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Author
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Topic: Cosmogony, Holography and Causality
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gedanken
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posted 23. September 2003 01:09
Rex, we appear to have discussed similar topics in the Kurzweil thread I linked just above.
But to clarify with respect to Russel’s point. I fully agree with the way you stated it.
However there are versions of the Turing machine recognition problem which show non-computability of certain problems (using that test structure very specifically stated). These relate to computability equivalents of Godel’s theorem.
However human “computation” seems to be able to deal with these problems—using the “analog” methods which could themselves in principle be “computed” in a Turing machine. In fact the same Turing machine that failed the logic test described.
The problem is a limited view of that logic test, and thinking that it implied the non-computability of those problems when we take a broader view. In fact this is very closely related to our subject—the inexactness of the match of the pure logic and the real world. The human (or an analog computation) could in principle solve these difficulties in ways that cannot be solved using strictly symbolic methods that are implied in the restricted version of the computability problem. The slightly “fuzzy” solution goes around the strictly “logical”, pointing the way to constructing a new “logic”.
Interesting Link
I wonder if there is some “Godelian” equivalent here. One can construct a logic that gets arbitrarily close to representing all the complexity in the real world at a given situation or point of discussion. But to get a more accurate description of every aspect of the situation requires going outside of either the logic description premises or outside of the “logic” itself. (And of course there could be “real-world” discussions that could include the features of the “halting problem” in their description—thus one must go outside of the “logic” itself previously used.)
(The basis of this includes following aspects: Quantum Mechanics has shown the relevance of the “observer” to the situation being observed. Therefore the observer is part of the situation. Therefore the observer, who is trying to represent the situation in logic must to get greater accuracy eventually account for the observer involvement in the situation. This eventually leads to the observer having to completely describe his own self in contribution to the situation. Computability shows this cannot be done, so one must go outside of that observer to get greater accuracy. Please note that if one is satisfied with approximation rather than a strict “isomorphic” mapping to the real world, the whole problem goes away.)
[ 23. September 2003, 01:51: Message edited by: gedanken ]
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Mark
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posted 23. September 2003 13:52
Ged wrote:
quote:
One last issue: How would those who were supportive of this “isomorphism” judge the discussion of Dennett and computability and human vs. machine reason? (Thread Ray Kurzweil’s Impossible Vision, which also discussed “frame problem” and Daniel Dennett’s “Robot’s dilemma”.) Because it would be very interesting if the same people thought that human reason had to go beyond that which was “computable” by a logic machine in that thread, and then here thought that the properties of the universe were isomorphic to the syntax processed by the “logic machine”. If the universe and the rules of logic are isomorphic, why is it so difficult to understand how the robot could use the rules of logic to figure out the problems, then?
I read that thread. I have nightmares of the robot in the room, holding the handle of the deadly wagon, feverishly going through computations in its efforts to frame the issue, then . . . .
Hence my question: Is cognition computational or something else (such as holographic)?
The frame problem suggests it is something other than computational, or at least extra-computational. If it is, does this mean there is not, or cannot be, some sort of isomorphism? After all, we do have knowledge of the world outside ourselves. There must be some isomorphism, based on some common medium, to permit the exchange.
This is the classic distinction between DeCartes' "thinking substance" and the "extended substance." As I understand Langan's CMTU, he is attempting to overcome this duality through the commonality of language between matter and consciousness.
I don't know if the Real is logical, and only the logical is Real. I remain agnostic. You have pointed to some salient facts which suggest that this tautology won't hold. There are other factors (continuity, coherence, limits) that suggest that it (or something like it) may hold.
But I do think Langan is asking the right question. The physicist David Bohm observed, in "Wholeness and the Implicate Order," p. 197:
"However, when we start, as Descartes did, with extension and separation in space as primary for matter, then we can see nothing in this notion that can serve as a basis for a relationship between matter and consciousness, whose orders are so different. Descartes clearly understood this difficulty and indeed proposed to resolve it by means of the idea that such a relationship is made possible by God, who being outside of and beyond matter and consciousness . . . is able to give the latter "clear and distinct notions' that are currently applicable to the former. Since then, the idea that God takes care of this requirement has generally been abandoned, but it has not commonly been noticed that thereby the possibility of comprehending the relationship between matter and consciousness has collapsed."
