Re: An invisible fuzzy amoral mindless blob, aka God

[Torgny Tholerus]

On 2016-12-28 23:56, John Mikes wrote:
I do not intend to participate in the discussion of this topic fpr 
more than one reason:

1. I am agnostic, so I just DO NOT KNOW what (who?) that "GOD" may be.


*You just have to ask God what she is.  Then she will answer.  But it 
may take two years to get the full answer.*



   1,A: is God a PERSON? (Or: many persons?)


*Yes, God is a person.  In the same way as your own personality is build 
up by trillions of brain cells, then Gods personality is build up by 
billions of human beeings.*


1,C Did He/She/It originate the World? (what draws the question: 
How was God originated?)


*No, she did not originate the world.  She is a result of the natural 
selection.*


3. A am also ignorant about my (or anyone else's) Subconscious. Have 
you ever M E T
yours? I figure it must be something limitless of which we fathom 
only a bit.
Or is all t his rather fitting the Superconscious? we have some 
idea about our 'conscious'?


*I have talked with my subconscious.  I do it every time I pray.  And 
sometimes my subconscious answer me.  And sometimes my subconscious 
talks directly to me, she reminds me when I have forgotten something.*



4. An immortal person? Cf. Wagner's Gotterdammerung.


*No, God is not immortal.  But God will live much longer than a human 
being.  God will *live *as long as the mankind exists.*


5. "Supernatural powers"? did you ever define the "natural ones" 
(beyond our ever changing concept of a system of our "physical" 
 explanations?


*No, God have no supernatural powers.  God can only do what a human 
being can do.*



John M


--
Torgny

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Re: An invisible fuzzy amoral mindless blob, aka God

[Torgny Tholerus]

On 2016-12-26 10:52, Stathis Papaioannou wrote:

On 25 December 2016 at 19:40, Torgny Tholerus <tor...@dsv.su.se 
<mailto:tor...@dsv.su.se>> wrote:


   I have found that God is exactly the same as my subconscious.  And
   my subconscious is connected to other peoples subconsciouses.

   When I pray, I talk to my own subconscious.  Then my subconscious
   talks to other peoples subconsciouses.  Then one persons
   subconscious is affecting this persons behavior, so that I get
   answer to my prayer.


How do you know that your subconscious talks to and affects other people?
--
Stathis Papaioannou

=
I have had several experiences of it. Not so often, only when needed. 
These experiences can be explained away as coincidence and chance. But 
it happens too often to be mere coincidence.


--
Torgny

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Re: An invisible fuzzy amoral mindless blob, aka God

[Torgny Tholerus]

On 2016-12-26 00:09, Brent Meeker wrote:


On 12/25/2016 12:40 AM, Torgny Tholerus wrote:


I have found that God is exactly the same as my subconscious. And my 
subconscious is connected to other peoples subconsciouses.


When I pray, I talk to my own subconscious.  Then my subconscious 
talks to other peoples subconsciouses.  Then one persons subconscious 
is affecting this persons behavior, so that I get answer to my prayer.




Psychiatrist:   "Look--how do you know you're God?"
Lord Gurney: "Well, every time I pray, I find that I'm talking to 
myself."

--- Peter Barnes, "The Ruling Class"



Yes, this is true.  I have a part of God inside me.  So I can say that I 
am (a part of) God.


The whole of God consists of the sum of all the subconsciouses of all 
human beeings.  Nothing more and nothing less than that.


--
Torgny

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Re: An invisible fuzzy amoral mindless blob, aka God

[Torgny Tholerus]

2016-12-25 03:07 skrev John Clark:

On Wed, Dec 14, 2016 at 9:56 AM, Bruno Marchal 
wrote:


​>>​ usage says that "God" means an immortal person with
supernatural power who wants, and deserves, to be worshipped.







​> ​That's the Christian use
​ ​. Why do atheists insist so much we use the christian notion,


Well... at least atheists have some notation in mind when they use the
word
​.​ It may not exist but at least "an immortal person with
supernatural power who wants and deserves to be worshiped" means
something.
​  Theists, at least most of those on this list, quite literally
don't know what they're talking about when they talk about "God".
​ ​As near as I can tell to them the word "God"  means an
invisible fuzzy amoral blob that does nothing and knows nothing and
thinks about nothing
​ that we can not effect and that does not effect our lives​. Why
even invent a word for a concept as useless as that?


I have found that God is exactly the same as my subconscious.  And my 
subconscious is connected to other peoples subconsciouses.


When I pray, I talk to my own subconscious.  Then my subconscious talks 
to other peoples subconsciouses.  Then one persons subconscious is 
affecting this persons behavior, so that I get answer to my prayer.


--
Torgny

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Re: MGA revisited paper + supervenience

[Torgny Tholerus]

LizR skrev 2014-10-01 01:44:
On 1 October 2014 04:23, Platonist Guitar Cowboy 
multiplecit...@gmail.com mailto:multiplecit...@gmail.com wrote:



Ultrafinitism then: set of all numbers is finite and whatever
weird logic they need to have numbers obey some weirder upper
limit, and I heard they issue fines and tickets for anybody who
states a bigger number.

Like the biggest number used by ultra finitists + 1 ... oops.




The biggest number + 1 is a number that does not belong to the set of 
all numbers...


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Re: Everything List Survey

[Torgny Tholerus]

Stathis Papaioannou skrev:

2010/1/14 Stathis Papaioannou stath...@gmail.com:

  

Interesting so far:
- people are about evenly divided on the question of whether computers
can be conscious
- no-one really knows what to make of OM's
- more people believe cats are conscious than dogs



Oh, and one person does not believe that they are conscious! Come on,
who's the zombie?


  


It's me.

(The question on whether computers can be conscious, should have three 
alternatives:


1)  Both computers and humans can be conscious.
2)  Humans, but not computers can be conscious.
3)  Neither humans nor computers can be conscious.

(The alternative: Computers, but not humans can be conscious, is not 
needed...))


--
Torgny Tholerus
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Re: Dreaming On

[Torgny Tholerus]

Bruno Marchal skrev:
   
 Then it is not RITSIAR in the sense of the discussion with David.
 Real in the sense that I am real. is ambiguous.
 Either the I refers to my first person, and then I have ontological  
 certainty.
 As I said on FOR, I can conceive that I wake up and realize that  
 quark, planet, galaxies and even my body were not real. I cannot  
 conceive that I wake up and realize that my consciousness is not real.
   

When I woke up this morning, I realized that my consciousness was not 
real...

-- 
Torgny Tholerus

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Re: Dreams and Machines

[Torgny Tholerus]

Bruno Marchal skrev:

 On 22 Jul 2009, at 14:12, Torgny Tholerus wrote:
 What do you think about the GoL-universes?  You can look at some of
 those at http://www.bitstorm.org/gameoflife/ .  If you have an initial
 condition and you have an unlimited board, then you can compute what
 will happen in the future in that universe.  

 What is an unlimited board for an ultrafinitist. (Ok, that was perhaps 
 easy).

An unlimited board is a board that is enough big.  How far away you 
look, you will see no border of the board.



 These universes are
 universes with a two-dimensional space and a one-dimensional time.  
 These GoL-universes are mathematial universes.  They have an initial
 condition and a mathematical rule that defines how that universe will
 look like in the next moment, and the next next moment, and so on.

 Does this make sense for you?

 Those are not universes, but computational histories.

What is wrong with computational histories?  If you can explain 
everything in our universe with a computational history, why do you need 
anything more?

 Assuming comp there is a first person indeterminacy, which makes 
 physical appearances or physical universe emerging from the 
 infinity of such computational and universal computation. I suggest 
 you read the UDA papers. I guess you were not yet on the list when I 
 explained why Wolfram sort of computational physics, based on 
 cellular automata, does not work.

Yes, I was not on the list then.  And all the time when I have been on 
the list, I have wondered what COMP is?

 And quantum mechanics confirms this by giving indirect but strong 
 evidences on the existence of many statistically interfering computations.

I do not believe in that quantum mechanics implies statistically 
interfering computations.  I believe that quantum mechanics is 
deterministic.  Microcosmos looks indeterministic just because we do not 
know yet what is happening at the Planck scale.  You must think of that 
a quark is 100.000.000.000.000.000.000 times bigger than the Planch 
length, so many things can happen in that interval.

-- 
Torgny Tholerus

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Re: Dreams and Machines

[Torgny Tholerus]

Rex Allen skrev:
 Brent,

 So my first draft addressed many of the points you made, but it that
 email got too big and sprawling I thought.

 So I've focused on what seems to me like the key passage from your
 post.  If you think there was some other point that I should have
 addressed, let me know.

 So, key passage:

   
 Do these mathematical objects really exist?  I'd say they have
 logico-mathematical existence, not the same existence as tables and
 chairs, or quarks and electrons.
 

 So which kind of existence do you believe is more fundamental?  Which
 is primary?  Logico-mathematical existence, or quark existence?  Or
 are they separate but equal kinds of existence?

   

The most general form of existence is: All mathematical possible 
universes exist.  Our universe is one of those mathematical possible 
existing universes.

The inside of a specific universe constitutes an other form of 
existence.  In a specific universe there are objects inside that 
universe.  In the Game of Life universe, you have the Glider object, the 
Glider gun object, the Exploder object, the Tumbler object, etc.  In a 
specific instance of the GoL-universe, there exist some objects and some 
objects does not exist there.

In our own universe, there exist tables and chairs and quarks and 
electrons.  This is the specific form of existence.  But the 
mathematical objects does not exist in our universe, in this form of 
existence.  You can not find the 17 object anywhere inside our universe.

Then we have the general form of existence saying that our universe 
exists because it is a mathematical possibility.

-- 
Torgny Tholerus

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Re: Dreams and Machines

[Torgny Tholerus]

Bruno Marchal skrev:
 Le 22-juil.-09, à 10:27, Torgny Tholerus a écrit :


 Rex Allen skrev:

 Brent:

 Do these mathematical objects really exist? I'd say they
 have
 logico-mathematical existence, not the same existence as
 tables and
 chairs, or quarks and electrons.


 So which kind of existence do you believe is more fundamental?
 Which
 is primary? Logico-mathematical existence, or quark existence? Or
 are they separate but equal kinds of existence?



 The most general form of existence is: All mathematical possible
 universes exist. Our universe is one of those mathematical possible
 existing universes.


 This is non sense. Proof: see UDA. Or interrupt me when you have an 
 objection in the current explanation. I have explained this many 
 times, but the notion of universe or mathematical universe just makes 
 no sense. The notion of our universe is too far ambiguous for just 
 making even non sense.

What do you think about the GoL-universes?  You can look at some of 
those at http://www.bitstorm.org/gameoflife/ .  If you have an initial 
condition and you have an unlimited board, then you can compute what 
will happen in the future in that universe.  These universes are 
universes with a two-dimensional space and a one-dimensional time.  
These GoL-universes are mathematial universes.  They have an initial 
condition and a mathematical rule that defines how that universe will 
look like in the next moment, and the next next moment, and so on.

Does this make sense for you?

Now look at a mathematical universe that have somewhat more complicated 
rules, and that mathematical universe looks exactly the same as our 
universe.  The same things happens as in our universe, and there is an 
object there that is calling himself Bruno, and there is another object 
calling himself Torgny...

(By the way, I think it is better to use the notion 010110 for 
strings.  Then B_1 will be {0, 1}, and B_0 will be {}.  Then it is 
more clear that B_0 contains one element.)

-- 
Torgny

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Re: The seven step-Mathematical preliminaries

[Torgny Tholerus]

Bruno Marchal skrev:
 Torgny,

 I agree with Quentin.
 You are just showing that the naive notion of set is inconsistent.  
 Cantor already knew that, and this is exactly what forced people to  
 develop axiomatic theories. So depending on which theory of set you  
 will use, you can or cannot have an universal set (a set of all sets).  
 In typical theories, like ZF and VBG (von Neuman Bernay Gödel) the  
 collection of all sets is not a set.

It is not the naive notion of set that is inconsistent.  It is the naive 
*handling* of sets that is inconsistent.

This problem has two possible solutions.  One possible solution is to 
deny that it is possible to create the set of all sets.  This solution 
is chosen by ZF and VBG.

The second possible solution is to be very careful of the domain of the 
All quantificator.  You are not allowed to substitute an object that is 
not included in the domain of the quantificator.  It is this second 
solution that I have chosen.

What is illegal in the two deductions below, is the substitutions.  
Because the sets A and B do not belong to the domain of the All 
quantificator.

You can define existence by saying that only that which is incuded in 
the domain of the All quantificator exists.  In that case it is correct 
to say that the sets A and B do not exist, because they are not included 
in the domain.  But I think this is a too restrictive definition of 
existence.  It is fully possible to talk about the set of all sets.  But 
you must then be *very* careful with what you do with that set.  That 
set is a set, but it does not belong to the set of all sets, it does not 
belong to itself.  It is also a matter of definition; if you define 
set as the same as belonging to the set of all sets, then the set of 
all sets is not a set.  This is a matter of taste.  You can choose 
whatever you like, but you must be aware of your choice.  But if you 
restrict yourself too much, then your life will be poorer...

  In NF, some have developed  
 structure with universal sets, and thus universe containing  
 themselves. Abram is interested in such universal sets. And, you can  
 interpret the UD, or the Mandelbrot set as (simple) model for such  
 type of structure.

 Your argument did not show at all that the set of natural numbers  
 leads to any trouble. Indeed, finitism can be seen as a move toward  
 that set, viewed as an everything, potentially infinite frame (for  
 math, or beyond math, like it happens with comp).

 The problem of naming (or given a mathematical status) to all sets  
 is akin to the problem of giving a name to God. As Cantor was  
 completely aware of. We are confused on this since we exist. But the  
 natural numbers, have never leads to any confusion, despite we cannot  
 define them.
   

The proof that there is no biggest natural number is illegal, because 
you are there doing an illegal deduction, you are there doing an illegal 
substitution, just the same as in the deductions below with the sets A 
and B.  You are there substituting an object that is not part of the 
domain of the All quatificator.

--
Torgny Tholerus

 You argument against the infinity of natural numbers is not valid. You  
 cannot throw out this little infinite by pointing on the problem  
 that some terribly big infinite, like the set of all sets,  leads  
 to trouble. That would be like saying that we have to abandon all  
 drugs because the heroin is very dangerous.
 It is just non valid.

 Normally, later  I will show a series of argument very close to  
 Russell paradoxes, and which will yield, in the comp frame,  
 interesting constraints on what computations are and are not.

 Bruno


 On 13 Jun 2009, at 13:26, Torgny Tholerus wrote:

   
 Quentin Anciaux skrev:
 
 2009/6/13 Torgny Tholerus tor...@dsv.su.se:

   
 What do you think about the following deduction?  Is it legal or  
 illegal?
 ---
 Define the set A of all sets as:

 For all x holds that x belongs to A if and only if x is a set.

 This is an general rule saying that for some particular symbol- 
 string x
 you can always tell if x belongs to A or not.  Most humans who think
 about mathematics can understand this rule-based definition.  This  
 rule
 holds for all and every object, without exceptions.

 So this rule also holds for A itself.  We can always substitute A  
 for
 x.  Then we will get:

 A belongs to A if and only if A is a set.

 And we know that A is a set.  So from this we can deduce:

 A beongs to A.
 ---
 Quentin, what do you think?  Is this deduction legal or illegal?

 
 It depends if you allow a set to be part of itselft or not.

 If you accept, that a set can be part of itself, it makes your
 deduction legal regarding the rules.
   
 OK, if we accept that a set can be part of itself, what do you think
 about the following deduction? Is it legal or illegal?

 ---
 Define the set B of all sets that do not belong to itself

Re: The seven step-Mathematical preliminaries

[Torgny Tholerus]

Quentin Anciaux skrev:
 2009/6/13 Torgny Tholerus tor...@dsv.su.se:
   
 What do you think about the following deduction?  Is it legal or illegal?
 ---
 Define the set A of all sets as:

 For all x holds that x belongs to A if and only if x is a set.

 This is an general rule saying that for some particular symbol-string x
 you can always tell if x belongs to A or not.  Most humans who think
 about mathematics can understand this rule-based definition.  This rule
 holds for all and every object, without exceptions.

 So this rule also holds for A itself.  We can always substitute A for
 x.  Then we will get:

 A belongs to A if and only if A is a set.

 And we know that A is a set.  So from this we can deduce:

 A beongs to A.
 ---
 Quentin, what do you think?  Is this deduction legal or illegal?
 

 It depends if you allow a set to be part of itselft or not.

 If you accept, that a set can be part of itself, it makes your
 deduction legal regarding the rules.

OK, if we accept that a set can be part of itself, what do you think 
about the following deduction? Is it legal or illegal?

---
Define the set B of all sets that do not belong to itself as:

For all x holds that x belongs to B if and only if x does not belong to x.

This is an general rule saying that for some particular symbol-string x 
you can always tell if x belongs to B or not.  Most humans who think 
about mathematics can understand this rule-based definition.  This rule 
holds for all and every object, without exceptions.

So this rule also holds for B itself.  We can always substitute B for 
x.  Then we will get:

B belongs to B if and only if B does not belong to B.
---
Quentin, what do you think?  Is this deduction legal or illegal?


