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Author
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Topic: Cosmogony, Holography and Causality
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jasonyoung
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Member # 432
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posted 05. November 2003 02:07
NT. Out.
[ 05. November 2003, 02:10: Message edited by: jasonyoung ]
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chimp
Member
Member # 333
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posted 05. November 2003 03:40
quote:
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.
The abstract structure must be self similar, in that reality is logically consistent with itself. So two electrons are the "same" are they not? I recall Richard Feynman proposed the idea that all electrons are just one electron. So there is a stratification of cognitive categories. Algebraic structures that are isomorphic.
So contents of the observable universe exhibit the underlying mathematical structures with their interrelations and interactions. Universal instantiations of physical law. Mathematics corresponds to reality as the universal corresponds to instantiated particular. I.e. mathematics corresponds to reality as pattern corresponds to patterned. Exemplifications of the logical correspondence[morphisms] to reality are discovered through the patterns in the mathematical structure among observable objects.
So now Gedankin will protest by saying that we are headed directly into a fuzzy logic explosion ![[Wink]](wink.gif)
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gedanken
Member
Member # 594
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posted 05. November 2003 10:36
Richard Feynman proposed a concept that there is “one electron”. Alright, so a scientist ‘proposed’ an idea. This makes the concept now an iso-morphism, that Feynman proposed such an idea?
One of the loose definitions of ‘isomorphism’ is this correspondence of structure of a physical law to structure of reality. That is why I asked much earlier about which definition of “isomorphism” was in use. The response has been consistently, and even apparently when the question has been asked elsewhere, that the precise mathematical definition of a bijective mapping preserving (mathematical) structure is the intended definition, not the loose definition of “correspondence”. So note the presence of the inverse as well as forward mapping that Kevin Langdon asked about (and apparently as far as I can tell never received an adequate answer).
I think it is very important not to get these issues mixed up. There are separate issues. One issue is about some sort of “replication”, wherein a separate copy of the lexically stated relationship of nature must be present to bijectively map to the instantiation of such a relationship. A separate issue is about the degree of accuracy of such relationships, stated in language, to actual performance in reality.
Let me ask a question that is related to this. You may or may not see the relation, but please bear with me. Are not classical mechanics “laws” correct? (Note that classical mechanics predictions can be used to put a man on the Moon, and many other physical measurements of classical mechanics can be done with many digits of precision in the measurements!) Then if classical mechanics is ‘correct’, how do you explain the anomalies seen as required for further theories like relativity, QM, etc. And if it is not ‘correct’, then describe why and now it is not correct, and why and how one gets such precise correspondence in so many peasurements, even sufficient to put a man on the Moon.
(On “fuzzy logic explosion”, I don’t recall using that terminology. And if I did, I apologize for the lack of clarity. I do discuss how in trying to accurately model the real world one hits limits of measurement, including combinatorial explosion of interacting factors that complicate getting a completely accurate statement of relationships in nature. “Fuzzy logic” application of notions like that such relationships are correct in degree are useful in that regard.)
[ 05. November 2003, 10:51: Message edited by: gedanken ]
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chimp
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Member # 333
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posted 05. November 2003 12:03
First, my apologies for all of the quotes, but Gedankin continues to demand strict definitions
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Gedankin:
Once one tries to introduce the higher order descriptions--then the combinatorial explosion occurs, and the "fuzzy logic" issues rear in greater degree, etc.
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Gedankin:
On “fuzzy logic explosion”, I don’t recall using that terminology.
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Gedankin:
One of the loose definitions of ‘isomorphism’ is this correspondence of structure of a physical law to structure of reality. That is why I asked much earlier about which definition of “isomorphism” was in use. The response has been consistently, and even apparently when the question has been asked elsewhere, that the precise mathematical definition of a bijective mapping preserving (mathematical) structure is the intended definition, not the loose definition of “correspondence”. So note the presence of the inverse as well as forward mapping that Kevin Langdon asked about (and apparently as far as I can tell never received an adequate answer).
Here is another "isomorphism" explanation on the web:
http://www.ctmu.org/CTMU/Discussions/Atheist.html
quote:
Christopher Langan:
What is “irreal” is the assumed veridical mapping of personalized fantasies onto general (perceptual) reality.