Can we agree that there is some "relationship between matter and consciousness"? If there is, how can we account for it? I don't pretend that I have an answer, or that anyone else does. But I do think that this is the question that Langan is attempting to answer, via his "logic is Real, the Real is logic" tautology (that is, he collapses the Cartesian dualism into an isomporphic syntax of logical language).
I don't disagree with any of your observations. And I do see the parallels with the Ray Kurzweil thread, and the problems that a logic-based (or perhaps I should say "bound by logic") syntax poses for cognition. There seems to be more to cognition than mere logical operations upon perceptions. These are extremely difficult problems for very smart people. I do think, however, that they are very interesting.
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gedanken
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posted 23. September 2003 17:24
Mark,
To get back to the discussion between Rex and myself about "computational", Rex suggested that the analog processes could be "computed". So would an analog, non-symbolic, and massively parallel process of making such a decision be "computational"? (It might depend on your definitions--please clarify.)
PS one hint that I am surprized nobody commented on, is whether a non symbolic evaluation could not then be subsequently checked by "logic". The issue of whether the presentation fits logic is independent of the procedure by which the presentation was arrived at. (A difference between computation as search and computation as verification.)
[ 23. September 2003, 17:26: Message edited by: gedanken ]
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Rex Kerr
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posted 23. September 2003 21:52
My impression is that dualism arises from a category mistake that is easy to make with nested models. As a rational being with perceptions, I must start with my rationality and perceptions. This is a model for how I must understand my perceptions. However, I might also be implemented entirely materialistically. This is a model for how I might understand my construction and functioning.
The mistake is conflating these two models and assuming that these two models must account for the same data at the same level. Voila, you have the problem of dualism.
One method of escaping dualism is to assume that there is some special relationship between rationality, perception, and the material that somehow conflates them all into the same sort of thing. My understanding is that Descartes and Langan both take this approach (albeit in different ways).
Another method of escaping dualism--the one I take--is to reject the premise that the two models are models of the same thing. Rather, at least one of the models should be embeddable as inside the other. For example, in a materialistic ontologic model, we might have a submodel of what epistemology would look like; and in our rational-perceptual epistemologic model, we might have a submodel of what ontology would look like. Achieving coherence between these model-nestings is what we are actually doing, I think, whether we realize it or not, and trying to view the problem un-nested is both (to my mind) ultimately nonsensical and the source of much confusion.
I agree that there is "some relationship between matter and consciousness", but I think that there is a layer of abstraction involved as well which is normally ignored.
And, in reply to gedanken, a computation of an analog non-symbolic massively parallel decision-making process is, under my definitions, computational. (It may be ridiculously inefficient to implement digitally, but it is still computational.) The only caveat that I know about is that there are some problems that are provably incomputable in finite time with a Turing machine which are soluble via quantum mechanics. There is little reason to believe that any of these processes are occuring in humans, but we could potentially solve incomputable problems by noticing that an incomputable problem is computable with QM and then building the right device to compute it. However, a Turing machine presumably could notice (compute) the same thing and, with access to the real world, build an appropriate device and read its output.
[ 23. September 2003, 21:54: Message edited by: Rex Kerr ]
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gedanken
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posted 24. September 2003 10:43
Thanks, Rex, this makes several things clear to me that I had not thought about.
But I still have an abiding question, one that I have thought about for years and still don't see answered. (And highly relevant to this thread!) That still gets in part to the definition of "computability", but does so in a way that is somewhat different from your above discussion.
My question is about the relationship of the "answer" to an understanding of points like computability theory themselves. Clearly the human can discuss computability theory at length. We can understand (not just search and terminate) the very idea of a process not being able to "understand" itself in completeness by way of a strict computation of all of its own bits (as in halting problem).