-- 
Torgny Tholerus

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Re: The seven step-Mathematical preliminaries

[Torgny Tholerus]

Jesse Mazer skrev:

  Date: Wed, 10 Jun 2009 09:18:10 +0200
  From: tor...@dsv.su.se
  To: everything-list@googlegroups.com
  Subject: Re: The seven step-Mathematical preliminaries
 
  Jesse Mazer skrev:
 
  Date: Tue, 9 Jun 2009 18:38:23 +0200
  From: tor...@dsv.su.se
  To: everything-list@googlegroups.com
  Subject: Re: The seven step-Mathematical preliminaries
 
  For you to be able to use the word all, you must define the domain
  of that word. If you do not define the domain, then it will be
  impossible for me and all other humans to understand what you are
  talking about.
 
  OK, so how do you say I should define this type of universe? Unless
  you are demanding that I actually give you a list which spells out
  every symbol-string that qualifies as a member, can't I simply provide
  an abstract *rule* that would allow someone to determine in principle
  if a particular symbol-string they are given qualifies? Or do you have
  a third alternative besides spelling out every member or giving an
  abstract rule?
 
  You have to spell out every member. 

 Where does this have to come from? Again, is it something you have a 
 philosophical or logical definition for, or is it just your aesthetic 
 preference?

It is, as I said above, for me and all other humans to understand what 
you are talking about.  It is also for to be able to decide what 
deductions or conclusions or proofs that are legal or illegal.  It has 
nothing to do with my aesthetic preference.


  Because in a *rule* you are 
  (implicitely) using this type of universe, and you will then get a
  circular definition.

 A good rule (as opposed to a 'bad' rule like 'the set of all sets that 
 do not contain themselves') gives a perfectly well-defined criteria 
 for what is contained in the universe, such that no one will ever have 
 cause to be unsure about whether some particular symbol-string they're 
 given at belongs in this universe. It's only circular if you say in 
 advance that there is something problematic about rules which define 
 infinite universes, but again this just seems like your aesthetic 
 preference and not something you have given any philosophical/logical 
 justification for.

What do you mean by some particular symbol-string?

I suppose that you mean by this is: If you take any particular 
symbol-string from this universe, then no one will ever have cause to be 
unsure about whether this symbol-string belongs in this universe.  So 
you are defining this universe by supposing that you have this 
universe to start with.  Is that not a typical circular definition?

-- 
Torgny Tholerus

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Re: The seven step-Mathematical preliminaries

[Torgny Tholerus]

Jesse Mazer skrev:


  Date: Tue, 9 Jun 2009 18:38:23 +0200
  From: tor...@dsv.su.se
  To: everything-list@googlegroups.com
  Subject: Re: The seven step-Mathematical preliminaries
 
  For you to be able to use the word all, you must define the domain
  of that word. If you do not define the domain, then it will be
  impossible for me and all other humans to understand what you are
  talking about.

 OK, so how do you say I should define this type of universe? Unless 
 you are demanding that I actually give you a list which spells out 
 every symbol-string that qualifies as a member, can't I simply provide 
 an abstract *rule* that would allow someone to determine in principle 
 if a particular symbol-string they are given qualifies? Or do you have 
 a third alternative besides spelling out every member or giving an 
 abstract rule?

You have to spell out every member.  Because in a *rule* you are 
(implicitely) using this type of universe, and you will then get a 
circular definition.  When you say that *every* number have a successor, 
you are presupposing that you already know what *every* means.

-- 
Torgny Tholerus

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Re: The seven step-Mathematical preliminaries

[Torgny Tholerus]

Jesse Mazer skrev:


  Date: Sat, 6 Jun 2009 21:17:03 +0200
  From: tor...@dsv.su.se
  To: everything-list@googlegroups.com
  Subject: Re: The seven step-Mathematical preliminaries
 
  My philosophical argument is about the mening of the word all. To be
  able to use that word, you must associate it with a value set.

 What's a value set? And why do you say we must associate it in 
 this way? Do you have a philosophical argument for this must, or is 
 it just an edict that reflects your personal aesthetic preferences?

  Mostly that set is all objects in the universe, and if you stay 
 inside the
  universe, there is no problems.

 *I* certainly don't define numbers in terms of any specific mapping 
 between numbers and objects in the universe, it seems like a rather 
 strange notion--shall we have arguments over whether the number 113485 
 should be associated with this specific shoelace or this specific 
 kangaroo?

When I talk about universe here, I do not mean our physical universe.  
What I mean is something that can be called everything.  It includes 
all objects in our physical universe, as well as all symbols and all 
words and all numbers and all sets and all other universes.  It includes 
everything you can use the word all about.

For you to be able to use the word all, you must define the domain 
of that word.  If you do not define the domain, then it will be 
impossible for me and all other humans to understand what you are 
talking about.

-- 
Torgny Tholerus

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Re: The seven step-Mathematical preliminaries

[Torgny Tholerus]

Jesse Mazer skrev:


  Date: Fri, 5 Jun 2009 08:33:47 +0200
  From: tor...@dsv.su.se
  To: everything-list@googlegroups.com
  Subject: Re: The seven step-Mathematical preliminaries
 
 
  Brian Tenneson skrev:
 
  How can BIGGEST+1 be a natural number but not belong to the set of all
  natural numbers?
 
  One way to represent natural number as sets is:
 
  0 = {}
  1 = {0} = {{}}
  2 = {0, 1} = 1 union {1} = {{}, {{}}}
  3 = {0, 1, 2} = 2 union {2} = ...
  . . .
  n+1 = {0, 1, 2, ..., n} = n union {n}
  . . .
 
  Here you can then define that a is less then b if and only if a belongs
  to b.
 
  With this notation you get the set N of all natural numbers as {0, 
 1, 2,
  ...}. But the remarkable thing is that N is exactly the same as
  BIGGEST+1. BIGGEST+1 is a set with the same structure as all the other
  natural numbers, so it is then a natural number. But BIGGEST+1 is not a
  member of N, the set of all natural numbers.

 Here you're just contradicting yourself. If you say BIGGEST+1 is then 
 a natural number, that just proves that the set N was not in fact the 
 set of all natural numbers. The alternative would be to say 
 BIGGEST+1 is *not* a natural number, but then you need to provide a 
 definition of natural number that would explain why this is the case.

It depends upon how you define natural number.  If you define it by: n 
is a natural number if and only if n belongs to N, the set of all 
natural numbers, then of course BIGGEST+1 is *not* a natural number.  In 
that case you have to call BIGGEST+1 something else, maybe unnatural 
number.

-- 
Torgny Tholerus

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Re: The seven step-Mathematical preliminaries

[Torgny Tholerus]

Jesse Mazer skrev:


  Date: Sat, 6 Jun 2009 16:48:21 +0200
  From: tor...@dsv.su.se
  To: everything-list@googlegroups.com
  Subject: Re: The seven step-Mathematical preliminaries
 
  Jesse Mazer skrev:
 
  Here you're just contradicting yourself. If you say BIGGEST+1 is then
  a natural number, that just proves that the set N was not in fact the
  set of all natural numbers. The alternative would be to say
  BIGGEST+1 is *not* a natural number, but then you need to provide a
  definition of natural number that would explain why this is the case.
 
  It depends upon how you define natural number. If you define it by: n
  is a natural number if and only if n belongs to N, the set of all
  natural numbers, then of course BIGGEST+1 is *not* a natural number. In
  that case you have to call BIGGEST+1 something else, maybe unnatural
  number.

 OK, but then you need to define what you mean by N, the set of all 
 natural numbers. Specifically you need to say what number is 
 BIGGEST. Is it arbitrary? Can I set BIGGEST = 3, for example? Or do 
 you have some philosophical ideas related to what BIGGEST is, like the 
 number of particles in the universe or the largest number any human 
 can conceptualize?

It is rather the last, the largest number any human can conceptualize.  
More natural numbers are not needed.


 Also, any comment on my point about there being an infinite number of 
 possible propositions about even a finite set,

There is not an infinite number of possible proposition.  You can only 
create a finite number of proposition with finite length during your 
lifetime.  Just like the number of natural numbers are unlimited but 
finite, so are the possible propositions unlimited but finte.

 or about my question about whether you have any philosophical/logical 
 argument for saying all sets must be finite,

My philosophical argument is about the mening of the word all.  To be 
able to use that word, you must associate it with a value set.  Mostly 
that set is all objects in the universe, and if you stay inside the 
universe, there is no problems.  But as soon you go outside universe, 
you must be carefull with what substitutions you do.  If you have all 
quantified with all object inside the universe, you can not substitute 
it with an object outside the universe, because that object was not 
included in the original statement.

 as opposed to it just being a sort of aesthetic preference on your 
 part? Do you think there is anything illogical or incoherent about 
 defining a set in terms of a rule that takes any input and decides 
 whether it's a member of the set or not, such that there may be no 
 upper limit on the number of possible inputs that the rule would 
 define as being members? (such as would be the case for the rule 'n is 
 a natural number if n=1 or if n is equal to some other natural number+1')

In the last sentence you have an implicite all:  The full sentence 
would be: For all n in the universe hold that n is a natural number if 
n=1 or if n is equal to some other natural number+1.  And you may now be 
able to understand, that if the number of objects in the universe is 
finite, then this sentence will just define a finite set.

-- 
Torgny Tholerus

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Re: The seven step-Mathematical preliminaries

[Torgny Tholerus]

Brian Tenneson skrev:


 On Thu, Jun 4, 2009 at 8:27 AM, Torgny Tholerus tor...@dsv.su.se 
 mailto:tor...@dsv.su.se wrote:


 Brian Tenneson skrev:
 
 
  Torgny Tholerus wrote:
  It is impossible to create a set where the successor of every
 element is
  inside the set, there must always be an element where the
 successor of
  that element is outside the set.
 
  I disagree.  Can you prove this?
  Once again, I think the debate ultimately is about whether or not to
  adopt the axiom of infinity.
  I think everyone can agree without that axiom, you cannot build or
  construct an infinite set.
  There's nothing right or wrong with adopting any axioms.  What
 results
  is either interesting or not, relevant or not.

 How do you handle the Russell paradox with the set of all sets
 that does
 not contain itself?  Does that set contain itself or not?

  
 If we're talking about ZFC set theory, then the axiom of foundation 
 prohibits sets from being elements of themselves.
 I think we agree that in ZFC, there is no set of all sets.

But there is a set of all sets.  You can construct it by taking all 
sets, and from them doing a new set, the set of all sets.  But note, 
this set will not contain itself, because that set did not exist before.

  



 My answer is that that set does not contain itself, because no set can
 contain itself.  So the set of all sets that does not contain
 itself, is
 the same as the set of all sets.  And that set does not contain
 itself.
 This set is a set, but it does not contain itself.  It is exactly the
 same with the natural numbers, *BIGGEST+1 is a natural number, but it
 does not belong to the set of all natural numbers.  *The set of
 all sets
 is a set, but it does not belong to the set of all sets.

 How can BIGGEST+1 be a natural number but not belong to the set of all 
 natural numbers?

One way to represent natural number as sets is:

0 = {}
1 = {0} = {{}}
2 = {0, 1} = 1 union {1} = {{}, {{}}}
3 = {0, 1, 2} = 2 union {2} = ...
. . .
n+1 = {0, 1, 2, ..., n} = n union {n}
. . .

Here you can then define that a is less then b if and only if a belongs 
to b.

With this notation you get the set N of all natural numbers as {0, 1, 2, 
...}.  But the remarkable thing is that N is exactly the same as 
BIGGEST+1.  BIGGEST+1 is a set with the same structure as all the other 
natural numbers, so it is then a natural number.  But BIGGEST+1 is not a 
member of N, the set of all natural numbers.  BIGGEST+1 is bigger than 
all natural numbers, because all natural numbers belongs to BIGGEST+1.

  


 
  What the largest number is depends on how you define natural
 number.
  One possible definition is that N contains all explicit numbers
  expressed by a human being, or will be expressed by a human
 being in the
  future.  Amongst all those explicit numbers there will be one
 that is
  the largest.  But this largest number is not an explicit number.
 
 
  This raises a deeper question which is this: is mathematics
 dependent
  on humanity or is mathematics independent of humanity?
  I wonder what would happen to that human being who finally expresses
  the largest number in the future.  What happens to him when he wakes
  up the next day and considers adding one to yesterday's number?

 This is no problem.  If he adds one to the explicit number he
 expressed
 yesterday, then this new number is an explicit number, and the number
 expressed yesterday was not the largest number.  Both 17 and 17+1 are
 explicit numbers.

 This goes back to my earlier comment that it's hard for me to believe 
 that the following statement is false:
 every natural number has a natural number successor
 We -must- be talking about different things, then, when we use the 
 phrase natural number.
 I can't say your definition of natural numbers is right and mine is 
 wrong, or vice versa.  I do wonder what advantages there are to the 
 ultrafinitist approach compared to the math I'm familiar with. 

The biggest advantage is that everything is finite, and you can then 
really know that the mathematical theory you get is consistent, it does 
not contain any contradictions.

-- 
Torgny Tholerus

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Re: The seven step-Mathematical preliminaries

[Torgny Tholerus]

Kory Heath skrev:
 On Jun 4, 2009, at 8:27 AM, Torgny Tholerus wrote:
   
 How do you handle the Russell paradox with the set of all sets that  
 does
 not contain itself?  Does that set contain itself or not?

 My answer is that that set does not contain itself, because no set can
 contain itself.  So the set of all sets that does not contain  
 itself, is
 the same as the set of all sets.  And that set does not contain  
 itself.
 This set is a set, but it does not contain itself.  It is exactly the
 same with the natural numbers, BIGGEST+1 is a natural number, but it
 does not belong to the set of all natural numbers.  The set of all  
 sets
 is a set, but it does not belong to the set of all sets.
 

 So you're saying that the set of all sets doesn't contain all sets.  
 How is that any less paradoxical than the Russell paradox you're  
 trying to avoid?
   

The secret is the little word all.  To be able to use that word, you 
have to define it.  You can define it by saying: By 'all sets' I mean 
that set and that set and that set and   When you have made that 
definition, you are then able to create a new set, the set of all sets.  
But you must be carefull with what you do with that set.  That set does 
not contain itself, because it was not included in your definition of 
all sets.

If you call the set of all sets for A, then you have:

For all x such that x is a set, then x belongs to A.
A is a set.

But it is illegal to substitute A for x, so you can not deduce:

A is a set, then A belongs to A.

This deductuion is illegal, because A is not included in the definition 
of all x.

-- 
Torgny Tholerus

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Re: The seven step-Mathematical preliminaries

[Torgny Tholerus]

Brian Tenneson skrev:
   
 How do you know that there is no biggest number?  Have you examined all 
 the natural numbers?  How do you prove that there is no biggest number?

   
 
 In my opinion those are excellent questions.  I will attempt to answer 
 them.  The intended audience of my answer is everyone, so please forgive 
 me if I say something you already know.

 Firstly, no one has or can examine all the natural numbers.  By that I 
 mean no human.  Maybe there is an omniscient machine (or a maximally 
 knowledgeable in some paraconsistent way)  who can examine all numbers 
 but that is definitely putting the cart before the horse.

 Secondly, the question boils down to a difference in philosophy: 
 mathematicians would say that it is not necessary to examine all natural 
 numbers.  The mathematician would argue that it suffices to examine all 
 essential properties of natural numbers, rather than all natural numbers.

 There are a variety of equivalent ways to define a natural number but 
 the essential features of natural numbers are that
 (a) there is an ordering on the set of natural numbers, a well 
 ordering.  To say a set is well ordered entails that every =nonempty= 
 subset of it has a least element.
 (b) the set of natural numbers has a least element (note that it is 
 customary to either say 0 is this least element or say 1 is this least 
 element--in some sense it does not matter what the starting point is)
 (c) every natural number has a natural number successor.  By successor 
 of a natural number, I mean anything for which the well ordering always 
 places the successor as larger than the predecessor.

 Then the set of natural numbers, N, is the set containing the least 
 element (0 or 1) and every successor of the least element, and only 
 successors of the least element.

 There is nothing wrong with a proof by contradiction but I think a 
 forward proof might just be more convincing.

 Consider the following statement:
 Whenever S is a subset of N, S has a largest element if, and only if, 
 the complement of S has a least element.

 By complement of S, I mean the set of all elements of N that are not 
 elements of S.

 Before I give a longer argument, would you agree that statement is 
 true?  One can actually be arbitrarily explicit: M is the largest 
 element of S if, and only if, the successor of M is the least element of 
 the compliment of S.
   

I do not agree that statement is true.  Because if you call the Biggest 
natural number B, then you can describe N as = {1, 2, 3, ..., B}.  If 
you take the complement of N you will get the empty set.  This set have 
no least element, but still N has a biggest element.

In your statement you are presupposing that N has no biggest element, 
and from that axiom you can trivially deduce that there is no biggest 
element.

-- 
Torgny Tholerus

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Re: The seven step-Mathematical preliminaries

[Torgny Tholerus]

Quentin Anciaux skrev:
 If you are ultrafinitist then by definition the set N does not
 exist... (nor any infinite set countably or not).
   

All sets are finite.  It it (logically) impossible to construct an 
infinite set.

You can construct the set N of all natural numbers.  But that set must 
be finite.  What the set N contains depends on how you have defined 
natural number.

