Fw: the world as mathematical. was pythagoras right after all ?

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Roger Clough

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Dec 24, 2012, 11:49:42 AM12/24/12
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My idea below is no doubt off-base, but
suggests the following idea.

As I understand quantum mechanics, it
uses only quantum (mathematical) fields,
so, at least as far as I can understand, the
physical (not the mental) universe is
a mathematical construction (perhaps of
strings in quantum form).

[Roger Clough], [rcl...@verizon.net]
12/24/2012
"Forever is a long time, especially near the end." -Woody Allen

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From: Roger Clough
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Time: 2012-12-24, 09:35:00
Subject: Arithmetic as true constructions of a fictional leggo set


Hi Bruno Marchal

It helps me if I can understand arithmetic as true
constructions of a fictional leggo set.

From what you say, the natural numbers and + and * (nn+*).
are not a priori members of Platonia (if indeed that makes
sense anyway). They can simply be invoked and used
as needed, as long as they don't produce contradictions.
That being the case, don't you need to add =, - , and
/ to the Leggo set ? Then we have (nn+-*/=).

I wonder if somebody could derive string theory from this set.
Then we might say that the universe is an arithmetic construction.
Probably an absurd idea.



[Roger Clough], [rcl...@verizon.net]
12/24/2012
"Forever is a long time, especially near the end." -Woody Allen

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From: Bruno Marchal
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Time: 2012-12-23, 09:17:09
Subject: Re: Can the physical brain possibly store our memories ? No.




On 22 Dec 2012, at 17:05, Telmo Menezes wrote:




Hi Bruno,

On Thu, Dec 20, 2012 at 1:01 PM, Roger Clough wrote:



> The infinite set of natural numbers is not stored on anything,


Which causes no problem because there is not a infinite number of anything in the observable universe, probably not even points in space.



Perhaps, we don't know.
It causes no problem because natural numbers does not have to be stored a priori. Only when universal machine want to use them.




Why do the natural numbers exist?




We cannot know that.


Precisely, if you assume the natural numbers, you can prove that you cannot derived the existence of the natural number and their + and * laws, in *any* theory which does not assume them, or does not assume something equivalent.


That is why it is a good reason to start with them (or equivalent).


Somehow, the natural numbers, with addition and multiplication, are necessarily "mysterious".


With the natural numbers and + and *, you can prove the existence of all universal machines, and vice versa, if you assume any other universal system (like the combinators K, S (K K), (K S), ...) you can prove the existence of the natural numbers and their laws.


We have to assume at least one universal system, and I chose arithmetic because it is the simpler one. The problem is that the proof of its universality will be difficult, but at least it can be found in good mathematical logic textbook, like Mendelson or Kleene, etc.


Bruno










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Richard Ruquist

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Dec 24, 2012, 12:07:36 PM12/24/12
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Roger,

Quantum mechanics is not physical nor is string theory.
How the physical world comes from the quantum world is a matter of
conjecture called interpretations.
Richard

Brian Tenneson

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Dec 24, 2012, 1:11:46 PM12/24/12
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What do you think of Tegmark's version of a mathematical Platoia?

meekerdb

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Dec 24, 2012, 3:05:14 PM12/24/12
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On 12/24/2012 9:07 AM, Richard Ruquist wrote:
Roger,

Quantum mechanics is not physical nor is string theory.
How the physical world comes from the quantum world is a matter of
conjecture called interpretations.
Richard

On Mon, Dec 24, 2012 at 11:49 AM, Roger Clough <rcl...@verizon.net> wrote:
> My idea below is no doubt off-base, but
> suggests the following idea.
>
> As I understand quantum mechanics, it
> uses only quantum (mathematical) fields,
> so, at least as far as I can understand, the
> physical (not the mental) universe is
> a mathematical construction (perhaps of
> strings in quantum form).

QM is a mathematical *description*, or more accurately a schema for a description. Don't take the map to be the territory.

Brent

Roger Clough

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Dec 25, 2012, 4:00:40 AM12/25/12
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Hi Richard Ruquist
 
Read what I said below again. I never said that the quantum
world is physical, quite the reverse.
 
Not to worry, I have made similar mistakes,
especially my inverted interpretation of the gini
index.
 
 
[Roger Clough], [rcl...@verizon.net]
12/25/2012
"Forever is a long time, especially near the end." -Woody Allen
 
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Roger Clough

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Dec 25, 2012, 9:34:45 AM12/25/12
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Hi Brian Tenneson
 
Tegmark has many many good ideas, but I am not a believer in multiverses,
which only a strict mechanistic 19th century type can believe. 
 
Multiverses defy reason. Just off the top of head:
 
1) For one reason because of Occam's razor: it is a needless complication,
and the universe (or its Creator) does not do needless things,
because IMHO the universe is purposeful. 
 
2) "Purposeful" meaning that Aristotle's end causes are needed for a
final collapse, as they are for life, which is not mechanistic.
 
3) As in life/mind/consciousness/intelligence, which  are also purposeful. 
 
4) In order for there to be multiple universes, there would
have to be multiple platonic Ones. But there can only be one One.
 
5) Multiverses are mechanistic and so in spacetime, but consciouss life
and all that other good stuff are outside of spacetime.  Would the
minds of multiverses be mashed together ?  And all particular lifes
would have to terminate at the same time.
 
6) There is no non-Boltzmann physics which is required for a final collapse.
Time has to begin to travel backwards as things reorganize,
in which case the final collapse should be a reflection of the initial creation.
That would be cool.
 
7) But each universes being differemnt, they would not be expected to
all terminate at the same time.
 
8) One might conjecture also that the presence of life, consciousness and
intelligence (which are all individual, personal, subjective) are not
mechanical and so cannot be part of a multiverse. It's each man
for himself.  Along these lines, because of natural selection and
different worlds not being all the same, evolution would not occur
in parallel.
 
9) Besides, there are alternate possibilities for a quantum wave collapse.
 
10) In a related matter, one of the multiverse sites cited William James
as a proponent. Because of his pragmatism, his multiverses arise
because there is no fixed general in pragmatism for each particular.
There are as many generals (additional universes) as you can think of.
These obviously would not be parallel.
 
[Roger Clough], [rcl...@verizon.net]
12/25/2012
"Forever is a long time, especially near the end." -Woody Allen
 
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Subject: Re: Fw: the world as mathematical. was pythagoras right after all ?

What do you think of Tegmark's version of a mathematical Platoia?

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Roger Clough

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Dec 25, 2012, 9:49:10 AM12/25/12
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Hi meekerdb
 
My description turns out to be essentially the same as Tegmark's,
namely that the world is mathematical at base.
 
Google that name to see.
 
 
[Roger Clough], [rcl...@verizon.net]
12/25/2012
"Forever is a long time, especially near the end." -Woody Allen
 
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Subject: Re: Fw: the world as mathematical. was pythagoras right after all ?

