Hi Bruno, -----Original Message----- From: everything-list@googlegroups.com [mailto:everything-l...@googlegroups.com] On Behalf Of Bruno Marchal Sent: Saturday, September 11, 2010 11:36 AM To: everything-list@googlegroups.com Subject: Re: What's wrong with this?
On 11 Sep 2010, at 00:42, Stephen P. King wrote: > Hi Bruno, > > -----Original Message----- > From: everything-list@googlegroups.com > [mailto:everything-l...@googlegroups.com] On Behalf Of Bruno Marchal > Sent: Friday, September 10, 2010 11:16 AM > To: everything-list@googlegroups.com > Subject: Re: What's wrong with this? > > > On 09 Sep 2010, at 14:37, Stephen P. King wrote: > >> Hi Bruno, >> >> My thought is to look at the transformation group around which some >> property is invariant to act as a generator of the properties of the, >> say, quark. > [BM] > Good idea. That is related with the importance of group theory and > (soon) category theory in physics. > > >> For simple numbers this would be a permutation over fields, one field >> per number, > > [BM] > Why? We may have use combinators instead of numbers. Their role are > intensional, and representational. Their intrinsic mathematical > structure certainly plays some role, but I don't see why to use them > directly to mirror physics. Even if that works (by chance) it would > hidden the mind-body problem. Of course it might be very interesting, > and the relation between physics and number theory suggest that such > approach have their merits. > > [SPK] > > YES!!! You nailed it! Let me paste a little note here that I just > wrote up. I apologize in advance for the crudeness of this. > *** > Integers as Arithmetic Equivalence Classes and implications > > by S. P. King > 9/10/2010 > > Zero-ness > _______ > 0 + 0 = 0 > 0 - 0 = 0 > 0^1 - 0^1 = 0 > 1 - 1 = 0 > 2 - 2 = 0 > 3 - 3 = 0 > ... > 0 x 0 = 0 > _______ > > One-ness > _______ > 0 + 1 = 1 > 1^1 + 0 = 1 > 1 - 0 = 1 > 1^1 - 0 = 1 > 2 - 1 = 1 > 3 - 2 = 1 > 4 - 3 = 1 > . > 1 x 1 = 1 > 2 / 2 = 1 > 3 / 3 = 1 > 4 / 4 = 1 > . > _____ > > Two-ness > ________ > 1 + 1 = 2 > 1^1 + 1^1 = 2 > 0 + 2 = 2 > 3 - 1 = 2 > 4 - 2 = 2 > 5 - 3 = 2 > . > 4 / 2 = 2 > 6 / 3 = 2 > 8 / 4 = 2 > .. > _______ > Etc. > > > External symmetry = 3rd person aspect. > > Each Class has aleph_null tuples and thus has the same cardinality. > We could use the permutation symmetry over the cardinality to > identify an > external or 3rd person notion of Integer. This would generate a > notion of > that is an Integer that is invariant to a change from one of the N > classes > to another. > > What would be the internal symmetry? > > Internal Symmetries = 1st person aspect. > > Note that we can substitute equivalent elements of the tuples with > each other by the use of bracketing or some other push/pop method. > This > would ultimately show that the tuples are combinations of "images" > of each > other's elements so that there is 1) no primitive atom and 2) that the > pattern of similarities and differences over this tapestry of > combinatorics > would encode the operations of Arithmetic. Property 1 is the reason > I use > non-well founded set theory, by the way... > ************* [BM] It is difficult for me to follow. In ZF there is no atom, yet it is well-founded. Non well-foundedness is motivate by introducing set having themselves as elements, or having elements having elements ... having elements having the starting set as an element. [SPK] Yes, in my example above it seems to be the case that the N-ness classes can have themselves as elements and so forth. For example, in the Zero-ness class, there is a couple of 0s that are equaling 0 when added, subtracted or multiplied. Is this not an example of an element having itself as an element? My wording might be incorrect according to the usual definition of class, etc. but I hope that my meanings are communicated. > > It is my suspicion that the mind-body problem is caused by a lack of > understanding of what is involved. It is far too easy to throw up > one's > hands and settle for some silly eliminatism; Ignorance is Bliss. > Notice that > both the internal and external symmetry notions here yield a kind of > indefiniteness that Plotinus would point to, as per your > discussions, to > define Matter. You should elaborate, but you should make clear the relation between math and philosophy/theology. [SPK]] Yes, I agree but I am sure that you can see that this is very difficult to do. > But what about the information content itself of the > relations themselves? Is Information identical to Indeterminateness? [BM] Information is a tricky word having different meaning in different theories. It can be a measure of surprise, like in the old Shannon theory, or something related to meaning, like in logics and in the press. We can relate all that, but then we have to be almost formal for not falling in the traps of non genuine analogies. [SPK] Let me quote something from Carlo Rovelli that I found in "Quo Vadis Quantum Mechanics?" referring to C. E. Shannon's 1949 book: "...the definition of Shannon, not the popular one, but the one in his book, where you have two systems with many states, and there is a possible state of the couple but there is only a restricted subset of all joint states. Information is simply the way of counting the allowed joint possible states. The fact that there is a common allowed state tells you that if you know something about one system you also know something about the other one. This is exactly what you need in communication theory when you have a channel, a receiver and a transmitter. So I have two systems. If there is a quantum correlation of the two, I can say that, if this system is UP, the other is DOWN, and vice versa. This is what I mean by information, period." I am attempting to be faithful to this definition. Interestingly, it seems that since the equivalence classes that I pointed out above are countably infinite then the property that any proper subset of infinity is isomorphic to the infinity would apply and this would make the notion of information for such classes to vanish, no? It would be a zero-information system of sorts! > It > seems to me that the answer is a resounding NO! I claim that it is > its Dual. > Thus I advocate a form of mind-matter dualism in terms of an > Information-Matter dualism following the lines of the Pontryagin and > Stone > dualities. http://en.academic.ru/dic.nsf/enwiki/327868 [SPK] You may elaborate, but Stone dualities are very technical hard matter. I guess