Brainstorms: Cosmogony, Holography and Causality

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Topic: Cosmogony, Holography and Causality

Aliet Jacob
Member
Member # 908

posted 03. November 2003 11:18

quote:
I have been assuming that by "isomorphism" he meant that...

OOh, then you have no aahdea whats coming at ya. nothing is what it looks...

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gedanken
Member
Member # 594

posted 03. November 2003 13:23

I realize that there is a colloquial use of "isomorphism" that is in fact used in the sense that Mr. Langan might be seeming to use it. That use is in relating of relationships or scientific "laws" to their real world expression. But the use of "up to isomorphism" with the mathematical “up to” usage seeming to be intended, and of substantial mathematical terminology elsewhere, implies to me that the more technical mathematical meaning was implied.

“That’s what isomorphism means: that mental objects are distributed over reality.” But “distributed” is in conflict with “one to one” and “onto”. (If you mean that isomorphism is used within showing that mental objects are distributed over reality, that would be different from “isomorphism means” that.)

quote:
Whats worse, Langan argues that the UBT is a pre-informational realm of unbound potential.
"Pre-informational", and "potential" are information, and if we can get them, then the UBT is not pre-informational. If its pre-informational, then no information can 'flow' from it to us or to anything.

Interesting that you mention Chaitin. Try this.

[ 03. November 2003, 13:32: Message edited by: gedanken ]

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chimp
Member
Member # 333

posted 04. November 2003 04:19

quote:

Gedankin:
“That’s what isomorphism means: that mental objects are distributed over reality.” But “distributed” is in conflict with “one to one” and “onto”. (If you mean that isomorphism is used within showing that mental objects are distributed over reality, that would be different from “isomorphism means” that.)

The laws of physics are mental objects and the laws of physics are perfectly distributed over reality. The law of conservation of energy is exact is it not? The laws are also diffeomorphism invariant, that is to say, they are invariant under a change of coordinates.

Freedom[UBT] is perfectly distributed over reality, in that there is "Heisenberg Uncertainty"

DxDp >= hbar/2 [Wink]

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Aliet Jacob
Member
Member # 908

posted 04. November 2003 04:58

"Up to" statements in the CTMU:

quote:

"the system is either deterministic or “random up to determinacy” p.6

"matter-information equivalence, an dentification (up to isomorphism) of concrete physical reality with information, the abstract currency of perception." p.8

"if there were something outside reality that were real enough to affect or influence reality, it would be inside reality, and this contradiction invalidates any supposition of
an external reality (up to observational or theoretical relevance)." p.16

"This shows that on some level, general covariance must hold. This is not merely true “up to isomorphism with X”; even if more than one valid set of laws can be distinguished, any one of which might be active at any given location..." p.18

"cognition and generic information transduction are identical up to isomorphism" p.33

"informational content are cross-refined through telic (syntax-state) feedback over the entire range of potential syntax-state relationships, up to and including all of spacetime and reality in general." p.38

"hunches or rules of thumb, and in fact share their syntaxes with the objects of theorization up to descriptive isomorphism, they are languages."
p.40

"if such a syntax were sufficiently relevant to this reality, i.e. sufficiently real, to support its existence, then it would be analytically included in reality (as defined up to perceptual relevance)." p.42

"First, it is supertautological; being constructed to mirror logical tautology up to the level of model theory and beyond" p.48

"In fact, they are identical up to an isomorphism beyond which the mental side, being the more
comprehensive of the two, outstrips the material." p.53

"Up to" seems to imply a progressive application of certain ideas (usually comparisons) to reach the required objective (isomorphism).

So, mental objects are "distributed" over reality up to "one on one" mapping.

Its patently false. Thats why I was saying that I put two inverses of a matrix in my bag but the matrix removed them and threw them in the river.

"Up to" creates the necessary wriggle room while at the same time leads readers to thinking that the isomorphism actually happens at some level. Its like in a movie, you show a scene with a trigger being pulled and then the next scene has someone on the ground bleeding. The audience is led to believe...

"Up to", guides you down the garden path. At the same time, its jelly. And you are armed with a nail and hammer. The wall behind the jelly is meaning. Wriggle room here means he can always say he never wrote that they map one on one (isomorphism), and that you are reading too much into what he wrote.

Now your task is to figure out the meaning of up to isomorphism. Pin the meaning "down" so to speak.

[ 04. November 2003, 05:07: Message edited by: Aliet Jacob ]

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Aliet Jacob
Member
Member # 908

posted 04. November 2003 05:04

Russel, tha laws of physics are not the only mental objects. I can fantasize about having sex with Madonna, that does not mean that there is me and Madonna having sex in reality.

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Aliet Jacob
Member
Member # 908

posted 04. November 2003 05:08

Unless you want to argue that I get to have sex with Madonna in another universe?

