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Author
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Topic: CTMU and the Axiom of Choice
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chimp
Member
Member # 333
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posted 20. May 2003 02:30
I am a great fan of the CTMU, but I try to invent counter arguments also ![[Wink]](wink.gif)
There is incredible conceptual difficulty with the "UBT(Unbound Telesis)" concept. UBT is postulated as a protean hypermedium with nil
constraint. The wellspring that gives birth TO perceptual reality.
Chris Langan explains that nil constraint means basically zero extension and zero duration i.e. zero space-time.
This makes sense in one respect, because all mathematical-physics relationships appear as intrinsic TO our universe ...so far.
On the other hand, zero extension and zero duration *IS* constraint, big time constraint. Actually, a condition of zero constraint means
infinite dimensions and infinite extension, infinite duration. Spatial extension *IS* freedom.
If zero extension and duration contains extension and duration, A MATHEMATICAL, NOT PHILOSOPHICAL PROOF, IS REQUIRED
MULTIVERSE:
The axiom of choice explains that for every set A there is a choice function, f, such that for any non-empty subset B of A, f(B) is a member of B. The choice function designates("chooses") a member from each set B. There may be infinitely many sets B within A. The axiom of
choice gives birth to the "Banach Tarski Paradox" where by mathematical derivations of n-dimensional Euclidean space, a sphere of
fixed radius can be decomposed into a finite number of parts and then be re-assembled into TWO spheres each with the same radius as the
original sphere. This leads to the question:
If a mathematical structure is isomorphic to total reality and if a real physical multiverse literally exists, then is the axiom of choice a
type of mathematical verification OF the ...multiverse?
You can't have your mathematical universe and eat it too
Russ
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chimp
Member
Member # 333
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posted 21. May 2003 03:42
Interesting...
The CTMU requires the Lowenheim Skolem theorem, which appears to be dependent on the Axiom of Choice...
http://www.cs.uu.nl/wais/html/na-dir/sci-math-faq/axiomchoice.html
quote:
And these statements depend on AC (i.e., they cannot be proved in ZF without AC):
* The union of countably many countable sets is countable.
* Every infinite set has a denumerable subset.
* The Loewenheim-Skolem Theorem: Any first-order theory which has a model has a denumerable model.
* The Baire Category Theorem: The reals are not the union of countably many nowhere dense sets (i.e., the reals are not meager).
* The Ultrafilter Theorem: Every Boolean algebra has an ultrafilter on it.
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Christopher M. Langan
Member
Member # 264
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posted 21. May 2003 13:09
Hello, Russell.
You say that as a fan of the CTMU, you try to invent counterarguments. That’s fine. But as I’m sure you realize, it can be hard to formulate a coherent counterargument to an argument of which you have not yet formed an adequate understanding. For example, you write that “there is incredible conceptual difficulty with the UBT (Unbound Telesis) concept.” If this is true, then it is true only in the minds of people whose conceptual limitations prevent them from understanding it.
Consider: in cybernetics and information theory, we speak of constraint as opposed to freedom. We quantify the constraints in “bits”, and the freedom in “degrees”. Immediately, this arithmetical quantification leads to the logical possibility of 0 constraint, i.e. 0 information, and infinite (unbounded) freedom. It’s part of the price of forming a coherent mathematical model.
Constraint is not the only existential necessity routinely taken to zero. Consider energy. Because physical existence entails energy, there is no such thing as a zero-energy state in physical reality. Yet physicists sometimes talk about zero energy as though it has meaning, e.g. when some of them maintain that positive energy and negative energy sum to 0. If one maintains that this only works in an unreal idealization of physical reality (rather than in physical reality itself), then one is asserting in effect that these physicists are working from an unreal model, are not modeling reality, and are not doing physics. Although I could be mistaken, I have a hunch that this isn’t really what you mean to imply.
Now to clear up a couple of other loose ends in your posts. You write that “zero extension and zero duration *IS* constraint, big time constraint.” Well, yes and no. When (and if) I’ve used the phrase “zero extension and duration”, it has been in simplified reference to undefined extension and duration. The reference is as plain as the nose on your face; since “undefined” means “unmeasurable”, and since any meaningful definition of extension and duration implies at least some degree of measurability, nondefinition precludes extension and duration with respect to the undefined domain. (I’ve explained this to you before, and I just did so again. Please try to remember that I'm usually too busy to enjoy repeating myself.)
