Re: Theory of Everything based on E8 by Garrett Lisi

[Bruno Marchal]

Le 30-nov.-07, à 20:21, Torgny Tholerus a écrit :

> Why can't our universe be modelled by a cellular automata?


By UDA, this is just  a priori impossible.

What *is* still possible, is that you can "modelize" the emergence of 
the appearance of a universe by modelling, with a cellular automata, a 
couple "observer + a quantum cellular automata", or by modelling all 
possible observers through universal dovetaling. Normally the 
appearance of the quantum will be generated as well.

If you are a machine, the physical universe (the sharable third person 
pov) is not describable in term of working machine. Unless you are the 
whole universe yourself, which I doubt.
If, you are the whole universe, and if you (the universe) exist, and if 
comp is false and ultrafinitism true, then you are right. But then, 
about the mind body problem, you are reintroducing the material bullet 
making even impossible to really addressed the question. Imo: it would 
be a regression.

This comment assumes a good understanding of the seven first steps of 
the UDA.



> Our universe
> is very complicated, but why can't it be modelled by a very complicated
> automata?


Because, by assuming comp, the (physical) universe has to emerge non 
locally from an infinity of infinite computations.


> 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?


Of course I talk here on exact emulation. FAPP, you can simulate 
electron and photon. About  "reality", I am not even sure there are 
photons and electrons, we have non local (in our local 
histories/branches) wavy interacting fields.
Note that Newton's law, taken seriously enough, are also not turing 
emulable, like almost everything in naïve math.


Bruno





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


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Re: Theory of Everything based on E8 by Garrett Lisi

[Bruno Marchal]

Le 30-nov.-07, à 20:00, Torgny Tholerus a écrit :

> 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.



Then you are physicalist before being ultrafinitist.

Now ultrafinitism implies comp (OK?, 'course comp does not imply 
ultrafinitism!)

But I have already argued that comp implies the falsity of physicalism 
(UDA), so?

BTW, you often quote wiki or other standard definition of math concept. 
But few are justifiable in the ultrafinitist realm, so many of your 
statements seems contradictory to me.

Bruno



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


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Re: Theory of Everything based on E8 by Garrett Lisi

[Quentin Anciaux]

Le Thursday 29 November 2007 19:28:05 Torgny Tholerus, vous avez écrit :
> 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 "no"set 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 
> has a 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.

And how this render the *set R* ]-infinity,infinity[ finite/limited or even 
the set N [0,infinity[ ?

If as you say you have elements/events/... after the last element/event/... it 
is totally contradictory and meaning less to call it last... If I take it as 
a demonstration by absurd, then you've just demonstrated that there exists no 
last element/event/... How can you avoid this contradiction ?

Regards,
Quentin Anciaux


-- 
All those moments will be lost in time, like tears in the rain.

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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]

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

[Bruno Marchal]

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

>
> 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.


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).

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.



Jesse wrote:

How would the set "omega-1" be defined? It doesn't make sense unless  
you believe in a "last finite ordinal", which of course a  
non-ultrafinitist will not believe in.

Actually this makes sense in what is called non standard model of  
arithmetic. In Peano Arithmetic you cannot define what is a finite  
number (the notion of finiteness is typically a second order notion).  
So it is consistent to add some "infinite numbers" in the model of PA.  
But you can prove in PA that any number, except zero, has a  
predecessor, so a non standard model of arithmetic can have infinite  
objects, but then also its predecessor, and all their successive  
predecessors. A non standard model will have the following order on it:

0 1 2 ... ... infinity-1  infinity  infinity+1    (and possibly  
other so called Z-chain).  Such order are NOT ordinals, note.

All this is not important now, but I say this in passing.


> 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).

