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Author Topic: Cosmogony, Holography and Causality
Rex Kerr
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Icon 1 posted 07. November 2003 01:18      Profile for Rex Kerr     Send New Private Message       Edit/Delete Post 
There seems to be a fundamental assumption here that some people are forgetting to question and others are perhaps forgetting to notice. It's a philosophical question: do objects exist?

As far as I can tell, Russel has completely accepted the premise that objects do exist. For example, there is some ideal Platonic form, and that such objects can be treated by their category, instead of individually. For example, a proton has position, momentum, and spin. All protons are identical, aside from the values of these three observables. They all have charge +1, they all have a certain mass, etc. etc..

It may indeed be possible to fashion an isomorphism of sorts between Chris's favored but largely arbitrary abstraction of mind, and between this particular view of reality.

But there are serious and apparently unresolved issues on both sides. The one that seems to be coming up here is that this view of reality can't robustly be supported. Sure, we can say, "Hey, let's suppose that there are no differences between protons, on any time scale, in any situation, aside from these QM observables." This doesn't mean that the universe is this way; it's just speculation. So far, it seems to be a fairly good representation. (It does not seem to work so well, however, with chairs.)

We could try to use quantum mechanics now to bolster our claim. But if we notice that QM replaced classical mechanics which replaced Aristotelian mechanics which replaced intuitive notions of mechanics--each with better preditive power than the last--we might doubt that QM is the final word. Indeed, we should doubt that QM is the final word. How elementary are the elementary particles, after all?

Please see gedankin's question about classical mechanics--it gets at the same point. And it's a very important point.

The other half of the failure is at least as bad, as far as the CTMU goes. If we can only comprehend that part of the universe that is isomorphic to some syntax that we use, the syntax cannot possibly be logic, because we're only able to understand the simplest logical constructs. Rather, the universe has to be isomorphic to our actual thought processes: fuzzy, sometimes logical, sometimes emotional, beset by error, etc.. This is, on the one hand, exactly right: we can only understand what we can understand. But on the other hand, it's an absurdly bad model for an external reality, since it is our experience that some things (e.g. mechanics) behave much more predictably than our cognition does. So this approach seems wrong in principle. Why is it any better in principle if we take an abstraction of human cognition, namely logic, than if we take the cognition itself? There are many logical things that are incomprehensible, so this hardly seems to help; if the analysis is correct (and I believe it is not), that would allow many things in the universe that we couldn't perceive or understand, and hence were not in the universe by definition. Oops.

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chimp
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Icon 1 posted 07. November 2003 03:05      Profile for chimp   Email chimp   Send New Private Message       Edit/Delete Post 
quote:

Deb Bebbington:
Can you explain what perception is? For example, is it the raw signals detected by human senses or the subjective experience of those senses.

Cognition and perception are languages based on the SCSPL syntax, as explained in the CTMU writings. Logical tautologies are then the basis of our cognitive and perceptual syntax. So anything that is beyond logic, is beyond cognition, which is then beyond perception, which is then beyond the senses.
Perception is a cognitive process, logical information processing with degrees of complexity, that is to say, perception is a self processing language. Mind and reality are linked in mutual dependence[isomorphism [Wink] ] on the most basic level of understanding. It is an interactive connection of the abstract and the concrete, the subjective and the objective, the internal and the external.
Therefore, it is impossible to separate mind from reality.

quote:

Gedankin:
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.)


Since mind equals reality, solipsism becomes a distributive identity. The mind of Gedankin is an SCSPL subprocessor in the universal information processor = mind, if my interpretation is correct...
quote:

Gedankin:
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.


Gedankin, do you have a point with regards to the Copenhagen interpretation of quantum mechanics?
The crisp 2V logic resides in the fact that potential is actualized, which becomes A or not-A. Particles of matter are also waves.

When the waves intersect, they don't disappear. A type of continuum must be generated by the interconnected waves. So an observation is the creation of standing waves. The logic becomes
[standing wave] or not[standing wave].

Waves are self similar.

quote:

Rex:
The other half of the failure is at least as bad, as far as the CTMU goes. If we can only comprehend that part of the universe that is isomorphic to some syntax that we use, the syntax cannot possibly be logic, because we're only able to understand the simplest logical constructs. Rather, the universe has to be isomorphic to our actual thought processes: fuzzy, sometimes logical, sometimes emotional, beset by error, etc.. This is, on the one hand, exactly right: we can only understand what we can understand. But on the other hand, it's an absurdly bad model for an external reality, since it is our experience that some things (e.g. mechanics) behave much more predictably than our cognition does. So this approach seems wrong in principle. Why is it any better in principle if we take an abstraction of human cognition, namely logic, than if we take the cognition itself? There are many logical things that are incomprehensible, so this hardly seems to help; if the analysis is correct (and I believe it is not), that would allow many things in the universe that we couldn't perceive or understand, and hence were not in the universe by definition.