Brian Tenneson

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Dec 25, 2012, 1:35:56 PM12/25/12
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At least in the video (skip to 43:14), Tegmark estimates that our doppelgangers are 2^10^118 meters away which probably puts it past the range of direct testing and, consequently, makes it not falsifiable.

Regarding (4), I think the disparity between you and Tegmark can be explained by having different definitions of universe and multiverse.  Of course, if you have a metauniverse, then you'd have a metametauniverse, ad infinitum.  There is only one "totality of all that exists" and I bet that if you were to explain what you mean by the One to him, he would agree that there is only one One.  When he uses an aphorism like "multiverse" he may as well be saying "poly mega galaxy cluster" or some such.  In other words I don't think Tegmark believes in multiple Ones.

In his mathematical universe paper and ultimate ensemble paper, he posits that there is only one type of existence which would simplify things (a la Occam's razor).  Instead of there being mathematical and physical existence, there is an identification between the two so they are seen to be one in the same.  This merges the spaces "mathematical objects" with "physical objects".  He argues this in those papers (though to me sometimes it seems to be merely a plausibility argument).

Now if ME=PE, then one natural question is which mathematical structure is "the totality of all that exists" isomorphic to?  In other words, what is the One?  What is the universe? Or to abuse language a bit, what is the multiverse?  This is a question that I've been thinking about for a while now and I'm really not sure.  The current idea is to take the category of all mathematical structures C (which is large, unfortunately), and embed that into a category of functors defined on that category (a la Yoneda's lemma), in such a way that every mathematical structure is embedded within that category of functors (called a "cocompletion" of C), a sort of "presheaf" category.  To have a single mathematical object that all mathematical structures can be embedded would give us an object that, in a sense, contains all structures.  If one follows Tegmark's idea that ME=PE, then a definition for universe just might be a mathematical object (which by ME=PE is a physical object) that contains, in a sense, all mathematical objects (i.e., all physical objects).  It's not super clear to me that the cocompletion of the category of all structures C exists though since C is not a small category and thus Yoneda's lemma doesn't apply.  I would have to fine-tune the argument to work in the case of the category C I have in mind.

If the cocompletion of C is the One, that which all mathematical structures can be embedded, then the parallel universe question would be a matter of logic and category theory; it would depend on how you defined "the visible universe" and "parallel" universe.

Richard Ruquist

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Dec 25, 2012, 3:46:47 PM12/25/12
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But you did imply that string theory was physical. Not true.
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Bruno Marchal

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Dec 26, 2012, 5:03:19 AM12/26/12
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On 24 Dec 2012, at 19:11, Brian Tenneson wrote:

What do you think of Tegmark's version of a mathematical Platoia?

Too much naive, and too much big. Then Tegmark ignore the fact that we are distributed in it, in a way which force the consciousness/matter relation to be in need to be derived from a very simple ontology (the sigma_1 arithmetical truth).
Tegmark is a physicist closer than others with respect to the computationalist hypothesis, but, despite his mathematicalism, consciousness, and the origin of the "matter stable illusion" is still under the rug.

Bruno





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Bruno Marchal

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Dec 26, 2012, 5:30:24 AM12/26/12
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On 25 Dec 2012, at 15:34, Roger Clough wrote:

Hi Brian Tenneson
 
Tegmark has many many good ideas, but I am not a believer in multiverses,
which only a strict mechanistic 19th century type can believe. 
 
Multiverses defy reason. Just off the top of head:
 
1) For one reason because of Occam's razor: it is a needless complication,
and the universe (or its Creator) does not do needless things,
because IMHO the universe is purposeful. 

I disagree. The multiverse is just the literal reading of the SWE. To get 1 universe from the SWE you need to add a complication in the form of a collapse or a reduction principle. Occam asks us to chose the simpler theory, not the simpler ontology.
Note that with comp we get both. The theory is the laws of + and *, and the ontology is the standard model of arithmetic: (N, +, *). 
But then in the 1p plural and singular we get the many dreams from which multiverses or quasi-multiverses emerge.





 
2) "Purposeful" meaning that Aristotle's end causes are needed for a
final collapse, as they are for life, which is not mechanistic.
 
3) As in life/mind/consciousness/intelligence, which  are also purposeful. 
 
4) In order for there to be multiple universes, there would
have to be multiple platonic Ones. But there can only be one One.


Not really. The ONE is "known" to let the multiple emanates from "him/her/it". 
The one remains one, but from inside and/or machine's epistemology you get the many internal views.



 
5) Multiverses are mechanistic and so in spacetime, but consciouss life
and all that other good stuff are outside of spacetime.  Would the
minds of multiverses be mashed together ?  And all particular lifes
would have to terminate at the same time.
 
6) There is no non-Boltzmann physics which is required for a final collapse.
Time has to begin to travel backwards as things reorganize,
in which case the final collapse should be a reflection of the initial creation.
That would be cool.
 
7) But each universes being differemnt, they would not be expected to
all terminate at the same time.
 
8) One might conjecture also that the presence of life, consciousness and
intelligence (which are all individual, personal, subjective) are not
mechanical and so cannot be part of a multiverse. It's each man
for himself.  Along these lines, because of natural selection and
different worlds not being all the same, evolution would not occur
in parallel.
 
9) Besides, there are alternate possibilities for a quantum wave collapse.

I have not yet find one, and besides, this would contradict the comp hypothesis.



 
10) In a related matter, one of the multiverse sites cited William James
as a proponent. Because of his pragmatism, his multiverses arise
because there is no fixed general in pragmatism for each particular.
There are as many generals (additional universes) as you can think of.
These obviously would not be parallel.

Parallel worlds are not really parallel. It is only a manner of speaking. 
The "real" structure is still unknown and is plausibly rather complex.

Bruno



 
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12/25/2012
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Subject: Re: Fw: the world as mathematical. was pythagoras right after all ?

What do you think of Tegmark's version of a mathematical Platoia?

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Roger Clough

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Dec 26, 2012, 9:53:47 AM12/26/12
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ROGER: Hi Brian Tenneson

BRIAN: At least in the video (skip to 43:14), Tegmark estimates that our doppelgangers
are 2^10^118 meters away which probably puts it past the range of direct testing and, consequently,
makes it not falsifiable.
 
ROGER: Things not falsifiable need not be true. And things that are true need not be falsifiable
if they are not always true (such as Popper is alive-- I think he died). His criteria do not hold water.

BRIAN: Regarding (4), I think the disparity between you and Tegmark can be explained by having different definitions
of universe and multiverse. Of course, if you have a metauniverse, then you'd have a metametauniverse, ad infinitum.
 