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.
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. 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!).
But there are version of ZF without foundation, or even with diverse  
versions of the negation of the foundation axiom, like Stephen Paul  
King appreciates 

RE: Theory of Everything based on E8 by Garrett Lisi

[Jesse Mazer]

> Date: Fri, 30 Nov 2007 09:00:17 +0100
> From: [EMAIL PROTECTED]
> To: [EMAIL PROTECTED]
> Subject: Re: Theory of Everything based on E8 by Garrett Lisi
> 
> 
> 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?

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.

Jesse
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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

[John Mikes]

Marc, please, allow me to write in plain language - not using those
fancy words of these threads.
Some time ago when the discussion was in commonsensically more
understandable vocabulary, I questioned something similar
to Günther, as pertaining to "numbers" - the alleged generators of
'everything' (physical, quality, ideation, process, you name it).
As Bruno then said: the positive integers do that - if applied in
sufficiently long expressions. (please, Bruno, correct this to a
bottom-low simplification) - I did not follow that and was promised
some more explanatory text in "not so technical" language. The
discussion over the past some weeks is even "more technical" for me.
Is not the distinction relevant what I hold, that there are two kinds
of 'number'-usage: the (pure, theoretical Math and the in sciences -
(quantity related) - "applied math" - that uses the formalism (the
results, even logics) of 'Math' to exercise 'math'? (Cap vs lower m)

Geometry seems to be in between() and symmetry can be both, I think.

I am no physicist AND no mathematician, (not even a logician), so I
pretend to keep an objective eye on things in which I am not
prejudiced by knowledge. ().

John M



On Nov 27, 2007 11:40 PM,  <[EMAIL PROTECTED]> wrote:
>
>
>
> On Nov 28, 1:18 am, Günther Greindl <[EMAIL PROTECTED]>
> wrote:
> > Dear Marc,
> >
> > > Physics deals with symmetries, forces and fields.
> > > Mathematics deals with data types, relations and sets/categories.
> >
> > I'm no physicist, so please correct me but IMHO:
> >
> > Symmetries = relations
> > Forces - could they not be seen as certain invariances, thus also
> > relating to symmetries?
> >
> > Fields - the aggregate of forces on all spacetime "points" - do not see
> > why this should not be mathematical relation?
> >
> > > The mathemtical entities are informational.  The physical properties
> > > are geometric.  Geometric properties cannot be derived from
> > > informational properties.
> >
> > Why not? Do you have a counterexample?
> >
> > Regards,
> > Günther
> >
>
> Don't get me wrong.  I don't doubt that all physical things can be
> *described* by mathematics.  But this alone does not establish that
> physical things *are* mathematical.  As I understand it, for the
> examples you've given, what happens is that based on emprical
> observation, certain primatives of geometry and symmetry are *attached
> to* (connected with) mathematical relations, numbers etc which
> successfully *describe/predict* these physical properties.  But it
> does not follow from this, that the mathematical relations/numbers
> *are* the geometric properties/symmetrics.
>
> In order to show that the physical properties *are* the mathematical
> properties (and not just described by or connected to the physical
> properties), it has to be shown how geometric/physical properties
> emerge from/are logically derived from sets/categories/numbers alone.
>

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RE: Theory of Everything based on E8 by Garrett Lisi

[Jesse Mazer]

> Date: Thu, 29 Nov 2007 19:55:20 +0100
> From: [EMAIL PROTECTED]
> To: [EMAIL PROTECTED]
> Subject: Re: Theory of Everything based on E8 by Garrett Lisi
> 
> 
> 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...)

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.

> 
>>  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?)


I would just define the criterion recursively by saying "1 is a natural number, 
and given a natural number n, n+1 is also a natural number".

Jesse
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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]

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 "no"set 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  
has a 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

[Jesse Mazer]

> Date: Thu, 29 Nov 2007 18:25:54 +0100
> From: [EMAIL PROTECTED]
> To: [EMAIL PROTECTED]
> Subject: Re: Theory of Everything based on E8 by Garrett Lisi
> 
> 
> 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.


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"? 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).