Again, we have the distinction between particular theoretic languages, which may indeed be fantastic, and the basic syntactic relations of which they are composed. With respect to ordinary theories, the map is not the terrain; with respect to cognitive and perceptual syntax, it sure as hell is, right up to isomorphism. (By the way, "up to isomorphism" is not an escape clause. Beyond the maximum scope and resolution at which the real universe can internally sustain a syntax <--> content, mind <--> reality, cognition <--> information, time<-->space isomorphism, there is no more reality; the isomorphism is the entire basis of the coherence of the real universe! This should readily become apparent to anyone who tries, logically of course, to find an alternative basis.)
I found the "cybernetics" definition of isomorphism that must agree with the CTMU, sinse CTMU is a model employing cybernetics terminology:
http://pespmc1.vub.ac.be/ASC/ISOMORPHISM.html
quote:
ISOMORPHISM
(l) A mapping of one entity into another having the same elemental structure, whereby the behaviors of the two entities are identically describable. (John Warfield) (2) A formal correspondence of general principles or even of special laws. (Bertalanffy) (3) A set of principles may be transferred from one field to another without need to duplicate the effort. (Weinberg) (4) a one-to-one correspondence between the elements of two sets such that the result of an operation on elements of one set corresponds to the result of the analogous operation on their images in the other set.
A one-to-one mapping representing a pattern in the domain of the mapping by another pattern in its range without loss of information. The product of applying an isomorphism is called an isomorphic system that is a model of another by virtue of an isomorphism offers no simplifications. This may be useful, e.g., when one seeks an electronic substitute for a cognitive process such as the automatic pilot for an airplane. The more common simpler models, from a street map to a simulation of economic processes call for homomorphisms not isomorphisms.
[ 05. November 2003, 12:04: Message edited by: Russell E. Rierson ]
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gedanken
Member
Member # 594
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posted 05. November 2003 13:19
Russell, I have most certainly used "fuzzy logic", and "combinatorial explosion" as relating. It was the complete sequence or phrase "fuzzy logic explosion" that I was questioning, as I don't recall that, and it does not seem to be a coherent expression with regard to its use above. The 'explosion' of terms primarily occurs if one tries to continually refine a crisp logic model to the seemingly infinite number of details of all the interactions that need to be considered. So "crisp logic explosion" makes sense. (And I have also, elsewhere, pointed out that even 'fuzzy logics' do not solve the problem--the only element of fuzzy logic I am taking as important is their recognition of matter of degree. Thus one could have an 'explosion' of fuzzy logic terms, thus "fuzzy logic explosion", due to particular fuzzy logic chosen still not being sufficient to model the real world--but I don't think that was what was meant.)
But then as to isomorphism:
First--this is strictly distinct from the issue of "fuzzy logic". (Don't confuse issues here.)
For a moment I thought we were in agreement on one-to-one and onto, which means bijective and thus strictly invertable. The "cybernetics" definition #2 is incoherent for the same reason as our discussion here seems to be, if it is intended to also incorporate bijectivity. The reason the "cybernetics" #2 definition (but with "bijectivity") is incoherent is that it uses or implies the conditions one-to-one and onto, but does not actually adhere to its own self proclaimed terminology. The relationship, which has multiple instantiations, is thus not one-to-one! (Thus violating their own self imposed terminology.)
But let's also be clear that I mentioned this definition (which is #2 here) before, but took it as not including bijectivity. This removes self-inconsistency, just is a fuzzy or less crsip definition, and is thus demonstrably not the definition used in CTMU.
The 'cybernetics' definition #2 (without further assuming bijectivity), which has multiple cases or instantiations mapping to a single relationship description (preserving structure) is more closely related to a different morphism than "iso-morphism", in that multiple instantiations map to the single relation description, preserving structure (at least in concept). This is close to homomorphism of the multiple instantiations to the single relationship description, but there are minor technical problems. That this is not the intended definition can be deduced from existing discussions which include recognition of homomorphism and explicitly distinguishing, and of existing discussions invoking bijectivity.
[ 05. November 2003, 13:41: Message edited by: gedanken ]
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chimp
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Member # 333
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posted 05. November 2003 14:00
quote:
For a moment I thought we were in agreement on one-to-one and onto, which means bijective and thus strictly invertable.
A Boolean algebra is any "lattice" that is isomorphic to a collection of sets closed under complementation and intersection. Gedankin rejects one definition[cybernetics 2] of isomorphism but an isomorphism is just a homomorphism that is one to one and onto.