A thought process such as an emotion, making errors, etc. is result of cognitive processing. The cognitive processing must be by definition logical. The brain processes information according to logical rules.

[ 07. November 2003, 04:39: Message edited by: Russell E. Rierson ]

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Aliet Jacob
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Icon 1 posted 07. November 2003 04:52      Profile for Aliet Jacob   Email Aliet Jacob   Send New Private Message       Edit/Delete Post 
Russel claimed: "Mind is isomorphic to reality in that mind and reality share the same cognitive and perceptual syntax"

He offered no support of that claim but when I pointed out that its incorrect, he asks me to explain with good evidence. I will ignore the double standard and indulge him.

First, Russel needs to explain what is the syntax of reality and then explain what is the syntax of the mind.

By the very fact that he juxtaposes reality from mind, it means that Russel is talking about the non-sentient part of reality like water or a rock or a dust particle.

The dust particle is not isomorphic to the mind because the mind is capable of conceptualizing while the dust particle is not. The dust particle has no desires while it is desires/purpose/instincts that drive the mind to action. When one sees a rock on a stool, one cannot imagine that the rock had any choice in its being there because rocks do not have choices and do not think.

The mind can see water where there is no water (mirage) and the mind will rush to the water only for the water to move further and further away. Thus reality in such cases is inconsistent with perception.
Thus the percept and percepient are not always on the same page.

From geocentricity to heliocentricity, one can see that cognition is not the same as reality as Langan argues. Reality theory is not equal to reality, but is a description of reality.

Russel's arguments can only hold for those that believe that electrons and atoms are sentient.

quote:
By design or logical necessity?
By design. A chair is not a chair by logical necessity. The laws of science are not the laws of science by logical necessity - we describe the phenomena in question as the laws of science. We dont get to prescribe them. A rose is not a rose by logical necessity.

You can call the laws of science "cupboard of stools" and they will still be the laws of science as we know them.

There is nothing logical by going to the toilet or having fever when we are sick. These are chain reactions that we have experienced over time and have come, via study, to integrate into our knowledge by knowing their causes. And even then, we still dont know plenty.

In making your arguments, like Langan, you have mightily confused force and energy with logic.

An electron does not attact another particle by logical necessity: its because of a force.

You need to define logic first before you start squandering it like you are doing. In failing to define it, you afford yourself an opportunity to abuse it and misapply its meaning, while buying the necessary wriggle room.

quote:
We perceive a logically consistent universe, Aliet's fantasies notwithstanding.
There is nothing logical about the universe. Its stable. Thats all. And because its stable, we can explain it and have our explanations 'matching' what we observe. But if gravity becomes a repulsive force, we can explain in also - so long as its constantly repulsive. It wont be less logical.

Consistency allows logic. But 'logically consistent' is not the same as 'logical'. The former is a description while the latter has intrinsic connotations.

The aspects of reality that are consistent have got nothing to do with logic. So, 'logically consistent' is an incorrect expression.

quote:
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.
Hology is an adoption of the cosmological principle under the cloak of holography.
There is nothing new or useful that it can offer. Hollow words like "spatiotemporal" are gramatically impressive but lack any useful concepts that we do not know. They are like rocking chairs: keep you busy but take you nowhere.

Please provide evidence that there is a part of reality that "generates" grammar. And why if such a 'phase' exists, it violates the cosmological principle.

And if you want to talk about automata, dont even try.

Yeah, ged's point about crispness is important. In advocating for hology over holography, Langan uses such terms as 'more powerful'. 'Powerful' means exactly nothing. Because it doesnt make a concept more correct or more explanatory and is not scientific. As such, its all hyperbole and aggrandizement of the arguments.

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chimp
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Icon 1 posted 07. November 2003 06:41      Profile for chimp   Email chimp   Send New Private Message       Edit/Delete Post 
quote:

Aliet:

First, Russel needs to explain what is the syntax of reality and then explain what is the syntax of the mind.

By the very fact that he juxtaposes reality from mind, it means that Russel is talking about the non-sentient part of reality like water or a rock or a dust particle.

The dust particle is not isomorphic to the mind because the mind is capable of conceptualizing while the dust particle is not. The dust particle has no desires while it is desires/purpose/instincts that drive the mind to action. When one sees a rock on a stool, one cannot imagine that the rock had any choice in its being there because rocks do not have choices and do not think.

A dust particle is a logical process composed of interacting quarks and leptons, which could be composed of even more fundamental particles like strings, or loops, etc. If my interpretation is correct, these fundamental entities are one type of SCSPL syntactic operator. Since the mind is an SCSPL, it is identical to reality. The dust particle has degrees of complexity, with the individual sentient mind being more complex than the dust particle, the rock, or vegtable... etc.
Syntax[reality] = Syntax[mind] :
Cognition and perception are languages based on the SCSPL syntax, as explained in the CTMU writings. Logical tautologies are then the basis of our cognitive and perceptual syntax. So anything that is beyond logic, is beyond cognition, which is then beyond perception, which is then beyond the senses.


quote:

Aliet:

The mind can see water where there is no water (mirage) and the mind will rush to the water only for the water to move further and further away. Thus reality in such cases is inconsistent with perception.
Thus the percept and percepient are not always on the same page.