> 
>>
>>   
>>> 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.


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?

Jesse
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Re: Theory of Everything based on E8 by Garrett Lisi

[Quentin Anciaux]

Le Thursday 29 November 2007 18:52:36 Torgny Tholerus, vous avez écrit :
> 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.

o_O

> >> 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 "no"set R ?
>
> How do you define "the set R"?

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

Choose your method...

Regards,
Quentin Anciaux
-- 
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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 "no"set R ?
>   

How do you define "the set R"?

-- 
Torgny

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Re: Theory of Everything based on E8 by Garrett Lisi

[Quentin Anciaux]

Le Thursday 29 November 2007 18:25:54 Torgny Tholerus, vous avez écrit :
> 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.  

Ok then the set R is also 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.

What is the production rules of the "no"set R ?

> >> 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.  

I don't get it.

> 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.

I don't accept and/or don't understand.

> >> 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.

There exists no last element in the set N.

> >> 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...   :-)

What you are saying seems like to me "So the best thing is to avoid words at 
all (and any languages)"... 

Regards,
Quentin Anciaux


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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

[Quentin Anciaux]

Le Thursday 29 November 2007 17:22:59 Torgny Tholerus, vous avez écrit :
> 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.

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".


> 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.

> 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 ?

> 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 ?

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

like everything ?

Regards,
Quentin Anciaux

-- 
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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

[marc . geddes]

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.
>
> --
> Torgny

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.  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.  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.

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.
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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

[Bruno Marchal]

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

> [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.


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?


Bruno



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

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Re: Theory of Everything based on E8 by Garrett Lisi

[Bruno Marchal]

Le 28-nov.-07, à 05:48, [EMAIL PROTECTED] a écrit :

>
>
>
> On Nov 28, 3:16 am, Bruno Marchal <[EMAIL PROTECTED]> wrote:
>> Le 27-nov.-07, à 05:47, [EMAIL PROTECTED] a écrit :
>>
>>> Geometric properties cannot be derived from
>>> informational properties.
>>
>> I don't see why. Above all, this would make the computationalist 
>> wrong,
>> or at least some step in the UDA wrong (but then which one?).
>
> I'll find the flaw in UDA in due course ;)


Thanks.






>
>> I recall that there is an argument (UDA) showing that if comp is true,
>> then not only geometry, but physics, has to be derived exclusively 
>> from
>> numbers and from what numbers can prove (and know, and observe, and
>> bet, ...) about themselves, that is from both extensional and
>> intensional number theory.
>> The UDA shows *why* physics *has to* be derived from numbers (assuming
>> CT + "yes doctor").
>> The Lobian interview explains (or should explain, if you have not yet
>> grasp the point) *how* to do that.
>>
>> Bruno
>>
>
> If the UDA is sound that would certainly refute what I'm claiming
> yes.
> I want to see how physics (which as far I'm concerned *is*
> geometry - at least I think pure physics=geometry) emerges *purely*
> from theories of sets/numbers/categories.

OK. Note that UDA says only why, not how.
"how" is given by the lobian interview, and gives only the 
"propositional physics" (as part
of the propositional "theology").


>
> I base my claims on ontological considerations (5 years of deep
> thought about ontology), which lead me to strongly suspect the
> irreducible property dualism between physical and mathematical
> properties.  Thus I'm highly skeptical of UDA but have yet to property
> study it.  Lacking resources to do proper study here at the
> moment :-(

We are in the same boat ...

Bruno

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


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Re: Theory of Everything based on E8 by Garrett Lisi

[Quentin Anciaux]

Hi,

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

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

Also why do you limit yourself to one computational model ? Turing Machine, 
Lambda calcul, cellular automata are all equivalents.

Regards,
Quentin Anciaux


-- 
All those moments will be lost in time, like tears in the rain.