A bijection is an association of two sets such, that every member of each set is uniquely paired with a member of the other. So the abstract structure of CTMU is stratified and the universal instantiations[concrete relations] are ismomorphic to distinct stratifications of SCSPL cognitive and perceptual syntax. Syntax and state are closed under complementation and intersection.
Syntax becomes state and state becomes syntax, so the strict invertability and thus the bijection are consistently explained, much to the chagrin of Gedankin?
[ 05. November 2003, 14:04: Message edited by: Russell E. Rierson ]
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gedanken
Member
Member # 594
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posted 05. November 2003 14:19
quote:
Syntax becomes state and state becomes syntax, so the strict invertability and thus the bijection are consistently explained, much to the chagrin of Gedankin?
Chagrin? So now you agree that if combinatorially exploding or infinite number of expressions are required to represent real world situations with complete accuracy, then the “universal instantiations[concrete relations]” must furthermore be combinatorially exploding or of infinite cardinality. Specifically, a new definition of “syntax” must be accommodated, one that allows for infinite quantity of language statements in the “cognitive and perceptual syntax” and of infinite number of elements for representation of “state” if the later case is required. And if the former, then “state” or “cognitive and perceptual syntax” requires a combinatorially exploding amount of syntactic information for each and every tiny aspect of reality, and thus not escaping Godelian problems after all.
To put it another way, consider each elementary particle (in a complete and accurate Theory Of Everything, such as a string theory can be found to be an accurate representation of elementary particle interaction). Each particle must include not only its own complete copy of the TOE, but also a complete description of the interaction of that particle with every other particle in the universe.
But if there is another layer of turtles under the so-called TOE, such that the TOE turns out not to be completely accurate description of reality, then even more and possibly recursive theories must also be instantiated. In that case, even to complete the TOE a possibly infinite amount of state “syntax” may be required. This is an unknown.
Russell, I note that you did not answer my question about classical mechanics, so I ask again.
Let me ask a question that is related to this. You may or may not see the relation, but please bear with me. Are not classical mechanics “laws” correct? (Note that classical mechanics predictions can be used to put a man on the Moon, and many other physical measurements of classical mechanics can be done with many digits of precision in the measurements!) Then if classical mechanics is ‘correct’, how do you explain the anomalies seen as required for further theories like relativity, QM, etc. And if it is not ‘correct’, then describe why and now it is not correct, and why and how one gets such precise correspondence in so many measurements, even sufficient to put a man on the Moon.
[ 05. November 2003, 14:35: Message edited by: gedanken ]
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chimp
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Member # 333
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posted 05. November 2003 14:38
quote:
Gedankin:
Specifically, a new definition of “syntax” must be accommodated, one that allows for infinite quantity of language statements in the “cognitive and perceptual syntax” and of infinite number of elements for representation of “state” if the later case is required.
In other words you are explaining that a theory must be exactly complete down to every last minute detail of a total completed reality?
Identity is distributive and it seems that it can be derived from first principles[Telic Principle?] and be explained in terms of relations that are necessarily true on logical or analytic grounds only. It would then take the form of a tautological set of relations via its own self referential identity variable. The content of theory would become the emerging content of the identity operator. Gedankin seems to be trying to explain that since there is Godelian incompleteness, there will never be an isomorphic interpretation[T.O.E] of reality?
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gedanken
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Member # 594
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posted 05. November 2003 19:57
quote:
In other words you are explaining that a theory must be exactly complete down to every last minute detail of a total completed reality?
No, it is not I who is saying that. Rather every person who says that strict isomorphism must occur, wherein isomorphism is not defined as the #2 definition above which is rather loose, rather isomorphism is the strict mathematically exact in every detail one to one and onto mapping preserving structure exactly in every detail.
Now if you're not saying that, then I guess I misunderstood quite a number of posts above--but that's possible.
[ 05. November 2003, 19:58: Message edited by: gedanken ]
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chimp
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posted 06. November 2003 02:28
quote:
Gedankin:
No, it is not I who is saying that. Rather every person who says that strict isomorphism must occur, wherein isomorphism is not defined as the #2 definition above which is rather loose, rather isomorphism is the strict mathematically exact in every detail one to one and onto mapping preserving structure exactly in every detail.
Mind is isomorphic to reality in that mind and reality share the same cognitive and perceptual syntax. If they did not, everyone would perceive disconnectedly different realities from the one all inclusive reality we now perceive. I recall Jason has kindly given you that definition several times.