 If you pose the assumption of a biggest number for N, you come to a
 contradiction because you use the successor operation which cannot
 admit a biggest number.(because N is well ordered any successor is
 strictly bigger and the successor operation is always valid *by
 definition of the operation*)
   

You have to define the successor operation.  And to do that you have to 
define the definition set for that operation.  So first you have to 
define the set N of natural numbers.  And from that you can define the 
successor operator.  The value set of the successor operator will be a 
new set, that contains one more element than the set N of natural 
numbers.  This new element is BIGGEST+1, that is strictly bigger than 
all natural numbers.

-- 
Torgny Tholerus

 So either the set N does not exists in which case it makes no sense to
 talk about the biggest number in N, or the set N does indeed exists
 and it makes no sense to talk about the biggest number in N (while it
 makes sense to talk about a number which is strictly bigger than any
 natural number).

 To come back to the proof by contradiction you gave, the assumption
 (2) which is that BIGGEST+1 is in N, is completely defined by the mere
 existence of BIGGEST. If BIGGEST exists and well defined it entails
 that BIGGEST+1 is not in N (but this invalidate the successor
 operation and hence the mere existence of N). If BIGGEST in contrary
 does not exist (as such, means it is not the biggest) then BIGGEST+1
 is in N by definition of N.

 Regards,
 Quentin

   


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Re: The seven step-Mathematical preliminaries

[Torgny Tholerus]

Brian Tenneson skrev:
 This is a denial of the axiom of infinity.  I think a foundational set 
 theorist might agree that it is impossible to -construct- an infinite 
 set from scratch which is why they use the axiom of infinity.
 People are free to deny axioms, of course, though the result will not 
 be like ZFC set theory.  The denial of axiom of foundation is one I've 
 come across; I've never met anyone who denies the axiom of infinity.

 For me it is strange that the following statement is false: every 
 natural number has a natural number successor.  To me it seems quite 
 arbitrary for the ultrafinitist's statement: every natural number has 
 a natural number successor UNTIL we reach some natural number which 
 does not have a natural number successor.  I'm left wondering what the 
 largest ultrafinist's number is.

It is impossible to lock a box, and quickly throw the key inside the box 
before you lock it.
It is impossible to create a set and put the set itself inside the set, 
i.e. no set can contain itself.
It is impossible to create a set where the successor of every element is 
inside the set, there must always be an element where the successor of 
that element is outside the set.

What the largest number is depends on how you define natural number.  
One possible definition is that N contains all explicit numbers 
expressed by a human being, or will be expressed by a human being in the 
future.  Amongst all those explicit numbers there will be one that is 
the largest.  But this largest number is not an explicit number.

-- 
Torgny Tholerus

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Re: The seven step-Mathematical preliminaries

[Torgny Tholerus]

Bruno Marchal skrev:
 On 02 Jun 2009, at 19:43, Torgny Tholerus wrote:

   
 Bruno Marchal skrev:
 
 4) The set of all natural numbers. This set is hard to define, yet I
 hope you agree we can describe it by the infinite quasi exhaustion by
 {0, 1, 2, 3, ...}.

   
 Let N be the biggest number in the set {0, 1, 2, 3, ...}.

 Exercise: does the number N+1 belongs to the set of natural numbers,
 that is does N+1 belongs to {0, 1, 2, 3, ...}?
 


 Yes. N+1 belongs to {0, 1, 2, 3, ...}.
 This follows from classical logic and the fact that the proposition N  
 be the biggest number in the set {0, 1, 2, 3, ...} is always false.  
 And false implies all propositions.
   

No, you are wrong.  The answer is No.

Proof:

Define biggest number as:

a is the biggest number in the set S if and only if for every element e 
in S you have e  a or e = a.

Now assume that N+1 belongs to the set of natural numbers.

Then you have N+1  N or N+1 = N.

But this is a contradiction.  So the assumption must be false.  So we 
have proved that N+1 does not belongs to the set of natural numbers.

-- 
Torgny Tholerus

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Re: The seven step-Mathematical preliminaries

[Torgny Tholerus]

Quentin Anciaux skrev:
 2009/6/3 Torgny Tholerus tor...@dsv.su.se:
   
 Bruno Marchal skrev:
 
 On 02 Jun 2009, at 19:43, Torgny Tholerus wrote:


   
 Bruno Marchal skrev:

 
 4) The set of all natural numbers. This set is hard to define, yet I
 hope you agree we can describe it by the infinite quasi exhaustion by
 {0, 1, 2, 3, ...}.


   
 Let N be the biggest number in the set {0, 1, 2, 3, ...}.

 Exercise: does the number N+1 belongs to the set of natural numbers,
 that is does N+1 belongs to {0, 1, 2, 3, ...}?

 
 Yes. N+1 belongs to {0, 1, 2, 3, ...}.
 This follows from classical logic and the fact that the proposition N
 be the biggest number in the set {0, 1, 2, 3, ...} is always false.
 And false implies all propositions.

   
 No, you are wrong.  The answer is No.

 Proof:

 Define biggest number as:

 a is the biggest number in the set S if and only if for every element e
 in S you have e  a or e = a.

 Now assume that N+1 belongs to the set of natural numbers.

 Then you have N+1  N or N+1 = N.

 But this is a contradiction.  So the assumption must be false.  So we
 have proved that N+1 does not belongs to the set of natural numbers.
 

 Hi,

 No, what you've demonstrated is that there is no biggest number (you
 falsified the hypothesis which is there exists a biggest number). You
 did a demonstration par l'absurde (in french, don't know how it is
 called in english). And you have shown a contradiction, which implies
 that your assumption is wrong (there exists a biggest number), not
 that this number is not in the set.
   

How do you know that there is no biggest number?  Have you examined all 
the natural numbers?  How do you prove that there is no biggest number?

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Re: The seven step-Mathematical preliminaries

[Torgny Tholerus]

Bruno Marchal skrev:
 4) The set of all natural numbers. This set is hard to define, yet I  
 hope you agree we can describe it by the infinite quasi exhaustion by  
 {0, 1, 2, 3, ...}.
   

Let N be the biggest number in the set {0, 1, 2, 3, ...}.

Exercise: does the number N+1 belongs to the set of natural numbers,  
that is does N+1 belongs to {0, 1, 2, 3, ...}?

-- 
Torgny Tholerus

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Re: Consciousness is information?

[Torgny Tholerus]

Bruno Marchal skrev:
 On 08 May 2009, at 19:15, Torgny Tholerus wrote:
   
 Bruno Marchal skrev:
 
 On 07 May 2009, at 18:29, Torgny Tholerus wrote:
   
 Yes it is right.  There is no infinity of natural numbers.  But the
 natural numbers are UNLIMITED, you can construct as many natural
 numbers as you want.  But how many numbers you construct, the  
 number of
 numbers will always be finite.  You can never construct an  
 infinite number of
 natural numbers.
 
 This is no more ultrafinitism. Just the usal finitism or  
 intuitionism.
 It seems I recall you have had a stronger view on this point.
 Ontologically I am neutral on this question. With comp I don't need
 any actual infinity in the third person ontology. Infinities are not
 avoidable from inside, at least when the inside view begins some  
 self-reflexion studies.
   
 I was an ultrafinitist before, but I have changed my mind.
 
 Excellent. The ability of changing its mind is a wonderful gift.
   


It was the Mathematical Universe that made me change my mind:

Earlier I was convinced that the number of time steps in the universe 
was explicitely finite, that time goes in a circle.

But the Mathematical Universe says that all mathematically possible 
universes exists.  And it is possible to construct an EXPANDING 
universe, where you have a simple rule stating that the status of a 
space-time point is a combination of the statuses of the neighboring 
space-time points in the previous time point.  In this universe there 
will never happen that the same space will be repeated at a later time, 
because the space consists of more space points at the later time.  So 
in that case the universe is UNLIMITED, it will never stop, but continue 
for ever...

-- 
Torgny Tholerus

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Re: Consciousness is information?

[Torgny Tholerus]

Quentin Anciaux skrev:
 Hi,

 2009/5/8 Torgny Tholerus tor...@dsv.su.se:
   
 I was an ultrafinitist before, but I have changed my mind.  Now I accept
 that you can say that the natural numbers are unlimited.  I only deny
 actual infinities.  The set of all natural numbers are always finite,
 but you can always increase the set of all natural number by adding more
 natural numbers to it.
 
 Then it's not the set of *all* natural numbers. You do nothing by
 adding a number... you don't create numbers by writing them down, you
 don't invent properties about them, it's absurd... especially for a
 zombie.
   

What do you mean by *all*?  How do you define *all*?  Can you give a 
definition that is not a circular definition?

-- 
Torgny

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Re: Consciousness is information?

[Torgny Tholerus]

Bruno Marchal skrev:
 On 07 May 2009, at 18:29, Torgny Tholerus wrote:

   
 Bruno Marchal skrev:
 

 you are human, all right?
   
 I look exactly as a human.  When you look at me, you will not be  
 able to know if I am a human or a zombie, because I behave exacly like a  
 human.
 
 So you believe that human are not zombie, and you agree that you are  
 not human.
 Where do you come from? Vega? Centaur?
   

I come from Stockholm, Sweden.  I was constructed by my parents.  In 
reality I think that all humans are zombies, but because I am a polite 
person, I do not tell the other zombies that they are zombies.  I do not 
want to hurt the other zombies by telling them the truth.

 Yes it is right.  There is no infinity of natural numbers.  But the
 natural numbers are UNLIMITED, you can construct as many natural  
 numbers as you want.  But how many numbers you construct, the number of  
 numbers will always be finite.  You can never construct an infinite number of
 natural numbers.
 
 This is no more ultrafinitism. Just the usal finitism or intuitionism.  
 It seems I recall you have had a stronger view on this point.
 Ontologically I am neutral on this question. With comp I don't need  
 any actual infinity in the third person ontology. Infinities are not  
 avoidable from inside, at least when the inside view begins some self- 
 reflexion studies.
   

I was an ultrafinitist before, but I have changed my mind.  Now I accept 
that you can say that the natural numbers are unlimited.  I only deny 
actual infinities.  The set of all natural numbers are always finite, 
but you can always increase the set of all natural number by adding more 
natural numbers to it.

 An ordinary computer can never be arithmetically unsound.
 
 ? (this seems to me plainly false, unless you mean perfect for  
 ordinary. But computers can be as unsound as you and me.
 There is no vaccine against soundness: all computers can be unsound  
 soo or later. there is no perfect computer. Most gods are no immune,  
 you have to postulate the big unnameable One and be very near to It,  
 to have some guaranty ... if any ...
   

OK, I misunderstood what you meant by unsound, I thougth you meant 
something like unlogical.  But now I see that you mean something like 
irrational.  And I sure am irrational.


 I do not want to be tortured, I behave as if I try to avoid that as
 strongly as I can.  Because I behave in this way, I answer no to  
 your question, because that answer will decrease the probability of you
 torturing me.
 
 Do you realize that to defend your point you are always in the  
 obligation, when talking about any first person notion, like  
 consciousness, fear, desire, to add I behave like . But if you  
 can do that successfully you will make me doubt that you are a zombie.
 Or ... do you think a zombie could eventually find a correct theory of  
 consciousness, so that he can correctly fake consciousness, and delude  
 the humans?
   

An intelligent zombie can correctly fake consciousness, and I am an 
intelligent zombie.

 3) Do you have any sort-of feeling, insight, dreams, impression,
 sensations, subjective or mental life, ... ?
   
 I behave as if I have sort-of feelings, I behave as if I have
 insights, I behave as if I have dreams, I behave as if I have
 impressions, I behave as if I have sensations, I behave as if I have a
 subjective or mental life, ...
 
 As I said. But if you know that, I mean if you can behave like if you  
 were knowing that, it would mean that such words do have some meaning  
 for you.

 How can you know that you are not conscious? Why do you behave like if  
 you are conscious, and then confess to us that you are not. Why  
 don't you behave like if you were not conscious. Should not a zombie  
 defend the idea that he is conscious, if he behaves like if he was  
 conscious.

If you ask me if I am conscious, I will reply yes.  But I am so 
intelligent that I can look at myself from the outside, and then I 
understand why I behave like I do.  I can see that all my behaviour is 
explained by chemical reactions in my brain, and there is no more than 
that.  So when I talk about myself on the meta level, then I can say 
that I have no consciousness.  But most people are not intelligent 
enough to realize that.

-- 
Torgny Tholerus

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Re: Consciousness is information?

[Torgny Tholerus]

Bruno Marchal skrev:
 On 06 May 2009, at 11:35, Torgny Tholerus wrote:

   
 Bruno Marchal skrev:
 
 Someone unconscious cannot doubt either ... (A zombie can only fake
 doubts)
   
 Yes, you are right.  I can only fake doubts...
 



 I suspect you are faking faking doubts, but of course I cannot provide  
 any argument.
 I mean it is hard for me to believe that you are a zombie, still less  
 a zombie conscious to be a zombie!
   

I am a zombie that behaves AS IF it knows that it is a zombie.






   
 
 When you say yes to the doctor, we
 assume the yes is related to the belief that you will survive. This
 means you believe that you will not loose consciousness, not become a
 zombie, nor will you loose (by assumption) your own consciousness, by
 becoming someone else you can't identify with.
   
 I can say yes to the doctor, because it will not be any difference  
 for me, I will still be a zombie afterwards...
 




   I don't know if you do this to please me, but you illustrate quite  
 well the Löbian consciousness theory.
 Indeed the theory says that consciousness can be very well  
 approximated logically by consistency.
 So a human (you are human, all right?

I look exactly as a human.  When you look at me, you will not be able to 
know if I am a human or a zombie, because I behave exacly like a human.

 ) who says I am a zombie, means  
 I am not conscious, which can mean I am not consistent.
 By Gödel's second theorem, you remain consistent(*), but you loose  
 arithmetical soundness, which is quite coherent with your  
 ultrafinitism. If I remember well, you don't believe that there is an  
 infinity of natural numbers, right?
   

Yes it is right.  There is no infinity of natural numbers.  But the 
natural numbers are UNLIMITED, you can construct as many natural numbers 
as you want.  But how many numbers you construct, the number of numbers 
will always be finite.  You can never construct an infinite number of 
natural numbers.

 We knew already you are not arithmetically sound.  Nevertheless it is  
 amazing that you pretend that you are a zombie. This confirms, in the  
 lobian frame, that you are a zombie. I doubt all ultrafinitists are  
 zombie, though.

 It is coherent with what I tell you before: I don't think a real  
 ultrafinitist can know he/she is an ultrafinitist. No more than a  
 zombie can know he is a zombie, nor even give any meaning to a word  
 like zombie.

 My diagnostic: you are a consistent, but arithmetically unsound,  
 Löbian machine. No problem.
   

An ordinary computer can never be arithmetically unsound.  So I am not 
arithmetically unsound.  I am build by a finite number of atoms, and the 
atoms are build by a finite number of elementary parts.  (And these 
elementary parts are just finite mathematics...)

 There are not many zombies around me, still fewer argue that they are  
 zombie, so I have some questions for you, if I may.

 1) Do you still answer yes to the doctor if he proposes to substitute  
 your brain by a sponge?
   

If the sponge behaves exactly in the same way as my current brain, then 
it will be OK.

 2) Do humans have the right to torture zombie?
   

Does an ordinary computer have the right to do anything?

I do not want to be tortured, I behave as if I try to avoid that as 
strongly as I can.  Because I behave in this way, I answer no to your 
question, because that answer will decrease the probability of you 
torturing me.

 3) Do you have any sort-of feeling, insight, dreams, impression,  
 sensations, subjective or mental life, ... ?
   

I behave as if I have sort-of feelings, I behave as if I have 
insights, I behave as if I have dreams, I behave as if I have 
impressions, I behave as if I have sensations, I behave as if I have a 
subjective or mental life, ...

 4) Does the word pain have a meaning for you? In particular, what if  
 the doctor, who does not know that you are a zombie, proposes to you a  
 cheaper artificial brain, but warning you that it produces often  
 unpleasant hard migraine? Still saying yes?
   

No, I will say no in this case, because I avoid things that causes 
pain.  I have an avoiding center in my brain, and when this center 
in my brain is stimulated, then my behavior will be to avoid those 
things that causes this center to be stimulated.  Stimulating this 
center will cause me to say: I feel pain.

-- 
Torgny Tholerus

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Re: Consciousness is information?

[Torgny Tholerus]

Bruno Marchal skrev:

 Something conscious cannot doubt about the existence of its 
 consciousness, I think, although it can doubt everything else it can 
 be conscious *about*.
 It is the unprovable (but coverable) fixed point of Descartes 
 systematic doubting procedure (this fit well with the self-reference 
 logics, taking consciousness as consistency).

 Someone unconscious cannot doubt either ... (A zombie can only fake 
 doubts)

Yes, you are right.  I can only fake doubts...


 We live on the overlap of a subjective un-sharable certainty (the 
 basic first person knowledge) and an objective doubtful but sharable 
 possible reality (the third person belief).

 To keep 3-comp, and to abandon consciousness *is* the correct 
 materialist step, indeed. But you cannot keep 1-comp(*) then, because 
 it is defined
 by reference to consciousness. When you say yes to the doctor, we 
 assume the yes is related to the belief that you will survive. This 
 means you believe that you will not loose consciousness, not become a 
 zombie, nor will you loose (by assumption) your own consciousness, by 
 becoming someone else you can't identify with.