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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

[marc . geddes]

On Nov 28, 3:16 am, Bruno Marchal <[EMAIL PROTECTED]> wrote:
> Le 27-nov.-07, à 05:47, [EMAIL PROTECTED] a écrit :
>
> > Geometric properties cannot be derived from
> > informational properties.
>
> I don't see why. Above all, this would make the computationalist wrong,
> or at least some step in the UDA wrong (but then which one?).

I'll find the flaw in UDA in due course ;)

> I recall that there is an argument (UDA) showing that if comp is true,
> then not only geometry, but physics, has to be derived exclusively from
> numbers and from what numbers can prove (and know, and observe, and
> bet, ...) about themselves, that is from both extensional and
> intensional number theory.
> The UDA shows *why* physics *has to* be derived from numbers (assuming
> CT + "yes doctor").
> The Lobian interview explains (or should explain, if you have not yet
> grasp the point) *how* to do that.
>
> Bruno
>

If the UDA is sound that would certainly refute what I'm claiming
yes.  I want to see how physics (which as far I'm concerned *is*
geometry - at least I think pure physics=geometry) emerges *purely*
from theories of sets/numbers/categories.

I base my claims on ontological considerations (5 years of deep
thought about ontology), which lead me to strongly suspect the
irreducible property dualism between physical and mathematical
properties.  Thus I'm highly skeptical of UDA but have yet to property
study it.  Lacking resources to do proper study here at the
moment :-(

Time will tell.
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Re: Theory of Everything based on E8 by Garrett Lisi

[marc . geddes]

On Nov 28, 1:18 am, Günther Greindl <[EMAIL PROTECTED]>
wrote:
> Dear Marc,
>
> > Physics deals with symmetries, forces and fields.
> > Mathematics deals with data types, relations and sets/categories.
>
> I'm no physicist, so please correct me but IMHO:
>
> Symmetries = relations
> Forces - could they not be seen as certain invariances, thus also
> relating to symmetries?
>
> Fields - the aggregate of forces on all spacetime "points" - do not see
> why this should not be mathematical relation?
>
> > The mathemtical entities are informational.  The physical properties
> > are geometric.  Geometric properties cannot be derived from
> > informational properties.
>
> Why not? Do you have a counterexample?
>
> Regards,
> Günther
>

Don't get me wrong.  I don't doubt that all physical things can be
*described* by mathematics.  But this alone does not establish that
physical things *are* mathematical.  As I understand it, for the
examples you've given, what happens is that based on emprical
observation, certain primatives of geometry and symmetry are *attached
to* (connected with) mathematical relations, numbers etc which
successfully *describe/predict* these physical properties.  But it
does not follow from this, that the mathematical relations/numbers
*are* the geometric properties/symmetrics.

In order to show that the physical properties *are* the mathematical
properties (and not just described by or connected to the physical
properties), it has to be shown how geometric/physical properties
emerge from/are logically derived from sets/categories/numbers alone.
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Re: Theory of Everything based on E8 by Garrett Lisi

[Bruno Marchal]

Le 27-nov.-07, à 05:47, [EMAIL PROTECTED] a écrit :


> Geometric properties cannot be derived from
> informational properties.


I don't see why. Above all, this would make the computationalist wrong, 
or at least some step in the UDA wrong (but then which one?).
I recall that there is an argument (UDA) showing that if comp is true, 
then not only geometry, but physics, has to be derived exclusively from 
numbers and from what numbers can prove (and know, and observe, and 
bet, ...) about themselves, that is from both extensional and 
intensional number theory.
The UDA shows *why* physics *has to* be derived from numbers (assuming 
CT + "yes doctor").
The Lobian interview explains (or should explain, if you have not yet 
grasp the point) *how* to do that.