Yet this understanding goes beyond the limitations of the halting problem in a very significant way. Now back to "computability" applied to ourselves. I'm not meaning to imply a contradiction--at least not in the strictly logical sense. Rather what I am implying is that this "understanding" itself needs to be defined or given category. I'm not sure that one can simply "up the anti" like one does with the halting problem, I think it goes beyond that.
I think that the definition of what it means to "recognize" the "answer" is at fault. I think that we are recognizing that Gestalt of a recursive aspect in a different way that is not strictly a solution to the problem in the way it was posed in the original halting problem.
In other words we have not violated the halting problem in our understanding, we are within the limits of the "computability", and it is the means of our answer that has changed to another category of understanding (well within computable limits). It may involve allowing less than crisp logic in our statement of what is understood—that may be involved in this “different category” of explanation.
This gets to the issue of how we can seem to solve problems which defy strict "computability" presentations. Intuitively people claim that we have gone "beyond computability" and I think this claim is in error.
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Mark
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posted 24. September 2003 11:24
Rex, with respect to your observation that we could potentially solve incomputable problems with QM, you may be interested in the following link: http:www.i-sis.org.uk/QuantumComputing.php. It is Mae-Wan Ho's review of a book by Gerard Milburn, "The Feynman Processor, Quantum Entanglement and the Computing Revolution."
A quote from her review:
quote:
Now, add quantum entanglement, the correlation between subsystems in a state of quantum superposition, to Feynman’s rule and one comes up with still stranger stuff, the e-bit, or information transfer through the entangled state, the possibilities of quantum crytography, teleportation (beam me up Scotty), and quantum computing.
The popular parable of the entangled state is Schrödinger’s cat, which is in superposition of being both dead and alive at the same time. In fact, Feynman’s rule already describes the superposition of indistinguishable alternatives, ie, the entangled state.
Quantum computing depends above all, on the coherent entangled state, or pure state that contains the superposition of multiple, even mutually exclusive alternatives. The more alternatives are entangled, the faster the quantum computing. It is the ability to ask many questions all at once, rather than one question at a time. . . .
Can a quantum computer simulate reality perfectly? Milburn asserts that "the physical world is a quantum world", which makes "a quantum computer not only possible, but inevitable." I agree only in the sense that the organism may already be a kind of quantum computer.
Ged, you asked what I mean by "computational." That's a good one. I have no definition that I have devised, or even one that I prefer; I try to reflect the use made of the term by those who should know. It seems the meaning of the term continually expands or changes through time. Perhaps there is no difference between a computational and holographic model of cognition, depending on definition of terms. I will accept any definition that you prefer.
With respect to Rex's comments on dualism, I tend to agree. I also asked a question (with respect to a "relationship between consciousness and matter") that was imprecise and concealed my assumptions. The question was asked in the context of any proposed isomorphism between the natural world and logical syntax, and the further proposal that an identity of syntax accounts for the possibility of perception and cognition (that is, some commonality of syntax accounts for the cognition of information). It was not intended as a metaphysical or philosophical inquiry. I operate on the assumption that perception and cognition are susceptible to rational investigation with rational categories and analysis, and that they have a materialist basis (and therefore a materialist explanation -- although we may not yet be in possession of the proper rational categories to acquire a meaningful understanding at this time).
I agree with your observation of the nesting problem, and the issue of what comes first, epistemology or ontology. One's epistemology inevitably influences, and even determines, one's ontology, and vice versa. We can go round and round with the question of what precedes what, and the degree of influence, and the "objectivity" of our epistemology, etc. For purposes of Brainstorms, I prefer to assume that consciousness (including perception and cognition) is a natural phenomenon susceptible, in some form, to our rational understanding (if not now, then at some point). To my mind, we have discussed in this thread what rational categories (for example, "logical syntax") are useful or appropriate for an understanding of the apparent operations of perception and cognition upon the natural world.
This is not to say that, if such a day of rational understanding arrives, that "computation," or some other model, will enable us to reproduce consciousness. We may be able at some point to mimic it, but I am not at all confident that we can reproduce it (but then, this conclusion is probably a personal metaphysical prejudice, with no basis in fact).
