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).
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From: Richard RuquistReceiver: everything-listTime: 2012-12-24, 12:07:36Subject: Re: Fw: the world as mathematical. was pythagoras right after all ?
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From: Brian TennesonReceiver: everything-listTime: 2012-12-24, 13:11:46
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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From: meekerdbReceiver: everything-listTime: 2012-12-24, 15:05:14
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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Hi Brian TennesonTegmark 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 afinal 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 wouldhave to be multiple platonic Ones. But there can only be one One.
5) Multiverses are mechanistic and so in spacetime, but consciouss lifeand all that other good stuff are outside of spacetime. Would theminds of multiverses be mashed together ? And all particular lifeswould 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 toall terminate at the same time.8) One might conjecture also that the presence of life, consciousness andintelligence (which are all individual, personal, subjective) are notmechanical and so cannot be part of a multiverse. It's each manfor himself. Along these lines, because of natural selection anddifferent worlds not being all the same, evolution would not occurin parallel.9) Besides, there are alternate possibilities for a quantum wave collapse.
10) In a related matter, one of the multiverse sites cited William Jamesas a proponent. Because of his pragmatism, his multiverses arisebecause 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----- Receiving the following content -----From: Brian TennesonReceiver: everything-listTime: 2012-12-24, 13:11:46Subject: 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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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.
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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.
[Roger Clough], [rcl...@verizon.net]
12/26/2012
"Forever is a long time, especially near the end." -Woody AllenFrom: Bruno Marchal
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Subject: Re: Ten top-of-my-head arguments against multiverses
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.
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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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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.
Brent
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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.
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.
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?
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From: Platonist Guitar CowboyReceiver: everything-list
Time: 2012-12-29, 14:43:11Subject: Re: Re: Re: Ten top-of-my-head arguments against multiversesHi 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
�
"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:
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?
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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
So is that a yes? If so, can you stipulate such a physical object?
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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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.
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