Bruno



>
>
>
> On Nov 27, 3:54 am, Bruno Marchal <[EMAIL PROTECTED]> wrote:
>
>>
>>> 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.
>>
>> I don't see why.
>
> Physics deals with symmetries, forces and fields.
> Mathematics deals with data types, relations and sets/categories.
>
> The mathemtical entities are informational.  The physical properties
> are geometric.  Geometric properties cannot be derived from
> informational properties.
>
>
>
>>
>>
>>
>>> Mathematics deals with logical properties,
>>
>> I guess you mean "mathematical properties". Since the filure of
>> logicism, we know that math is not really related to logic in any way.
>> It just happens that a big part of logic appears to be a branch of
>> mathemetics, among many other branches.
>
> I would classify logic as part of applied math - logic is a
> description of informational systems from the point of view of
> observers inside time and space.
>
>>
>>> physics deals with spatial
>>> (geometric) properties.  Although geometry is thought of as math, it
>>> is actually a branch of physics,
>>
>> Actually I do think so. but physics, with comp, has to be the science
>> of what the observer can observe, and the observer is a mathematical
>> object, and observation is a mathematical object too (with comp).
>
>
>>
>>> since in addition to pure logical
>>> axioms, all geometry involves 'extra' assumptions or axioms which are
>>> actually *physical* in nature (not purely mathematical) .
>>
>> Here I disagree (so I agree with your preceding post where you agree
>> that we agree a lot but for not always for identical reasons).
>> Arithmetic too need extra (non logical) axioms, and it is a matter of
>> taste (eventually) to put them in the branch of physics or math.
>>
>> Bruno
>>
>
> I don't think it's a matter of taste.  I think geoemtry is clearly
> physics, arithmetic is clearly pure math.  See above.  Geometry is
> about fields, arithmetic (in the most general sense) is about
> categories/sets.
>
>
> >
>
http://iridia.ulb.ac.be/~marchal/


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Re: Theory of Everything based on E8 by Garrett Lisi

[Günther Greindl]

Dear Marc,

> Physics deals with symmetries, forces and fields.
> Mathematics deals with data types, relations and sets/categories.

I'm no physicist, so please correct me but IMHO:

Symmetries = relations
Forces - could they not be seen as certain invariances, thus also 
relating to symmetries?

Fields - the aggregate of forces on all spacetime "points" - do not see 
why this should not be mathematical relation?

> The mathemtical entities are informational.  The physical properties
> are geometric.  Geometric properties cannot be derived from
> informational properties.

Why not? Do you have a counterexample?

Regards,
Günther



-- 
Günther Greindl
Department of Philosophy of Science
University of Vienna
[EMAIL PROTECTED]
http://www.univie.ac.at/Wissenschaftstheorie/

Blog: http://dao.complexitystudies.org/
Site: http://www.complexitystudies.org

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Re: Theory of Everything based on E8 by Garrett Lisi

[marc . geddes]

On Nov 27, 3:54 am, Bruno Marchal <[EMAIL PROTECTED]> wrote:

>
> > 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.
>
> I don't see why.

Physics deals with symmetries, forces and fields.
Mathematics deals with data types, relations and sets/categories.

The mathemtical entities are informational.  The physical properties
are geometric.  Geometric properties cannot be derived from
informational properties.



>
>
>
> > Mathematics deals with logical properties,
>
> I guess you mean "mathematical properties". Since the filure of
> logicism, we know that math is not really related to logic in any way.
> It just happens that a big part of logic appears to be a branch of
> mathemetics, among many other branches.

I would classify logic as part of applied math - logic is a
description of informational systems from the point of view of
observers inside time and space.

>
> > physics deals with spatial
> > (geometric) properties.  Although geometry is thought of as math, it
> > is actually a branch of physics,
>
> Actually I do think so. but physics, with comp, has to be the science
> of what the observer can observe, and the observer is a mathematical
> object, and observation is a mathematical object too (with comp).