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Rex Kerr
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posted 24. September 2003 12:00
Gedanken, it sounds to me as if you've answered your own question: we get around problems of computability by changing, for example, our level of abstraction of the problem and, much of the time, what counts as an answer.
This leaves us with questions we know we can't answer ("Will this Turing machine terminate its execution?"), questions we do know the answer to ("truth is undecidable under Peano's axioms"), and questions that are uncomputed/undecided so far ("x(i+1) = 3x(i)+1 if x(i) is odd, x(i)/2 otherwise; for finite n, does the chain starting with x(0)=n always terminate at x(i)=1 for some finite i?")
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gedanken
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posted 24. September 2003 13:25
Rex, I agree that I have established a quality of the answer to my question—that we have changed the “level of abstraction of the problem and, much of the time, what counts as an answer.”
However I am not satisfied. Especially with regard to this thread and its history.
Specifically have we introduced a “fuzzy” measure of what it means to have an answer? In other words we have not satisfied the strict logical “termination” of the search according to the original strictly logical terms? (But rather satisfied a “fuzzy” recognition of a solution which is not strictly logical conclusion of the original question.)
Because if that is accepted by the readers here, we have demonstrated the approximation and some form of “fuzzy” logic aspects applying. If not, then what have I missed?
[ 24. September 2003, 13:27: Message edited by: gedanken ]
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Rex Kerr
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posted 24. September 2003 20:31
Whether it is sharp or fuzzy is up to your axiomatization of the situation.
One could have crisp definitions that a problem is understood if it is either provably computable or we have a proof that it is not; a problem is considered if it has been classified as either understood or not understood after expending at least some minimal effort to understand it.
We then can be satisfied when a problem becomes understood, even if it is not computable; and possibly even if a problem is considered, but not understood. There is no fuzzy logic here; everything is crisp boolean logic. I've just invented new categories instead.
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gedanken
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posted 25. September 2003 00:27
That's what I'm trying to figure out.
We have, of course posed "fuzzy" logics as alternative logics, along side of alternate crisp logics that might be useful. And they may all be useful.
My question is whether in the "approximation" of choosing to be satisfied we must use some "fuzzy" element. And I'll take your word on the reformulation of the problem as providing a "crisp" logic positive result.
I'm just wondering whether the process is not still inherently dependent on a "fuzzy" element. Can it be strictly computable with crisp logic computation, for example, to come up with the choice of the alternate reformulation and choose to be satisfied. (In other words did we get out of the halting problem with "crisp logic"? Or was a fuzzy calculation necessary to come up with the "new categories" for example?)
Obviously we can simulate arbitrary precision analog with crisp operators, so this could be considered to "go away". But I don't think this was an out. Because if the original question was not answered, there had to be a decision to accept alternate "answers", and in part I am wondering if that must not depend on some form of "fuzzy" (meaning analog) evaluation which cannot be reduced to strictly digital except by simulation of same analog.
Yet another aspect, have we in essence posed a logical question, then allowed (equivalently) a "fuzzy" resolution by having a partial truth answer as our satisfaction criterion. This could be an "isormorphism" issue--e.g. the computation has to be isomorphic to an analog simulation of a fuzzy logic in order to have a solution.
I'm afraid we would have to expand a specific case out in detaill, a lot of effort.
By the way, Rex's "algorithm" can always terminate, as in a time out that gives up with the "no understanding" case. That can be done with "crisp logic". It is guaranteed to meet that spec, even if it always gives up. My question is whether the human "satisfaction" criterion must be analog in a complex manner, or a simulation isomorphic thereto.
It may in fact be that such issues are comparable to a fractal-like problem. It can never really be answered, only tunnel into finer zig-zags that get more refined but occupy more and more detials.