From geocentricity to heliocentricity, one can see that cognition is not the same as reality as Langan argues. Reality theory is not equal to reality, but is a description of reality.

Russel's arguments can only hold for those that believe that electrons and atoms are sentient.


I will repeat:
Perception is a cognitive process, logical information processing with degrees of complexity, that is to say, perception is a self processing language. Mind and reality are linked in mutual dependence[isomorphism ] on the most basic level of understanding. It is an interactive connection of the abstract and the concrete, the subjective and the objective, the internal and the external.

Therefore, it is impossible to separate mind from reality.

Yes, atoms and electrons are CTMU syntactic operators. Information processors that operate according to their allowed degrees of freedom.


quote:
quote:

By design or logical necessity?

By design. A chair is not a chair by logical necessity. The laws of science are not the laws of science by logical necessity - we describe the phenomena in question as the laws of science. We dont get to prescribe them. A rose is not a rose by logical necessity.

You can call the laws of science "cupboard of stools" and they will still be the laws of science as we know them.

A chair, like the dust particle, is an information processing system composed of interacting particles. Therefore the chair is a logically consistent aspect of a self contained reality. A thought process such as an emotion, making errors, etc. is result of cognitive processing. The cognitive processing must be by definition logical. The brain processes information according to logical rules. Laws of science must be logically consistent.
Repeat [Wink]
Cognition and perception are languages based on the SCSPL syntax, as explained in the CTMU writings. Logical tautologies are then the basis of our cognitive and perceptual syntax. So anything that is beyond logic, is beyond cognition, which is then beyond perception, which is then beyond the senses.

quote:

There is nothing logical by going to the toilet or having fever when we are sick. These are chain reactions that we have experienced over time and have come, via study, to integrate into our knowledge by knowing their causes. And even then, we still dont know plenty.

In making your arguments, like Langan, you have mightily confused force and energy with logic.

An electron does not attact another particle by logical necessity: its because of a force.

You need to define logic first before you start squandering it like you are doing. In failing to define it, you afford yourself an opportunity to abuse it and misapply its meaning, while buying the necessary wriggle room.

If a human being has the standard digestive system, then it is logical that their body produces waste products at the end of the digestive process, and it is therefore logical that they complete the digestive process at the appropriate location.

If a person is sick, one possible symptom of sickness is a high temperature i.e. a fever.
It is therefore logical for certain sick prople to have a fever.

All of the laws of physics are based on mathematics and mathematics is based on logic. Therefore descriptions of force and energy are logical. Therefore force and energy are logical.
Energy is conserved. [1 Newton of force] = [1 Newton of force]. Very logical [Wink]

quote:
quote:

We perceive a logically consistent universe, Aliet's fantasies notwithstanding.

There is nothing logical about the universe. Its stable. Thats all. And because its stable, we can explain it and have our explanations 'matching' what we observe. But if gravity becomes a repulsive force, we can explain in also - so long as its constantly repulsive. It wont be less logical.

Consistency allows logic. But 'logically consistent' is not the same as 'logical'. The former is a description while the latter has intrinsic connotations.

The aspects of reality that are consistent have got nothing to do with logic. So, 'logically consistent' is an incorrect expression.

Is Aliet trying to say that logical consistency is not logical???. Tautologies of logic are absolute truths, consistency could not exist without them.

quote:
quote:

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.

Hology is an adoption of the cosmological principle under the cloak of holography.
There is nothing new or useful that it can offer. Hollow words like "spatiotemporal" are gramatically impressive but lack any useful concepts that we do not know. They are like rocking chairs: keep you busy but take you nowhere.

Hology is a generalization of holography. A perfect fractal? would be isomorphic to succsessive magnifications of itself, so there is no associated cloak and dagger with respect to the hology principle [Wink]


quote:


Please provide evidence that there is a part of reality that "generates" grammar. And why if such a 'phase' exists, it violates the cosmological principle.

According to physicist Lee Smolin, a description of any entity inside the real universe can only refer to other things within the universe. Space is then relational. For example, if an object has a momentum, that momentum can only be explained with respect to another object. Space then becomes an aspect of the relationships between things in the real universe. Space becomes analogous to a sentence, and Smolin says it is absurd to say that a sentence has no words in it. So the grammatical structure of each sentence[space] is defined by the relationships that hold between the words in it. For example, relationships like object-subject or adjective-noun. So there are many different grammatical structures composed of different arrangements of words, and the varied relationships between them.
SCSPL starts with a first principle and the forward[inward] direction of time is a deductive process of generating the SCSPL grammar. The generative grammar of SCSPL does not violate the cosmological principle since the CP must be the direct consequence of SCSPL generative grammar.

quote:

And if you want to talk about automata, dont even try.