There is only one "totality of all that exists" and I bet that if you were to explain what you mean by the One to him,
he would agree that there is only one One. When he uses an aphorism like "multiverse" he may as well be saying
"poly mega galaxy cluster" or some such. In other words I don't think Tegmark believes in multiple Ones.
In his mathematical universe paper and ultimate ensemble paper, he posits that there is only one type of existence
which would simplify things (a la Occam's razor). Instead of there being mathematical and physical existence, there
is an identification between the two so they are seen to be one in the same. This merges the spaces "mathematical objects"
with "physical objects". He argues this in those papers (though to me sometimes it seems to be merely a plausibility argument).
ROGER: Tegmark is wrong there. According to Descartes, there are TWO types of existence, physical and mental.
He defined physical existence as whatever is present in spacetime (that has extension in space).
Mental existence has no extension in space. The One and indeed mathematics itself are not extended in space,
and so are not physical. They exist in a completely different way (as Mind). They have no physical borders
or location so that one cannot be sure if one has the physical "Totality".  
 
The rest that you discuss below then has meaning only to a materialist.
Materialists don't follow Descartes so that IMHO their philosophy is bad science, it is a cult.
 
 
BRIAN: Now if ME=PE, then one natural question is which mathematical structure is "the totality of all that exists" isomorphic to? In other words, what is the One? What is the universe? Or to abuse language a bit, what is the multiverse? This is a question that I've been thinking about for a while now and I'm really not sure. The current idea is to take the category of all mathematical structures C (which is large, unfortunately), and embed that into a category of functors defined on that category (a la Yoneda's lemma), in such a way that every mathematical structure is embedded within that category of functors (called a "cocompletion" of C), a sort of "presheaf" category. To have a single mathematical object that all mathematical structures can be embedded would give us an object that, in a sense, contains all structures. If one follows Tegmark's idea that ME=PE, then a definition for universe just might be a mathematical object (which by ME=PE is a physical object) that contains, in a sense, all mathematical objects (i.e., all physical objects). It's not super clear to me that the cocompletion of the category of all structures C exists though since C is not a small category and thus Yoneda's lemma doesn't apply. I would have to fine-tune the argument to work in the case of the category C I have in mind.
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Roger Clough

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Dec 26, 2012, 10:17:11 AM12/26/12
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Hi Bruno Marchal

It all boils down to this: is something that is mathematically true necessarily physically true ?
This question can be restated as "are mathematical truth and pragmatic truth
the same ?" IMHO No, because theory can be wrong but what works works.


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12/26/2012
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Subject: Re: Ten top-of-my-head arguments against multiverses

Bruno Marchal

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Dec 26, 2012, 12:13:10 PM12/26/12
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On 25 Dec 2012, at 19:35, Brian Tenneson wrote:

At least in the video (skip to 43:14), Tegmark estimates that our doppelgangers are 2^10^118 meters away which probably puts it past the range of direct testing and, consequently, makes it not falsifiable.

Regarding (4), I think the disparity between you and Tegmark can be explained by having different definitions of universe and multiverse.  Of course, if you have a metauniverse, then you'd have a metametauniverse, ad infinitum.  There is only one "totality of all that exists" and I bet that if you were to explain what you mean by the One to him, he would agree that there is only one One.  When he uses an aphorism like "multiverse" he may as well be saying "poly mega galaxy cluster" or some such.  In other words I don't think Tegmark believes in multiple Ones.

In his mathematical universe paper and ultimate ensemble paper, he posits that there is only one type of existence which would simplify things (a la Occam's razor).  Instead of there being mathematical and physical existence, there is an identification between the two so they are seen to be one in the same.  This merges the spaces "mathematical objects" with "physical objects".  He argues this in those papers (though to me sometimes it seems to be merely a plausibility argument).

Now if ME=PE, then one natural question is which mathematical structure is "the totality of all that exists" isomorphic to?  In other words, what is the One? 


With comp, any first order logical specification of a Turing universal system will do. 

Now if we start from a system having physicalist attribute (like the plane of GOL, for example, or like String Theory), we introduce a pedagogical difficulty in the derivation of the physical laws, and we make harder taking account the difference between the 3p and the 1p, or the quanta and the qualia.





What is the universe? Or to abuse language a bit, what is the multiverse?  This is a question that I've been thinking about for a while now and I'm really not sure.  The current idea is to take the category of all mathematical structures C (which is large, unfortunately), and embed that into a category of functors defined on that category (a la Yoneda's lemma), in such a way that every mathematical structure is embedded within that category of functors (called a "cocompletion" of C), a sort of "presheaf" category. 


Why not take the categories of all categories (besides that Lawyere tried that without to much success, except rediscovering Grothendieck topoi).

But if you assume comp, elementary arithmetic is enough, and it is better to keep the infinities and categories into the universal machine's mind tools. 



To have a single mathematical object that all mathematical structures can be embedded would give us an object that, in a sense, contains all structures.  If one follows Tegmark's idea that ME=PE, then a definition for universe just might be a mathematical object (which by ME=PE is a physical object) that contains, in a sense, all mathematical objects (i.e., all physical objects). 

I think that this is deeply flawed. We cannot identify the physical and the mathematical. We might try theory on the physical, or on the mental, or on the mathematical, which might suggest relation between those thing, but I doubt any non trivial theory would identify them, unless enlarging the sense of the words like mental, physical.

With computationalism, the coupling consciousness/physical is a phenomenon, person perceptible through numbers relations when they (the persons) bet on their relative self-consistency. This explains the appearance of the physical, without going out of the arithmetical. It works thanks to Church thesis and the closure of the comp everything (UD*, sigma_1 completeness).



It's not super clear to me that the cocompletion of the category of all structures C exists though since C is not a small category and thus Yoneda's lemma doesn't apply.  I would have to fine-tune the argument to work in the case of the category C I have in mind.

The n-categories might be interesting, but we don't need so rich ontology. If we are machine, the cardinality of the basic TOE is absolutely undecidable from inside. Omega is enough.



If the cocompletion of C is the One, that which all mathematical structures can be embedded, then the parallel universe question would be a matter of logic and category theory; it would depend on how you defined "the visible universe" and "parallel" universe.

You will have to define an observer, its points of view, and to take into account its many distributions in that super-mathematical structure, but you can't do that, as you will need an even bigger structure to define and study the indeterminacy. So you will have to limit your notion of observer and use some "comp" hypothesis (an infinite variant if you want).

With comp, it is easier: you cannot really take more than arithmetic. God created the Natural Numbers, all the rest belong to the (singular and collective) number's imagination. If nature refutes this, it will still remain time to add the infinities needed. I think.

Bruno


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Platonist Guitar Cowboy

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Dec 26, 2012, 12:53:21 PM12/26/12
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On Wed, Dec 26, 2012 at 4:17 PM, Roger Clough <rcl...@verizon.net> wrote:
Hi Bruno Marchal

It all boils down to this: is something that is mathematically true necessarily physically true ?
This question can be restated as "are mathematical truth and pragmatic truth
the same ?"  IMHO No, because theory can be wrong but what works works.