You also make reference to the axiom of choice, a postulate of standard set theory. As I’ve explained on multiple occasions, the CTMU utilizes another approach to set theory, and in this new (SCSPL) approach, the axiom of choice doesn’t necessarily mean what it used to mean (neither, for that matter, do terms like “set” and “inclusion”). Thus, when you wax philosophical about the Banach-Tarski paradox, your speculations have only limited relevance to the CTMU (and likewise for the relationship between the CTMU and the Lowenheim-Skolem theorem).
By the way, there’s another moral to this story: mathematics is philosophy. Anyone who has ever cracked a book about modern analytic-linguistic philosophy knows that it consists largely of mathematics of the most unforgiving sort...the kind of math that one can’t really get a handle on simply by browsing the Internet. Please try to keep this in mind the next time you want to belabor the supposed distinction between mathematical and philosophical proof.
Thanks for your consideration.
[ 21. May 2003, 13:23: Message edited by: Christopher M. Langan ]
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chimp
Member
Member # 333
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posted 21. May 2003 14:30
quote:
Hello, Russell.
You say that as a fan of the CTMU, you try to invent counterarguments. That’s fine. But as I’m sure you realize, it can be hard to formulate a coherent counterargument to an argument of which you have not yet formed an adequate understanding. For example, you write that “there is incredible conceptual difficulty with the UBT (Unbound Telesis) concept.” If this is true, then it is true only in the minds of people whose conceptual limitations prevent them from understanding it.
The conceptual difficulty resides in the interpretation of "non-existensial and non-durational" *containing* existensial and durational. I agree that mathematical ideas do not always agree with our observational experiences.
quote:
Consider: in cybernetics and information theory, we speak of constraint as opposed to freedom. We quantify the constraints in “bits”, and the freedom in “degrees”. Immediately, this arithmetical quantification leads to the logical possibility of 0 constraint, i.e. 0 information, and infinite (unbounded) freedom. It’s part of the price of forming a coherent mathematical model.
Respectfully I ask, is this a purely discrete model? There is difficulty postulating a totally discrete "disconnected" reality. How can reality be disconnected from itself in some fundamental way?
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Constraint is not the only existential necessity routinely taken to zero. Consider energy. Because physical existence entails energy, there is no such thing as a zero-energy state in physical reality. Yet physicists sometimes talk about zero energy as though it has meaning, e.g. when some of them maintain that positive energy and negative energy sum to 0. If one maintains that this only works in an unreal idealization of physical reality (rather than in physical reality itself), then one is asserting in effect that these physicists are working from an unreal model, are not modeling reality, and are not doing physics. Although I could be mistaken, I have a hunch that this isn’t really what you mean to imply.
If my understanding is correct, scientists start with "ideal" hypothetical models and then adjust them to the real world.
quote:
Now to clear up a couple of other loose ends in your posts. You write that “zero extension and zero duration *IS* constraint, big time constraint.” Well, yes and no. When (and if) I’ve used the phrase “zero extension and duration”, it has been in simplified reference to undefined extension and duration. The reference is as plain as the nose on your face; since “undefined” means “unmeasurable”, and since any meaningful definition of extension and duration implies at least some degree of measurability, nondefinition precludes extension and duration with respect to the undefined domain. (I’ve explained this to you before, and I just did so again. Please try to remember that I'm usually too busy to enjoy repeating myself.)
Your writings in the past have explained UBT as a *non-existential*, *non-durational* hyper- medium and that the infocognitive *seed crystal* the Telic Principle, is the starting symbol that is *in* the UBT, where I interpret the word "in" to mean *contained by*.
Does non-existential mean "zero extension"?
Does non-durational mean "zero duration"?
quote:
You also make reference to the axiom of choice, a postulate of standard set theory. As I’ve explained on multiple occasions, the CTMU utilizes another approach to set theory, and in this new (SCSPL) approach, the axiom of choice doesn’t necessarily mean what it used to mean (neither, for that matter, do terms like “set” and “inclusion”). Thus, when you wax philosophical about the Banach-Tarski paradox, your speculations have only limited relevance to the CTMU (and likewise for the relationship between the CTMU and the Lowenheim-Skolem theorem).