Yeah, ged's point about crispness is important. In advocating for hology over holography, Langan uses such terms as 'more powerful'. 'Powerful' means exactly nothing. Because it doesnt make a concept more correct or more explanatory and is not scientific. As such, its all hyperbole and aggrandizement of the arguments.

It appears that SCSPL is more advanced than the cellular automata, in that SCSPL can explain its own genesis? and cellular automata cannot. But that brings us back to the UBT, and we cannot say anything about UBT because that would be giving UBT a constraint. Then it would no longer be pure freedom. But then again, the UBT can be explained as a perfect self cancellative symmetry and SCSPL would be a process of symmetry breaking. Yes?

"Ged" appears to totally miss the point about the 2 valued logic of the CTMU. According to ged, reality is not logical. Since all theories and explanations of reality must be logical, ged's illogical musings about reality being illogical appear to be incorrect along with being illogical [Wink]

[ 07. November 2003, 07:06: Message edited by: Russell E. Rierson ]

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gedanken
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Icon 1 posted 07. November 2003 14:51      Profile for gedanken         Edit/Delete Post 
quote:
If a human being has the standard digestive system, then it is logical that their body produces waste products at the end of the digestive process, and it is therefore logical that they complete the digestive process at the appropriate location.
What is the "standard digestive system"? It definitely appears that Rex is correct, you make these assumptions that objects exist in their Platonic ideal.

quote:
"Ged" appears to totally miss the point about the 2 valued logic of the CTMU. According to ged, reality is not logical. Since all theories and explanations of reality must be logical, ged's illogical musings about reality being illogical appear to be incorrect along with being illogical
Russell, do you believe that everything you say is logical? Do you believe that everything everyone says is "logical"? If not, then you must accept that parts of reality are not "logical". So now we do not have that "reality" per se is "logical," rather that some aspect or portion of reality is "logical". That would be deductive using the logic you appear to be using. (If it is not 'logical,' then perhaps my point was made just there.) Now we have that only a portion of reality at most is "logical", how much? How do we separate the "logical" portion from the portion that is not "logical"?

If (by definition) "all theories and explanations of reality must be logical", then how do we know that there are any theories or any explanations? Our argument will go back into a circle if you try to demonstrate one of them, and I poke a little hole in the explanation by showing that it is not perfectly "logical".

Or do you mean that there are theories and explanations of reality, and that some of them exist and by definition are "logical", but that these theories and explanations are not known to conform to reality? (For if they are known to conform to reality, I suggest showing that, and showing that they have no points whatsoever of divergence from strictly and completely "logical" conformance to observation. If that cannot be shown, you have not made that point.)

Or lastly, are you simply claiming (as I think Rex pointed out) that there might be some theory or explanation of reality that is completely logical. But this has not been demonstrated.

But Russell, I suggest looking at my statement above in terms of paradox. One cannot state that No statement is completely and crisply "logical", and do so within "logic". I think that Godelian issues apply.

[ 07. November 2003, 17:00: Message edited by: gedanken ]

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chimp
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Icon 1 posted 08. November 2003 02:52      Profile for chimp   Email chimp   Send New Private Message       Edit/Delete Post 
quote:

If (by definition) "all theories and explanations of reality must be logical", then how do we know that there are any theories or any explanations? Our argument will go back into a circle if you try to demonstrate one of them, and I poke a little hole in the explanation by showing that it is not perfectly "logical".

Or do you mean that there are theories and explanations of reality, and that some of them exist and by definition are "logical", but that these theories and explanations are not known to conform to reality? (For if they are known to conform to reality, I suggest showing that, and showing that they have no points whatsoever of divergence from strictly and completely "logical" conformance to observation. If that cannot be shown, you have not made that point.)

Or lastly, are you simply claiming (as I think Rex pointed out) that there might be some theory or explanation of reality that is completely logical. But this has not been demonstrated.

Logical-mathematical existence, simply means freedom from contradiction. Reality does not contradict itself. Therefore a theory that can prove both a statement and its negation is nonsensical and useless, because its statements and their negations can both be true.
Every aspect of reality is isomorphic to a description and theories are descriptions of reality [Wink]
Language describes things, so reality is isomorphic to a language.

quote:

But Russell, I suggest looking at my statement above in terms of paradox. One cannot state that No statement is completely and crisply "logical", and do so within "logic". I think that Godelian issues apply.

Goedel's Completness Theorem:
http://en2.wikipedia.org/wiki/G%F6del%27s_completeness_theorem
quote:

Gödel's completeness theorem is a fundamental theorem in mathematical logic proved by Kurt Gödel in 1929 . It states, in its most familiar form, that in first-order predicate calculus every universally valid formula can be proved.