Dear Roger,

What's wrong with:

Theory always works (in some mind, no matter truth) and pragmatism can be used to justify or conceal discrimination, violence, false problems and examples like US style conservative rhetoric that pretends to be Christian, with its elements of compassion, love thy neighbor, share your wealth, anti-materialism etc. but in fact is pushing for policies that deny health to weak/poor, consolidate power and horde wealth, and promote the myth of people as isolated Islands, defending only their own interests, implying some Citizen Kane ideal, that everybody should aspire to?

It's a rather transparent trick for this rhetoric to mask its anti-Christian individualism with the Christian cloak of truth, faith, piety, charity, and probity; while "pragmatically" reasoning to themselves that it's advantageous to pose with the moral authority of ruling Christian dogma + liberty of individual, freedom from tyrannical forces. For this reason, this form of "Christian-conservative rhetoric" is not an expression of liberty; it's more an instrument of control to stop people from entering political process via distraction and shared moral indignation at "what's wrong".

I do not buy anymore "left vs. right" as ecology and energy problems make resource management much more complex and freedom/monitoring of internet activity enters the picture to which both Adam Smith and Marx/Engels were mute... but I do know that, if anything, Jesus was a socialist or communist.

Hence, the above mentioned nonsense of rhetoric framing conservative Christians as guardians of faith, piety, probity, and charity, while they horde their wealth and complain about higher taxes is merely noise to me. People parrots. Single function machine. Of course it "works", as you say, as anything does when you allow this kind of blatant contradiction. But it still is bs.

Ironically, the "atheist left" fights for Christian (New Testament) ideals... damn heathens! So the heathens will be judged, for doing Jesus' work without believing in him; and the "right" will be judged for pretending to believe in him, but for pragmatism sake they do devil's job á la "I am God, my wealth, myself and I won't share or show solidarity with people in need, because it's their fault in my final judgement of them, even though only God can judge, for practical reason because I cannot see him, I will judge them when I vote."

This disparity, the blatant fundamental contradiction in both camps, is quite hilarious I must admit, even though it's stupid how many have to suffer because of policy decisions based on this charade, and how much cash is wasted in keeping these narratives alive. Pragmatism has a coarser bs filter than arithmetic truth, anywhere in the multiverse I'd guess.

PGC


 
[Roger Clough], [rcl...@verizon.net]
12/26/2012
"Forever is a long time, especially near the end." -Woody Allen

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Subject: Re: Ten top-of-my-head arguments against multiverses

Bruno Marchal

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On 26 Dec 2012, at 16:17, Roger Clough wrote:

> Hi Bruno Marchal
>
> It all boils down to this: is something that is mathematically true
> necessarily physically true ?

I cannot even understand what that could mean.

I don't think that any mathematical truth is ever physically true. It
is a category error (a point where I agree with Bill)

I don't think there is a general notion of "mathematical truth", nor
do I think there is a primitive notion of "physical truth".

Assuming comp, we do have, by a sort of miracle, a rather clear notion
of truth: arithmetical truth. It is quasi definable, and everybody
seems to agree on the elementary base (except sunday philosophers).

Assuming comp, and assuming there is no logical flaw in UDA, we can
bet on truth = arithmetical truth, and then derive, in the UDA way,
and using the canonical self-reference logic, the witnessing of the
existence of a rich psychology, and theology, including physics and
cosmogonies.

But physics is described as the theory predicting result of
observation, and observation is described by the interaction of a
universal machine relatively to its most probable universal
neighborhood.

Given that the basic reality is arithmetic, it is not astonishing that
the physical has mathematical aspect.

It is even normal, here, that the psychological and theological hide
their mathematical aspect, as they are not completely available to us
from our perspective.




> This question can be restated as "are mathematical truth and
> pragmatic truth
> the same ?"

The truth that your government tries to hide to you: 1 + 1 = 2.

The pragmatic truth: 1 + 1 = 2 + taxes.




> IMHO No, because theory can be wrong but what works works.

Which reminds me what Charles said on the FOR, or FOAR, list:

In theory, practice and theory fit well.
In practice, they don't.

The problem is that, in practice, we have only theories, and when you
say 'what works works,' you are just betting on your oldest theories
which have never been disconfirmed by experience (like the ground can
support me).
(Of course, "you" are (1p) betting from your ultimate ineffable
undoubtable (but hidden from the public) conscious lever).

So we can only propose, publicly, but even to ourselves on any matter,
theories, and we can only live the "pragmatic", which is itself the
result of billions years, if not much longer complex universal machine
histories in arithmetic. And we can only measure the imbalance between
what we live and what we theorize (even theorizing on what we have
theorized unconsciously in some possible past).

Keep in mind this theory protects the person from any reductionism,
and is eventually far closer to Plato, Plotinus, and perhaps Descartes
and Leibniz than to Aristotle, Metaphysical Naturalism, Physicalism,
Weak Materialism, which is unfortunately often presented as the
rationalist position. Today, we have theories and facts which makes
Plato more rational than Aristotle, imo, for the big picture.

And then the Church Turing thesis, or Emil Post law, rehabilitates the
more Pythagorean form of (Neo)Platonism.

If you don't like Number, you can use Word instead. The primitive
ontology needs only to be Turing complete, equivalently, capable of
proving all true sigma_1 sentences, as I am sure you and everybody
can. That will already contains the computation involving more rich
observers, not only sigma_1 complete, but Löbian, which means that
they can know that they are Turing universal, and that they can get
the "frightening" consequences (no prevention against crashing,
looping, dreaming, hallucinating, etc. DBf, in G*.

The physical becomes the border of the number's observability (=
bettable prediction for measurement) ability.

Arithmetic is an Indra net of universal entities not only reflecting
each others, but interacting in all possible ways. Universal numbers
can put masks and stop recognizing themselves, getting sleepy for
awhile. This often makes shit happens more than usually and this can
grow up to awaken them, momentarily, sometimes only relatively, etc.
> http://iridia.ulb.ac.be/~marchal/
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Bruno Marchal

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Dec 26, 2012, 2:25:23 PM12/26/12
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On 25 Dec 2012, at 19:35, Brian Tenneson wrote:

At least in the video (skip to 43:14), Tegmark estimates that our doppelgangers are 2^10^118 meters away which probably puts it past the range of direct testing and, consequently, makes it not falsifiable.


But this is in the "many worlds" of one world being infinite and sufficiently homegenous. It is not the Everett, nor the comp Doppelgangers. 

Also, it is not clear why would this be not testable, as we can test first person indeterminacies on such "Garden of Eden" configuration, and compare with the observation.

May be *that* can win the 1p-(plural)- measure battle, but I guess this is today just speculation.

I don't think Tegmark takes the 1p indeterminacy into account, except in the quantum wave, but not on math in general or in arithmetic.

Bruno





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Richard Ruquist

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Dec 26, 2012, 2:46:09 PM12/26/12
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Bruno, you are getting closer to string theory than I have noticed
before now. Richard
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Roger Clough

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Hi Richard Ruquist
 
String theory is a physical theory, yes, but it itself is not physical.
 
