subject:"Prime Numbers"

Re: Prime numbers

2013-05-26 Thread Bruno Marchal

John,

On 26 May 2013, at 00:54, John Mikes wrote:

Bruno and others:
did you read

http://www.slate.com/articles/health_and_science/do_the_math/2013/05/yitang_zhang_twin_primes_conjecture_a_huge_discovery_about_prime_numbers.single.html

the information about prof. Zhang's discovery (U of New Hampshire)?
It is still in the conjecture of mathematical proof and 'truth' with
a position of "primes are greater
than 1" - with the interesting conclusion that 'primes' are the
ATOMS of the number world.

Any thoughts?

Primes (1 is usually not considered as a prime number) are atoms of
the numbers when conceived multiplicatively, because all numbers can
be described uniquely as a product of primes. That is the existence
and unicity of decomposition of numbers into prime factors (without
taking the order of the multiplication into account). This is the so
called fundamental theorem of arithmetic. It is easy to prove the
existence of the decomposition into primes, but less easy to prove the
uniqueness.

For the twin conjecture, (it exists an infinity of pair of primes p
and q with p - q = 2) it looks like an important step has been proved,
(the case with p - q just bounded) but we are still far from proving
the twin one. Most mathematician believe that the twin conjecture is
true (like most believe that the Riemann conjecture is true). If they
were false, the distribution of primes would not be "statistically
random", and that would mean something very special is at play, a bit
like a number conspiracy! Why not, of course. We just don't know, but
a non random behavior of the primes is a bit like the UFO of number
theory. Well, except that for the UFO, there are (at least) some
evidences (from time to time, most are eventually explained in
general), but there is no evidence at all that the primes behave non-
randomly (in the statistical sense, not in Chaitin-Kolmogorov sense as
we can generate mechanically the distribution of primes).

Bruno

http://iridia.ulb.ac.be/~marchal/

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Re: Prime numbers

2013-05-25 Thread meekerdb

http://www.newscientist.com/article/dn23595-weinsteins-theory-of-everything-is-probably-nothing.html

Brent

On 5/25/2013 3:54 PM, John Mikes wrote:

Bruno and others:
did you read

http://www.slate.com/articles/health_and_science/do_the_math/2013/05/yitang_zhang_twin_primes_conjecture_a_huge_discovery_about_prime_numbers.single.html

the information about prof. Zhang's discovery (U of New Hampshire)?
It is still in the conjecture of mathematical proof and 'truth' with a position of
"primes are greater

than 1" - with the interesting conclusion that 'primes' are the ATOMS of the
number world.
Any thoughts?
JM
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Re: An additional observation-- But only the prime numbers can bemonads. Cool.

2012-12-08 Thread Bruno Marchal



On 08 Dec 2012, at 14:23, Roger Clough wrote:


Hi Bruno Marchal

By "universal numbers" are you referring to the numbers
as seen by Pythagoras ? I'm a little hesistant to get
into that stuff or anything esoteric since becoming a Christian.


Good!

No, by universal numbers I mean a code for a universal Turing machine  
(what a physical computers approximate very well).


Enumerate all the programs in some fixed universal programming  
language: p_0, p_1, p_2, p_3, ...
Call phi_i the corresponding partial computable function. u is said to  
be a universal number if phi_u() = phi_x(y). u is the computer, x  
is the program, and y is the data.  is a bijection from NXN to N,  
so as to keep the phi_i having all one input/variable.


Nothing esoteric here, it is computer science.

Bruno




There is a short video of these at

http://www.youtube.com/watch?v=i7AyNFpJ6DA


[Roger Clough], [rclo...@verizon.net]
12/8/2012
"Forever is a long time, especially near the end." -Woody Allen

- Receiving the following content -
From: Bruno Marchal
Receiver: everything-list
Time: 2012-12-08, 05:09:15
Subject: Re: An additional observation-- But only the prime numbers  
can bemonads. Cool.


On 07 Dec 2012, at 14:57, Roger Clough wrote:

>
>
> Here's an additional observation-- Only the prime numbers can be
> monads,
> because all other integers can not be subdivided and still remain
> integers.