Definition of first order predicate calculus:
http://en.wikipedia.org/wiki/First-order_predicate_calculus
quote:

Nevertheless, first-order logic is strong enough to formalize all of set theory and thereby virtually all of mathematics . It is the classical logical theory underlying mathematics. It is a stronger theory than sentential logic , but a weaker theory than arithmetic , set theory, or Second-order logic.

Propositional logic posesses mathematical closure:
http://en.wikipedia.org/wiki/Propositional_logic
Boolean Algebra:
http://en.wikipedia.org/wiki/Boolean_algebra

quote:

It can be shown that every finite Boolean algebra is isomorphic to the Boolean algebra of all subsets of a finite set; in particular, the number of elements of every finite Boolean algebra is a power of two.

According to physicist Lee Smolin, a description of any entity inside the real universe can only be with reference to other things in the universe. Space is then relational. For example, if an object has a momentum, that momentum can only be explained with respect to another object. Space then becomes an aspect of the relationships between things in the real universe. Space becomes analogous to a sentence, and Smolin says it is absurd to say that a sentence has no words in it. So the grammatical structure of each sentence[space] is defined by the relationships that hold between the words in it. For example, relationships like object-subject or adjective-noun. So there are many different grammatical structures composed of different arrangements of words, and the varied relationships between them.

Language describes the universe. The universe is isomorphic to a description and reality can only refer to itself, because, there is nothing outside of ...reality.
Since descriptions make distinctions, or references to other entities, and distinctions are tautologically logical, [A or ~A], reality is logical, in that its contents can be described by a language. The contents within reality are distinctive objects, individually different from the others.
You make a very good point about the theory of relativity Gedankin, when you say that relativity is really a theory of invariants. Tautologies of logic are also invariance principles, and it appears that the concept of an invariance is more general and ...powerful, than the concept of absolute truth, as expressed by the tautologies of logic...
That could be the ultimate failure of the CTMU? It relies on the logic of Aristotle, which is very riddled with paradox
[Wink]

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gedanken
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Icon 1 posted 08. November 2003 03:07      Profile for gedanken         Edit/Delete Post 
I'm going to concentrate on this "isomorphism" issue for the moment.

quote:
The universe is isomorphic to a description...
Alright, this is not taken with a lot of escape clauses about definitions given by others. (It may relate to CTMU, but given in this form is not a reference to CTMU paper definitions of terms.)

So (assuming that), Russell how can you continue to assert that? You have agreed over and over that "isomorphic" means one to one and onto. A description has fewer parts than the universe. Therefore it cannot possibly be "onto", because a bijective mapping must be between sets of equal cardinality. In the world of models where mathematically defined logic is crisp, a crisp relationship here is important.

---

Russell, relating to the other subject, I still note that you did not answer my question about classical mechanics, so I ask even yet again. (Rex has even asked for this as well.) It is highly relevant to other points, and other points can be put in context of the answer to this question (as example). If you value this discussion as a real attempt for us to understand one another, then the question is worth answering.

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.

[ 08. November 2003, 03:17: Message edited by: gedanken ]

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chimp
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Icon 1 posted 08. November 2003 04:16      Profile for chimp   Email chimp   Send New Private Message       Edit/Delete Post 
quote:

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.


Einstein:

R_uv - [1/2]g_uv R = 8pi G T_uv

is more correct than

Newton:

F = G m1 m2 /r^2

The Einstein field equations look very elegant and they contain much more information in their tensor formulations with regards to structure of spacetime and its relation to matter and energy, than does the Newtonian law of gravity. Tensors are a generalization of the "vector" concept. So, generalizations can be more "isomorphic" to reality than the more primitive abstract constructs.

So the exact description becomes a type of limit, in the compression of information via powerful generalizations.

Here is another relevant CTMU quote:

http://www.iomas.com/gina/ultrahiq/Mega-Society/NoesisJan02/CTMU.asp

quote:


A closed formal system may be stratified, including variables and metavariables of arbitrary logical order. This makes the system self-referential, enabling it to internally express high-level truths regarding itself while leaving no level of truth internally unsubstantiated (provided that there exists a mechanism for transfinite referential closure, e.g. conspansive self-axiomatizing grammar and a form of logical self-similarity called “hology”). In other words, no ultimate level of truth is left in need of external validation; self-containment is satisfied.




[ 08. November 2003, 04:22: Message edited by: Russell E. Rierson ]

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primate
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Icon 1 posted 09. November 2003 10:49      Profile for primate     Send New Private Message       Edit/Delete Post 
Logical mysticism. Perfect.
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Gambit
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Icon 1 posted 09. November 2003 14:46      Profile for Gambit     Send New Private Message       Edit/Delete Post 
quote:
A description has fewer parts than the universe. Therefore it cannot possibly be "onto", because a bijective mapping must be between sets of equal cardinality. In the world of models where mathematically defined logic is crisp, a crisp relationship here is important.