 
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Roger Clough

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Hi Platonist Guitar Cowboy

Pragmatism is does not provide truth in, say a Platonic or Aristotelian sense.
It only provides truth as pragmatists define truth: namely that if A causes B,
B is the truth of A. This is the same as scientific truth or experimental truth.


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Time: 2012-12-26, 12:53:21
Subject: Re: Re: Ten top-of-my-head arguments against multiverses




On Wed, Dec 26, 2012 at 4:17 PM, Roger Clough wrote:

Hi Bruno Marchal

It all boils down to this: is something that is mathematically true necessarily physically true ?
This question can be restated as "are mathematical truth and pragmatic truth
the same ?" ?MHO No, because theory can be wrong but what works works.




Dear Roger,

What's wrong with:

Theory always works (in some mind, no matter truth) and pragmatism can be used to justify or conceal discrimination, violence, false problems and examples like US style conservative rhetoric that pretends to be Christian, with its elements of compassion, love thy neighbor, share your wealth, anti-materialism etc. but in fact is pushing for policies that deny health to weak/poor, consolidate power and horde wealth, and promote the myth of people as isolated Islands, defending only their own interests, implying some Citizen Kane ideal, that everybody should aspire to?

It's a rather transparent trick for this rhetoric to mask its anti-Christian individualism with the Christian cloak of truth, faith, piety, charity, and probity; while "pragmatically" reasoning to themselves that it's advantageous to pose with the moral authority of ruling Christian dogma + liberty of individual, freedom from tyrannical forces. For this reason, this form of "Christian-conservative rhetoric" is not an expression of liberty; it's more an instrument of control to stop people from entering political process via distraction and shared moral indignation at "what's wrong".

I do not buy anymore "left vs. right" as ecology and energy problems make resource management much more complex and freedom/monitoring of internet activity enters the picture to which both Adam Smith and Marx/Engels were mute... but I do know that, if anything, Jesus was a socialist or communist.

Hence, the above mentioned nonsense of rhetoric framing conservative Christians as guardians of faith, piety, probity, and charity, while they horde their wealth and complain about higher taxes is merely noise to me. People parrots. Single function machine. Of course it "works", as you say, as anything does when you allow this kind of blatant contradiction. But it still is bs.

Ironically, the "atheist left" fights for Christian (New Testament) ideals... damn heathens! So the heathens will be judged, for doing Jesus' work without believing in him; and the "right" will be judged for pretending to believe in him, but for pragmatism sake they do devil's job ? la "I am God, my wealth, myself and I won't share or show solidarity with people in need, because it's their fault in my final judgement of them, even though only God can judge, for practical reason because I cannot see him, I will judge them when I vote."

This disparity, the blatant fundamental contradiction in both camps, is quite hilarious I must admit, even though it's stupid how many have to suffer because of policy decisions based on this charade, and how much cash is wasted in keeping these narratives alive. Pragmatism has a coarser bs filter than arithmetic truth, anywhere in the multiverse I'd guess.

PGC


?
[Roger Clough], [rcl...@verizon.net]
12/26/2012

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Subject: Re: Ten top-of-my-head arguments against multiverses


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Roger Clough

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Dec 26, 2012, 3:50:16 PM12/26/12
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Hi Bruno Marchal
 
By that I meant that what is theoretically true
does not mean that it will happen as theorized.
 
 
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12/26/2012
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Subject: Re: Ten top-of-my-head arguments against multiverses

observers, not only sigma_1 complete, but L鯾ian, which means that
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Richard Ruquist

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Wrong Roger,

String theory predicts quantum field theory which is closer to MWI or
CTM or monads or the mind than the physical world.
Richard
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meekerdb

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On 12/26/2012 11:25 AM, Bruno Marchal wrote:
I don't think Tegmark takes the 1p indeterminacy into account, except in the quantum wave, but not on math in general or in arithmetic.

I thought his idea was that in the infinite universe there are infinitely many Max Tegmarks for whom indeterminancy is realized by different ones seeing different outcomes of quantum measurements - just like your Moscow/Washington indeterminacy.

Brent

Bruno Marchal

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Dec 27, 2012, 7:07:57 AM12/27/12
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That seems to be what I said. Tegmark applies correctly the 1p-indterminacy in the Quantum wave, but fails to appreciate it applies already in elementary arithmetic, and that CTM forces us to derive the wave from arithmetic, (and to not postulate it, nor anything (even math) above arithmetic).

Bruno




Brent

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Platonist Guitar Cowboy

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Dec 29, 2012, 2:43:11 PM12/29/12
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Hi Roger,

On Wed, Dec 26, 2012 at 9:46 PM, Roger Clough <rcl...@verizon.net> wrote:
Hi Platonist Guitar Cowboy

Pragmatism is does not provide truth in, say a Platonic or Aristotelian sense.
It only provides truth as pragmatists define truth: namely that if A causes B,
B is the truth of A. This is the same as scientific truth or experimental truth.




I don't think that pragmatists like Dewey, which is how I'd frame "pragmatism" semantically, would agree with that.

Whenever the word pops up, I raise an eyebrow: "Let's be pragmatic here..." used for argument's sake, I do not take to be a valid move, unless the party making the statement specifies some context they are referring to + some degree of congruence with the same. Without that, I find it usually nonsense, referring to some unspecified universe that is inflated to "absolute reality which necessitates x". And everybody knows cui bono with x.

And if Christian rhetoric makes such a pragmatic move, say republicans for denying healthcare to poor, my question is naturally: "Your universe is based on that book, that you guys use to ceremonially inaugurate presidents, instantiate judicial laws, make statements in courts etc. Why is your policy in direct contradiction with Jesus teachings, á la love thy neighbor, help the poor and so on?"

I have yet to hear a convincing answer to that one. But I'm patient (unless I sense they're ripping me off) with such things.

Platonistically pragmatic Guitar Cowboy


 

Brian Tenneson

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Dec 29, 2012, 2:51:19 PM12/29/12
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Why not take the categories of all categories (besides that Lawyere tried that without to much success, except rediscovering Grothendieck topoi).

I'm more interested in the smallest mathematical object in which all mathematical structures are embedded but the category of all categories will do.
 

But if you assume comp, elementary arithmetic is enough, and it is better to keep the infinities and categories into the universal machine's mind tools. 

Enough for what, in what sense?


To have a single mathematical object that all mathematical structures can be embedded would give us an object that, in a sense, contains all structures.  If one follows Tegmark's idea that ME=PE, then a definition for universe just might be a mathematical object (which by ME=PE is a physical object) that contains, in a sense, all mathematical objects (i.e., all physical objects). 

I think that this is deeply flawed. We cannot identify the physical and the mathematical. We might try theory on the physical, or on the mental, or on the mathematical, which might suggest relation between those thing, but I doubt any non trivial theory would identify them, unless enlarging the sense of the words like mental, physical.