>
> > since in addition to pure logical
> > axioms, all geometry involves 'extra' assumptions or axioms which are
> > actually *physical* in nature (not purely mathematical) .
>
> Here I disagree (so I agree with your preceding post where you agree
> that we agree a lot but for not always for identical reasons).
> Arithmetic too need extra (non logical) axioms, and it is a matter of
> taste (eventually) to put them in the branch of physics or math.
>
> Bruno
>

I don't think it's a matter of taste.  I think geoemtry is clearly
physics, arithmetic is clearly pure math.  See above.  Geometry is
about fields, arithmetic (in the most general sense) is about
categories/sets.


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Re: Theory of Everything based on E8 by Garrett Lisi

[marc . geddes]

>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.




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Re: Theory of Everything based on E8 by Garrett Lisi

[Russell Standish]

Could we have a stop to HTML-only postings please! These are hard to read.

On Mon, Nov 26, 2007 at 10:51:36AM +0100, Torgny Tholerus wrote:

-- 


A/Prof Russell Standish  Phone 0425 253119 (mobile)
Mathematics  
UNSW SYDNEY 2052 [EMAIL PROTECTED]
Australiahttp://www.hpcoders.com.au


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Re: Theory of Everything based on E8 by Garrett Lisi

[John Mikes]

Listers, (Bruno, Torgny, et al.):

some (lay) remarks from another mindset (maybe I completely miss your
points - perhaps even my own ones).
I go with Bruno in a lack of clear understanding what "physical world"
may be. It can be extended into entirely mathematical ideas beside the
likable assumption of it being 'geometrical '  as well as geometry
'completely physical'. I don't see these terms agreed upon as crystal
clearly (maybe my ignorance).
*
Then again "pure"(?) Math, the logical entirety, is in my views
different from the "applied"(?) math of the diverse sciences,
(please note the cap vs lower case distinction, as borrowed from the
late mathematician Robert Rosen)  the latter applying the former's
results to quantities. (I don't want to digress here into my views
about the restricted (topical) aspects of those sciences, omitting the
rest of the totality that, however, may have an effect of those
figments derived as 'scientific quantities' within their boundaries.
It may come up in a separate (different) thread).
To (I think) Torgny's remark
 "> > reality and hence everything could not be expressed solely in
terms of physical substance and properties.<<"  I would add:
also depends on a possible extension of the meaning 'physical'.
*
Then there is the reference to 'axioms'. These "true" postulates are
formed AFTER a theory was thought through to maintain the validity of
that theory. So I don't consider them "proof", rather as a consequence
for the statement it is supposed to underlie.
I believe these are Bruno's (supporting?) words:
> Arithmetic too need extra (non logical) axioms, and it is a matter of taste 
> (eventually) to put them in the branch of physics or math.<
*
Please, excuse my 'out-of-context' remarks, I wanted to illustrate a
different line of thoughts - also generated in a "human" mind.

John M



On Nov 26, 2007 9:54 AM, Bruno Marchal <[EMAIL PROTECTED]> wrote:
>
>
> Le 26-nov.-07, à 04:17, [EMAIL PROTECTED] a écrit :
>
> >
> >
> >
> > On Nov 23, 8:49 pm, Torgny Tholerus <[EMAIL PROTECTED]> wrote:
> >> [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...
> >
> > 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.
>
>
> Are you not begging a bit the question here?
>
>
>
> >
> > 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.
>
>
> I don't see why.
>
>
>
> >
> > Mathematics deals with logical properties,
>
> I guess you mean "mathematical properties". Since the filure of
> logicism, we know that math is not really related to logic in any way.
> It just happens that a big part of logic appears to be a branch of
> mathemetics, among many other branches.
>
>
> > physics deals with spatial
> > (geometric) properties.  Although geometry is thought of as math, it
> > is actually a branch of physics,
>
> Actually I do think so. but physics, with comp, has to be the science
> of what the observer can observe, and the observer is a mathematical
> object, and observation is a mathematical object too (with comp).
>
>
>
> > since in addition to pure logical
> > axioms, all geometry involves 'extra' assumptions or axioms which are
> > actually *physical* in nature (not purely mathematical) .
>
> Here I disagree (so I agree with your preceding post where you agree
> that we agree a lot but for not always for identical reasons).
> Arithmetic too need extra (non logical) axioms, and it is a matter of
> taste (eventually) to put them in the branch of physics or math.
>
> Bruno
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
> >
>