A description has fewer parts than that described by definition and would seem to generalize that which is described. An isomorphism is itself a description of sets of equal cardinality. This logic of generalization allows mapping a description to that which is described by implicitly reaching an equality between the two sets. Further, the implicit equality of these sets represents their logical interconnection.
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gedanken
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Icon 1 posted 10. November 2003 01:28      Profile for gedanken         Edit/Delete Post 
quote:
An isomorphism is itself a description of sets of equal cardinality.
Gambit, your point is relevant, but your statement quoted is about mappings from one model space to another model space. The issue we were discussing was of a possible meaning for a mapping from “description” of a physical relationship, to the actual physical. In the second term, one cannot use an arbitrary abstracted model as a substitute for the “physical”, as that is avoiding the question and discussing some other question (namely mapping from one model space to another model space).

Now I think what you are describing is more along these lines:

A generalized description (of a physical “law”) can form a mathematically defined generator of detail description. We call the generated detail descriptions a “production”. At least one instantiation of those detailed descriptions (in the expanded or generated production or set of specific relationships) could then (in principle) map one to one with some other large set of details (and here we are considering the actual “reality” as that target, considering it as a “set”).

Now I have specific problems with considering the target “reality” a “set”—and for that see several pages near start of this thread—but we can leave that issue for later.

The primary problem I am having is the claim that the relationship itself is “isomorphic” to the target set! It is not the original stated “law” (such as a scientific law) that is “isomorphic”, rather it is some expanded production that could be isomorphic, and that is a very different statement. Only the production has the potential for having the same cardinality—not the original relationship statement per se.

Presumably the mapping of the original relationship to the production is one to many, and its inverse could be a homomorphism from the production to the original relationship or “law”. Thus the inverse of the final isomorphism (as bijective mapping), composed with the first homomorphism, is itself a non-bijective homomorphism from the target back to the original relationship description or “law”. This is why I described the relationship of law description to (at least some detailed model of) physical reality as a “reverse homomorphism”, because it is at best in reverse a homomorphism from realty to the law description, and is in forward direction a one to many mapping.

But we still have problems, even now. Under what conditions do such a production actually match exactly any aspect of reality? This will be discussed more below.

--

Russell said:

quote:
Einstein:

R_uv - [1/2]g_uv R = 8pi G T_uv

is more correct than

Newton:

F = G m1 m2 /r^2

The Einstein field equations look very elegant and they contain much more information in their tensor formulations with regards to structure of spacetime and its relation to matter and energy, than does the Newtonian law of gravity. Tensors are a generalization of the "vector" concept. So, generalizations can be more "isomorphic" to reality than the more primitive abstract constructs.

So the exact description becomes a type of limit, in the compression of information via powerful generalizations.

First I draw attention to phrases “..is more correct than..”, and “..generalizations can be more ‘isomorphic’ to reality than..” (my emphasis.) First note my emphasizing “more” which is a quantifying concept.

I thought that “correct” was “logical”, as in “binary” or 1/0 or “true”/“false”. How can one statement be more “true” than another? How can one system be more “isomorphic” than another? (Isomorphic is a mathematically defined model statement, it is either ‘true’ or ‘false’!) But of course it can—that has been precisely what I was talking about for several pages here. Logic as actually used in human conversation has degree, logic is “fuzzy”, not crisp! (At least the logic that Russell appears to be using in this argument!)

Now I appreciate the link to other statements on Mr. Langan’s CTMU, as it does help clarify issues with respect to that concept. (I had been more concentrating on Russel’s statements here than on reference to CTMU versions of definitions of terms.)

But the response about self-generating of axioms (is that what “self-axiomatizing grammar” means?) does not demonstrate an escape from infinite quantity of syntactic data needed to represent that “limit”!

I have never claimed that an amount of syntactically represented binary or crisp logic statements which increases in limit to infinity could not approximate reality (or all of reality) to any arbitrary degree of precision. Does SCSPL require infinite quantity of syntactic language?

What I find most significant, however, is Russell’s backtracking on use of “logic” as crisp terminology, not subject to matters of degree.

Furthermore we must consider this aspect of modeling represented by the progression of cases, first Newtonian, second Einsteinian laws. Now is the Einsteinian law final and completely correct? Of course not, and we all recognize that. First Newtonian mechanics is very useful fiction, accurately representing many situations with great accuracy. Then Einsteinian relationships cover more cases in two manners: One they cover the old cases with at least as great of accuracy. Second they cover many cases that were not covered by the Newtonian mechanics with a great deal of accuracy. But since neither has reached the end of error, neither has essentially changed the characteristic that they are matters of degree.

Russell, distance from point A to point B is r=1/t, for all t>1.0. Now in the limit as t approaches infinity, r=0. So do the points A and B touch? Do they touch as the approach the limit?