Isn't it simpler to assume there is only one type of existence?  What are the actual flaws of a mathematical universe?  A physical system can be mathematically encoded by its corresponding set of world lines.  This encoding is an isomorphism.  A very simple example of what I mean is the nearly parabolic path taken by a projectile.  The set of world lines would be some subset of R^4 or R^n if it turns out that n != 4.  I am aware that indeterminacy due to Heisenberg's uncertainty principle kicks in here so we may never "know" which subset of R^n a physical system is isomorphic to but by a pigeonhole principle, the physical system must be isomorphic to some subset of R^n, several in fact.


 
With computationalism, the coupling consciousness/physical is a phenomenon, person perceptible through numbers relations when they (the persons) bet on their relative self-consistency. This explains the appearance of the physical, without going out of the arithmetical. It works thanks to Church thesis and the closure of the comp everything (UD*, sigma_1 completeness).


How are you defining consciousness here?

It's not super clear to me that the cocompletion of the category of all structures C exists though since C is not a small category and thus Yoneda's lemma doesn't apply.  I would have to fine-tune the argument to work in the case of the category C I have in mind.

The n-categories might be interesting, but we don't need so rich ontology. If we are machine, the cardinality of the basic TOE is absolutely undecidable from inside. Omega is enough.

Do you have an argument that proves that our minds can't transcend "inside"?


If the cocompletion of C is the One, that which all mathematical structures can be embedded, then the parallel universe question would be a matter of logic and category theory; it would depend on how you defined "the visible universe" and "parallel" universe.

You will have to define an observer, its points of view, and to take into account its many distributions in that super-mathematical structure, but you can't do that, as you will need an even bigger structure to define and study the indeterminacy. So you will have to limit your notion of observer and use some "comp" hypothesis (an infinite variant if you want).

With comp, it is easier: you cannot really take more than arithmetic. God created the Natural Numbers, all the rest belong to the (singular and collective) number's imagination. If nature refutes this, it will still remain time to add the infinities needed. I think.


How is the arithmetical structure going to give rise to a description of reality that takes into account observer, its points of view, and its many distributions without the need to study the indeterminacy?

Stephen P. King

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Dec 29, 2012, 4:12:12 PM12/29/12
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On 12/29/2012 2:51 PM, Brian Tenneson wrote:



Why not take the categories of all categories (besides that Lawyere tried that without to much success, except rediscovering Grothendieck topoi).

I'm more interested in the smallest mathematical object in which all mathematical structures are embedded but the category of all categories will do.

Hi Brian,

    Check out this proposed structure: a compressed PS file: boole.stanford.edu/pub/gamut.ps.gz or pdf: http://boole.stanford.edu/pub/gamut.pdf


 

But if you assume comp, elementary arithmetic is enough, and it is better to keep the infinities and categories into the universal machine's mind tools. 

Enough for what, in what sense?


To have a single mathematical object that all mathematical structures can be embedded would give us an object that, in a sense, contains all structures.  If one follows Tegmark's idea that ME=PE, then a definition for universe just might be a mathematical object (which by ME=PE is a physical object) that contains, in a sense, all mathematical objects (i.e., all physical objects). 

I think that this is deeply flawed. We cannot identify the physical and the mathematical. We might try theory on the physical, or on the mental, or on the mathematical, which might suggest relation between those thing, but I doubt any non trivial theory would identify them, unless enlarging the sense of the words like mental, physical.


Isn't it simpler to assume there is only one type of existence?  What are the actual flaws of a mathematical universe?  A physical system can be mathematically encoded by its corresponding set of world lines.  This encoding is an isomorphism.  A very simple example of what I mean is the nearly parabolic path taken by a projectile.  The set of world lines would be some subset of R^4 or R^n if it turns out that n != 4.  I am aware that indeterminacy due to Heisenberg's uncertainty principle kicks in here so we may never "know" which subset of R^n a physical system is isomorphic to but by a pigeonhole principle, the physical system must be isomorphic to some subset of R^n, several in fact.

    Is it possible that this isomorphism is one example of a more general relation?




 
With computationalism, the coupling consciousness/physical is a phenomenon, person perceptible through numbers relations when they (the persons) bet on their relative self-consistency. This explains the appearance of the physical, without going out of the arithmetical. It works thanks to Church thesis and the closure of the comp everything (UD*, sigma_1 completeness).


How are you defining consciousness here?

It's not super clear to me that the cocompletion of the category of all structures C exists though since C is not a small category and thus Yoneda's lemma doesn't apply.  I would have to fine-tune the argument to work in the case of the category C I have in mind.

The n-categories might be interesting, but we don't need so rich ontology. If we are machine, the cardinality of the basic TOE is absolutely undecidable from inside. Omega is enough.

Do you have an argument that proves that our minds can't transcend "inside"?

    ISTM, that to transcend from 'inside' would be to contradict Godel's incompleteness theorems, no?




If the cocompletion of C is the One, that which all mathematical structures can be embedded, then the parallel universe question would be a matter of logic and category theory; it would depend on how you defined "the visible universe" and "parallel" universe.

You will have to define an observer, its points of view, and to take into account its many distributions in that super-mathematical structure, but you can't do that, as you will need an even bigger structure to define and study the indeterminacy. So you will have to limit your notion of observer and use some "comp" hypothesis (an infinite variant if you want).

With comp, it is easier: you cannot really take more than arithmetic. God created the Natural Numbers, all the rest belong to the (singular and collective) number's imagination. If nature refutes this, it will still remain time to add the infinities needed. I think.


How is the arithmetical structure going to give rise to a description of reality that takes into account observer, its points of view, and its many distributions without the need to study the indeterminacy?
--

    I think that Bruno is assuming an ensemble or collection of possible encodings within the relations between numbers (or equivalent) to account for every possible description and thus would include any observer, its points of view and its many distributions. All of it exists a priori in Platonia. No?

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Onward!

Stephen

Roger Clough

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Hi Platonist Guitar Cowboy
 
Dewey has always fascinated me because of the sweeping power
of his ideas, his blunt originality, and his emphasis on "doing".
But his relativism is nowadays a bit too much for me (IMHO),
in my conservative old age. He might be called the father of
progressivism, so I can understand your more positive view of him.
He would be the darling of progressive politics.
 
 
Unfortunately for me, Dewey differs from Peirce and James in
defining truth too relatively. His relativism seems to me to say
that for him, whatever works is true, period. He doesn't qualify
that with "true in this particular pragmatic sense", but
true, period. This is a bit too heavy-handed for me.
 
P and J are much tighter with their definition, namely that the
result of an action is merely the truth of that action, not
the absolute truth. I find this to be more in line with what
I would call "classic pragmatism", which is suspicious of all truth,
but does not deny all of it.  They admitted the possible existence of
God, while Dewey, in his heavy-handed manner, simply
said that God does not exist, period.
 