I can say yes to the doctor, because it will not be any difference for 
me, I will still be a zombie afterwards...

-- 
Torgny Tholerus

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Re: Mathematical methods for the discrete space-time.

[Torgny Tholerus]

Jason Resch skrev:
 I am not sure how related this is to what you ask in your original 
 post, but as for a model (and candidate TOE) of physics which is 
 discrete, there is a theory known as Hiem Theory 
 ( http://en.wikipedia.org/wiki/Heim_Theory ) which posits there are 
 six discrete dimensions.  Interestingly, the theory is able to predict 
 the masses of many subatomic particles entirely from some force 
 constants, something which even the standard model is unable to explain.

I have now looked at Heim Theory, but it does not look enough serious to 
me.  Every theory that compute the masses of the elementary particles 
from nothing, must be wrong.  Because in different possible universa the 
masses of the elementary particles are different.  Besides, the Heim 
Theory could not explain the quarks.

But from the Heim Theory article I followed a link to Difference 
operator ( http://en.wikipedia.org/wiki/Difference_operator ), and that 
article was much more interesting, because there you could find the 
extended Leibniz rule.

And from that article I found a link to Umbral calculus ( 
http://en.wikipedia.org/wiki/Umbral_calculus ), that look like exactly 
what I am looking for.  The Umbral calculus seems to be a good candidate 
for a tool for handling discrete space-time!

-- 
Torgny Tholerus


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Re: Mathematical methods for the discrete space-time.

[Torgny Tholerus]

Torgny Tholerus skrev:

 What I want to know is what result you will get if you start from the 
 axiom that *everything in universe is finite*.
   

One important function in Quantum Theory is the harmonic oscillator.  So 
I want to know: What is the corresponding function in discrete mathematics?

In continuous mathematics you have the harmonic oscillator defined by 
the differential equation D^2(f) + k^2*f = 0, which will have one of its 
solutions as:

f(t) = exp(i*k*t) = cos(k*t) + i*sin(k*t), where i is sqrt(-1).

In discrete mathematics you have the corresponding oscillator defined by 
the difference equation D^2(f) + k^2*f = 0, which will have one of its 
solutions as:

f(t) = (1 + i*k)^t = dcos(k*t) + i*dsin(k*t), where dcos() och dsin() 
are the corresponding discrete functions of the continuous functions 
cos() and sin().

So what is dcos() and dsin()?

If you do Taylor expansion of the continuos function you get:

exp(i*k*t) = Sum((i*k*t)^n/n!) = Sum((-1)^m*k^(2*m)*t^(2*m)/(2*m)!) + 
i*Sum((-1)^m*k^(2*m+1)*t^(2*m+1)/(2*m+1)!)

And if you do binominal expansion of the discrete function you get:

(1 + i*k)^t = Sum(t!/((t-n)!*n!)*(i*k)^n) = 
Sum((-1)^m*k^(2*m)*(t!/(t-2*m)!)/(2*m)!) + 
i*Sum((-1)^m*k^(2*m+1)*(t!/(t-2*m-1)!)/(2*m+1)!)

When you compare these two expession, you see a remarkable resemblance!  
If you replace t^n in the upper expression with t!/(t-n)! you will then 
get exactly the lower expression!

This suggest the general rule:

If the Taylor expansion of a continuous function f(x) is:

f(x) = Sum(a(n)*x^n) = Sum(a(n)*Prod(n;x)),

then the corresponding discrete funtion f(x) is:

f(x) = Sum(a(n)*x!/(x-n)!) = Sum(a(n)*Prod(n;x-m)),

where Prod(n;x-m) = x*(x-1)*(x-2)* ... *(x-n+2)*(x-n+1) is a finite product.

I have no strict proof of this general rule.  But this rule is such a 
beautifil result, that it simply *must* be true!

-- 
Torgny


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Re: Mathematical methods for the discrete space-time.

[Torgny Tholerus]

Torgny Tholerus skrev:

 Exercise: Show that the extended Leibniz rule in the discrete 
 mathematics: D(f*g) = f*D(g) + D(f)*g + D(f)*D(g), is correct!
   


Another way to see both form of the Leibniz rule is in the graphical set 
theory, where you represent the sets by circles on a paper.  Here I will 
represent the union of the sets A and B with A + B, and the 
intersection as A*B.

Then you can represent the D operator as the border of the circle.

Then you will have:

D(A*B) = A*D(B) + D(A)*B, ie the Leibniz rule, ie the border of the area 
of the intersection is the union of the border of B inside A, and the 
border of A inside B.  I can not show this figure in this message, but 
you can draw two circles on a paper before you, and you will then see 
what I mean.

Now the interesting thing is what will happen if the circles have 
*thick* borders:  Then the set A is represented by two circles inside 
each other, and the border will then be the area between the two 
circles.  The set A will then be the interior of the inner circle, and 
the outside of A will be the outside of the outer circle.

What will you then get if you look at the border of the intersection of 
A and B?

This time you will get:

D(A*B) = A*D(B) + D(A)*B + D(A)*D(B), ie the extended Leibniz rule.  The 
extra term then comes from the two small squares you get where the two 
borders cross each other.  (Do draw this figure om the paper before you, 
and you will understand.)

This picture with the circles with thick borders is a way to represent 
intiutionistic logic.  The interior of the inner circle is the objects 
that represent A (such as red), and the outside of the outer circle 
represent not-A (such as not red).  Inside the border you will have 
all that is neither A nor not-A (such as red-orange, where you don't 
know if it is red or not...)

-- 
Torgny Tholerus

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Re: QTI euthanasia (brouillon)

[Torgny Tholerus]

Bruno Marchal skrev:
 For example, a zombie is just some entity which looks like you and me,  
 i.e. has all the appearance of a human, and who has no consciousness.   
 There is no *need* to make them a priori fundamentally material. Now a  
 materialist can and even should interpret this as a zombie in the  
 sense of Dennett, but the definition continues to make sense for a non  
 materialist, who for example just consider itself that physics is  
 implemented or emerge from something else. It shows that the notion of  
 zombie does not depend on the materialist or non materialist belief. A  
 zombie is just something NON conscious despite it has all the  
 appearance of a human like you and me (and thus is material for a  
 materialist, and immaterial for an immaterialist).
   

If you want a concrete example of a zombie, you can just think of me.  I 
am an entity that have all the appearance of a human, but I have no 
consciousness...

-- 
Torgny Tholerus

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Re: Mathematical methods for the discrete space-time.

[Torgny Tholerus]

Bruno Marchal skrev:
 I have to think. I think that to retrieve a Leibniz rule in discrete 
 mathematics, you have to introduce an operator and some non 
 commutativity rule. This can be already found in the book by Knuth on 
 numerical mathematics. This has been exploited by Kauffman and one of 
 its collaborator, and they have published a book which I have ordered 
 already two times ... without success. It is a very interesting matter. 
 Dirac quantum relativistic wave equation can almost be retrieved form 
 discrete analysis on complex or quaternion. It is worth investigating 
 more. Look at Kauffman page (accessible from my url), and download his 
 paper on discrete mathematics.


I will look closer at the Kauffman paper on Non-commutative Calculus and 
Discrete Physics.  It seems interesting, but not quite what I am looking 
for.  Kauffman only gets the ordinary Leibniz rule, not the extended 
rule I have found.

What I want to know is what result you will get if you start from the 
axiom that *everything in universe is finite*.

For this you will need a function calculus.  A function is then a 
mapping from a (finite) set of values to this set of values.  Because 
this value set is finite, you can then map the values on the numbers 
0,1,2,3, ... , N-1.

So a function calculus can be made starting from a set of values 
consisting of the numbers 0,1,2,3, ... , N-1, where N is a very large 
number, but not too large.  N should be a number of the order of a 
googol, ie 10^100.  Because the size of our universe is 10^60 Planck 
units, and our universe has existed for 10^60 Planck times.  As the 
arithmetic, we can count modulo N, ie (N-1) + 1 = 0.  This makes it 
possible for the calculus to describe our reality.

A function can then be represented as an ordered set of N numbers, namely:

f = [f(0), f(1), f(2), f(3), ... , f(N-1)].

This means that S(f) becomes:

S(f) = [f(1), f(2), f(3), ... , f(N-1), f(0)].

The sum or the product of two functions is obtained by adding or 
multiplying each element, namely:

f*g = [f(0)*g(0), f(1)*g(1), f(2)*g(2), ... , f(N-1)*g(N-1)].

and to apply a function f on a function g then becomes:

f(g) = [f(g(0)), f(g(1)), f(g(2)), ... , f(g(N-1))].

Exercise: Show that the extended Leibniz rule in the discrete 
mathematics: D(f*g) = f*D(g) + D(f)*g + D(f)*D(g), is correct!

-- 
Torgny Tholerus

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Mathematical methods for the discrete space-time.

[Torgny Tholerus]

When you are going to do exact mathematical computations for the 
discrete space-time, then the continuous mathematics is not enough, 
because then you will only get an approximation of the reality.  So 
there is a need for developing a special calculus for a discrete 
mathematics.

One difference between continuous and discrete mathematics is the rule 
for how to derívate the product of two functions.  In continuous 
mathematics the rule says:

D(f*g) = f*D(g) + D(f)*g.

But in the discrete mathematics the corresponding rule says:

D(f*g) = f*D(g) + D(f)*g + D(f)*D(g).

In discrete mathematics you have difference equations of type: x(n+2) = 
x(n+1) + x(1), x(0) = 0, x(1) = 1, which then will give the number 
sequence 0,1,1,2,3,5,8,13,21,34,55,... etc.  For a general difference 
equation you have:

Sum(a(i)*x(n+i)) = 0, plus a number of starting conditions.

If you then introduce the step operator S with the effect: S(x(n)) = 
x(n+1), then you can express the difference equation as:

Sum((a(i)*S^i)(x(n)) = 0.

You will then get a polynom in S.  If the roots (the eigenvalues) to 
this polynom are e(i), you will then get:

Sum(a(i)*S^i) = Prod(S - e(i)) = 0.

This will give you the equations S - e(i) = 0, or more complete: (S - 
e(i))(x(n)) = S(x(n)) - e(i)*x(n) = x(n+1) - e(i)*x(n) = 0, which have 
the solutions x(n) = x(0)*e(i)^n.

The general solution to this difference equation will then be a linear 
combination of these solutions, such as:

x(n) = Sum(k(i)*e(i)^n), where k(i) are arbitrary constants.

To get the integer solutions you can then build the eigenfunctions:

x(j,n) = Sum(k(i,j)*e(i)^n) = delta(j,n), for n  the grade of the 
difference equation.

With the S-operator it is then very easy to define the difference- or 
derivation-operator D as:

D = S-1, so D(x(n)) = x(n+1) - x(n).

What do you think, is this a good starting point for handling the 
mathematics of the discrete space-time?

-- 
Torgny Tholerus

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Re: QTI euthanasia

[Torgny Tholerus]

Bruno Marchal skrev:
 On 09 Nov 2008, at 20:29, Brent Meeker wrote:

   
 Many physicists think that an ultimate theory would be
 discrete,
 
 This is highly implausible, assuming comp. I know that if we want  
 quantize gravitation, then space and time should be quantized, but  
 then I hope other things will remain continuous, like the statistics  
 (hoping it is enough).
 But for the reason above, the first persons cannot escape the  
 feeling or the appearances of continua (assuming mech.).
   

You do not need anything continuous.  When you look at a movie, you are 
shown 24 pictures every second, but you feel like it is a continuous 
movie.  But in reality it is just 24 discrete events every second.

-- 
Torgny Tholerus

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Re: UDA paper

[Torgny Tholerus]

Bruno Marchal skrev:
 Hi Torgny,

 Le 29-févr.-08, à 15:25, Torgny Tholerus a écrit :

   

 I have just tested to upload a file to the group (PofSTorgny1.doc).  
 You
 can try to see if you can see that file.  (You have to log in to Google
 groups first.)
 

 I see (and did print) your file. I have put the movie there, in two 
 version but I cannot retrieve it. With the first I get the code, and 
 with the other (the one with .mpeg) I get the QuickTime logo with an 
 interrogation mark. If you or someone can see the movie from there, 
 just tell me.

   

I have not succeeded to view your movie.  I have downloaded your files 
to my computer.  But it seems as if your files are corrupted in some 
way.  I have tried three different movie players (Windows Media Player, 
RealPlayer, and QuickTime), but no one was able to recognize your files.

-- 
Torgny

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Re: UDA paper

[Torgny Tholerus]

Bruno Marchal skrev:
 Hi Wei,

 I have not succeeded to upload the movie, nor do I have seen files 
 which I heard should have been already uploaded by people on the list. 
 The system complains that I am not a member of the list.
 I will try again Monday, because it looks like the discussion are not 
 currently available too, so the problem is perhaps with the 
 Googlegroups.

 But if that works it is of course the good idea, thanks,

   

I have just tested to upload a file to the group (PofSTorgny1.doc).  You 
can try to see if you can see that file.  (You have to log in to Google 
groups first.)

-- 
Torgny Tholerus

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Re: Theory of Everything based on E8 by Garrett Lisi

[Torgny Tholerus]

Bruno Marchal skrev:


 Le 29-nov.-07, à 17:22, Torgny Tholerus a écrit :

 There is a difference between unlimited and infinite. Unlimited
 just says that it has no limit, but everything is still finite. If
 you
 add something to a finite set, then the new set will always be
 finite.
 It is not possible to create an infinite set.

 Come on! Now you talk like a finitist, who accepts the idea of 
 potential infinity (like Kronecker, Brouwer and the intuitionnist) 
 and who rejects only the so called actual infinities, like ordinal and 
 cardinal numbers (or sets).

Yes, I am more like a finitist than an ultrafinitist in this respect.  I 
accept that something can be without limit.  But I don't want to use the 
word potential infinity, because infinity is a meaningless word for me.


 At the ontic level, (or ontological, I mean the minimum we have to bet 
 on at the third person pov), comp is mainly finitist. Judson Webb put 
 comp (he calls it mechanism) in Finitism. But that is no more 
 ultrafinitism. With finitism: every object of the universe is 
 finite, but the universe itself is infinite (potentially or actually). 
 With ultrafinitism, every object is finite AND the universe itself is 
 finite too.

Here I am an ultrafinitist.  I believe that the universe is strictly 
finite.  The space and time are discrete.  And the space today have a 
limit.  But the time might be without limit, that I don't know.


 Jesse wrote:

 My instinct would be to say that a well-defined criterion is one
 that, given any mathematical object, will give you a clear answer
 as to whether the object fits the criterion or not. And obviously
 this one doesn't, because it's impossible to decide where R fits
 it or not! But I'm not sure if this is the right answer, since my
 notion of well-defined criteria is just supposed to be an
 alternate way of conceptualizing the notion of a set, and I don't
 actually know why the set of all sets that are not members of
 themselves is not considered to be a valid set in ZFC set theory.

 Frege and Cantor did indeed define or identify sets with their 
 defining properties. This leads to the Russell's contradiction. (I 
 think Frege has abandoned his work in despair after that).
 One solution (among many other one) to save Cantor's work from that 
 paradox consists in formalizing set theory, which means using 
 belongness as an undefined symbol obeying some axioms. Just two 
 examples of an axiom of ZF (or its brother ZFC = ZF + axiom of 
 choice): is the extensionality axiom:
 AxAyAz ((x b z - y b z) - x = y) b is for belongs. It says that 
 two sets are equal if they have the same elements.
 AxEy(z included-in x - z b y) with z included-in x is a macro for 
 Ar(r b z - r b x). This is the power set axiom, saying that the set 
 of all subsets of some set is also a set).

For me belongness is not a problem, because everything is finite.  For 
me the axiom of choice always is true, because you can always do a 
chioce in a finite world.


 Paradoxes a-la Russell are evacuated by restricting Jesse's 
 well-defined criteria by
 1) first order formula (in the set language, that is with b as 
 unique relational symbols (+ equality) ... like the axioms just above.
 2) but such first order formula have to be applied only to an already 
 defined set.

This 2) rule is a very important restriction, and it is just this that 
my type theory is about.  When you construct new things, those things 
can only be constructed from things that are already defined.  So when 
you construct the set of all sets, then that new set will not be 
included in the new set.

 For example, you can defined the set of x such that x is in y and has 
 such property P(x). With P defined by a set formula, and y an already 
 defined set.

 Also, ZFC has the foundation axiom which forbids a set to belong to 
 itself.

This is a natural consequence of my type theory.  When you construct a 
set, that set can never belong to itself, because that set is not 
defined before it is constructed.

 In particular the informal collection of all sets which does not 
 belongs to themselves is the universe itself, which cannot be a set 
 (its power set would be bigger than the universe!).

Yes, the set of all sets which does not belongs to themselves is the 
universe itself.  But this is not a problem for me, because you can 
always extend the universe by creating new objects.  So you can create 
the power set, and the power set will then be bigger than the universe.  
But this power set will not be part of the universe.

-- 
Torgny

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Re: Theory of Everything based on E8 by Garrett Lisi

[Torgny Tholerus]

[EMAIL PROTECTED] skrev:
 On Nov 28, 9:56 pm, Torgny Tholerus [EMAIL PROTECTED] wrote:

   
 You only need models of cellular automata.  If you have a model and
 rules for that model, then one event will follow after another event,
 according to the rules.  And after that event will follow another more
 event, and so on unlimited.  The events will follow after eachother even
 if you will not have any implementation of this model.  Any physics is
 not needed.  You don't need any geometric properties.