Hmm... numbers are monad when seen as index of a partial computable
function. the monad are the program, which you can see as a number
relative to a universal number. Keep in mind I use comp (renamed CTM
for Computationalist theory of Mind).

Bruno



>
> Cool.
>
>
>
> - Have received the following content -
> Sender: Roger Clough
> Receiver: everything-list
> Time: 2012-12-07, 08:33:37
> Subject: Fw: Whoopie ! The natural INTEGERS are indeed monads
>
>
>
> Obviously, I meant the natural integers, not the natural numbers,
> whatever they be.
>
>
> - Have received the following content -
> Sender: Roger Clough
> Receiver: everything-list
> Time: 2012-12-07, 08:18:36
> Subject: Whoopie ! The natural numbers are indeed monads
>
>
> Hi Bruno Marchal
>
>
> 1) We in fact agree about what 1p is, except IMHO it is the
> Supreme Monad viewing the world THROUGH an individual's
> 1p that I would call the inner God. Or any God.
>
> 2) Previously I dismissed numbers as being monads because I
> thought that all monads had to refer to physical substances.
>
> But natural numbers are different because
> even though they are only mental substances, they're still
> substances, by virtue of the fact that they can't be subdivided.
> So they are of one part each.
>
> Thus the natural numbers are monads, even though they have no
> physical correlates. Sorry I've be so slow to see that.
>
> That reallyiopens doors Then numbers can see each other with 1p.
>
> WHOOPEE !
>
> [Roger Clough], [rclo...@verizon.net]
> 12/7/2012
> "Forever is a long time, especially near the end." -Woody Allen
>
> - Receiving the following content -
> From: Bruno Marchal
> Receiver: everything-list
> Time: 2012-12-06, 12:44:46
> Subject: Re: On the need for perspective and relations in modelling
> the mind
>
>
>
>
> On 05 Dec 2012, at 11:05, Roger Clough wrote:
>
>
> Hi Bruno Marchal
>
> Indeed, we can not code for [1p]. But we need not abandon
> itr entirely, as you seem to have done, and as cognitive
> theory has done.
>
>
> On the contrary, I define it is a simple way (the owner of the
> diary) the the self-multiplication thought experiment (UDA). It is
> enough to understand that physics emerge from the way the "numbers
> see themselves".
>
>
> But in the math part, I define it by using the fact that the
> incompleteness phenomenon redeemed the Theatetus definition. The Bp
> & p definition. It is a bit technical.
>
>
> Don't worry. The 1p is the inner god, the first person, the knower,
> and it plays the key role for consciousness and matter.
>
>
>
>
>
>
>
>
> We can replace [1p] by its actions -
> those of perception, in which terms are relational (subject:  
object).

> You seem to deal with everything from the 3p perspective.
>
>
> That's science. But don't confuse the level. My object of study is
> the 1p, that we can attribute to machine, or person emulated by
> machines. I describe the 3p and the 1ps (singular and plural), and
> indeed their necessary statistical relation at some level.
>
>
>
>
>
>
>
> That is my argument for using semiotics, which includes 1p (or
> interprant) as a necessary and natural

Re: Re: An additional observation-- But only the prime numbers can bemonads. Cool.

2012-12-08 Thread Roger Clough

Hi Bruno Marchal 

By "universal numbers" are you referring to the numbers
as seen by Pythagoras ? I'm a little hesistant to get
into that stuff or anything esoteric since becoming a Christian.

There is a short video of these at

http://www.youtube.com/watch?v=i7AyNFpJ6DA


[Roger Clough], [rclo...@verizon.net]
12/8/2012 
"Forever is a long time, especially near the end." -Woody Allen

- Receiving the following content - 
From: Bruno Marchal 
Receiver: everything-list 
Time: 2012-12-08, 05:09:15
Subject: Re: An additional observation-- But only the prime numbers can 
bemonads. Cool.


On 07 Dec 2012, at 14:57, Roger Clough wrote:

>
>
> Here's an additional observation-- Only the prime numbers can be 
> monads,
> because all other integers can not be subdivided and still remain 
> integers.






Hmm... numbers are monad when seen as index of a partial computable 
function. the monad are the program, which you can see as a number 
relative to a universal number. Keep in mind I use comp (renamed CTM 
for Computationalist theory of Mind).

