Le 20-juin-06, à 01:18, Russell Standish a écrit :
So we a need a name. Bitstrings is too specific, since we could also
be referring to strings from other alphabets. The word description
seems to fit the concept, and wasn't otherwise used in literature.
Why not saying just strings then?
Le 20-juin-06, à 06:00, Tom Caylor a écrit (replying to Norman Samish) :
Norman Samish wrote:
Gentlemen:
I've endured this thread long enough! Let's get back to something I
can understand!
Why? you'll ask.
I'll reply, Because your audience is shrinking! I've plotted the
On Thu, Jun 22, 2006 at 11:24:22AM +0200, Bruno Marchal wrote:
Whereas I don't think it does. It can be applied in an absolute way
(such as you refer) or in a relative subjective way (which is how I do
it). In fact I make the point that absolute measures aren't meaningful
- there just
Le 19-juin-06, à 15:31, Russell Standish a écrit :
I'm not so sure. At heart, I suspect he is a computationalist, however
what he assumes in his papers is that the universe (that we see) is a
single
specific computation selected from the dovetailer algorithm. With COMP
(and
with
Le 20-juin-06, à 04:04, Norman Samish a écrit :
I've endured this thread long enough! Let's get back to something I can understand!
Why? you'll ask.
I'll reply, Because your audience is shrinking! I've plotted the Audience vs. Topic, and find that, in 12.63 months, there is a 91%
James,
Le 17-juin-06, à 20:10, James N Rose a écrit :
Bruno,
Sometimes gedankenexperiments - or even theoretical
contemplations - include unvoiced/unconsidered
presumptions and biases that a system may not
be self-aware of. Benj Whorf brought this aspect
of systemic nature into
Le 18-juin-06, à 01:55, Russell Standish a écrit :
A description is an infinite length (bit)string (bits in brackets,
because any other alphabet will do also). This use does sometimes fly
in face of what people expect,
Certainly.
but I define this explicitly - it is a
useful
Le 18-juin-06, à 06:35, Tom Caylor a écrit :
I don't know much about Church Thesis, but I want to learn more. Even
though it seems easy to recite, as in the existence of a Universal
Language, it seems very deep and mysterious.
I think so.
Almost like stating a
Unified Field Thesis.
On Mon, Jun 19, 2006 at 11:12:52AM +0200, Bruno Marchal wrote:
?
I'm not sure which bit you were having trouble with. A description is
an infinite length bitstring. It is therefore equivalent to a point in
the unit interval [0,1] (modulo a little bit of funny stuff on a set of
measure zero).
Gentlemen:
I've endured this thread long enough! Let's get back
to something I can understand!
"Why?" you'll ask.
I'll reply, "Because your audience is shrinking!
I've plotted the Audience vs. Topic, and find that, in 12.63 months, there is a
91% probability that, if the topic doesn't
Norman Samish wrote:
Gentlemen:
I've endured this thread long enough! Let's get back to something I can
understand!
Why? you'll ask.
I'll reply, Because your audience is shrinking! I've plotted the Audience
vs. Topic, and find that, in 12.63 months, there is a 91% probability that,
Le 15-juin-06, à 17:57, Tom Caylor a écrit :
An even simpler case is the following:
inputs
1 2 3 4 5 6 7 8 9
f1:1 2 3 4 5 6 7 8 9 ... (identity)
f2:2 1 3 4 5 6 7 8 9 ... (switch 1 and 2)
f3:3 2 1 4 5 6 7 8 9 ... (switch 1 and 3)
f4:4 2 3 1 5 6 7 8 9
Le 15-juin-06, à 18:40, Tom Caylor a écrit :
Bruno Marchal wrote:
Let us be specific (also for the others).
Let us continue to write f1 f2 f3 f4 f5 f6 f7 ... for the sequence of
total computable functions.
