
video exists in the computer - the data of the video could be other
data as
well. We would indeed just find computation.
At the level of the chip, notions like definition, proving, inductive
interference don't exist. And if we believe the church-turing
thesis, they
can't exist in any computation (since all are equivalent to a
computation of
a turing computer, which doesn't have those notions), they would be
merely
labels that we use in our programming language.
All computers are equivalent with respect to computability. This does
not entail that all computers are equivalent to respect of
provability. Indeed the PA machines proves much more than the RA
machines. The ZF machine proves much more than the PA machines. But
they do prove in the operational meaning of the term. They actually
give proof of statements. Like you can say that a computer can play
chess.
Computability is closed for the diagonal procedure, but not
provability, game, definability, etc.
That is the reason that I don't buy turings thesis, because it
intends to
reduce all computation to a turing machine
... to a Turing machine activity (as defined in math, I don't mean
physical activity).
just because it can be
represented using computation. But ultimately a simple machine can't
compute
the same as a complex one, because we need a next layer to interpret
the
simple computations as complex ones (which is possible). That is,
assembler
isn't as powerful as C++, because we need additional layers to
retrieve the
same information from the output of the assembler.
That depends how you implement C++. It is not relevant. We might
directly translate C++ in the physical layer, and emulate some
assembler in the C++.
But assembler and C++ are computationally equivalent because their
programs exhaust the computable function by a Turing universal machine.
You are right that we can confuse the levels in some way,
Better not to confuse the levels ever, except when using fixed point
theorem justifying precisely how to fuse levels.
basically because
there is no way to actually completely seperate them.
When we look at an unknown machine, yes.
But in this case we
can also confuse all symbols and definitions, in effect deconstructing
language. So as long as we rely on precise, non-poetic language it
is wise
to seperate levels.
OK. I agree with this.
Bruno
Bruno Marchal wrote:
but then this can be said for us too, and that would be a confusion
of
level.
Only if we assume we are computational. I don't.
Bruno Marchal wrote:
The fact that a computer is universal for computation does not
imply logically that a computer can do only computations. You could
say that a brain can only do electrical spiking, or that molecules
can
only do electron sharing.
You have a point here. Physical computers must do more then
computation,
because they must convert abstract information into physical signals
(which
don't exist at the level of computation).
But if we really are talking about the abstract aspect of computers,
I think
my point is still valid. It can only do computations, because all we
defined
it as is in terms of computationl.
benjayk
--
View this message in context:
http://old.nabble.com/Simple-proof-that-our-intelligence-transcends-that-of-computers-tp34330236p34333663.html
Sent from the Everything List mailing list archive at Nabble.com.
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com
.
For more options, visit this group at http://groups.google.com/group/everything-list?hl=en
.
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to
everything-list+unsubscr...@googlegroups.com.
For more options, visit this group at
http://groups.google.com/group/everything-list?hl=en.