Bruno



>
> Cool.
>
>
>
> - Have received the following content -
> Sender: Roger Clough
> Receiver: everything-list
> Time: 2012-12-07, 08:33:37
> Subject: Fw: Whoopie ! The natural INTEGERS are indeed monads
>
>
>
> Obviously, I meant the natural integers, not the natural numbers, 
> whatever they be.
>
>
> - Have received the following content -
> Sender: Roger Clough
> Receiver: everything-list
> Time: 2012-12-07, 08:18:36
> Subject: Whoopie ! The natural numbers are indeed monads
>
>
> Hi Bruno Marchal
>
>
> 1) We in fact agree about what 1p is, except IMHO it is the
> Supreme Monad viewing the world THROUGH an individual's
> 1p that I would call the inner God. Or any God.
>
> 2) Previously I dismissed numbers as being monads because I
> thought that all monads had to refer to physical substances.
>
> But natural numbers are different because
> even though they are only mental substances, they're still
> substances, by virtue of the fact that they can't be subdivided.
> So they are of one part each.
>
> Thus the natural numbers are monads, even though they have no
> physical correlates. Sorry I've be so slow to see that.
>
> That reallyiopens doors Then numbers can see each other with 1p.
>
> WHOOPEE !
>
> [Roger Clough], [rclo...@verizon.net]
> 12/7/2012
> "Forever is a long time, especially near the end." -Woody Allen
>
> - Receiving the following content -
> From: Bruno Marchal
> Receiver: everything-list
> Time: 2012-12-06, 12:44:46
> Subject: Re: On the need for perspective and relations in modelling 
> the mind
>
>
>
>
> On 05 Dec 2012, at 11:05, Roger Clough wrote:
>
>
> Hi Bruno Marchal
>
> Indeed, we can not code for [1p]. But we need not abandon
> itr entirely, as you seem to have done, and as cognitive
> theory has done.
>
>
> On the contrary, I define it is a simple way (the owner of the 
> diary) the the self-multiplication thought experiment (UDA). It is 
> enough to understand that physics emerge from the way the "numbers 
> see themselves".
>
>
> But in the math part, I define it by using the fact that the 
> incompleteness phenomenon redeemed the Theatetus definition. The Bp 
> & p definition. It is a bit technical.
>
>
> Don't worry. The 1p is the inner god, the first person, the knower, 
> and it plays the key role for consciousness and matter.
>
>
>
>
>
>
>
>
> We can replace [1p] by its actions -
> those of perception, in which terms are relational (subject: object).
> You seem to deal with everything from the 3p perspective.
>
>
> That's science. But don't confuse the level. My object of study is 
> the 1p, that we can attribute to machine, or person emulated by 
> machines. I describe the 3p and the 1ps (singular and plural), and 
> indeed their necessary statistical relation at some level.
>
>
>
>
>
>
>
> That is my argument for using semiotics, which includes 1p (or
> interprant) as a necessary and natural part of its triad of relations.
> Your responses seem to leave out such relations. I cannot find
> again the quote I should have bookmarked, but in an argument
> for using semiotics on the web, it was said that modern cognitive
> theory has abandoned the self in an effort to depersonalize
> cognition. While this is a valid scientific reason, it doesn't work
> when living breathing humans are concerned.
>
>
> I use computer and mathematical logic semantic. That's the advantage 
> of comp. You have computer science.
>
>
>
>
&

Re: An additional observation-- But only the prime numbers can be monads. Cool.

2012-12-08 Thread Bruno Marchal



On 07 Dec 2012, at 14:57, Roger Clough wrote:




Here's an additional observation-- Only the prime numbers can be  
monads,
because all other integers can not be subdivided and still remain  
integers.







Hmm... numbers are monad when seen as index of a partial computable  
function. the monad are the program, which you can see as a number  
relative to a universal number. Keep in mind I use comp (renamed CTM  
for Computationalist theory of Mind).


Bruno





Cool.



- Have received the following content -
Sender: Roger Clough
Receiver: everything-list
Time: 2012-12-07, 08:33:37
Subject: Fw: Whoopie ! The natural INTEGERS are indeed monads



Obviously, I meant the natural integers, not the natural numbers,  
whatever they be.