Now consider the following (and I’m starting over, forget the previous equations) :

At time t=1, we have r=1.0
At time t=2, we have r=0.5
At time t=4, we have r=0.25
At time t=8, we have r=0.125
Will points touch? In fact, do we know that we even have a limiting case? (e.g. do we know that we have the case r=1/t, or do we simply have a model that seems to accurately represent measurement r for many cases that are known?

Of course this is a model concept—I’m just making a point. The existence of the limit per se is not demonstrated by the example points, it is only suggested.

It is possible that there is a theory of everything as a physics theory. Will it be deterministic, or probabilistic? If it is probabilistic, what does that notion of a limit mean, as the basic concept is itself fuzzy? Is the TOE the only aspect that would be computed in the SCSPL? (No higher order logical relationships?)

How do we know that a TOE, to be really about “everything” as in completely accurate, must not be described with an infinite number of statements. (Rather that the number of TOE statements must tend to infinite as the accuracy tends to zero.)

[ 10. November 2003, 01:58: Message edited by: gedanken ]

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chimp
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Icon 1 posted 10. November 2003 04:03      Profile for chimp   Email chimp   Send New Private Message       Edit/Delete Post 
quote:

Gedankin:
I thought that “correct” was “logical”, as in “binary” or 1/0 or “true”/“false”. How can one statement be more “true” than another? How can one system be more “isomorphic” than another? (Isomorphic is a mathematically defined model statement, it is either ‘true’ or ‘false’!) But of course it can—that has been precisely what I was talking about for several pages here. Logic as actually used in human conversation has degree, logic is “fuzzy”, not crisp! (At least the logic that Russell appears to be using in this argument!)

If my interpretation is correct, the "exact" correspondence[isomorphism] is a limit. Theories are mental constructs that approach this limit. My apologies for the confusion, and consequent Gedankin "hair splitting" [Wink]
The phrase should be: "closer to isomorphism" instead of "more isomorphic" but thanks very much for the correction Gedankin [Wink]
Now Gedankin keeps mentioning the "combinatorial explosion" of terms that invariably must result from a description that is exactly isomorphic to the described universe. But the Riemann tensors are able to "compress" the information. So a large number of terms becomes informationally compressible, getting closer to the correspondence that is one to one and onto.
The exact "crisp" correspondence exists at the limit. We see that the limit is a convergence. Can Gedankin, or Rex, prove otherwise?

quote:

Gedankin:
But the response about self-generating of axioms (is that what “self-axiomatizing grammar” means?) does not demonstrate an escape from infinite quantity of syntactic data needed to represent that “limit”!

I have never claimed that an amount of syntactically represented binary or crisp logic statements which increases in limit to infinity could not approximate reality (or all of reality) to any arbitrary degree of precision. Does SCSPL require infinite quantity of syntactic language?


The SCSPL utilizes transfinite algebra. The infinite number of terms could be represented as "variables and metavariables of arbitrary logical order"... SCSPL is a dynamic that generates its own axioms as it evolves.

quote:

Gedankin:
Of course this is a model concept—I’m just making a point. The existence of the limit per se is not demonstrated by the example points, it is only suggested.

It is possible that there is a theory of everything as a physics theory. Will it be deterministic, or probabilistic? If it is probabilistic, what does that notion of a limit mean, as the basic concept is itself fuzzy? Is the TOE the only aspect that would be computed in the SCSPL? (No higher order logical relationships?)


If my understanding is correct, the "CTMU" is a framework designed to incorperate the increasingly more correct theoretical constructs. [Wink] The syntax is a set of rules governing the contextual structure of cognition and perception, where cognition and perception are defined as languages.
The syntax does not need to be completely specified as long as that which IS specified is necessary and logical.

[ 10. November 2003, 05:47: Message edited by: Russell E. Rierson ]

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gedanken
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Icon 1 posted 10. November 2003 15:01      Profile for gedanken         Edit/Delete Post 
Little time, but very short:

The Holy Grail of the physics TOE, as a hope for a "final theory" is indeed a hope for such a theory that does not rest upon more subdivisions. Of course I cannot prove it cannot occur--many physicists are searching for just such a theory and may indeed find it.

On the other hand many statements have been made that indicate that such a theory could not be tested, or at least not entirely tested, to see if it was fully "accurate". In other words, there might be still further subdivisions (layers of turtles?) complicating the supposed TOE, and we would never know it because noise corrupts all measurement at the level in question. So we could have a TOE that seems correct, but we never know if it is fully accurate representation, or just an approximation. It could be just an approximaiton, just as Newtonian mechanics, relativity, Quantum Mechanics are now known to be approximations!

So answer is maybe yes, maybe no--can't "prove" either. Why this interest in "proving" that there could not be such a case?

Of interest is that even if the TOE existed, it still has some aspects: Only the TOE at the bottom is accurate (if one were possible), and higher order theories still have the same complexity explosion they always had. And that TOE may still be "fuzzy" in the same sense that QM is "fuzzy"--not specifying relationships accurately but rather in a fuzzy manner. Thus the TOE is still at most just a probabilistic constraint, or a fuzzy constraint, on relationships at the most fundamental particle level--nothing more.

