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
> > - ther
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
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" the
On Tue, Jun 20, 2006 at 11:43:08AM +0200, Bruno Marchal wrote:
>
>
> 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
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% probab
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 fu
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% probabi
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
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).
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 Thesi
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
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 int
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.
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
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,
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 not
Le 17-juin-06, à 07:56, Stathis Papaioannou a écrit :
Bruno,
I'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 looks like "A" in the example under consideration means "all
Le 15-juin-06, à 21:03, Jesse Mazer a écrit :
>
> Tom Caylor wrote:
>
>>
>> So apparently we are still missing something. You need to tell us
>> *why* this is not the right reason. The set of instructions for g is
>> precisely a big "case" statement (if you will) on n, like this:
>>
>> switch
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
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
Bruno,
I'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 looks like "A" in the example under consideration means "all the computable functions", but in fact there is a furthe
Tom Caylor wrote:
>
>So apparently we are still missing something. You need to tell us
>*why* this is not the right reason. The set of instructions for g is
>precisely a big "case" statement (if you will) on n, like this:
>
>switch n:
>begin
>case 1:
>set of instructions for f1:
>case 2:
>set o
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
>
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)
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 ... (s
Le 15-juin-06, à 14:40, Stathis Papaioannou a écrit :
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 gro
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 ve
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
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 numbers.
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
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 prog
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 nee
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
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
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
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 tro
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 int
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
> 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
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
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
>so
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
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
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 t
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
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 se
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
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,
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?
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 Om
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 th
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
> > > pro
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 su
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.
Re
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.
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 programs(
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 computab
al Message-
From: Bruno 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.
S
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 sh
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 bot
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/fun
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