- Have received the following content -
Sender: Roger Clough
Receiver: everything-list
Time: 2012-12-07, 08:18:36
Subject: Whoopie ! The natural numbers are indeed monads


Hi Bruno Marchal


1) We in fact agree about what 1p is, except IMHO it is the
Supreme Monad viewing the world THROUGH an individual's
1p that I would call the inner God. Or any God.

2) Previously I dismissed numbers as being monads because I
thought that all monads had to refer to physical substances.

But natural numbers are different because
even though they are only mental substances, they're still
substances, by virtue of the fact that they can't be subdivided.
So they are of one part each.

Thus the natural numbers are monads, even though they have no
physical correlates. Sorry I've be so slow to see that.

That reallyiopens doors Then numbers can see each other with 1p.

WHOOPEE !

[Roger Clough], [rclo...@verizon.net]
12/7/2012
"Forever is a long time, especially near the end." -Woody Allen

- Receiving the following content -
From: Bruno Marchal
Receiver: everything-list
Time: 2012-12-06, 12:44:46
Subject: Re: On the need for perspective and relations in modelling  
the mind





On 05 Dec 2012, at 11:05, Roger Clough wrote:


Hi Bruno Marchal

Indeed, we can not code for [1p]. But we need not abandon
itr entirely, as you seem to have done, and as cognitive
theory has done.


On the contrary, I define it is a simple way (the owner of the  
diary) the the self-multiplication thought experiment (UDA). It is  
enough to understand that physics emerge from the way the "numbers  
see themselves".



But in the math part, I define it by using the fact that the  
incompleteness phenomenon redeemed the Theatetus definition. The Bp  
& p definition. It is a bit technical.



Don't worry. The 1p is the inner god, the first person, the knower,  
and it plays the key role for consciousness and matter.









 We can replace [1p] by its actions -
those of perception, in which terms are relational (subject: object).
You seem to deal with everything from the 3p perspective.


That's science. But don't confuse the level. My object of study is  
the 1p, that we can attribute to machine, or person emulated by  
machines. I describe the 3p and the 1ps (singular and plural), and  
indeed their necessary statistical relation at some level.








That is my argument for using semiotics, which includes 1p (or
interprant) as a necessary and natural part of its triad of relations.
Your responses seem to leave out such relations. I cannot find
again the quote I should have bookmarked, but in an argument
for using semiotics on the web, it was said that modern cognitive
theory has abandoned the self in an effort to depersonalize
cognition. While this is a valid scientific reason, it doesn't work
when living breathing humans are concerned.


I use computer and mathematical logic semantic. That's the advantage  
of comp. You have computer science.






IMHO leaving out [1p ] in such a way will forever prevent
computer calculations from emulating the mind.


The 1p is not left out. Eventually comp singles out eight person  
points of view. If you think comp left out the person, you miss the  
meaning of the comp hope, or the comp fear.



Bruno








[Roger Clough], [rclo...@verizon.net]
12/5/2012
"Forever is a long time, especially near the end." -Woody Allen

- Receiving the following content -
From: Bruno Marchal
Receiver: everything-list
Time: 2012-12-03, 13:03:12
Subject: Re: Semantic vs logical truth




On 03 Dec 2012, at 00:04, meekerdb wrote:


On 12/2/2012 7:27 AM, Bruno Marchal wrote:
The 1p truth of the machine is not coded in the machine. Some actual  
machines knows already that, and can justified that If there are  
machine (and from outside we can know this to correct) then the 1p- 
truth is not codable. The 1p truth are more related to the relation  
between belief and reality (not necessarily physical reality, except  
for observation and sensation).



Even the simple, and apparently formal Bp & p is NOT codable.
Most truth about machine, including some that they can kno

An additional observation-- But only the prime numbers can be monads. Cool.

2012-12-07 Thread Roger Clough



Here's an additional observation-- Only the prime numbers can be monads,
because all other integers can not be subdivided and still remain integers. 

Cool.