Let us continue to write F1 F2 F3 F4 F5 F6 F7 ... for the sequence of
partial
Le 17-juin-06, à 07:56, Stathis Papaioannou a écrit :
x-tad-bigger /x-tad-bigger
x-tad-bigger Bruno,/x-tad-bigger
x-tad-biggerI'll rephrase the problem - let me know if I get it wrong. It is proposed that all the functions f with certain attributes A be enumerated in a list: f1, f2, f3 etc. It
Bruno,
Sometimes gedankenexperiments - or even theoretical
contemplations - include unvoiced/unconsidered
presumptions and biases that a system may not
be self-aware of. Benj Whorf brought this aspect
of systemic nature into consideration, in the 1930's,
when he applied Einstein/Reichenbach
On Thu, Jun 15, 2006 at 04:29:18PM +0200, Bruno Marchal wrote:
Le 14-juin-06, à 07:31, Russell Standish a écrit :
On Mon, Jun 12, 2006 at 03:52:15PM +0200, Bruno Marchal wrote:
In general, an infinite programs can still be written with a finite
number of symbols, like a real
Bruno Marchal wrote:
Le 15-juin-06, à 18:40, Tom Caylor a écrit :
Bruno Marchal wrote:
Let us be specific (also for the others).
Let us continue to write f1 f2 f3 f4 f5 f6 f7 ... for the sequence of
total computable functions.
Let us continue to write F1 F2 F3 F4 F5 F6 F7 ...
Bruno Marchal wrote:
Le 15-juin-06, à 13:53, Tom Caylor a écrit :
OK. I think I understand what you are saying, on a surface level. Of
course a surface level will never be able to expose any contradictions.
I'm just riding this wave as long as I can before deciding to get off.
It
Bruno,
I'll rephrase the problem - let me know if I get it wrong. It is proposed that all the functions fwith certainattributes "A" be enumerated in a list: f1, f2, f3 etc. It looks like "A" in theexample under considerationmeans "all the computable functions", but in fact there is a
Bruno Marchal wrote:
...
OK, you and Quentin have already solve this, I will not comment. Just a
little summary in two points:
1) The deep reason why we can hope (pray, bet on, ...) in the universal
dovetailer is just Church thesis which is possible thanks to the fact
the set of
Bruno Marchal wrote:
...
Let us be specific (also for the others).
Let us continue to write f1 f2 f3 f4 f5 f6 f7 ... for the sequence of
total computable functions.
Let us continue to write F1 F2 F3 F4 F5 F6 F7 ... for the sequence of
partial computable functions (this includes the fi but
I've always wondered (from a position of relative mathematical naivete, please understand)
about the process in arguments like this whereby reasoning about arithmetic comes to
include the labels applied to arithmetical statements, on the grounds that these labels happen
themselves to be
Le 14-juin-06, à 07:31, Russell Standish a écrit :
On Mon, Jun 12, 2006 at 03:52:15PM +0200, Bruno Marchal wrote:
In general, an infinite programs can still be written with a finite
number of symbols, like a real number can be written with a finite
number of symbols chosen among
Le 15-juin-06, à 13:53, Tom Caylor a écrit :
OK. I think I understand what you are saying, on a surface level. Of
course a surface level will never be able to expose any contradictions.
I'm just riding this wave as long as I can before deciding to get off.
It seems that there are very
Le 15-juin-06, à 14:40, Stathis Papaioannou a écrit :
x-tad-biggerI've always wondered (from a position of relative mathematical naivete, please understand)/x-tad-bigger
x-tad-bigger about the process in arguments like this whereby reasoning about arithmetic comes to/x-tad-bigger
x-tad-bigger
An even simpler case is the following:
inputs
1 2 3 4 5 6 7 8 9
f1:1 2 3 4 5 6 7 8 9 ... (identity)
f2:2 1 3 4 5 6 7 8 9 ... (switch 1 and 2)
f3:3 2 1 4 5 6 7 8 9 ... (switch 1 and 3)
f4:4 2 3 1 5 6 7 8 9 ... (switch 1 and 4)
f5:5 2 3 4 1 6 7 8 9 ...
Tom Caylor wrote:
An even simpler case is the following:
inputs
1 2 3 4 5 6 7 8 9
f1:1 2 3 4 5 6 7 8 9 ... (identity)
f2:2 1 3 4 5 6 7 8 9 ... (switch 1 and 2)
f3:3 2 1 4 5 6 7 8 9 ... (switch 1 and 3)
f4:4 2 3 1 5 6 7 8 9 ... (switch 1 and 4)
f5:
Bruno Marchal wrote:
Le 11-juin-06, à 08:49, Tom Caylor a écrit :
Bruno Marchal wrote:
There is just no algorithm which can generate
the sequence of codes of the computable functions from N to N. So,
although each fn is a computable function (from N to N), you cannot
diagonalize it
Le 13-juin-06, à 03:04, George Levy a écrit :
Bruno Marchal wrote:
Proceeding that way you will run into trouble. But it is very easy to
find the k.