It seems that the existence of a 'correct' TOE at the bottom of physics is not sufficient to justify many claims in CTMU.

What sort of language system only approximately processes its constructs? I mean mathematically defined precise processing of such a language? Or is CTMU just a statement of a bunch of fuzzy relationships, not clearly and crisply defined?

[ 10. November 2003, 15:07: Message edited by: gedanken ]

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Icon 1 posted 11. November 2003 02:17      Profile for chimp   Email chimp   Send New Private Message       Edit/Delete Post 
quote:

What sort of language system only approximately processes its constructs? I mean mathematically defined precise processing of such a language? Or is CTMU just a statement of a bunch of fuzzy relationships, not clearly and crisply defined?


The language system is described to a certain degree at this page:

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

A language system must be free of paradoxes if it is to be "true". The current useful fictions called theories of reality, are plagued with paradoxes.

Fictions, useful or not, are basically falsehoods. So the "fuzzy unclear relationships", are the conventional models, for example, many world's theory.

http://www.ctmu.org/CTMU/Articles/OnAbsoluteTruth.html

quote:


That a tautology constitutes absolute truth can be proven as follows. First, logic is absolute within any system for which (a) the complementary truth values T (true) and F (false) correspond to systemic inclusion and exclusion, a semantic necessity without which meaningful reference is impossible; and (b) lesser predicates and their complements equal subsystemic inclusion and exclusion. Because a tautology is an axiom of 2-valued logic, violating it disrupts the T/F distinction and results in the corruption of informational boundaries between perceptual and cognitive predicates recognized or applied in the system, as well as between each predicate and its negation. Thus, the observable fact that perceptual boundaries are intact across reality at large implies that no tautology within its syntax, or set of structural and functional rules, has been violated; indeed, if such a tautology ever were violated, then reality would disintegrate due to corruption of the informational boundaries which define it. So a tautology is "absolute truth" not only with respect to logic, but with respect to reality at large.
What does this mean? Uncertainty or non-absoluteness of truth value always involves some kind of confusion or ambiguity regarding the distinction between the sentential predicates true and false. Where these predicates are applied to a more specific predicate and its negation - e.g., "it is true that the earth is round and false that the earth is not-round" - the confusion devolves to the contextual distinction between these lesser predicates, in this case round and not-round within the context of the earth. Because all of the ambiguity can be localized to a specific distinction in a particular context, it presents no general problem for reality at large; we can be uncertain about whether or not the earth is round without disrupting the logic of reality in general. However, where a statement is directly about reality in general, any disruption of or ambiguity regarding the T/F distinction disrupts the distinction between reality and not-reality. Were such a disruption to occur at the level of basic cognition or perception, reality would become impossible to perceive, recognize, or acknowledge as something that "exists".
By definition, this is the case with regard to our cognitive-perceptual syntax, the set of structural and inferential rules governing perception and cognition in general. Since a tautology is a necessary and universal element of this syntax, tautologies can under no circumstances be violated within reality. Thus, they are "absolute knowledge". We may not be able to specify every element of absolute knowledge, but we can be sure of two things about it: that it exists in reality to the full extent necessary to guarantee its non-violation, and that no part of it yet to be determined can violate absolute knowledge already in hand. Whether or not we can write up an exhaustive itemized list of absolute truths, we can be sure that such a list exists, and that its contents are sufficiently "recognizable" by reality at large to ensure their functionality. Absolute truth, being essential to the integrity of reality, must exist on the level of reference associated with the preservation of global consistency, and may thus be duly incorporated in a theory of reality.




[ 11. November 2003, 02:20: Message edited by: Russell E. Rierson ]

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gedanken
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Icon 1 posted 11. November 2003 08:29      Profile for gedanken         Edit/Delete Post 
So does the CTMU document postulate the possibility that there might be a set of 'absolutely' crisply consistent set of relationships, or does it claim to describe such a consistent set of relationships?

This is a very short post, but I have already described problems with completely and
'absolute' claims of crispness of logic applying to real world situations. If CTMU depends on the existence of such crisp relationships in the real world, then I believe I have come upon a difficulty in the premises. If it does not, then we have other issues to discuss, and suggest we quit debating whether 'absolutely' crisp logical distinctions have much use in the real world.

quote:
Were such a disruption to occur at the level of basic cognition or perception, reality would become impossible to perceive, recognize, or acknowledge as something that "exists".
This is a statement that I wholeheartedly disagree with. For example if cognition occurs with "neural network" like system processes, then it is inherently fuzzy, and clarity comes from a notion of approximation and not inherent crispness of "logic". Read the Churchland paper mentioned several posts before (page 12). Mr. Langan makes a false dichotomy--one does not imply the other.

Has anybody looked at this paper I referred to many pages ago?

[ 11. November 2003, 09:07: Message edited by: gedanken ]

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