 In this model you may have a person called Torgny writing a message on a
 google group, and that event may be followed by a person called Marc
 writing a reply to this message.  And you don't need any implementation
 of that model.

 
 A whole lot of unproven assumptions in there.   For starters, we don't
 even know that the physical world can be modelled solely in terms of
 cellular automata at all.

Why can't our universe be modelled by a cellular automata?  Our universe 
is very complicated, but why can't it be modelled by a very complicated 
automata?  An automata where you have models for protons and electrons 
and photons and all other elementary particles, that obey the same laws 
as the particles in our universe?

   Digital physics just seems to be the latest
 'trendy' thing, but actual evidence is thin on the ground.
 Mathematics is much richer than just discrete math.  Discrete math
 deals only with finite collections, and as such is just a special case
 of algebra.

Isn't it enough with this special case?  You can do a lot with finite 
collections.  There is not any need for anything more.

   Algebraic relations extend beyond computational models.
 Finally, the introduction of complex analysis, infinite sets and
 category theory extends mathematics even further, beyond even
 algebraic relations.  So you see that cellular automata are only a
 small part of mathematics as a whole.  There is no reason for thinking
 for that space is discrete and in fact physics as it stands deals in
 continuous differential equations, not cellular automata.
   

The reason why physics deals in continuous differential equations is 
that they are a very good approximation to a world where the distance 
between the space points and the time points are very, very small.  And 
if you read a book in Quantum Field Theory, they often start from a 
discrete model, and then take the limit when the distances go to zero.

 Further, the essential point I was making is that an informational
 model of something is not neccesserily the same as the thing itself.
 An informational model of a person called Marc would capture only my
 mind, not my body.  The information has to be super-imposed upon the
 physical, or embodied in the physical world.
   
If the model models every atom in your body, then that model will 
describe your body.  That model will describe how the atoms in your body 
react with eachother, and they will describe all your actions.

-- 
Torgny

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Re: Theory of Everything based on E8 by Garrett Lisi

[Torgny Tholerus]

Jesse Mazer skrev:


   
 Date: Thu, 29 Nov 2007 19:55:20 +0100
 From: [EMAIL PROTECTED]

 
 As soon as you say the set of ALL numbers, then you are forced to 
 define the word ALL here.  And for every definition, you are forced to 
 introduce a limit.  It is not possible to define the word ALL without 
 introducing a limit.  (Or making an illegal circular definition...)
 

 Why can't you say If it can be generated by the production rule/fits the 
 criterion, then it's a member of the set? I haven't used the word all 
 there, and I don't see any circularity either.

What do you mean by a well-defined criterion?  Is this a well-defined 
criterion? :

The set R is defined by:

(x belongs to R) if and only if (x does not belong to x).

If it fits the criterion (x does not belong to x), then it's a member of 
the set R.

Then we ask the question: Is R a member of the set R?.  How shall we 
use the criterion to answer that question?

If we substitute R for x in the criterion, we will get:

(R belongs to R) if and only if (R does not belong to R)...

What is wrong with this?

-- 
Torgny

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Re: Theory of Everything based on E8 by Garrett Lisi

[Torgny Tholerus]

Quentin Anciaux skrev:
 Hi,

 Le Wednesday 28 November 2007 09:56:17 Torgny Tholerus, vous avez écrit :
   

 You only need models of cellular automata.  If you have a model and
 rules for that model, then one event will follow after another event,
 according to the rules.  And after that event will follow another more
 event, and so on unlimited.  The events will follow after eachother even
 if you will not have any implementation of this model.  Any physics is
 not needed.  You don't need any geometric properties.

 
 Sure, but you can't be ultrafinitist and saying things like And after that 
 event will follow another more event, and so on unlimited.
   


There is a difference between unlimited and infinite.  Unlimited 
just says that it has no limit, but everything is still finite.  If you 
add something to a finite set, then the new set will always be finite.  
It is not possible to create an infinite set.

So it is OK to use the word unlimited.  But it is not OK to use the 
word infinite.  Is this clear?

Another important word is the word all.  You can talk about all 
events.  But in that case the number of events will be finite, and you 
can then talk about the last event.  But you can't deduce any 
contradiction from that, because that is forbidden by the type theory.  
And there will be more events after the last event, because the number 
of events is unlimited.  As soon as you use the word all, you will 
introduce a limit - all up to this limit.  And you must then think of 
only doing conclusions that are legal according to type theory.

So the best thing is to avoid the word all (and all synonyms of that 
word).

-- 
Torgny


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Re: Theory of Everything based on E8 by Garrett Lisi

[Torgny Tholerus]

Quentin Anciaux skrev:
 Le Thursday 29 November 2007 17:22:59 Torgny Tholerus, vous avez écrit :
   

 There is a difference between unlimited and infinite.  Unlimited
 just says that it has no limit, but everything is still finite.  If you
 add something to a finite set, then the new set will always be finite.
 It is not possible to create an infinite set.
 

 I'm sorry I don't get it... The set N as an infinite numbers of elements 
 still 
 every element in the set is finite. Maybe it is an english subtility that I'm 
 not aware of... but in french I don't see a clear difference between infini 
 and illimité.
   

As soon as you talk about the set N, then you are making a closure 
and making that set finite.  The only possible way to talk about 
something without limit, such as natural numbers, is to give a 
production rule, so that you can produce as many of that type of 
objects as you want.  If you have a natural number n, then you can 
produce a new number n+1, that is the successor of n.


   
 So it is OK to use the word unlimited.  But it is not OK to use the
 word infinite.  Is this clear?
 

 No, I don't see how a set which have not limit get a finite number of 
 elements.
   

It is not possible for a set to have no limit.  As soon as you 
construct a set, then that set will always have a limit.  Either you 
have to accept that the set N is finite, or you must stop talking about 
the set N.  It is enough to have a production rule for natural numbers.

   
 Another important word is the word all.  You can talk about all
 events.  But in that case the number of events will be finite, and you
 can then talk about the last event.  But you can't deduce any
 contradiction from that, because that is forbidden by the type theory.
 And there will be more events after the last event, because the number
 of events is unlimited.  
 

 If there are events after the last one, how can the last one be the last ?
   

The last event is the last event in the set of all events.  But 
because you have a production rule for the events, it is always possible 
to produce new events after the last event.  But these events do not 
belong to the set of all events.

   
 As soon as you use the word all, you will 
 introduce a limit - all up to this limit.  And you must then think of
 only doing conclusions that are legal according to type theory.
 

 o_O... could you explain what is type theory ?
   

Type theory is one of the solutions of Russel's paradox.  You have a 
hierarchy of types.  Type theory says that the all quantifiers only 
can span objects of the same type (or lower types).  When you create 
new objects, such that the set of all sets that do not belong to 
themselves, then you will get an object of a higher type, so that you 
can not say anything about if this set belongs to itself or not.  The 
same thing with the set of all sets.  You can not say anything about 
if it belongs to itself.

   
 So the best thing is to avoid the word all (and all synonyms of that
 word).
 

 like everything ?
   
Yes...   :-)

-- 
Torgny

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Re: Theory of Everything based on E8 by Garrett Lisi

[Torgny Tholerus]

Quentin Anciaux skrev:
 Le Thursday 29 November 2007 18:25:54 Torgny Tholerus, vous avez écrit :
   

 As soon as you talk about the set N, then you are making a closure
 and making that set finite.  
 

 Ok then the set R is also finite ? 
   

Yes.

   
 The only possible way to talk about 
 something without limit, such as natural numbers, is to give a
 production rule, so that you can produce as many of that type of
 objects as you want.  If you have a natural number n, then you can
 produce a new number n+1, that is the successor of n.
 

 What is the production rules of the noset R ?
   

How do you define the set R?

-- 
Torgny

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Re: Theory of Everything based on E8 by Garrett Lisi

[Torgny Tholerus]

Quentin Anciaux skrev:
 Le Thursday 29 November 2007 18:52:36 Torgny Tholerus, vous avez écrit :
   
 Quentin Anciaux skrev:
 

 What is the production rules of the noset R ?
   
 How do you define the set R?
 

 http://en.wikipedia.org/wiki/Construction_of_real_numbers

 Choose your method...
   

The most important part of that definition is:

4. The order ? is /complete/ in the following sense: every non-empty 
subset of *R* bounded above http://en.wikipedia.org/wiki/Upper_bound 
has a least upper bound http://en.wikipedia.org/wiki/Least_upper_bound.

This definition can be translated to:

If you have a production rule that produces rational numbers that are 
bounded above, then this production rule is producing a real number.

This is the production rule for real numbers.

-- 
Torgny

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Re: Theory of Everything based on E8 by Garrett Lisi

[Torgny Tholerus]

Jesse Mazer skrev:

   
 From: [EMAIL PROTECTED]

 
 As soon as you talk about the set N, then you are making a closure 
 and making that set finite.
 


 Why is that? How do you define the word set? 


   The only possible way to talk about 
   
 something without limit, such as natural numbers, is to give a 
 production rule, so that you can produce as many of that type of 
 objects as you want.  If you have a natural number n, then you can 
 produce a new number n+1, that is the successor of n.
 


 Why can't I say the set of all numbers which can be generated by that 
 production ruler?

As soon as you say the set of ALL numbers, then you are forced to 
define the word ALL here.  And for every definition, you are forced to 
introduce a limit.  It is not possible to define the word ALL without 
introducing a limit.  (Or making an illegal circular definition...)

  It almost makes sense to say a set is *nothing more* than a criterion for 
 deciding whether something is a member of not, although you would need to 
 refine this definition to deal with problems like Russell's set of all sets 
 that are not members of themselves (which could be translated as the 
 criterion, 'any criterion which does not match its own criterion'--I suppose 
 the problem is that this criterion is not sufficiently well-defined to decide 
 whether it matches its own criterion or not).
   

A well-defined criterion is the same as what I call a production 
rule.  So you can use that, as long as the criterion is well-defined.

(What does the criterion, that decides if an object n is a natural 
number, look like?)

   

 It is not possible for a set to have no limit.  As soon as you 
 construct a set, then that set will always have a limit.
 


 Is there something intrinsic to your concept of the word set that makes 
 this true? Is your concept of a set fundamentally different than my concept 
 of well-defined criteria for deciding if any given object is a member or not?
   

Yes, the definition of the word all is intrinsic in the concept of the 
word set.

-- 
Torgny

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Re: Theory of Everything based on E8 by Garrett Lisi

[Torgny Tholerus]

[EMAIL PROTECTED] skrev:
   
 When I talk about pure mathematics I mean that kind of mathematics you 
 have in GameOfLife.  There you have gliders that move in the 
 GameOfLife-universe, and these gliders interact with eachother when they 
 meet.  These gliders you can see as physical objects.  These physical 
 objects are reducible to pure mathematics, they are the consequences of the 
 rules behind GameOfLife.
 

 --
 Torgny

 That kind of mathematics - models of cellular automata -  is the
 domain of the theory of computation.  These are just that - models.
 But there is no reason for thinking that the models or mathematical
 rules are identical to the physical entities themselves just because
 these rules/models can precisely predict/explain the behaviour of the
 physical objects.
   

You only need models of cellular automata.  If you have a model and 
rules for that model, then one event will follow after another event, 
according to the rules.  And after that event will follow another more 
event, and so on unlimited.  The events will follow after eachother even 
if you will not have any implementation of this model.  Any physics is 
not needed.  You don't need any geometric properties.

In this model you may have a person called Torgny writing a message on a 
google group, and that event may be followed by a person called Marc 
writing a reply to this message.  And you don't need any implementation 
of that model.

-- 
Torgny

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Re: Theory of Everything based on E8 by Garrett Lisi

[Torgny Tholerus]

Bruno Marchal skrev:


 Le 28-nov.-07, à 09:56, Torgny Tholerus a écrit :

 You only need models of cellular automata.  If you have a model
 and rules for that model, then one event will follow after another
 event, according to the rules.  And after that event will follow
 another more event, and so on unlimited.  The events will follow
 after eachother even if you will not have any implementation of
 this model.  Any physics is not needed.  You don't need any
 geometric properties.

 In this model you may have a person called Torgny writing a
 message on a google group, and that event may be followed by a
 person called Marc writing a reply to this message.  And you don't
 need any implementation of that model.



 OK. Do you agree now that the real Torgny, by which I mean you from 
 your first person point of view, cannot known if it belongs to a state 
 generated by automata 345 or automata 6756, or automata 6756690003121, 
 or automata 65656700234676611084899 , and so one ...
 Do you agree we have to take into account this first person 
 indeterminacy when making a first person prediction?

I agree that the real Torgny belongs to exactly one of those automata, 
but I don't know which one.  So I can not tell what will happen to the 
real Torgny in the future.  I can not do any prediction.

If we call the automata that the real Torgny belongs to, for automata 
X, then I can look at automata X from the outside, and I will then see 
that all that the real Torgny will do in the future is completely 
determined.  There is no indeterminacy in automata X.

-- 
Torgny

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Re: Theory of Everything based on E8 by Garrett Lisi

[Torgny Tholerus]

rafael jimenez buendia skrev:

  Sorry, but I think Lisi's paper is fatally flawed. Adding
altogether fermions and bosons is plain wrong. Best


What is wrong with adding fermions and bosons together?  Xiao-Gang Wen
is working with a condensed string-net where the waves behave just like
bosons (fotons) and the end of the open strings behave just like
fermions (electrons).

-- 
Torgny Tholerus

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Re: Theory of Everything based on E8 by Garrett Lisi

[Torgny Tholerus]

[EMAIL PROTECTED] skrev:

  

On Nov 23, 8:49 pm, Torgny Tholerus [EMAIL PROTECTED] wrote:
  
  
I think that everything is reducible to physical substances and
properties.  And I think that all of physics is reducible to pure
mathematics...

  
  
You can't have it both ways.  If physics was reducible to pure
mathematics, then physics could not be the 'ontological base level' of
reality and hence everything could not be expressed solely in terms of
physical substance and properties.

Besides which, mathematics and physics are dealing with quite
different distinctions.  It is a 'type error' it try to reduce or
identity one with the other.

Mathematics deals with logical properties, physics deals with spatial
(geometric) properties.  Although geometry is thought of as math, it
is actually a branch of physics, since in addition to pure logical
axioms, all geometry involves 'extra' assumptions or axioms which are
actually *physical* in nature (not purely mathematical) .
  


When I talk about "pure mathematics" I mean that kind of mathematics
you have in GameOfLife. There you have "gliders" that move in the
GameOfLife-universe, and these gliders interact with eachother when
they meet. These gliders you can see as physical objects. These
physical objects are reducible to pure mathematics, they are the
consequences of the rules behind GameOfLife.

-- 
Torgny

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Re: Theory of Everything based on E8 by Garrett Lisi

[Torgny Tholerus]

[EMAIL PROTECTED] skrev:

 As far as I tell tell, all of physics is ultimately
 geometry.  But as we've pointed out on this list many times, a theory
 of physics is *not* a theory of everything, since it makes the
 (probably false) assumption that everything is reducible to physical
 substances and properties.

I think that everything is reducible to physical substances and 
properties.  And I think that all of physics is reducible to pure 
mathematics...

I have now read Garrett Lisis paper.  It was interesting, but it is 
still to early to say if it is important.  There is a lot of symmetries 
in the elementary particles, and there is a lot of symmetries in the E8 
Lie group.  So it is not any suprise that they both can be mapped on 
each other.  Lisi has mapped 222 elementary particles on the 242 
elements of E8, and he has predicted that the rest of the 20 elements 
correspond to 20 yet to be discovered elementary particles.  If it is 
true, then Lisi will have the Nobel price.  If it is not, then we will 
have to look for another TOE.

But it is possible that we will never find any TOE.  Because there is 
10^500 different possiblities for our universe, and all of these 10^500 
universes exist in the same way.  By experiments we will have to decide 
which of those that is our universe, but we will never reach the correct 
answer, the number of experiments needed will be too many.

-- 
Torgny

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Re: Cantor's Diagonal

[Torgny Tholerus]

Bruno Marchal skrev:

  
Le 20-nov.-07,  23:39, Barry Brent wrote :

  
  
You're saying that, just because you can *write down* the missing
sequence (at the beginning, middle or anywhere else in the list), it
follows that there *is* no missing sequence.  Looks pretty wrong to me.

  Cantor's proof disqualifies any candidate enumeration.  You respond
by saying, "well, here's another candidate!"  But Cantor's procedure
disqualified *any*, repeat *any* candidate enumeration.

Barry Brent

  
  

Torgny, I do agree with Barry. Any bijection leads to a contradiction, 
even in some effective way, and that is enough (for a classical 
logician).
  


What do you think of this "proof"?:

Let us have the bijection:

0  {0,0,0,0,0,0,0,...}
1  {1,0,0,0,0,0,0,...}
2  {0,1,0,0,0,0,0,...}
3  {1,1,0,0,0,0,0,...}
4  {0,0,1,0,0,0,0,...}
5  {1,0,1,0,0,0,0,...}
6  {0,1,1,0,0,0,0,...}
7  {1,1,1,0,0,0,0,...}
8  {0,0,0,1,0,0,0,...}
...
omega --- {1,1,1,1,1,1,1,...}

What do we get if we apply Cantor's Diagonal to this?