- Have received the following content -  
Sender: Roger Clough  
Receiver: everything-list  
Time: 2012-12-07, 08:33:37 
Subject: Fw: Whoopie ! The natural INTEGERS are indeed monads 



Obviously, I meant the natural integers, not the natural numbers, whatever they 
be.  


- Have received the following content -  
Sender: Roger Clough  
Receiver: everything-list  
Time: 2012-12-07, 08:18:36  
Subject: Whoopie ! The natural numbers are indeed monads  


Hi Bruno Marchal  


1) We in fact agree about what 1p is, except IMHO it is the  
Supreme Monad viewing the world THROUGH an individual's  
1p that I would call the inner God. Or any God.  

2) Previously I dismissed numbers as being monads because I  
thought that all monads had to refer to physical substances.  

But natural numbers are different because  
even though they are only mental substances, they're still  
substances, by virtue of the fact that they can't be subdivided.  
So they are of one part each.  

Thus the natural numbers are monads, even though they have no  
physical correlates. Sorry I've be so slow to see that.  

That reallyiopens doors Then numbers can see each other with 1p.  

WHOOPEE !  

[Roger Clough], [rclo...@verizon.net]  
12/7/2012  
"Forever is a long time, especially near the end." -Woody Allen  

- Receiving the following content -  
From: Bruno Marchal  
Receiver: everything-list  
Time: 2012-12-06, 12:44:46  
Subject: Re: On the need for perspective and relations in modelling the mind  




On 05 Dec 2012, at 11:05, Roger Clough wrote:  


Hi Bruno Marchal  

Indeed, we can not code for [1p]. But we need not abandon  
itr entirely, as you seem to have done, and as cognitive  
theory has done.  


On the contrary, I define it is a simple way (the owner of the diary) the the 
self-multiplication thought experiment (UDA). It is enough to understand that 
physics emerge from the way the "numbers see themselves".  


But in the math part, I define it by using the fact that the incompleteness 
phenomenon redeemed the Theatetus definition. The Bp & p definition. It is a 
bit technical.  


Don't worry. The 1p is the inner god, the first person, the knower, and it 
plays the key role for consciousness and matter.  








  We can replace [1p] by its actions -  
those of perception, in which terms are relational (subject: object).  
You seem to deal with everything from the 3p perspective.  


That's science. But don't confuse the level. My object of study is the 1p, that 
we can attribute to machine, or person emulated by machines. I describe the 3p 
and the 1ps (singular and plural), and indeed their necessary statistical 
relation at some level.  







That is my argument for using semiotics, which includes 1p (or  
interprant) as a necessary and natural part of its triad of relations.  
Your responses seem to leave out such relations. I cannot find  
again the quote I should have bookmarked, but in an argument  
for using semiotics on the web, it was said that modern cognitive  
theory has abandoned the self in an effort to depersonalize  
cognition. While this is a valid scientific reason, it doesn't work  
when living breathing humans are concerned.  


I use computer and mathematical logic semantic. That's the advantage of comp. 
You have computer science.  





IMHO leaving out [1p ] in such a way will forever prevent  
computer calculations from emulating the mind.  


The 1p is not left out. Eventually comp singles out eight person points of 
view. If you think comp left out the person, you miss the meaning of the comp 
hope, or the comp fear.  


Bruno  








[Roger Clough], [rclo...@verizon.net]  
12/5/2012  
"Forever is a long time, especially near the end." -Woody Allen  

- Receiving the following content -  
From: Bruno Marchal  
Receiver: everything-list  
Time: 2012-12-03, 13:03:12  
Subject: Re: Semantic vs logical truth  




On 03 Dec 2012, at 00:04, meekerdb wrote:  


On 12/2/2012 7:27 AM, Bruno Marchal wrote:  
The 1p truth of the machine is not coded in the machine. Some actual machines 
knows already that, and can justified that If there are machine (and from 
outside we can know this to correct) then the 1p-truth is not codable. The 1p 
truth are more related to the relation between belief and reality (not 
necessarily physical reality, except for observation and sensation).  


Even the simple, and apparently formal Bp & p is NOT codable.  
Most truth about machine, including some that they can know, are not codable.  
Many things true about us is not codable either.  

Let me see if I understand that. I think you are saying that p, i.e. that "p" 
describes a fact about the world, a meta-le

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