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Re: Theory of Everything based on E8 by Garrett Lisi

[Bruno Marchal]

Le 26-nov.-07, à 04:17, [EMAIL PROTECTED] a écrit :

>
>
>
> On Nov 23, 8:49 pm, Torgny Tholerus <[EMAIL PROTECTED]> wrote:
>> [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...
>
> 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.


Are you not begging a bit the question here?



>
> 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.


I don't see why.



>
> Mathematics deals with logical properties,

I guess you mean "mathematical properties". Since the filure of 
logicism, we know that math is not really related to logic in any way. 
It just happens that a big part of logic appears to be a branch of 
mathemetics, among many other branches.


> physics deals with spatial
> (geometric) properties.  Although geometry is thought of as math, it
> is actually a branch of physics,

Actually I do think so. but physics, with comp, has to be the science 
of what the observer can observe, and the observer is a mathematical 
object, and observation is a mathematical object too (with comp).



> since in addition to pure logical
> axioms, all geometry involves 'extra' assumptions or axioms which are
> actually *physical* in nature (not purely mathematical) .

Here I disagree (so I agree with your preceding post where you agree 
that we agree a lot but for not always for identical reasons).
Arithmetic too need extra (non logical) axioms, and it is a matter of 
taste (eventually) to put them in the branch of physics or math.

Bruno

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


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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]

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

[marc . geddes]

On Nov 23, 8:49 pm, Torgny Tholerus <[EMAIL PROTECTED]> wrote:
> [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...

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) .


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RE: Theory of Everything based on E8 by Garrett Lisi

[rafael jimenez buendia]

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

> Date: Thu, 22 Nov 2007 18:30:03 -0800> Subject: Re: Theory of Everything 
> based on E8 by Garrett Lisi> From: [EMAIL PROTECTED]> To: [EMAIL PROTECTED]> 
> > > > > On Nov 23, 1:10 am, Bruno Marchal <[EMAIL PROTECTED]> wrote:> > >> > 
> Now such work raises the remark, which I don't really want to develop> > now, 
> which is that qualifiying "TOE" a theory explaining "only" forces> > and 
> particles or field, is implicit physicalism, and we know (by UDA)> > that 
> this is incompatible with comp.> > Yes indeed Bruno. 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. Thus we both are in agreement on this, 
> but> for different reasons (you because, you think math is the ultimate> 
> basis of everything aka COMP, me, because of my property dualism, aka> the 
> need for a triple-aspect explanation of physical/teleological/> mathematical 
> properties as the basis for everything).> > We keep telling mainstream 
> scients, but mainstream scients are not> listening to us. *sigh*.> > > Yet I 
> bet Lisi is quite close to the sort of physics derivable by> > machine's or 
> number's introspection. Actually, getting physics from so> > "few" symmetries 
> is a bit weird (I have to study the paper in detail).> > With comp, we have 
> to explain the symmetries *and* the geometry, and> > the quantum logic, from 
> the numbers and their possible stable> > discourses ... If not, it is not a 
> theory of everything, but just a> > classification, a bit like the Mendeleev 
> table classifies atoms without> > really explaining. But Lisi's theory seems 
> beautiful indeed ...> >> > Bruno> >> > > There's too many people mucking 
> around with physics - I do wish more> people were working on computer 
> science. Physics is the most advanced> of our sciences, but computer science 
> lags behind. It just seems to> be an unfortunate historical accident that 
> physical theories developed> first and then lots of social status got 
> attached to theoretical> physics (stemming from the glorification of Newton 
> in Europe).> > As a result, physics has advanced well ahead of comp-sci, and 
> there's> lots of money and status attached to physics breakthroughs. But 
> comp-> sci is actually far more important to us in practical sense -> 
> artificial general intelligence would be way way more valuable than> any 
> fundamental physics breakthrough. We would have had real AGI long> ago if 
> there was the same money and glory for comp-sci as there is for> physics 
> *sigh*.> > > > > 
> _
Tecnología, moda, motor, viajes,…suscríbete a nuestros boletines para estar a 
la última
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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: Theory of Everything based on E8 by Garrett Lisi