-- 
Torgny

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Re: Bijections (was OM = SIGMA1)

[Torgny Tholerus]

Bruno Marchal skrev:

 To sum up; finite ordinal and finite cardinal coincide. Concerning 
 infinite number there are much ordinals than cardinals. In between 
 two different infinite cardinal, there will be an infinity of ordinal. 
 We have already seen that omega, omega+1, ... omega+omega, 
 omega+omega+1, 3.omega, ... 4.omega  omega.omega . 
 omega.omega.omega, .omega^omega . are all different ordinals, 
 but all have the same cardinality.
   
Was it not an error there?  2^omega is just the number of all subsets of 
omega, and the number of all subsets always have bigger cardinality than 
the set.  So omega^omega can not have the same cardinality as omega.

-- 
Torgny

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Re: Bijections (was OM = SIGMA1)

[Torgny Tholerus]

Bruno Marchal skrev:

 But infinite ordinals can be different, and still have the same 
 cardinality. I have given examples: You can put an infinity of linear 
 well founded order on the set N = {0, 1, 2, 3, ...}.
 The usual order give the ordinal omega = {0, 1, 2, 3, ...}. Now omega+1 
 is the set of all ordinal strictly lesser than omega+1, with the 
 convention above. This gives {0, 1, 2, 3, ... omega} = {0, 1, 2, 3, 4, 
 {0, 1, 2, 3, 4, }}. As an order, and thus as an ordinal, it is 
 different than omega or N. But as a cardinal omega and omega+1 are 
 identical, that means (by definition of cardinal) there is a bijection 
 between omega and omega+1. Indeed, between  {0, 1, 2, 3, ... omega} and 
 {0, 1, 2, 3, ...}, you can build the bijection:

 0omega
 10
 21
 32
 ...
 n --- n-1
 ...

 All right?- represents a rope.
   
An ultrafinitist comment:

In the last line of this sequence you will have:

? - omega-1

But what will the ? be?  It can not be omega, because omega is not 
included in N...

-- 
Torgny

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Re: Cantor's Diagonal

[Torgny Tholerus]

Bruno Marchal skrev:
But then the complementary sequence (with the 0 and 1
permuted) is
also well defined, in Platonia or in the mind of God(s)
  
  
  0 1 1 0
  1 1 ...
  
  
But this infinite sequence cannot be in the list, above.
The "God" in question has to ackonwledge that. 
The complementary sequence is clearly different 
-from the 0th sequence (1, 0, 0,
1, 1, 1, 0 ..., because it differs at the first (better the 0th) entry.
  
-from the 1th sequence (0, 0, 0,
1, 1, 0, 1 ... because it differs at the second (better the 1th) entry.
  
-from the 2th sequence (0, 0, 0,
1, 1, 0, 1 ... because it differs at the third (better the 2th) entry.
  
and so one.
  
So, we see that as far as we consider the bijection above well
determined (by God, for example), then we can say to that God that the
bijection misses one of the neighbor sheep, indeed the "sheep"
constituted by the infinite binary sequence complementary to the
diagonal sequence cannot be in the list, and that sequence is also
well determined (given that the whole table is).
  
  
But this means that this bijection fails. Now the reasoning did not
depend at all on the choice of any particular bijection-candidate. Any
conceivable bijection will lead to a well determined infinite
table of binary numbers. And this will determine the diagonal sequence
and then the complementary diagonal sequence, and this one cannot be
in the list, because it contradicts all sequences in the list when
they cross the diagonal (do the drawing on paper).
  
  
Conclusion: 2^N, the set of infinite binary sequences, is not
enumerable.
  
  
All right?
  


An ultrafinitist comment to this:
==
You can add this complementary sequence to the end of the list. That
will make you have a list with this complementary sequence included.

But then you can make a new complementary sequence, that is not
inluded. But you can then add this new sequence to the end of the
extended list, and then you have a bijection with this new sequence
also. And if you try to make another new sequence, I will add that
sequence too, and this I will do an infinite number of times. So you
will not be able to prove that there is no bijection...
==
What is wrong with this conclusion?

-- 
Torgny

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Re: Cantor's Diagonal

[Torgny Tholerus]

meekerdb skrev:

  Torgny Tholerus wrote:
  
  
An ultrafinitist comment to this:
==
You can add this complementary sequence to the end of the list.  That 
will make you have a list with this complementary sequence included.

But then you can make a new complementary sequence, that is not 
inluded.  But you can then add this new sequence to the end of the 
extended list, and then you have a bijection with this new sequence 
also.  And if you try to make another new sequence, I will add that 
sequence too, and this I will do an infinite number of times.  So you 
will not be able to prove that there is no bijection...
==
What is wrong with this conclusion?

  
  
You'd have to insert the new sequence in the beginning, as there is no 
"end of the list".

  


Why can't you add something to the end of the list? In an earlier
message Bruno wrote:

"Now omega+1 is the set of all ordinal strictly lesser than omega+1,
with the convention above. This gives {0, 1, 2, 3, ... omega} = {0, 1,
2, 3, 4, {0, 1, 2, 3, 4, }}."

In this sentence he added omega to the end of the list of natural
numbers...

-- 
Torgny

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Re: Bijections (was OM = SIGMA1)

[Torgny Tholerus]

Quentin Anciaux skrev:

  Hi,

Le Thursday 15 November 2007 14:45:24 Torgny Tholerus, vous avez écrit :
  
  

What do you mean by "each" in the sentence "for each natural number"?  How
do you define ALL natural numbers?

  

  
  
There is a natural number 0.
Every natural number a has a natural number successor, denoted by S(a).
  


What do you mean by "Every" here?  Can you give a *non-circular*
definition of this word?  Such that: "By every natural number I mean
{1,2,3}" or "By every naturla number I mean every number between 1 and
100".  (This last definition is non-circular because here you can
replace "every number" by explicit counting.)


  

How do you prove that each x in N has a corresponding number 2*x in E?
If m is the biggest number in N,

  
  
By definition there exists no biggest number unless you add an axiom saying 
there is one but the newly defined set is not N.
  


I can prove by induction that there exists a biggest number:

A) In the set {m} with one element, there exists a biggest number, this
is the number m.
B) If you have a set M of numbers, and that set have a biggest number
m, and you add a number m2 to this set, then this new set M2 will have
a biggest number, either m if m is bigger than m2, or m2 if m2 is
bigger than m.
C) The induction axiom then says that every set of numbers have a
biggest number.

Q.E.D.

-- 
Torgny Tholerus

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The big-black-cloud-interpretation.

[Torgny Tholerus]

Bruno Marchal skrev:

  
Le 15-nov.-07,  14:45, Torgny Tholerus a crit :
  
  
  
  Do you have the big-black-cloud interpretation of "..."?
By that I
mean that there is a big black cloud at the end of the visible part of
universe, 
  
  
Concerning what I am trying to convey, this is problematic. The word
"universe" is problematic. The word "visible" is also problematic.
  
  
  
  and the sequence of numbers is disappearing into the
cloud,
so that you can only see the numbers before the cloud, but you can
not see what happens at the end of the sequence, because it is hidden
by the cloud.

  
  
I don't think that math is about seeing. I have never seen a number.
It is a category mistake. I can interpret sometimes some symbol as
refering to number, but that's all.
  
  


A way to prove the consistency of a theory is to make a "visualization"
of the theory. If you can visualize all that happens in the theory,
then you know the theory is consistent.

To visualize the natural numbers, you can think of them as a long
sequence {0,1,2,3,4,5,...}, and this sequence is going far, far, away.

But you can only visualize finite sequences. So you can think that you
have a finite sequence of numbers, and you have a big black cloud far,
far, away. You see the first part of the sequence {0,1,2,...,m} before
the cloud. But inside the cloud you can imagine that you have the
finite sequence {m+1,m+2,...,4*m-1,4*m}. This whole sequence
{0,1,2,...,m,m+1,...4*m} is what you call the set N of all natural
numbers.

>From that set N you construct the true subset
{0,2,4,6,...,2*m,2*m+2,...,4*m}, which you call the set E of all even
numbers. The visible part of the set E is then {0,2,4,...,2*m}, and
the hidden part of that sequence is {2*m+2,...,4*m}.

Now you define a new concept INNFINITE, that is defined by:

If you have a bijection from all visible numbers of a set S, to all
visible numbers of a true subset of S, then you say that the set S in
INNFINITE.

Then you can use this concept INNFINITE, and you will get a consistent
theory with no contradictions, because you have a finite visualization
of this theory.

-- 
Torgny

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Re: Bijections (was OM = SIGMA1)

[Torgny Tholerus]

Bruno Marchal skrev:

  
Le 15-nov.-07,  14:45, Torgny Tholerus a crit :
  
  
  But m+1 is not a number. 
  
  
This means that you believe there is a finite sequence of "s" of the
type
  
  
A =
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(
s(0)...)
  
  
where "..." here represents a finite sequence, and which is such that
s(A) is not a number.
  


Yes, exactly. When you construct the set of ALL natural numbers N, you
have to define ALL these numbers. And you can only define a finite
number of numbers. See more explanations below.


BTW, do you agree that 100^(100^(100^(100^(100^(100^(100^(100^100)],
and 100^(100^(100^(100^(100^(100^(100^(100^100)] +1 are numbers? I am
just curious,
  


Yes, I agree. All explicitly given numbers are numbers. The biggest
number is bigger than all by human beeings explicitly given numbers.

If you define the set of all natural numbers N, then you can pull out
the biggest number m from that set. But this number m has a different
"type" than the ordinary numbers. (You see that I have some sort of
"type theory" for the numbers.) The ordinary deduction rules do not
hold for numbers of this new type. For all ordinary numbers you can
draw the conclusion that the successor of the number is included in N.
But for numbers of this new type, you can not draw this conclusion.

You can say that all ordinary natural numbers are of type 0. And the
biggest natural number m, and all numbers you construct from that
number, such that m+1, 2*m, m/2, and so on, are of type 1. And you can
construct a set N1 consisting of all numbers of type 1. In this set
there exists a biggest number. You can call it m1. But this new
number is a number of type 2.

There is some sort of "temporal" distinction between the numbers of
different type. You have to "first" have all numbers of type 0,
"before" you can construct the numbers of type 1. And you must have
all numbers of type 1 "before" you can construct any number of type 2,
and so on.

The construction of numbers of type 1 presupposes that the set of all
numbers of type 0 is fixed. When the set N of all numbers of type 0 is
fixed, then you can construct new numbers of type 1.

It may look like a contradiction to say that m is included in N, and to
say that all numbers in N have a successor in N, and to say that m have
no successor in N. But it is not a constrdiction because the rule "all
numbers in N have a successor in N" can be expanded to "all numbers of
type 0 in N have a successor in N". And because m is a number of type
1, then that rule is not applicable to m.

-- 
Torgny

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Re: Bijections (was OM = SIGMA1)

[Torgny Tholerus]

Bruno Marchal skrev:

  
Le 14-nov.-07,  17:23, Torgny Tholerus a crit :

  
  
What do you mean by "..."?

  
  

Are you asking this as a student who does not understand the math, or 
as a philospher who, like an ultrafinist, does not believe in the 
potential infinite (accepted by mechanist, finistist, intuitionist, 
etc.).
  


I am asking as an ultrafinitist.


  
I have already explained that the meaning of "...'" in {I, II, III, 
, I, II, III, , I, ...}  is *the* 
mystery.
  


Do you have the big-black-cloud interpretation of "..."? By that I
mean that there is a big black cloud at the end of the visible part of
universe, and the sequence of numbers is disappearing into the cloud,
so that you can only see the numbers before the cloud, but you can not
see what happens at the end of the sequence, because it is hidden by
the cloud.


  

  
  

  For
example, the function which sends x on 2*x, for each x in N is such a
bijection.

  

What do you mean by "each x" here?

  
  

I mean "for each natural number".
  


What do you mean by "each" in the sentence "for each natural number"?
How do you define ALL natural numbers?


  

  
  
How do you prove that each x in N has a corresponding number 2*x in E?
If m is the biggest number in N,

  
  

There is no biggest number in N. By definition of N we accept that if x 
is in N, then x+1 is also in N, and is different from x.
  


How do you know that m+1 is also in N? You say that for ALL x then x+1
is included in N, but how do you prove that m is included in "ALL x"?

If you say that m is included in "ALL x", then you are doing an illegal
deduction, and when you do an illegal deduction, then you can prove
anything. (This is the same illegal deduction that is made in the
Russell paradox.)


  

  
  
then there will be no corresponding
number 2*m in E, because 2*m is not a number.

  
  

Of course, but you are not using the usual notion of numbers. If you 
believe that the usual notion of numbers is wrong, I am sorry I cannot 
help you.
  


I am using the usual notion of numbers. But m+1 is not a number. But
you can define a new concept: "number-2", such that m+1 is included in
that new concept. And you can define a new set N2, that contains all
natural numbers-2. This new set N2 is bigger than the old set N, that
only contains all natural numbers.

-- 
Torgny Tholerus

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Re: Bijections (was OM = SIGMA1)

[Torgny Tholerus]

Bruno Marchal skrev:
 0) Bijections

 Definition: A and B have same cardinality (size, number of elements) 
 when there is a bijection from A to B.

 Now, at first sight, we could think that all *infinite* sets have the 
 same cardinality, indeed the cardinality of the infinite set N. By N, 
 I mean of course the set {0, 1, 2,  3,  4,  ...}
   
What do you mean by ...?
 By E, I mean the set of even number {0, 2, 4, 6, 8, ...}

 Galileo is the first, to my knowledge to realize that N and E have the 
 same number of elements, in Cantor's sense. By this I mean that 
 Galileo realized that there is a bijection between N and E. For 
 example, the function which sends x on 2*x, for each x in N is such a 
 bijection.
   
What do you mean by each x here?

How do you prove that each x in N has a corresponding number 2*x in E?

If m is the biggest number in N, then there will be no corresponding 
number 2*m in E, because 2*m is not a number.
 Now, instead of taking this at face value like Cantor, Galileo will 
 instead take this as a warning against the use of the infinite in math 
 or calculus.
   
-- 
Torgny Tholerus

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Re: No(-)Justification Justifies The Everything Ensemble

[Torgny Tholerus]

Bruno Marchal skrev:

  
Le 19-sept.-07,  09:59, Youness Ayaita wrote (in two posts):

  
  
Probably, we
won't find the set of natural numbers within this universe, the number
of identical particles (as far as we can talk about that) of any kind
is finite.

  
  
Not in all "models" (cf type 1 multi-realty of Tegmark).
  


The type 1 multi-reality of Tegmark does not require infinity. The
type 1 multi-reality is true also in a finite universe, that is
*enough* big...

-- 
Torgny Tholerus

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Re: Space-time is a liquid!

[Torgny Tholerus]

John Mikes skrev:

 JM: Then what makes them into a continuous 'string'? OR: do those 
 individual points arrange in unassigned directions they just wish? If 
 they only fluctuate by themselves, what reference do they 
 (individually) follow to be callable 'string' -'fluctuate' - or just 
 vibrate on their own?
 (below you said it: there the strings consist of discrete points.)

 JM: so THOSE (discrete) points are SPACE and also VACUUM. Now what 
 keeps them 'discrete' if there is NO space between them? They mold 
 together into an 'undivided' continuum - without any divider in 
 between. Two discrete points have got to be discretized by something 
 interstitial  separational - in the geometrical view: their spatial 
 image (what they do not have, because they ARE space).
 In this same image vacuum is also a bunch of discontinuous points that 
 move. Vibrate. Fluctuate. Undulate into waves. But without anything 
 interstitial they melt into a continuum?

If you look at a meter, then there is a finite number of space points in 
that meter (it is about 10^35 space points in this meter).  There is no 
space between two space points, because the space is the space points.

The best way to imagine this discrete space and discrete time, is to 
look at the Game of Life.  There you have discrete space points, that 
can have two states, on/off (or black/white or spin up/spin down).  In 
this discrete space-time, you can see the gliders move.  It is the same 
thing with the vibrating strings in the string-net liquid.  There you 
have string-like structures, waving back and forth.  These string-like 
structure is the wacuum.  And the elementary particles are macroscopic 
vawes in this string-net liquid, just like sound waves in water.


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Re: Space-time is a liquid!

[Torgny Tholerus]

John Mikes skrev:

  
1.- Q: What are light and fermions? 
A: 
Light is a fluctuation of closed strings of arbitrary sizes.
Fermions are ends of open strings. 
2.- Q: Where do light and fermions come from? 
A: 
Light and fermions come from the collective motions of string-like
objects that form nets and fill our vacuum. 
3.- Q: Why do light and fermions exist? 
A: 
Light and fermions exist because our vacuum is a quantum
liquid of string-nets.
  
This is from the introduction of the URL so kindly provided by Torgny.
It looks very interesting, a gteat idea indeed. I like better a
'liquid' of spacetime than a 'fabric'. 
  