If the SCSPL is a powerful generalization OF set theory and it clarifies the definition of the "Axiom of choice", the SCSPL formalism is a major discovery of epic proportions.
Interesting...
quote:
By the way, there’s another moral to this story: mathematics is philosophy. Anyone who has ever cracked a book about modern analytic-linguistic philosophy knows that it consists largely of mathematics of the most unforgiving sort...the kind of math that one can’t really get a handle on simply by browsing the Internet. Please try to keep this in mind the next time you want to belabor the supposed distinction between mathematical and philosophical proof.
Thanks for your consideration.
Mathematics is a language, and philosophy requires a linguistic structure to interpret its concepts. Which came first? the philosophical chicken or the mathematical egg?
Thanks again for the helpful information.
Russ
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Parallel
Member
Member # 744
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posted 21. May 2003 23:48
Christopher M. Langan wrote:
quote:
When (and if) I’ve used the phrase “zero extension and duration”, it has been in simplified reference to undefined extension and duration. The reference is as plain as the nose on your face; since “undefined” means “unmeasurable”, and since any meaningful definition of extension and duration implies at least some degree of measurability, nondefinition precludes extension and duration with respect to the undefined domain. (I’ve explained this to you before, and I just did so again. Please try to remember that I'm usually too busy to enjoy repeating myself.)
Because zero is a defined quantity it should not be obvious to Mr. Rierson or anyone that "zero extension and duration" is a "simplified reference to undefined extension and duration". Your argument based on unmeasurability is also erroneous. n/0 is undefined and immeasurable, yet it does not therefore follow that it is zero. Any mathematics professor would inform you that "zero" does not refer to "undefined", and no amount of semantic finagling will change that fact. Your noting that you previously explained the same (error) also fails to make your argument persuasive.
Mr. Langan chides Russell when saying, "I'm sure you realize, it can be hard to formulate a coherent counterargument to an argument of which you have not yet formed an adequate understanding." Langan would do well to heed his own advice in reference to his argument about undefined that runs afoul of basic mathematics.
"The universe ... is both One and Many." Dionysius The Areopagite
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Pim van Meurs
Member
Member # 541
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posted 22. May 2003 00:17
Parellel: Mr. Langan chides Russell when saying, "I'm sure you realize, it can be hard to formulate a coherent counterargument to an argument of which you have not yet formed an adequate understanding." Langan would do well to heed his own advice in reference to his argument about undefined that runs afoul of basic mathematics.
While I understand that a busy man as Langan can sometimes feel frustrated at his perceived lack of understanding of others of his ideas, it should not be used as a blanket approach to criticism, good or bad. Let's focus on the arguments and show their value or lack thereof. If we can avoid the rethoric (I know it can be hard sometimes) we may even find the opportunity to comprehend Langan's ideas to Langan's likings. Lets give Russell the chance to elaborate on his ideas in a manner befitting the goals of ISCID
quote:
All posts on the first page of a thread must be what Edward de Bono calls of the "green hat" type. The earliest posts must be confined to positive construction, re-construction and modification of the ideas in the original post. In other words, on the first page of a thread, participants are required to show that they have an interest in helping the argument to be developed and not just in shooting it down.
[ 22. May 2003, 00:20: Message edited by: Pim van Meurs ]
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Moderator
Administrator
Member # 1
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posted 22. May 2003 08:04
Chris, at Brainstorms we expect that the principle of charity will be observed. When you see someone misunderstanding your work, try to understand what they are stabbing at, rather than beat down their misunderstanding.
The goal at Brainstorms is to have an environment of cooperation.
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Christopher M. Langan
Member
Member # 264
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posted 22. May 2003 15:17
OK. I'm going to try very hard to display the proper spirit of intellectual charity here, and explain exactly how something that is undefined might as well be zero.