So in the end, while the "sweeping power" of his ideas still
holds some fascination to me, I think he tended more to being
a dictator than a modest seeker of truth, whatever that is.
But there is much in his thought to yet consider.
 
 
 
[Roger Clough], [rcl...@verizon.net]
12/30/2012
"Forever is a long time, especially near the end." - Woody Allen
----- Receiving the following content -----
Time: 2012-12-29, 14:43:11
Subject: Re: Re: Re: Ten top-of-my-head arguments against multiverses

Hi Roger,

On Wed, Dec 26, 2012 at 9:46 PM, Roger Clough <rcl...@verizon.net> wrote:
Hi Platonist Guitar Cowboy

Pragmatism is does not provide truth in, say a Platonic or Aristotelian sense.
It only provides truth as pragmatists define truth: namely that if A causes B,
B is the truth of A. This is the same as scientific truth or experimental truth.




I don't think that pragmatists like Dewey, which is how I'd frame "pragmatism" semantically, would agree with that.

Whenever the word pops up, I raise an eyebrow: "Let's be pragmatic here..." used for argument's sake, I do not take to be a valid move, unless the party making the statement specifies some context they are referring to + some degree of congruence with the same. Without that, I find it usually nonsense, referring to some unspecified universe that is inflated to "absolute reality which necessitates x". And everybody knows cui bono with x.

And if Christian rhetoric makes such a pragmatic move, say republicans for denying healthcare to poor, my question is naturally: "Your universe is based on that book, that you guys use to ceremonially inaugurate presidents, instantiate judicial laws, make statements in courts etc. Why is your policy in direct contradiction with Jesus teachings, � la love thy neighbor, help the poor and so on?"


I have yet to hear a convincing answer to that one. But I'm patient (unless I sense they're ripping me off) with such things.

Platonistically pragmatic Guitar Cowboy


[Roger Clough], [rcl...@verizon.net]
12/26/2012
"The one thing a woman looks for in a man is to be needed." - "Ethan Frome", by Edith Wharton
----- Receiving the following content -----
From: Platonist Guitar Cowboy
Receiver: everything-list
Time: 2012-12-26, 12:53:21
Subject: Re: Re: Ten top-of-my-head arguments against multiverses




On Wed, Dec 26, 2012 at 4:17 PM, Roger Clough 爓rote:

Bruno Marchal

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Dec 30, 2012, 8:57:29 AM12/30/12
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On 29 Dec 2012, at 20:51, Brian Tenneson wrote:




Why not take the categories of all categories (besides that Lawyere tried that without to much success, except rediscovering Grothendieck topoi).

I'm more interested in the smallest mathematical object in which all mathematical structures are embedded but the category of all categories will do.

Except that it is too big, and eventually lawvere extract the topi from this, which model well, not the mathematical reality, but the mathematician itself.

Also, we have already discuss this, but the embedding notion does not seem the right think to study, compared to emulation, at least with the comp hypothesis.



 

But if you assume comp, elementary arithmetic is enough, and it is better to keep the infinities and categories into the universal machine's mind tools. 

Enough for what, in what sense?

Enough for a basic ontology (and notion of existence) to explain all the different sort of existence, notably of persons, consciousness, matter appearances, etc. See my papers, as I pretend that with comp we have no choice in those matter, except for pedagogical variants and practice.







To have a single mathematical object that all mathematical structures can be embedded would give us an object that, in a sense, contains all structures.  If one follows Tegmark's idea that ME=PE, then a definition for universe just might be a mathematical object (which by ME=PE is a physical object) that contains, in a sense, all mathematical objects (i.e., all physical objects). 

I think that this is deeply flawed. We cannot identify the physical and the mathematical. We might try theory on the physical, or on the mental, or on the mathematical, which might suggest relation between those thing, but I doubt any non trivial theory would identify them, unless enlarging the sense of the words like mental, physical.


Isn't it simpler to assume there is only one type of existence? 

It seems to me part of the data that this is not the case. My pain in a leg has a type of existence different from a quark. The game of bridge as a different type of existence than the moon material constitution. 
Then for machine, once we distinguish their different points of view (intuoitively like in UDA) or formally like in AUDA, we get many different sort of existence.
The ontic one is the simpler ExP(x), but we have also []ExP(x), []Ex[]P(x), []<>P(x), []<>Ex[]<>P(x), etc. All this in 8 different modal logics extracted from self-reference. 



What are the actual flaws of a mathematical universe? 

Too big. It is a metaphor.



A physical system can be mathematically encoded by its corresponding set of world lines.  This encoding is an isomorphism.  A very simple example of what I mean is the nearly parabolic path taken by a projectile.  The set of world lines would be some subset of R^4 or R^n if it turns out that n != 4.  I am aware that indeterminacy due to Heisenberg's uncertainty principle kicks in here so we may never "know" which subset of R^n a physical system is isomorphic to but by a pigeonhole principle, the physical system must be isomorphic to some subset of R^n, several in fact.

May be. But I am driven by the mind-body problem, and what you show above is mathematical physics. With comp, by UDA, we have to extract the belief in such physical idea by ultimately explaining them in term probabilities on computations (that the result I invite you to study and criticize).





 
With computationalism, the coupling consciousness/physical is a phenomenon, person perceptible through numbers relations when they (the persons) bet on their relative self-consistency. This explains the appearance of the physical, without going out of the arithmetical. It works thanks to Church thesis and the closure of the comp everything (UD*, sigma_1 completeness).


How are you defining consciousness here?

I can't define it. I just hope you know what I mean. Basically something true but non provable about yourself, and, by comp, invariant for some local digital substitution.






It's not super clear to me that the cocompletion of the category of all structures C exists though since C is not a small category and thus Yoneda's lemma doesn't apply.  I would have to fine-tune the argument to work in the case of the category C I have in mind.

The n-categories might be interesting, but we don't need so rich ontology. If we are machine, the cardinality of the basic TOE is absolutely undecidable from inside. Omega is enough.

Do you have an argument that proves that our minds can't transcend "inside"?

The mind can do that. Math, by diagonalization, does that, actually, even in a 3p way. 
But the fact that "number's mind" can do that invite us to not reify the transcendental. This is what lead to superstition and non necessarily complex ontologies.






If the cocompletion of C is the One, that which all mathematical structures can be embedded, then the parallel universe question would be a matter of logic and category theory; it would depend on how you defined "the visible universe" and "parallel" universe.

You will have to define an observer, its points of view, and to take into account its many distributions in that super-mathematical structure, but you can't do that, as you will need an even bigger structure to define and study the indeterminacy. So you will have to limit your notion of observer and use some "comp" hypothesis (an infinite variant if you want).

With comp, it is easier: you cannot really take more than arithmetic. God created the Natural Numbers, all the rest belong to the (singular and collective) number's imagination. If nature refutes this, it will still remain time to add the infinities needed. I think.


How is the arithmetical structure going to give rise to a description of reality that takes into account observer, its points of view, and its many distributions without the need to study the indeterminacy?