Let us be specific and let us imagine you have already written in
Fortran a generator of all programs of the one-variable partial
On Mon, Jun 12, 2006 at 03:52:15PM +0200, Bruno Marchal wrote:
In general, an infinite programs can still be written with a finite
number of symbols, like a real number can be written with a finite
number of symbols chosen among {0,1,2,3,4,5,6,7,8,9}. Of course in
general it will need an
Le 11-juin-06, à 02:00, Tom Caylor a écrit :
If I may, I'd like to revisit why (the motivation) we are considering
functions from N to N. I guess it is because all computations are
equivalent to taking a number from N (i.e. each uniquely meaningful
input of a computation can be put into a
Le 11-juin-06, à 08:49, Tom Caylor a écrit :
Bruno Marchal wrote:
...
It looks like g is computable isn't it. All fn are computable and can
be computed on each n, and certainly adding one (the + 1) is
computable too. Right?
Well, if you say all right here, we are in trouble. Because if
Le 12-juin-06, à 00:23, George Levy a écrit :
Ok. G(n) = Fn(n)+1 is computable.
I guess you mean programmable, or at least partial computable. OK.
The hard part is finding the k such
that G(k)=Fk(k). I could try scanning all instances of Fk(k) from k=0
to
a very large number. The scan
Bruno Marchal wrote:
Proceeding that way you will run into trouble. But it is very easy to
find the k.
Let us be specific and let us imagine you have already written in
Fortran a generator of all programs of the one-variable partial
computable functions: F1 F2 F3 F4 F5 F6 F7 ...
The list of
Bruno Marchal wrote:
...
It looks like g is computable isn't it. All fn are computable and can
be computed on each n, and certainly adding one (the + 1) is
computable too. Right?
Well, if you say all right here, we are in trouble. Because if g is
really computable, then g is in the
Tom Caylor wrote:
...
I guess even if this was the Universal Dovetailer computing the fi's
interspersed with non-computable Fi's, it would still compute the fi's
in a finite amount of time, along with a finite amount of the
non-computable Fi's computation (even though it will not finish the
Hi Tom,
Le Dimanche 11 Juin 2006 02:00, Tom Caylor a écrit :
I've been wondering about this in the background for a while, so now I
can ask this question. OK, I think I understand everything so far.
But... if there are functions (in the list of *all* programmable
functions) which will run
I went on a 10 day trip during which I had no access to email... a lot
has happened on this list since then.
Bruno Marchal wrote:
And fortran programs
are fortran generable, so I can generate a sequence of all fortran
one-variable program F1 F2 F3 F4 F5 F6 F7 F8 (all means that
soon or
Hi Tom,
Le Dimanche 11 Juin 2006 02:00, Tom Caylor a écrit :
I've been wondering about this in the background for a while, so now I
can ask this question. OK, I think I understand everything so far.
But... if there are functions (in the list of *all* programmable
functions) which will run
it generate the second
program, execute the first instruction of the second program, then the
*SECOND* instruction of the first program, then it generates the third one,
executing its first instruction, the second instruction of the second
program, the *THIRD* of the first and so on ad
Quentin Anciaux wrote:
it generate the second
program, execute the first instruction of the second program, then the
*SECOND* instruction of the first program, then it generates the third one,
executing its first instruction, the second instruction of the second
program, the *THIRD*
Bruno Marchal wrote:
Hi,
Ok Tom, put your security belt because we will leave the constructive
area, because it is the price we need to pay, in front of machine, for
NOT leaving the finite area.
Let me recall the problem.
1) Obviously the set of all computable function from the set of
Russell Standish wrote:
On Thu, Jun 08, 2006 at 04:24:51AM +0200, Quentin Anciaux wrote:
Le Jeudi 8 Juin 2006 02:56, Russell Standish a écrit :
On Wed, Jun 07, 2006 at 03:56:32PM +0200, Quentin Anciaux wrote:
Hi Bruno,
what I undestand about the UD is that it generates all
Indeed obtaining the tape with Omega on it would be equivalent to solving
the Halting problem, but obtaining an arbitrary random noncomputable sequence
tape is as simple as hooking up a random source to your TM.
In what way is the random source not a program?