First, Parallel (with the apparent support of Pim) says that "Because zero is a defined quantity it should not be obvious to Mr. Rierson or anyone that zero extension and duration is a simplified reference to undefined extension and duration."
I find it hard to understand how Parallel can speak definitively about what anyone in particular, other than himself, finds obvious. As it happens, Mr. Rierson and I have already had extensive discussions on this particular point, and I think I'm within my rights to ask that I not be forced to repeat myself in other forums. In any case, the scarcity of my time forces me to insist on it.
Parallel goes on to say that "my argument based on unmeasurability is also erroneous." But it isn't, at least not in the context at hand (the CTMU). In scientific parlance, to say that the spatial or temporal distance between objects or events is unmeasurable due to lack of syntactic support amounts to saying that it "might as well" be zero. That is, the objects or events are either identical or coincident for all practical purposes. If one denies this, then one is obliged to demonstrate that they are in fact separated. Obviously, this would be hard to do without some kind of measurement or formal demonstration of necessity.
To attribute extension and duration to some part of nature, even approximately or in some infinitesimal or infinitary sense, one needs to be able to observe it or consistently define it within some formal system to which nature demonstrably conforms. But as any quantum theorist understands, observation is measurement. So to attribute extension or duration to some part of nature, one must have some kind of measurement, at least in principle, and if one does not, then one has no business ascribing nonzero values to spatial and temporal distinctions associated with extension and duration.
Unfortunately, where something is undefined due to its lack of expressive syntax, it is totally unmeasurable even in principle. Therefore, there are no extensional or durational distinctions to be made, and this means that for practical and theoretical purposes, extension and duration are zero. (As Russell and some others are aware, I generally use terms like "virtual zero extension" and "zero infocognitive radius" instead of just plain "zero" to make this point; it's a subtle distinction, but it's been there all along.)
As for Parallel's example - "n/0 is undefined and immeasurable, yet it does not therefore follow that it is zero" - it doesn't really fit the context at hand. However, it is relevant to the extent that a quotient of the form "n/0" might as well be zero for all practical purposes. That is, quotients of the form "n/0" have no real, identifiable formal or physical existence in empirical science or (standard) arithmetic. This, however, does not preclude a systemic extension in which such quotients are allowed.
There's an interesting aside here: intuitively, (nonzero n)/0 "diverges to infinity". To some extent, this mirrors the relationship between constraint and freedom, whereby taking constraint to 0 takes freedom to infinity.
As far as concerns 0 being a defined quantity, of course it's defined...in the syntax of arithmetic. Without an underlying conceptual syntax, it would be undefined...and the absence of syntax is what UBT is all about.
[ 22. May 2003, 15:36: Message edited by: Christopher M. Langan ]
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Pim van Meurs
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Member # 541
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posted 22. May 2003 15:35
Let me first state that I appreciate Mr Langan's expressed efforts to show the proper intellectual charity in his discussions but despite some progress I still see some problems with what may very well be the definition of the term proper.
Chris states "Parallel, with the apparent support of Pim"
How can Chris speak definitively about what I in particular, support? In fact I did not make any such claim AFAIK. But perhaps Mr Langan can tell us what I was thinking.
Chris, if your time is so scarce then I propose you may want to consider to limit your responses to statements which help move forward the discussion and refrain from what I consider to be unnecessary snipes at people. This really is becoming detrimental to any serious discussion in this thread, just when things were getting interesting.
Lets try to move the original discussion forward in which Mr Rierson raised some interesting issues to consider. I would in fact have expected Mr Langan to be enthusiased by the interest in his ideas, even from a critical perspective. I am certainly interested in a (critical) evaluation of the CTMU and am thrilled to find someone who seems to understand it much better than I do.
[ 22. May 2003, 16:11: Message edited by: Pim van Meurs ]
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Christopher M. Langan
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Member # 264
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posted 22. May 2003 15:46
First, Pim, it's rude to repeatedly misspell the names of those you address. Please stop it.
Second, your post says very clearly that you support the content of Parallel's post. So I guess the answer to your question might be, "I can tell what you support because I'm somebody who can read."
Third, please refrain from giving me personal advice. I don't think it's your place to do so, and in any case, I have no use for it. Thanks for your consideration.