You might take a look on my paper(s)(°), or my posts here, as this is what I keep trying to explain here.  I am not sure how you can study the relation between the first person and its possible realities without using the first person indeterminacy, which is the building block of the physical realities.
The observer are the (Turing) universal numbers. Physics is given by the measure on the computations going through their state. This extends Everett on arithmetic. It leads to a many-dream view of arithmetic, and can be shown to be developed by almost all universal numbers.

Bruno




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Brian Tenneson

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Dec 30, 2012, 2:23:40 PM12/30/12
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Is there a "physical" object that exists physically which is not isomorphic to a mathematical object, having mathematical existence?

meekerdb

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Dec 31, 2012, 12:08:27 AM12/31/12
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On 12/30/2012 11:23 AM, Brian Tenneson wrote:
> Is there a "physical" object that exists physically which is not isomorphic to a
> mathematical object, having mathematical existence?

If it exists physically then it has at least one attribute that no mathematical "object" has.

Brent

Bruno Marchal

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Dec 31, 2012, 5:04:53 AM12/31/12
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Indeed.
If it exists *primitively-physically* then it has at least one
attribute that no mathematical "object" has.

If it exist *non-primitively-physically* then it "existing physically"
will be a non trivial mathematical notion, which will distinguish
physical and mathematical existence.

That the case with comp. A physical object becomes a stable emerging,
from infinities of computations, pattern, as seen from a universal
number first person (sharable) point of view.

Bruno





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Roger Clough

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Dec 31, 2012, 8:05:21 AM12/31/12
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Hi Bruno Marchal and Brian,

"Bigness" can only limit physical entities (those extended in space),
but is irrelevant with regard to nonphysical or mental entities,
as these are not extended in space.



[Roger Clough], [rcl...@verizon.net]
12/31/2012
"Forever is a long time, especially near the end." - Woody Allen
----- Receiving the following content -----
From: Bruno Marchal
Receiver: everything-list
Time: 2012-12-30, 08:57:29
Subject: Re: Ten top-of-my-head arguments against multiverses




You might take a look on my paper(s)(?), or my posts here, as this is what I keep trying to explain here. I am not sure how you can study the relation between the first person and its possible realities without using the first person indeterminacy, which is the building block of the physical realities.
The observer are the (Turing) universal numbers. Physics is given by the measure on the computations going through their state. This extends Everett on arithmetic. It leads to a many-dream view of arithmetic, and can be shown to be developed by almost all universal numbers.


Bruno


(?) http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html

Bruno Marchal

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Dec 31, 2012, 8:20:44 AM12/31/12
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On 31 Dec 2012, at 14:05, Roger Clough wrote:

> Hi Bruno Marchal and Brian,
>
> "Bigness" can only limit physical entities (those extended in space),
> but is irrelevant with regard to nonphysical or mental entities,
> as these are not extended in space.

?

Is is not natural to say that 10^100 is bigger than 0? And 2^Aleph_0
bigger than Aleph_0?

Bruno

Roger Clough

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Dec 31, 2012, 10:12:54 AM12/31/12
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Hi Bruno Marchal
 
Yes, but those numbers are not extended in space, so
they have no physical size.
 
 
[Roger Clough], [rcl...@verizon.net]
12/31/2012
"Forever is a long time, especially near the end." - Woody Allen
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http://iridia.ulb.ac.be/~marchal/



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Brian Tenneson

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So is that a yes? If so, can you stipulate such a physical object?

Craig Weinberg

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Dec 31, 2012, 1:52:36 PM12/31/12
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On Monday, December 31, 2012 8:20:44 AM UTC-5, Bruno Marchal wrote:

On 31 Dec 2012, at 14:05, Roger Clough wrote:

> Hi Bruno Marchal and Brian,
>
> "Bigness" can only limit physical entities (those extended in space),
> but is irrelevant with regard to nonphysical or mental entities,
> as these are not extended in space.

?

Is is not natural to say that 10^100 is bigger than 0? And 2^Aleph_0  
bigger than Aleph_0?

Bruno

It's natural because it is a metaphor. Like it's natural to say that you have a big test coming up, or a big problem with a neighbor.

To say that one number is larger than another is figurative. When we say 'five is bigger than four', what we mean is 'since the quantity of five exceeds the quantity of four*, it is _as if_ this understood relation could be expressed as an inequality in physical size.

*five only exceeds the quantity of four as a mathematical generalization, which is also figurative based on the idealization of solid objects. If we deal with fluids or gases as a model instead, it does not necessarily have much meaning to say that one quantity is greater than or less than another.

Craig

meekerdb

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Dec 31, 2012, 2:59:54 PM12/31/12
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On 12/31/2012 9:55 AM, Brian Tenneson wrote:
So is that a yes? If so, can you stipulate such a physical object?

I don't know.  Can you define a "mathematical object" that is "isomorphic" to the chair you're sitting in?  I'm not even sure I know what that would mean; much less whether we can know one.  Isomorphism is usually a relation between two mathematical structures.

Brent


On Sunday, December 30, 2012 9:08:27 PM UTC-8, Brent wrote:
On 12/30/2012 11:23 AM, Brian Tenneson wrote:
> Is there a "physical" object that exists physically which is not isomorphic to a
> mathematical object, having mathematical existence?

If it exists physically then it has at least one attribute that no mathematical "object" has.

Brent
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Bruno Marchal

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On 31 Dec 2012, at 19:52, Craig Weinberg wrote:



On Monday, December 31, 2012 8:20:44 AM UTC-5, Bruno Marchal wrote:

On 31 Dec 2012, at 14:05, Roger Clough wrote:

> Hi Bruno Marchal and Brian,
>
> "Bigness" can only limit physical entities (those extended in space),
> but is irrelevant with regard to nonphysical or mental entities,
> as these are not extended in space.

?

Is is not natural to say that 10^100 is bigger than 0? And 2^Aleph_0  
bigger than Aleph_0?

Bruno

It's natural because it is a metaphor. Like it's natural to say that you have a big test coming up, or a big problem with a neighbor.

To say that one number is larger than another is figurative. When we say 'five is bigger than four', what we mean is 'since the quantity of five exceeds the quantity of four*, it is _as if_ this understood relation could be expressed as an inequality in physical size.

*five only exceeds the quantity of four as a mathematical generalization, which is also figurative based on the idealization of solid objects. If we deal with fluids or gases as a model instead, it does not necessarily have much meaning to say that one quantity is greater than or less than another.


Assuming metaphysical naturalism, and non realism in math. I prefer to not assume physics as it is what I want to explain. 
5 is bigger than 4 just because there is a positive number z such that 4 + z = 5.

Bruno




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Bruno Marchal

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Assuming weak-materialism, or physicalism,  Brent answer makes sense. And it easy for a (weak) materialist to stipulate such a physical object, as any physical object will do (the moon, the electron here or there, etc.).

Bruno






Brent

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