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chimp
Member
Member # 333

posted 04. November 2003 05:25

quote:

Russel, tha laws of physics are not the only mental objects. I can fantasize about having sex with Madonna, that does not mean that there is me and Madonna having sex in reality.

There are also incorrect derivations of laws that are much less probable than your fantasized liaison with Madonna.

Not all mental objects are isomorphic to reality. [Wink]

[ 04. November 2003, 05:26: Message edited by: Russell E. Rierson ]

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Aliet Jacob
Member
Member # 908

posted 04. November 2003 06:53

quote:
Not all mental objects are isomorphic to reality

That is what I have been arguing for over 8 months now!
Russel, do you remember me arguing over this with you ar ARN, infidels...?
Are we now on the same page over M=R?

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gedanken
Member
Member # 594

posted 04. November 2003 09:56

Since the terms are not explicitly defined, and are used in mathematical sounding language including in locations with very precise mathematical symbology such as on pages 39 through 45, I hope readers will understand my confusion if I thought precise mathematical definitions of terms were being used.

(But then of course one must remember my previous comments about "absolute precision" of meaning being relegated to models, and not being directly and completely applicable to the real world. I guess that since even modeling is a function of humans in the real world, that I should apply my own concept that logic is not crisp here.)

Anyway, here is a definition of "up to" as it us used in mathematics. And here is definition of isomorphism and homomorphism. And contained here is description of subgraph isomorphism.

In any case, sorry for having thought that precise mathematical terminology was in use.

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chimp
Member
Member # 333

posted 04. November 2003 14:29

The [M = R] principle:

http://www.hology.net/

quote:

Mind Equals Reality Principle (M=R) asserts that mind and reality are ultimately inseparable to the extent that they share common rules of structure and processing..

According to M = R, objective and subjective reality are identified on the level of cognitive and perceptual syntax. So certain logic statements[tautologies] have corresponding[qualitative] physical instantiations in the real world. Gedankin and Aliet are confusing M = R with exact quantitative isomorphism.

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gedanken
Member
Member # 594

posted 04. November 2003 22:21

Wow, look at the various links and web pages.

Is this a religion?

--

quote:
Gedankin and Aliet are confusing M = R with exact quantitative isomorphism.

Yes, It seems we were confusing these various statements about isomorphism as having a precisely defined meaning, perhaps the meaning commonly used elsewhere for the same terms.

Are you saying that there is not a mapping that is one to one and onto in the precise mathematical meaning?

In light of all the comments about the existence of absolute logical quantities, it is amusing the comment of confusion with an "exact" mathematical relationship.

[ 04. November 2003, 22:30: Message edited by: gedanken ]

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Gambit
Member
Member # 558

posted 04. November 2003 23:27

The CTMU discusses an isomorphism between events. The M = R concept is relating events only. Specifically, events M = events R, when isomorphic.

This relationship is interesting because it can be used beyond "common" temporal and physical bounds of description.

The question about how a "fundamental causality check" is avoided by a biologist for example is almost rhetorical. If the CTMU's "set of all sets" (the universe) must contain events M and events R and say "C" (the causality check event) then where C = M (the causality check) this carries over to C = R. Reality equals this causality check a.k.a. it has taken place in the mind of the beholder. Someone avoiding this causality check won't be in isomorphism with "C".

The question on this topic is how is causal avoidance possible for a biologist who works with causality all the time? For if a biologist is working with causality are they not in isomorphism with it? It is suggested that this causality is not really causality at all!

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jasonyoung
Member
Member # 432

posted 05. November 2003 00:56

"mental objects are "distributed" over reality up to "one on one" mapping."

Generally speaking, when I encounter statements which I determine to be "patently false" I immediately re-read them as a corrective measure. People, I have found, especially those whose intelligence is manifest, do not typically make 'patently false' statements. Apparently intellectual hubris (whence it issues, I know not) has robbed you of this willingness to question your own interpretative abilities. Too bad.

"That is what I have been arguing for over 8 months now! [that not all mental objects are isomorphic to reality]"

It states no where in the paper that semantic and interpretational disjunctions with reality are not permitted. In fact, Chris appears to go out of his way to emphasize that the isomorphism resides on the level of cognitive and perceptual syntax.

[ 05. November 2003, 00:58: Message edited by: jasonyoung ]

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chimp
Member
Member # 333

posted 05. November 2003 01:28

Here is a discussion where Christopher M. Langan gives a definition of isomorphism:

http://www.polymath-systems.com/intel/hiqsocs/megasoc/noes154/isomorph.html

quote:

3. The proper algebraic definition of isomorphism goes
> something like this: If , are monoids, m:A-->A'
> a map of A into A' such that m(a*b) = ma *' mb for each a,b
> in A, then m is a homomorphism of the monoid A into the
> monoid A'. If m:A-->A' is a homomorphism, then m is:
> a monomorphism if it is injective (one-to-one)
> an epimorphism if it is surjective (onto)
> an isomorphism if it is bijective (one-to-one onto).
> This is taken from the nearest abstract algebra text I could
> grab, "Algebra" by Goldhaber and Erlich (Macmillan, 1970).
> Notice that since reality has algebraic structure, consisting not
> just of sets but of operations among their elements, we have
> to talk in terms of algebra. So as we see, when Kevin says
> "isomorphism", what he really means is "monomorphism"
> (even if he claims that in some strange way, this means that
> he means "isomorphism" after all).
[...]