Fourth, I don't particularly agree with your suggestion that we "move the discussion forward" on terms unfavorable to the author of the theory which forms the subject matter of this thread. In fact, I find it more than a little disingenuous.
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Pim van Meurs
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Member # 541
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posted 22. May 2003 16:10
Chris: It may have occured to you that a repeated misspelling of a name may be a mistake rather than rudeness? Some charity should be observed in our discussions here and if my mistake offends you then I apologize for misremembering your last name.
I would appreciate if you can show me where my posting clearly supports the content of Parallel's post when in fact I was pointing out that the back and forth quibbling was not leading anywhere fruitful. We may be reading this through differently colored glasses here since I did not intend to express any support for the content of parallel's post.
I think it is all our responsibility to make this forum hospitable for critical analysis, new ideas.
Finally your last paragraph suggest a miscommunication and misunderstanding. I am not stating that the terms should be unfavorable to the author of the theory under discussion and unless me asking such author to focus on the discussion at hand is unfavorable to said author I fail to see how such a conclusion could have been reached. I am more worried why you have to jump immediately to a conclusion of 'disingeneous'. Remember the principle of charity pointed out by the moderator?
The goal of this forum is to encourage cooperation and a forum in which to explore new and interesting ideas.
I see little reason to continue this discussion with Mr Langan which serves little to further the discussion per my earlier suggestions.
Mr Rierson, I encourage you to expand on your ideas and applaud your attempts to look at the CTMU in a critical manner despite being a fan of the CTMU. I find such approach refreshening and helpful to my understanding of the concepts of the CTMU which I hate to admit have remained somewhat elusive to me so far.
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David Garrett
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Member # 759
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posted 22. May 2003 18:03
Anyone reading these forums (not just Pim, Parallel, and the Moderator) should understand a little background before jumping on Chris. Russell and Chris have had a relationship, albeit an unusual one, which stretches back a little ways. Chris has probably spent more time explaining the CTMU to Russ than anyone else.
Chris has tried on numerous occassions to try and explain UBT to Russ but Russ just can't seem to fully grasp the concept. How else can you color this?
It is also quite funny to see people take offense at something Chris said to Russ while Russ himself never seemed to take offense. I suggest that in the future, before jumping in to defend someone you think was offended, that first you find out if that person was, in fact, offended.
Dave
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Alix Nenuphar
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Member # 686
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posted 22. May 2003 19:26
David Garrett:
While I appreciate that the exchange between Russell and Chris may be a continuation of a more protracted and complex discussion that began on another forum - a discussion that may include a number of frustrating miscommunications on both sides, I cannot agree that the tenor of Chris' reponse is appropriate as a page one response at ISCID.
Chris has the option, after all, of not responding and thus avoiding the entire acrimonious exchange. This would also allow others on the board to expand upon Russel's original concept and possibly refine it to the point where Chris' involvement becomes both necessary and interesting.
To the latter point, Pim's willingness to 'move the discussion forward' is appreciated, while Chris' characterisation of Pim's attitude appears counterproductive.
However, to return to the OP... I am puzzled by a tendency in the CTMU to equate 'zero distance' and 'undefined distance' - in the context in which the issue has been raised, they would appear not to be synonymous concepts. One could certainly argue that a zero displacement is fundamentally different from an undefined displacement - whether in time or space. And stating that 0/n might as well be zero is incorrect, unless the context relates to limit functions. Any clarification on this point would be appreciated.
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Pim van Meurs
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Member # 541
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posted 22. May 2003 19:57
David: Chris has tried on numerous occassions to try and explain UBT to Russ but Russ just can't seem to fully grasp the concept. How else can you color this?
I feel for Russ since I as well have some problems understanding the concepts of CTMU. But even assuming that this all is true, this forum is not the place to respond to Russell in the manner Chris did. As Alix points out Chris has the option to just not respond.
Whether or not Russ takes offense or not is not relevant imho.
Let's move on in a more constructive manner in which perhaps we can all learn what this elusive CTMU is all about. I am interested to learn but somewhat taken back by the idea that my ignorance will evoke a response in Chris which will destroy any further interest of mine in pursuing the ideas surrounding the CTMU.
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