Xiao-Gang Wen looks like a very open-minded wise man. 
I wonder if he made the circularity of his Q#1 and Q#3 deliberately?
(if, of course, we include Q#2). 
Originally - before reading Q#3 I wanted to ask 'what is OUR vacuum?
but here it is: a QUANTUM liqud and it has the substance of
"string-nets". 
He also postulates closed strings and open ones. (What-s?)
the closed ones fluctuate in waves (=photons) and the open ones have
endings we consider electrically charged (also callable: particles). 
In my original (uneducted) question I wanted to ask what kind of a
vacuum is "filled"? is it still a (full) vacuum? Do the 'strings' have
a 'filling' quale? or is a 'string-filled' plenum still empty (as in
vacuum)? If the strings fluctuate into waves, what fluctuates? I am
afraid that ANY answer will start another string of questions. 
  
The vocabulary is not so clear, then again it is the nth consequence of
the mth consequential result of an old assumption: the assumption of
the physical world. 
  
Please, do not reply! I just realizes that this entire topic is way
above my preparedness and just have "let it out". 


Some clarifications:

The vacuum IS a string-net liquid. But the strings are not continous.
As you can see in the picture in Figure 1.8 at page 9 (page 14 in the
pdf file) in Xiao-Gang Wen: "Introduction to Quantum Many-boson Theory
(-: a theory of almost
everything :-)", that can be found at http://dao.mit.edu/~wen/pub/intr-frmb.pdf
, and in the 10th slide of his talk "An unification of light and
electron" at
http://dao.mit.edu/~wen/talks/06TDLee.pdf
, there the strings consist of discrete points. And it is these
discrete points that ARE the space. There is no space between the
points. The vacuum IS these points.

This might be hard to understand. But this is the same thing that
there were no time "before" the Big Bang. The time started with Big
Bang. And there is the same thing with the space points in the strings
in the discrete space. There is no space "between" the space points.
This is hard to understand mentally, but it can be understood
mathematically.

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Space-time is a liquid!

[Torgny Tholerus]

(From the swedish Allting List:)

The discrete space-time is a liquid.  This explains why the space is 
isomorph in all directions.

The one that discovered that the space-time is a liquid, was Xiao-Gang 
Wen (Home Page: http://dao.mit.edu/~wen ).  He has found that elementary 
particles are not the fundamental building blocks of matter.  Instead, 
they emerge as defects or whirlpools in the deeper organized structure 
of space-time.  The space-time is a string-net liquid, and the photons, 
the light, are waves in this liquid.  And the charged electrons are the 
the ends of open-ended strings.

Xiao-Gang Wen has written a lot of articles about this, and they can all 
be found from his home page.  But most of the articles are *very* 
mathematical.  But there is an easy-to-read article at 
https://dao.mit.edu/~wen/NSart-wen.html .  And there is a 
rather-easy-to-read article in 12 pages at 
https://dao.mit.edu/~wen/pub/intr-frmb.pdf , that explains more about 
these very interesting theories.


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Re: Why Objective Values Exist

[Torgny Tholerus]

[EMAIL PROTECTED] skrev:

 (7)  From (3) mathematical concepts are objectively real.  But there
 exist mathematical concepts (inifinite sets) which cannot be explained
 in terms of finite physical processes.

How can you prove that infinite sets exists?

-- 
Torgny Tholerus



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Message to swedish language members.

[Torgny Tholerus]

This is a message to the swedish language members of the Everything List:

Efersom jag har svårt att uttrycka det jag vill säga på engelska, så har 
jag nu startat en svenskspråkig sublista till Everything List, som jag 
har kallat Allting List.  Du hittar den nya listan på: 
http://groups.google.com/group/allting-list?hl=sv .  Gå gärna med i den 
listan, och hjälp mej förklara universum.

Jag har redan lagt in 11 (korta) inlägg i denna lista, som en startpunkt 
för diskussionerna.

Resultaten som vi kommer fram till i sublistan ska sedan överföras till 
den övergripande Everything List.

-- 
Torgny Tholerus


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Re: Asifism revisited.

[Torgny Tholerus]

Brent Meeker skrev:

 Torgny Tholerus wrote:

 That is exactly what I wanted to say.  You don't need to have a complete
 description of arithmetic.  Our universe can be described by doing a
 number of computations from a finite set of rules.  (To get to the
 current view of our universe you have to do about 10**60 computations
 for every point of space...)

 How did you arrive at that number?

It is the number of Planck times since the birth of Universe.  The age of
Universe is 13,7 billion years, number of seconds in a year is 31 million,
and the Planck time is 5,4 * 10**-44 seconds.  That gives 13,7*10**9 *
31*10**6 / (5,4*10**-44) = 8*10**60.

-- 
Torgny


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Re: Asifism revisited.

[Torgny Tholerus]

Brent Meeker skrev:

  Bruno Marchal wrote:
  
  

Le 09-juil.-07,  17:41, Torgny Tholerus a crit :

  
  ...
  
  
Our universe is the result of some set of rules. The interesting
thing is to discover the specific rules that span our universe.




Assuming comp, I don't find plausible that "our universe" can be the 
result of some set of rules. Even without comp the "arithmetical 
universe" or arithmetical truth (the "ONE" attached to the little Peano 
Arithmetic Lobian machine) cannot be described by finite set of rules.

  
  
But it can be "the result of" a finite set of rules. Arithmetic results from Peano's axioms, but a complete description of arithmetic is impossible.
  

That is exactly what I wanted to say. You don't need to have a
complete description of arithmetic. Our universe can be described by
doing a number of computations from a finite set of rules. (To get to
the current view of our universe you have to do about 10**60
computations for every point of space...)

-- 
Torgny

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Re: Asifism revisited.

[Torgny Tholerus]

Bruno Marchal skrev:

Le 09-juil.-07,  17:41, Torgny Tholerus a crit :
  
  
  
   Bruno Marchal skrev:
 


  I agree with you (despite a notion as "universe" is
not primitive in my 
opinion, unless you mean it a bit like the logician's notion of model 
perhaps). As David said, this is arithmetical realism.
  
  


Yes, you can see a universe as the same thing as a model.


When you have a (finite) set of rules, you will always get a universe
from that set of rules, by just applying those rules an unlimited
number of times. And the result of these rules is existing, in the
same way as our universe is existing.

  
  
The problem here is that an effective syntactical description of a
intended model ("universe") admits automatically an infinity of non
isomorphic models (cf Lowenheim-Skolem theorems, Godel, ...).
  

Yes, you are right, the word "model" is not quite appropriate here.
The universe is not a model that satisfies a set of axioms.

The kind of rules I am thinking of, is rather that kind of rules you
have in Game of Life. When you have a situation at one moment of time
and at one place in space, you can compute the situation the next
moment of time at the same place by using the situations near this
place. The important thing is that the rules uniquely describes the
whole universe by applying the rules over and over again.

(But I want something more general than GoL-like rules, because the
GoL-rules presupposes that you have a space-time from the beginning. I
want a set of rules that are such that the space-time is a result of
the rules. But I don't know how to get there...)

  
  
Our universe is the result of some set of rules. The interesting
thing is to discover the specific rules that span our universe.

  
  
  
Assuming comp, I don't find plausible that "our universe" can be the
result of some set of rules. Even without comp the "arithmetical
universe" or arithmetical truth (the "ONE" attached to the little
Peano Arithmetic Lobian machine) cannot be described by finite set of
rules.
  
The Universal Dovetailer Argument (UDA) shows that even a cup of
coffee is eventually described by the probabilistic interferences of
an infinity of computations occurring in the Universal deployment
(UD*), which by the way explains why we cannot really duplicate
exactly any piece of apparent matter (comp-no cloning).
  
It is an open question if those theoretical interferences correspond
to the quantum one. Studying the difference between the comp
interference and the quantum interferences gives a way to measure
experimentally the degree of plausibility of comp.
  

I claim that "our universe" is the result of a finite set of rules.
Just as a GoL-universe is the result of a finite set of rules, so is
our universe the result of a set of rules. But these rules are more
complicated than the GoL-rules...

-- 
Torgny Tholerus

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Re: Asifism revisited.

[Torgny Tholerus]

Quentin Anciaux skrev:
  I claim that our universe is the result of a finite set of rules.  Just
 as a GoL-universe is the result of a finite set of rules, so is our universe
 the result of a set of rules.  But these rules are more complicated than the
 GoL-rules...
 
 What are your proofs or set of evidences that our universe as it is
 is 1) resulting from a finite set of rules 2) by 1) computable.
   
There are two proofs:

A)  Everything is finite.  So our universe must be the result from a 
finite set of rules.
B)  Occams razor.  Because we can explain everything in our universe 
from this finite set of rules, we don't need anything more complicated.
 If 2) is true what difference do you make between functionnaly
 equivalent model of your set of rules ? is it the same universe ?
   
Our universe has nothing to do with different models of our universe.  A 
model is more like a picture of our universe.  You can make a model of a 
GoL-universe with red balls, or you can make a model with black dots, 
but still there will hold the same relations in both these models.  It 
is the relations that are the important things.

-- 
Torgny Tholerus


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Re: Some thoughts from Grandma

[Torgny Tholerus]

David Nyman skrev:

  On 11/07/07, Brent Meeker [EMAIL PROTECTED] wrote:

  
  
(quite contrary to the premise of the everything-list, but one that I'm glad to entertain).

  
  
For what it's worth, I really don't see that this is necessarily
contrary to the premise of this list.  The proposition is that all
POSSIBLE worlds exist, not that anything describable in words (or for
that matter mathematically) 'exists'.  My analysis is an attempt to
place a constraint on what can be said to exist in any sense strong
enough to have any discernible  consequences, either for us, or for
any putative denizens of such 'worlds'.  So I would argue that
non-reflexive worlds are not possible in any consequential sense of
the term.
  

What do you mean with a POSSIBLE world?

One exemple of a possible world is that GoL-universe, of which there is
a picture of on the Wikipedia page.

One interesting thing about this particular GoL-universe is that it is
finite, the time goes in a circle in that universe. That universe only
consists of 14 situations. After the 14th situation follows the 1st
situation again.

This GoL-universe exists, but it is a non-reflexive world, I can not
see anything reflexive in that universe.

-- 
Torgny Tholerus

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Re: Asifism revisited.

[Torgny Tholerus]

David Nyman skrev:

  On 09/07/07, [EMAIL PROTECTED] [EMAIL PROTECTED] wrote:

  
  
There can be no dynamic time.  In the space-time, time is always
static.

  
  
Then you must get very bored ;)

David
  

But I am not bored, because I don't know what will happen tomorrow. If
I look at our universe from the outside, I see that I will do something
tomorrow, and I see what will happen in one million years. There will
never be any changes in the situations that will happen in the future.

But it is impossible to know today what will happen in the future,
because we can not have total knowledge about how the universe looks
like just now. If we try to find the exact position and the exact
speed of an electron, then that electron will be disturbed by me
looking at it. So it is impossible for me to compute how our universe
will look like tomorrow. But the rules of our universe decide what our
universe will look like tomorrow.
-- 
Torgny Tholerus

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Re: Asifism revisited.

[Torgny Tholerus]

David Nyman skrev:
 Consequently we can't 'interview' B-Universe objects.
   
It is true that we can not interview objects in B-Universe.  One object 
in one universe can not affect any object in some other universe.

But we can look at the objects in an other universe.  Just in the same 
way that we can look at a GoL-universe.  So we in the A-Universe can 
look at the objects in B-Universe, and see what they are doing.

One way to interview the objects in B-Universe is to do interviewing in 
the A-Universe.  If A-Torgny is interviewing A-David in the A-Universe, 
then B-Torgny will be interviewing B-David in the B-Universe.  Because 
everything that happens in A-Universe will also happen in B-Universe.  
All objects in A-Universe obey the laws of physics, and all objects in 
B-Universe obey the same laws, so the same things will happen in both 
universes.

-- 
Torgny Tholerus


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Re: Asifism revisited.

[Torgny Tholerus]

Bruno Marchal skrev:

  
Le 05-juil.-07,  14:19, Torgny Tholerus wrote:
  
  
David Nyman skrev:


  You have however drawn our attention to something very interesting and
important IMO.  This concerns the necessary entailment of 'existence'.
  

1.  The relation 1+1=2 is always true.  It is true in all universes.
Even if a universe does not contain any humans or any observers.  The
truth of 1+1=2 is independent of all observers.

  
  
I agree with you (despite a notion as "universe" is not primitive in my 
opinion, unless you mean it a bit like the logician's notion of model 
perhaps). As David said, this is arithmetical realism.
  


Yes, you can see a universe as the same thing as a model.

When you have a (finite) set of rules, you will always get a universe
from that set of rules, by just applying those rules an unlimited
number of times. And the result of these rules is existing, in the
same way as our universe is existing.

Our universe is the result of some set of rules. The interesting thing
is to discover the specific rules that span our universe.

-- 
Torgny Tholerus

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Re: Some thoughts from Grandma

[Torgny Tholerus]

David Nyman skrev:
 You're right, we must distinguish zombies.  The kind I have in mind
 are the kind that Torgny proposes, where 'everything is the same' as
 for a human, except that 'there's nothing it is like' to be such a
 person.  My key point is that this must become incoherent in the face
 of self-relativity.  My reasoning is that a claim for the 'existence'
 of something like Torgny's B-Universe is implicitly a claim for
 self-relative existence: i.e. independent of other causality, like the
 One.  When Torgny proposed the Game of Life as an example of 'another
 universe', I pointed out that GoL clearly doesn't possess independent
 existence: it's just a part of the A-Universe.
It is intresting to study the GoL-universe we can see on the Wikipedia 
page.  What will happen if we stop the program that shows this 
GoL-universe?  Will the GoL-universe stop to exist then?

No, the GoL-universe will not stop, it will continue for ever.  The 
rules for this GoL-universe makes it possible to compute all future 
situations.  It is this that is important.  This GoL-universe is not 
dependent of the A-Universe.  What we see when we look at the Wikipedia 
page is just a picture of a part of this GoL-universe.

-- 
Torgny Tholerus


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Re: Asifism revisited.

[Torgny Tholerus]

David Nyman skrev:
 You have however drawn our attention to something very interesting and 
 important IMO.  This concerns the necessary entailment of 'existence'.
1.  The relation 1+1=2 is always true.  It is true in all universes.  
Even if a universe does not contain any humans or any observers.  The 
truth of 1+1=2 is independent of all observers.

2.  If you have a set of rules and an initial condition, then there 
exist a universe with this set of rules and this initial condition.  
Because it is possible to compute a new situation from a situation, and 
from this new situation it is possible to compute another new situation, 
and this can be done for ever.  This unlimited set of situations will be 
a universe that exists independent of all humans and all observers.  
Noone needs to make these computations, the results of the computations 
will exist anyhow.

3.  All mathmatically possible universes exists, and they all exist in 
the same way.  Our universe is one of those possible universes.  Our 
universe exists independant of any humans or any observers.

4.  For us humans are the universes that contain observers more 
interesting.  But there is no qualitaive difference between universes 
with observers and universes without observers.  They all exist in the 
same way.  The GoL-universes (every initial condition will span a 
separate universe) exist in the same way as our universe.  But because 
we are humans, we are more intrested in universes with observers, and we 
are specially interested in our own universe.  But otherwise there is 
noting special with our universe.

-- 
Torgny Tholerus


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Re: Asifism revisited.

[Torgny Tholerus]

Jason skrev:
 Note that you did not say thought was non-existent in B-universe, I
 think one can construct complex conscious awareness to the collection
 of a large number of simultaneous thoughts.
I had the intention to include thoughts, but I was unsure about how to 
spell that word (where to put all those h:s...), so I included the 
thoughts in all that kind of stuff.  The B-Universe should not include 
any thouths(!).  The B-Universe should be a strictly materialistic Universe.

-- 
Torgny Tholerus



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Re: Asifism revisited.

[Torgny Tholerus]

David Nyman skrev:
On 04/07/07, Stathis
Papaioannou [EMAIL PROTECTED]
wrote:
  
SP: We can imagine an external observer looking at two model universes
A
  
and B side by side, interviewing their occupants.
  
DN: Yes, and my point precisely is that this is an illegitimate
sleight of imagination where the thought experiment goes amiss. When
one imagines the 'external' observer 'looking' at two universes, one
constructs precisely the false relationship that is the source of the
confusion with respect to consciousness. Any possible observer must in
fact be integral to their own universe.
  

You can look at the Game-of-Life-Universe, where you can see how the
"gliders" move. If you look at "Conway's game of Life" in Wikipedia,
you can look at how the Glider Gun is working in the top right corner.
This is possible although there is no observer integral to that
Universe.

The same is true about the B-Universe. You can look at it as an
outside observer.

-- 
Torgny Tholerus

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Re: Justifying the Theory of Everything

[Torgny Tholerus]

Jason skrev:
 I have seen two main justifications on this list for the everything
 ensemble, the first comes from information theory which says the
 information content of everything is zero (or close to zero).  The
 other is mathematicalism/arithmatical realism which suggests
 mathematical truth exists independandly of everything else and is the
 basis for everything.

 My question to the everything list is: which explaination do you
 prefer and why?  Are these two accounts compatible, incompatible, or
 complimentary?  Additionally, if you subscribe to or know of other
 justifications I would be interesting in hearing it.
   
Both justifications are true.  All mathematical possible universes 
exist.  (Game of Life is one possibility...)  But this theory doesn't 
say anything about our universe.  So the information content is zero.