[marc . geddes]

On Nov 23, 1:10 am, Bruno Marchal <[EMAIL PROTECTED]> wrote:

>
> Now such work raises the remark, which I don't really want to develop
> now, which is that qualifiying "TOE" a theory explaining "only" forces
> and particles or field, is implicit physicalism, and we know (by UDA)
> that this is incompatible with comp.

Yes indeed Bruno.  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.  Thus we both are in agreement on this, but
for different reasons (you because, you think math is the ultimate
basis of everything aka COMP, me, because of my property dualism, aka
the need for a triple-aspect explanation of physical/teleological/
mathematical properties as the basis for everything).

We keep telling mainstream scients, but mainstream scients are not
listening to us.  *sigh*.

> Yet I bet Lisi is quite close to the sort of physics derivable by
> machine's or number's introspection. Actually, getting physics from so
> "few" symmetries is a bit weird (I have to study the paper in detail).
> With comp, we have to explain the symmetries *and* the geometry, and
> the quantum logic, from the numbers and their possible stable
> discourses ... If not, it is not a theory of everything, but just a
> classification, a bit like the Mendeleev table classifies atoms without
> really explaining. But Lisi's theory seems beautiful indeed ...
>
> Bruno
>


There's too many people mucking around with physics - I do wish more
people were working on computer science.  Physics is the most advanced
of our sciences, but computer science lags behind.  It just seems to
be an unfortunate historical accident that physical theories developed
first and then  lots of social status got attached to theoretical
physics (stemming from the glorification of Newton in Europe).

As a result, physics has advanced well ahead of comp-sci, and there's
lots of money and status attached to physics breakthroughs.  But comp-
sci is actually far more important to us in practical sense -
artificial general intelligence would be way way more valuable than
any fundamental physics breakthrough.  We would have had real AGI long
ago if there was the same money and glory for comp-sci as there is for
physics *sigh*.




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Re: Theory of Everything based on E8 by Garrett Lisi

[Bruno Marchal]

Le 21-nov.-07, à 19:54, George Levy a écrit :


>  A theory of everyting is sweeping the Physics community.
>
>
>  The theory by Garrett Lisi is explained in this Wiki entry.
>
>
>  A simulation of E8 can be found a the New Scientist.
>
>
>  The Wiki entry on E8 is also interesting.


Thanks, very interesting indeed. Note that the original paper is 
accessible from the  New Scientist entry. Not so easy to read (need of 
differential geometry, simple groups, etc.
Quite close to the idea of the importance of 24 which I mention 
periodically ... :)

Now such work raises the remark, which I don't really want to develop 
now, which is that qualifiying "TOE" a theory explaining "only" forces 
and particles or field, is implicit physicalism, and we know (by UDA) 
that this is incompatible with comp.

Yet I bet Lisi is quite close to the sort of physics derivable by 
machine's or number's introspection. Actually, getting physics from so 
"few" symmetries is a bit weird (I have to study the paper in detail). 
With comp, we have to explain the symmetries *and* the geometry, and 
the quantum logic, from the numbers and their possible stable 
discourses ... If not, it is not a theory of everything, but just a 
classification, a bit like the Mendeleev table classifies atoms without 
really explaining. But Lisi's theory seems beautiful indeed ...

Bruno


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

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