Hology is a powerful form of self similarity. Specifications of bijections between sets of combinatoric objects can be recursively defined and become generalizations of context free grammars. Recursive descriptions of objects defined by means of terminal objects is called an object grammar. These object grammars are isomorphic. So if my interpretation is correct, the SCSPL algebraic language is a type of universal algebra of which categorized object grammars belong to its domain. The context free variable is known as the identity operator. Identity distrubutes over the self referential reality, recursively. Spatio temporal self similarity is then a fractal effect.
Geometric reductions are substituted for the elementary relations as the sentenial variables of a tautology, are substituted for the tautology itself. Reality evolves inwardly, evolving as a language, a process in which specific elements are substituted for more general elements.
It appears that the CTMU definition of "isomorphism" is rigorously defined, yes?
[ 06. November 2003, 02:44: Message edited by: Russell E. Rierson ]
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Aliet Jacob
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Member # 908
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posted 06. November 2003 06:35
quote:
Is this a religion?
The first (pseudo) Mathematical Theology: Church of Teleology of Multiplex Unity.
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Aliet Jacob
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Member # 908
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posted 06. November 2003 06:43
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Mind is isomorphic to reality in that mind and reality share the same cognitive and perceptual syntax.
This is incorrect.
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Hology is a powerful form of self similarity.
Are there weak forms of self-similarity? This is hyperbole.
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These object grammars are isomorphic.
By design. This is like marvelling at the fact that a circle is actually a round shape.
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chimp
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posted 06. November 2003 14:07
quote:
quote:
Mind is isomorphic to reality in that mind and reality share the same cognitive and perceptual syntax.
This is incorrect.
Your philosophic opinion? Proof please... no more overly simplistic Madonna analogy-counterexamples.
Elementary categories of cognition and perception are the syntactic elements of cognitive and perceptual languages. SCSPL.
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Hology is a powerful form of self similarity.
Are there weak forms of self-similarity? This is hyperbole.
Good point about the word "powerful", does it leave room for ambiguity in the interpretation? Not if all the CTMU material has been assimilated. What is the difference between a form and a powerful form? Is hology a logical generalization of holography? It is defined as a cybernetic, and therefore logical, form of self-similarity in which the global structure of a self referential, self-containing, self-interactive system is also its own self-distributed self-transductive syntax; justified by the obvious fact that for a self-containing system, no other structure exists, or is available, for that purpose.
Since there is no other structure available for a self containing universe, it is not hyperbole as Aliet Jacob incorrectly and desperately, tries to argue.
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These object grammars are isomorphic.
By design. This is like marvelling at the fact that a circle is actually a round shape.
By design or logical necessity? The nomology is isomorphic at time T and time T_n. We perceive a logically consistent universe, Aliet's fantasies notwithstanding. The SCSPL's general spatiotemporal structure is hologically replicated everywhere within itself as self-transductive syntax. Thus, the generative phase of reality is reduced to the generative grammar of SCSPL.
[ 06. November 2003, 14:12: Message edited by: Russell E. Rierson ]
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Dene Bebbington
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Member # 168
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posted 06. November 2003 18:58
Russell Rierson wrote:
quote:
Mind is isomorphic to reality in that mind and reality share the same cognitive and perceptual syntax. If they did not, everyone would perceive disconnectedly different realities from the one all inclusive reality we now perceive.
Can you explain what perception is? For example, is it the raw signals detected by human senses or the subjective experience of those senses.
People with eyesight problems perceive the world differently to those with "normal" eyesight, and people who are colour blind perceive colours differently than those who are not colour blind. Can you explain how you know whether it's syntax or semantics that determines perception?
In other words, in the CTMU where does syntax end and semantics begin?
--
Dene
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gedanken
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Member # 594
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posted 06. November 2003 19:20
It may be claimed that mind is iso-morphic to reality. But that would eaither mean that every mind is omniscient, or is suportive of solipsism. (Solipsism because our limited minds "ISO-" morphic thus one to one onto all of reality means a very small and private reality. Remembrer this case is not omnicient mind, for which a one to one and onto of all of reality might be reasonable.)
quote:
powerful form of ...
But this is just what I have pointed out over many pages. This is not crisp logic. Rather it is argument with matter of degree.
[ 06. November 2003, 20:00: Message edited by: gedanken ]
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