> Kevin's confusion comes down to this. In the context of
> simple sets, we can get away with saying that an isomorphism
> is "one-to-one" because, if this is applied to both sets,
> surjection (onto) is logically implied. That is, if one has two
> sets A and B and says that there is a 1-to-1 mapping between
> them, one is saying that for every element of either set there is
> another (unique) element in the other. It follows that the sets
> A and B contain an equal number of elements, and that the
> mapping is surjective (onto) no matter what its direction.
[...]

Thus, Kevin has not only failed to properly track the logical
> implications of his set-theoretic definition of "isomorphism"
> in the context of set theory itself, but he has failed to account
> for the additional structure that algebra brings to set theory.
> Reality includes not just sets, but algebraic operations within
> them. And that's the first installment of Kevin's math and
> reality lesson for today.

The most general definition of isomorphism that I know of is the definition given by category theory:

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

According to my CTMU interpretation, the laws of mathematics distribute over the laws of physics. S1 distributes over S2. A particle of matter is an instantiation of physical law. Gedankin or Aliet cannot refute this. Can they try to give oversimplistic counter examples in a futile effort to create confusion? [Wink]

Here is what appears to be one of the earliest CTMU papers, from 1990, where computation theory is used to describe the resolution of "Newcomb's paradox":

http://www.polymath-systems.com/intel/hiqsocs/megasoc/noes44/newcomb.html

I have reached the limits of my CTMU knowledge [Wink]

and there are probably many mistakes in my interpretation. So thanks for the thorough grilling but I am not the expert in the CTMU [Wink]

I recall Aliet proclaiming himself to be a computer programmer? Perhaps he can critique the mathematics contained within the "resolution of Newcomb's paradox", or are he, and Gedankin? full of wind ? [Wink]

LOL

Thanks for the discussion.

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gedanken
Member
Member # 594

posted 05. November 2003 01:46

quote:
A particle of matter is an instantiation of physical law.

Key word: "instantiation"

That means that a particle obeys (and I would assume within limits) a physical "law". But that is not an isomorphism of law to reality, rather it is possibly a connection of the structure of model ("law") to the structure of physical reality in a specific instance, but with that instance somehow removed or abstracted out of the larger picture of reality. This is the only way to have a bijective mapping!

Take to "instantiations" of particles obeying the same "physical law". We no longer have one to one, because the one "law" (in the degree it maps with structure of reality) is now mapping to two instantiations.

Now this may seem of minor importance, and it is tangential to the real point. But the resolution of this issue gets nearer to the heart of the issue I consider important, so it is important to resolve this issue first.

The problem is that one must now deal in some sort of "copy" of the so-called "physical law", such that each copy is involved in an individual mapping, such that all the copies map into the entirety of physical reality, and (as is a bijective mapping) the inverse of each aspect of physical reality must map back to the "copy".

Now I expect that is discussed in the sense of "distribute" that was referenced--no problem there per se. But in the "polymath-systems" link, the issue of bijective or 1 to 1 is not resolved. It was apparently clearly stated very early. But where is the resolution? I can't find it in that link!

A problem is that the physical laws are not exact! (At least not so far, as they have been expressed in language.) Furthermore they must work in combination. Now there are a couple of interesting possibilities:

1) That reality is really simple at heart, such as a simple (in relative terms) string theory of everything approach completely describing all interactions of physical reality.

2) That reality is not reducible to such simplicity at heart, in that the complexity of relationships grows as one refines the representation--and even below the complexity of string theory (which lies under particle theories, etc.) there is yet another theory. (Tower of turtles...?)

But even this does not capture the essence of my claim. Because the essence is that the combinatoric interaction of all the factors that must describe all the particle interactions is not something that I think can be represented in a finite language description. It is the language description that I am questioning.

(If one is willing to go beyond "language" description, and deal in some other level--then I might be willig to accept other aspects of the concepts more readily.)

Furthermore consider that case "1" above is correct, and that furthermore that one can construct an equivalent of "language" in which the interactions of each particle is fully described. The problem here is that is a very "thin" layer of language description that actually maps to reality! No higher order descriptions are introduced, only the elementary particle interactions. Once one tries to introduce the higher order descriptions--then the combinatorial explosion occurs, and the "fuzzy logic" issues rear in greater degree, etc.

And beyond that, even the basic TOE of case 1 might not escape "fuzzy logic" issues, just within the description of particle interactions!

[ 05. November 2003, 02:04: Message edited by: gedanken ]

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