On another point, 10,000 bits of
Russell Standish wrote:
Indeed obtaining the tape with Omega on it would be equivalent to solving
the Halting problem, but obtaining an arbitrary random noncomputable
sequence
tape is as simple as hooking up a random source to your TM.
In what way is the random source not a program?
True,
Hi Quentin,
Le 07-juin-06, à 15:56, Quentin Anciaux a écrit :
Hi Bruno,
what I undestand about the UD is that it generates all programs, a
program
being simply a number from the set N.(1)
This is right. Programs or digital machine are supposed to be
(grammatically) well-defined, and
Le 08-juin-06, à 02:56, Russell Standish a écrit :
On Wed, Jun 07, 2006 at 03:56:32PM +0200, Quentin Anciaux wrote:
Hi Bruno,
what I undestand about the UD is that it generates all programs, a
program
being simply a number from the set N.(1)
No - halting programs are a subset of N,
Hi,
Ok Tom, put your security belt because we will leave the constructive
area, because it is the price we need to pay, in front of machine, for
NOT leaving the finite area.
Let me recall the problem.
1) Obviously the set of all computable function from the set of natural
number N to the
Le 06-juin-06, à 20:50, [EMAIL PROTECTED] a écrit :
Given a
(countably infinite) sequence of functions f1, f2, ..., you say that
fn(n)+1 must either be in the sequence OR not in the sequence.
I am just showing constructively that if f1, f2,f3, ... is a well
defined sequence of computable
Hi Bruno,
what I undestand about the UD is that it generates all programs, a program
being simply a number from the set N.(1)
There exists an infinity of program which generates a set of growing function
(different set), all the computable growing function are generated by all
these
On Wed, Jun 07, 2006 at 03:56:32PM +0200, Quentin Anciaux wrote:
Hi Bruno,
what I undestand about the UD is that it generates all programs, a program
being simply a number from the set N.(1)
No - halting programs are a subset of N, but there are uncountably
infinite non-halting ones.
On Tue, Jun 06, 2006 at 03:05:26PM +0200, Bruno Marchal wrote:
Alas this is only partially true. Well, perhaps it is due to my use of
both english and french all the time, but I have a tendency to mess up
the s in french too. The s rule are 90% opposed in french and
english.
Really?
Le Jeudi 8 Juin 2006 02:56, Russell Standish a écrit :
On Wed, Jun 07, 2006 at 03:56:32PM +0200, Quentin Anciaux wrote:
Hi Bruno,
what I undestand about the UD is that it generates all programs, a
program being simply a number from the set N.(1)
No - halting programs are a subset of N,
On Thu, Jun 08, 2006 at 04:24:51AM +0200, Quentin Anciaux wrote:
Le Jeudi 8 Juin 2006 02:56, Russell Standish a écrit :
On Wed, Jun 07, 2006 at 03:56:32PM +0200, Quentin Anciaux wrote:
Hi Bruno,
what I undestand about the UD is that it generates all programs, a
program being
Le 05-juin-06, à 18:37, Tom Caylor a écrit :
Not to try to answer the Puzzle, but just some thoughts for the
conversation:
That's the right spirit!
At one glance, it seems that the argument is trying to transcend
Godel's Incompleteness theorems. The Universal Language is trying to
be
Hi,
Here is a little test, just for singling out a typical non
intuitionistic (non constructive) argument.
Such kind of argument makes me recall the tale: The Little Prince
written by the French pilot and novelist St-Exupery, where the Little
Prince asked the narrator (a pilot) to draw a
Marchal [EMAIL PROTECTED]
To: everything-list@googlegroups.com
Sent: Tue, 6 Jun 2006 16:38:28 +0200
Subject: Re: *THE* PUZZLE (was: ascension, Smullyan, ...)
Hi,
Here is a little test, just for singling out a typical non
intuitionistic (non constructive) argument.
Such kind of argument makes me
More comments on George Levy + *THE PUZZLE*.
Le 30-mai-06, à 20:42, George Levy a écrit :
To speak only for myself, I think I have a sufficient understanding of
the thread. Essentially you have shown that one cannot form a set of
all
numbers/functions because given any set of
Bruno Marchal wrote:
More comments on George Levy + *THE PUZZLE*.
Le 30-mai-06, à 20:42, George Levy a écrit :
To speak only for myself, I think I have a sufficient understanding of
the thread. Essentially you have shown that one cannot form a set of
all
numbers/functions because
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