[ 25. September 2003, 00:39: Message edited by: gedanken ]
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Rex Kerr
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posted 25. September 2003 01:41
Human satisfaction is graded, and thus inherently not meaningfully separable into "satisfied" and "not satisfied". The statement "x is satisfied" is not well represented by boolean logic. You can cope with this, even without any non-boolean values, by generating satisfied_level_0 through satisfied_level_N as categories and then spreading your truth values across them. (This is basically discretizing a continuous variable, and then having categories saying "the variable value is between x_i and x_(i+1)".) Is this efficient? Certainly not! But this option is available to a purely binary logic system as an alternative to fuzziness.
I don't think humans do it this way. But I don't see why a self-modeling system couldn't come up with this. For example, our Turing machine tries to prove P, but that's not *all* it does. It also tries to prove that a Turing machine can prove P, and that a Turing machine can't prove P. And it can try to prove that a Turing machine can prove that a Turing machine can prove P, etc.. It's possible to set up this system so it spirals out of control in self-analysis, but the system itself can tell when it's spiralling out of control, so there's no particular reason to suppose that it couldn't represent things at the level of "I know I can't solve this" or decide "this one category doesn't work, let's split it into two".
Fuzzy and non-fuzzy logic are equivalent to arbitrary precision. Therefore, the process can't be inherently dependent on a fuzzy element--but it may be inherently dependent on something that is trivially represented in a fuzzy way and difficult to represent in a non-fuzzy way.
I'm not sure if this helps or not.
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chimp
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posted 25. September 2003 01:42
Interesting...
The quantum computer agrees with the idea:
[symmetry] = [invariance] = [identity] = [qualia]
When the probability amplitudes are summed an [invariant interval]^2 is the result.
a^2 + b^2 + ... + n^2 = [probability amplitude]^2
Yes qualia is an invariance, because it is a type of distributive identity. For example the set of "green objects" has an invariant property, in that it retains its identity when green objects are removed or added to the set. Chris langan explains it[qualia] as a distributive predicate. I see it as an invariance, i.e. a symmetry principle.
A serial computation? :
A--->B--->C---> ... X = answer
A quantum computation? Reduced to two variables :
[Y-infinite-selections]
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|-------------------->[X-infinite-selections]
X^2 + Y^2 = [invariant]^2 = optimal selection
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RBH
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posted 25. September 2003 02:06
Rex Kerr wrote quote:
Fuzzy and non-fuzzy logic are equivalent to arbitrary precision. Therefore, the process can't be inherently dependent on a fuzzy element--but it may be inherently dependent on something that is trivially represented in a fuzzy way and difficult to represent in a non-fuzzy way.
This is a quick observation/question, because I'm too tired to do the necessary research. My understanding of "fuzzy" logic from reading Bart Kosko years ago is not that it refers to uncertain class membership or probabilistic class membership, but that it incorporates genuinely graded class membership. For example, I'm 5'11", which makes me a low-value member (say 0.1) of the class of short men, a fairly high-value member (say 0.8) of the class of average height men, and a low-ish member (say 0.2) of the class of tall men. The values (which need not sum to 1.0) reflect my degree of membership in the various classes, not to an uncertainty of classification or probability of classification. Hence crisp logic (where class memberships are all or nothing) is the special case of fuzzy logic in which all values are 1 or 0.
RBH
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gedanken
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posted 25. September 2003 09:29
Thanks to Rex and RBH.
RBH is correct about "Fuzzy". But then Rex is speaking about what amounts to "rule explosion" which can approximate the continuous "fuzzy" function rule to arbitrary precision. And in fact in many circumstances may not "explode" rather just makes a category shift. But RBH is correct to note the essential "fractional truth" as opposed to a "certainty" measure--a definitie distinction. (In fact "certainty" in terms of probability can be argued to be subsumed in "fuzzy" as one particular kind of partial truth among many.)
I too should not spend the time necessary to refine this. It's just been an intuition, however, that the huaman does use a "feeling" (meaning fuzzy evaluation) of something seeming to be in the correct direction--approximately the notion of hueristics as an analog search helper. I'd wondered if this was an "essence", but it may not be able to be demonstrated. Thanks all.
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