-- 
Torgny Tholerus


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Re: Asifism

[Torgny Tholerus]

Bruno Marchal skrev:

 But nobody really doubts about his own consciousness 
 (especially going to the dentist), despite we cannot define it nor 
 explain it completely.
That sentence is wrong.  There is at least one person (me...) that 
really doubts about my own consciousness.  I am conscious about that I 
am not conscious.  I know that I does not know anything.  When I go to 
the dentist I behave as if I am feeling strong pain, because my pain 
center is directly stimulated by the dentist, which is causing my behaviour.

Consciouslike behaviour is good for a species to survive.  Therefore 
human beings show that type of behaviour.

-- 
Torgny Tholerus


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Re: Asifism

[Torgny Tholerus]

Quentin Anciaux skrev:

  On Thursday 28 June 2007 16:52:12 Torgny Tholerus wrote:
  
  
Consciouslike behaviour is good for a species to survive.  Therefore
human beings show that type of behaviour.

  
  I don't know what is consciouslike behaviour without consciousness in the 
first place.
  

An animal can show a consciouslike behaviour. When a dog sees a
rabbit, then the dog behaves as if he is conscious about that there is
food in front of him. He starts running after the rabbit as quick as
he can.

-- 
Torgny Tholerus

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Re: Asifism

[Torgny Tholerus]

Mohsen Ravanbakhsh skrev:
The "subjective experience" is
just some sort of behaviour. You can
make computers show the same sort of behavior, if the computers are
enough complicated.
  
But we're not talking about 3rd person point of view. I can not see how
you reduce the subjective experience of first person to the behavior
that a third person view can evaluate! All the problem is this first
person experience.
  

What you call "the subjective experience of first person" is just some
sort of behaviour. When you claim that you have "the subjective
experience of first person", I can see that you are just showing a
special kind of behaviour. You behave as if you have "the subjective
experience of first person". And it is possible for an enough
complicated computer to show up the exact same behaviour. But in the
case of the computer, you can see that there is no "subjective
experience", there are just a lot of electrical fenomena interacting
with each other.

There is no first person experience problem, because there is no first
person experience.

-- 
Torgny Tholerus

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Re: Asifism

[Torgny Tholerus]

 On Tuesday 19 June 2007 11:37:09 Torgny Tholerus wrote:
  What you call the subjective experience of first person is just some
 sort of behaviour.  When you claim that you have the subjective
 experience
 of first person, I can see that you are just showing a special kind of
 behaviour.  You behave as if you have the subjective experience of
 first
 person.  And it is possible for an enough complicated computer to show
 up
 the exact same behaviour.  But in the case of the computer, you can see
 that there is no subjective experience, there are just a lot of
 electrical fenomena interacting with each other.

  There is no first person experience problem, because there is no first
 person experience.

 In all your reasoning you implicitely use consciousness for example when
 you
 says When you claim that you have the subjective experience
 of first person, *I* can see that you are just showing a special kind of
 behaviour.

 Who/what is I ? Who/what is seeing ? What does it means for you to see
 if
 you have no inner representation of what you (hmmm if you're not
 conscious,
 you is not an appropriate word) see, what does it means to see at all ?

 In all your reasonning you allude to I, this is what 1st pov is about
 not
 about you (the conscious being/knower) looking at another person as if
 there
 was no obsever (means you) in the observation.

 Quentin

Our language is very primitive.  You can not decribe the reality with it.

If you have a computer robot with a camera and an arm, how should that
robot express itself to descibe what it observes?  Could the robot say: I
see a red brick and a blue brick, och when I take the blue brick and
places it on the red brick, then I see that the blue brick is over the red
brick.?

But if the robot says this, then you will say that this proves that the
robot is conscious, because it uses the word I.

How shall the robot express itself, so it will be correct?  It this
possible?  Or is our language incapable of expressing reality?

We human beings are slaves under our language.  The language restricts out
thinking.

-- 
Torgny Tholerus


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Re: Asifism

[Torgny Tholerus]

Bruno Marchal skrev:
Le 07-juin-07,  15:47, Torgny Tholerus a crit :
  
  What is the philosophical term for persons like me, that
totally deny
the existence of the consciousness?
  
An eliminativist.
  

"Eliminativist" is not a good term for persons like me, because that
term implies that you are eliminating an important part of reality.
But you can't eliminate something that does not exists. If you don't
believe in ghosts, are you then an eliminativist? If you don't believe
in Santa Claus, are you then an eliminativist, eliminating Santa Claus?

-- 
Torgny Tholerus


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Re: Asifism

[Torgny Tholerus]

Quentin Anciaux skrev:

  2007/6/14, Stathis Papaioannou [EMAIL PROTECTED]:
  
  
On 14/06/07, Quentin Anciaux [EMAIL PROTECTED] wrote:

  Sure but I still don't understand what could mean 'to know', 'to
believe' for an entity which is not conscious. Also if you're not
conscious, there is no 'me', no 'I', so there exists no 'person like
you' because then you're not a person.

Sure, but Torgny is just displaying the person-like behaviour of claiming to
be a person.

  
  Yes, in this case his writing is just garbage because it doesn't have
any meaning. I can't understand what it means for an unconscious thing
(for example a rock) to know something, to believe in something, to
have thought (especially this one, because it could be a definition of
consciousness, ie: something which has thought).
  

If the rock behaves as if it knows something (if you say something to
the rock, and the rock gives you an intelligent answer), then you can
say that the rock knows something. When the rock behaves as if it
believes in something, then you can say that the rock believes in
something. If the rock behaves as if it has thought, then you can say
that the rock has thought.

If a rock shows the same behavior as a human being, then you should be
able to use the same words ("know", believe", "think") to describe this
behaviour.

-- 
Torgny Tholerus

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Re: Asifism

[Torgny Tholerus]

Quentin Anciaux skrev:
 2007/6/14, Torgny Tholerus [EMAIL PROTECTED]:
   
 If a rock shows the same behavior as a human being, then you should be able
 to use the same words (know, believe, think) to describe this
 behaviour.
 
 If the rock know something and it behaves like it knows it, then it is
 conscious.
   
If the rock does *not* know anything, *but* the rock behaves as if it 
knows it, then it is reasonable to say that the rock knows it.

-- 
Torgny Tholerus


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Re: Asifism

[Torgny Tholerus]

Mohsen Ravanbakhsh skrev:
What is the subjective experience then?

The "subjective experience" is just some sort of behaviour. You can
make computers show the same sort of behavior, if the computers are
enough complicated.
-- 
Torgny Tholerus

  On 6/8/07, Torgny
Tholerus [EMAIL PROTECTED]
wrote:
  
The question, as I see it, is
if there is anything "more" than just
atoms reacting with each other in our brains. I claim that there is
not anything "more". The atoms reacting with each other explain fully
my (and your...) behaviour. Our brains are very complicated
structures, but it is nothing supernatural with them. Physics explains
everything.

  
  



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Re: Asifism

[Torgny Tholerus]

Mark Peaty skrev:
 MP: There is possibly a loose end or two here and perhaps 
 clarification is needed, yet again:

 * Or this could conceivably be construed as a 'state of grace' 
 in that Torgny is operating with no mental capacity being wasted 
 on self-talk or internal commentary: 'just doing' whatever needs 
 to be done and 'just being' what he needs to be; very Zen!
   
To discuss the nature of consciousness is waste of time, because 
consciousness or mind is not an entity that exists in the real world.  
The only thing that exists in the real world is matter.  What you can 
talk about is consciouslike behaviour, objects that behave as if they 
were conscious, objects that claim that they are conscious.
 * Then again it may be that I have misunderstood TT's grammar 
 and that what he is denying is simply the separate existence of 
 something called 'consciousness'. If that be the case then I 
 would not argue because I agree that the subjective impression 
 of being here now is simply what it is like to be part of the 
 processing the brain does, ie updating the model of self in the 
 world.
   
Yes, I simpy deny the separate existence of something called 
'consciousness'.

-- 
Torgny Tholerus



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Re: Asifism

[Torgny Tholerus]

Quentin Anciaux skrev:
 Beside, I don't see how denying consciousness answer the problem... 
 Redefining terms does not make the problem goes away.
   
What is the problem?

If a computer behaves as if it knows anything, what is the problem with 
that?  That type of behaviour increases the probability for the computer 
to survive, so the natural selection will favour that type of behaviour.

-- 
Torgny Tholerus



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Re: Asifism

[Torgny Tholerus]

Quentin Anciaux skrev:

  On Friday 08 June 2007 17:37:06 Torgny Tholerus wrote:
  
  
What is the problem?

If a computer behaves as if it knows anything, what is the problem with
that?  That type of behaviour increases the probability for the computer
to survive, so the natural selection will favour that type of behaviour.

  
  I claim that if it behaves as if, then it means it has consciousness... 
Philosophical zombie (which is what it is all about) are not possible... If 
it is impossible to discern it with what we define as conscious (and when I 
say impossible, I mean there exists no test that can show between the 
presuposed zombie and a conscious being a difference of behavior) then there 
is no point whatsover you can say to prove that one is conscious and one is 
not. Either both are conscious or both aren't... While you say you're not 
conscious... I am, therefore you're conscious.
  

The question, as I see it, is if there is anything "more" than just
atoms reacting with each other in our brains. I claim that there is
not anything "more". The atoms reacting with each other explain fully
my (and your...) behaviour. Our brains are very complicated
structures, but it is nothing supernatural with them. Physics explains
everything.

-- 
Torgny Tholerus


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Re: Asifism

[Torgny Tholerus]

Bruno Marchal skrev:
Le 04-juin-07,  14:10, Torgny Tholerus a crit :
  
  Pain is the same thing as the pain center in the brain
being
stimulated. 
  
If you are really unconscious or not conscious, you could say this,
indeed, but I hardly believe you are unconscious.
  
In the best case your theory will work for you and other "zombie". It
cannot work for those who admit the 1/3 distinction or the mind/body
apparent distinction.
  
You are on the fringe of being an eliminativist philosopher. What I do
appreciate is that you offer your theory for yourself. Let me ask you
explicitly this question, which I admit is admittedly weird to ask to
a zombie, but: do you think *we* are conscious?
  

I am constructed in such a way (my brain connections is such that...) I
very strongly claim that I am conscious, I very strongly claim that I
have feelings, I very strongly claim that I have a mind, I very
strongly claim that I have perceptions. But I know (intellectually)
that I am wrong, and I know why I am wrong.

When I look at you (in 3rd person view), I see that you are constructed
in exactly the same way as I am. So I know why you say that you are
conscious. I know nothing sure about you, but the most probable
conclusion is that you are equally unconscious as I am.

What is the philosophical term for persons like me, that totally deny
the existence of the consciousness?
(I also deny the existence of infinity...)

-- 
Torgny Tholerus


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Re: How would a computer know if it were conscious?

[Torgny Tholerus]

Tom Caylor skrev:

 I think that IF a computer were conscious (I don't believe it is
 possible), then the way we could know it is conscious would not be by
 interviewing it with questions and looking for the right answers.
 We could know it is conscious if the computer, on its own, started
 asking US (or other computers) questions about what it was
 experiencing.  Perhaps it would saying things like, Sometimes I get
 this strange and wonderful feeling that I am special in some way.  I
 feel that what I am doing really is significant to the course of
 history, that I am in some story.  Or perhaps, Sometimes I wish that
 I could find out whether what I am doing is somehow significant, that
 I am not just a duplicatable thing, and that what I am doing is not
 'meaningless'.
   
public static void main(String[] a) {

println(Sometimes I get this strange and wonderful feeling);
println(that I am 'special' in some way.);
println(I feel that what I am doing really is significant);
println(to the course of history, that I am in some story.);
println(Sometimes I wish that I could find out whether what);
println(I am doing is somehow significant, that I am not just);
println(a duplicatable thing, and that what I am doing);
println(is not 'meaningless'.);

}

You can make more complicated programs, that is not so obvious, by 
genetic programming.  But it will take rather long time.  The nature 
had to work for over a billion years to make the human beings.  But with 
genetic programming you will succeed already after only a million 
years.  Then you will have a program that is equally conscious as you are.

-- 
Torgny Tholerus



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Re: Asifism

[Torgny Tholerus]

Bruno Marchal skrev:

  Le 01-juin-07,  18:47, Torgny Tholerus a crit :
  
  When I am tortured, my pain center in my
brain will be stimulated. 
This
will cause me to try to avoid this situation (being tortured).  One
(good) way to archive this is to start talking about "ethics".  If I 
can
make other human beings to "believe" that it is ethically wrong to
torture objects, that behave as if they were conscious, then the
probability that somebody will torture me decreases.

  
  But if "me" is not conscious, why should us try to diminish that 
probability?
  

My brain is constructed in such a way, that if my pain center is
stimulated, then I will not repeat those action that caused the pain
center to be stimulated. (And if my lust center is stimulated, then I
will repeat those actions that caused my lust center to be
stimulated.) My neurons in my brain are interconnected in such a way,
causing this behavoiur.

  
  
This is all ethics is about: Trying to avoid stimulating the pain 
center
in our brains.

  
  Could pain exist without consciousness?
Do you agree that the sensation of pain is different from acting like 
if having that sensation of pain?
If not movie actors would complain!
  

Pain is the same thing as the pain center in the brain being
stimulated. When movie actors behave as if they were feeling pain,
then it is not pain, because their pain center in their brains are not
being stimulated. Only their outer behaviour is the same, inside their
brains there will be different.

-- 
Torgny Tholerus


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Re: Asifism

[Torgny Tholerus]

Stathis Papaioannou skrev:

  On 01/06/07, Torgny Tholerus [EMAIL PROTECTED] wrote:
  
  
  
I behave AS IF I am conscious
because the natural
selection
has favored that type of behavior.
  
  
Which implies you really are conscious, because otherwise why would
evolution have gone to the trouble of making *me* conscious if it could
have got away without it?
  
  
  

It did got away without it... ;-)

-- 
Torgny Tholerus


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Re: Asifism

[Torgny Tholerus]

Bruno Marchal skrev:
 One more question: supposing you are correct, is it ethically wrong to 
 torture you? Is it ethically wrong to torture an entity without 
 consciousness (supposing we could be sure of that) even if it acts 
 like it was conscious?
This is an interesting question.  And the answer is:

When I am tortured, my pain center in my brain will be stimulated.  This 
will cause me to try to avoid this situation (being tortured).  One 
(good) way to archive this is to start talking about ethics.  If I can 
make other human beings to believe that it is ethically wrong to 
torture objects, that behave as if they were conscious, then the 
probability that somebody will torture me decreases.

This is all ethics is about: Trying to avoid stimulating the pain center 
in our brains.

-- 
Torgny Tholerus



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Re: Asifism

[Torgny Tholerus]

Bruno Marchal skrev:
Le 01-juin-07,  14:35, Torgny Tholerus a crit :
  
  
  The only thing that exists is a lot of protons, neutrons,
and
electrons reacting with each other inside my brain.
  
Are you *sure*?
  
By the way, are you more sure about proton than about your belief in
proton? What would that mean?
  


I look at myself in the third person view. I then see a lot of protons
reacting with eachother, and I see how they explain my behavior and the
words I produce. I see how they cause me saying "I am conscious! I
have a free will! I am happy!". This is all that is. This explains
everything.

-- 
Torgny Tholerus


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Re: A sequel to my 1996 ultimate ensemble theory paper

[Torgny Tholerus]

Max skrev:

  Hi Folks,

After a decade of procrastination, I've finally finished writing up a
sequel to that paper that I wrote back in 1996 (Is "the theory of
everything'' merely the ultimate ensemble theory?) that's been the
subject of so much interesting discussion in this group.
It's entitled "The Mathematical Universe", and you'll find it at
http://arxiv.org/pdf/0704.0646 and http://space.mit.edu/home/tegmark/toe.html
- I'd very much appreciate any comments that you may have.
  

I have now read your new paper more carefully, and I have then found
one error in it. I the top of page 6 you write:



But there is a length scale "1" of special significance in our physical
space, namely the Planck length:

  meter.
And there is a time period of special significance, namely the Planck
time:
  


  .
(Source: Wikipedia.)
  

So when you look for the mathematical system that is our universe, you
have to look at the mathematical systems that have a special unit
length and a special unit time.

  -- 
  
  Torgny Tholerus
  
  



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Re: A sequel to my 1996 ultimate ensemble theory paper

[Torgny Tholerus]

Max skrev:
 Hi Folks,

 After a decade of procrastination, I've finally finished writing up a
 sequel to that paper that I wrote back in 1996 (Is the theory of
 everything'' merely the ultimate ensemble theory?) that's been the
 subject of so much interesting discussion in this group.
 It's entitled The Mathematical Universe, and you'll find it at
 http://arxiv.org/pdf/0704.0646 and http://space.mit.edu/home/tegmark/toe.html
 - I'd very much appreciate any comments that you may have.
   
I have now read The Mathematical Universe, and I have found it very 
good.  I agree with everything you write there.  I found the CUH 
(Computable Universe Hypothesis) very good, and most interesting was VII 
G 2 (Abandoning the continuum altogether), that is exactly what I 
believe in.

One problem I have not yet solved, is how to get all directions isomorph 
if you have a discrete space-time.  Maybe someone on this this list can 
help me solve that problem?

Max, a suggestion to you is to skip the concept of infinity totally.  
Your reasoning will be true even if you have a finite, but enough big, 
universe.  You don't need the infinity.

-- 
Torgny Tholerus



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