you are alluding to Vaughan Pratt's work on Chu Spaces. [SPK] Yes, it is Pratt's idea that inspires this thinking. What he has found is that is possible to solve the problem of Cartesian Dualism, but in solving the problem we chance the notion of "substance" into one that is emergent from underlying Process and not taken to be a primitive. What convinced me of the validity of his idea is that it offers a very neat and novel solution to the measurement problem of QM. To me it is the utility of a metaphysical principle in advancing understanding that goes toward the necessity of its assumptions/axiom, just as you have shown how the ideas of Plato ,Plotinus and Theaetetus are useful. > > >> but this seems to not really resolve the question entirely. > > [BM] > I am not sure I have a clear idea of the question, here. > > [SPK] > > Am I making any sense so far? > >> It >> makes me suspicious of the entire Platonic program, for what would >> act >> as the universal generator of "twoness" as distinguished from >> "threeness" be in-itself? Why not some kind of nominalism that >> transforms asymptotically into universalism? > [BM] > You lost me. > > You know how I work. I start from an assumption about some link > between > consciousness and Turing 'machine', and from this I derived step by > step a > frame which is closer to Plato and Plotinus than to Aristotle, at > least on > the "Matter" notion. > > [SPK] > Yes and I use the assumption that any 1st person "content" of > consciousness can be show to be equivalent to the content of some > virtual > reality generated by a Turing Machine (given with sufficient physical > resources) [BM] But this has been shown not working. You cannot both capture consciousness by Turing machine states, and at the same time to invoke a notion of physical resource. It is the whole point of most of my posts. Physical resource including space and time have to be recovered from the math of (abstract) computer science. [SPK] No no no! I am not "capturing consciousness by Turing machine"! I am pointing at the content, using Descartes' brain in a vat and related gedankenexperiments to show how there is an equivalence relation between the content of experience (minus "agency" notions, self-awareness, etc.) and the content of what can be generated by universal Virtual reality machines, as explained by D. Deutsch in Fabric of Reality, that can be used. The notion of a physical resource is allowed because I am assuming that both mind (crudely an information structure, like a Boolean algebra) and matter (crudely as a Cantor dust or completely disconnected Hausdorff space) are both equally existent and "real". The idea in Pratt's work is that Logic and Time (the evolution of physical systems) form a duality see: http://boole.stanford.edu/pub/dti.pdf > and following your arguments will agree that while the content > itself is computable, *which one of the computations it is* that is > the > actual generator of the particular content of a particular point of > view is not computational. [BM] I am OK, here. [SPK] OK, so if we can extract the symmetry groups from the possible relations between 'many' and find that those include the symmetry groups that we find in physics, would this not give us a way to think of physical laws as emergent from interactions in a way that is parallel to Kant's idea? But for this to work, two conditions must be show to be of prior necessity: a plurality of systems that we can associate with observers (in a generic non-anthropomorphic sense) and a means to derive notions of "substance exchange". That is what I am working towards. > These thoughts tie back to the point about > indeterminateness that Plotinus brilliantly made and you point out. [BM] Yes. Note that the idea of relating matter to indeterminacy is already in Aristotle. Alas, Aristotle and/or its successors have reified it metaphysically. That is, imo, what makes the mind-body problem insolvable. [BM] I disagree. What makes the mind-body problem insoluble is the assumption that 'substance' is primitive. We can see this in Descartes attempt at dualism. By taking res extensa and res cognitas as primitive substances, Descartes was unable to close the gap between them, for within the notion of substance one must have another substance that is of both aspects to bridge between them and this necessity stultifies the entire project; what is the point of separate substances if there is a third substance that is both? Cartesian dualism fails because it is just an incoherent monism. OTOH, if we consider Mind and Matter in terms of their logics and dynamics and see that there is a relation between these two aspects that preserves their differences all the while there is a parallelism a solution can obtain. But this alternative requires a different metaphysical underpinning; this point is what I am arguing below. > > Your modelization so far seems to only consider a "frozen" > perspective and there is scant mention of how the model is extended > to cover > a plurality of entities, except for the diamond^alpha aspect mentioned > below. As far as I can tell, your Model offers a logical structure > to a new > version of the individual Leibnizian Monad ( > http://www.iep.utm.edu/leib-met/#H8 ) that I am trying to develop, > but only > in the static sense. There is no dynamic in it. [BM] The 'sensible' modalities, like Bp & p, and Bp & Dp & p, introduces an internal dynamic. S4Grz is not just a logic of knowledge, it is a logic of evolving knowledge, or time. It is due to the "& p". It makes the first person intuitionist, the builder of its mental reality. [SPK] It may exist there Bruno, but it is by no means explicit. The fact that we can map Bp & p, etc. to some abstract structure and use the orderings of those relations to act as a quotienting does nothing to obtain the experiential transitivity that is explicit in the 1st person. This is just a very sophisticated form of eliminatism unless we assume, even tacitly, a fundamental Becoming. We find explicit examples of this in discussions of Chris Isham's paper on Topos. See: Isham, C. J. (1993), “Canonical Quantum Gravity and the Problem of Time”, in L. A. Ibort and M. A. Rodríguez (eds.), Integrable Systems, Quantum Groups, and Quantum Field theories. Dordrecht: Kluwer Academic Publishers, 157-288. And http://philsci-archive.pitt.edu/archive/00001915/01/SptPhilChallQG=9903072.p df http://philsci-archive.pitt.edu/archive/00001914/01/EmergTimeQG=9901024.pdf My problem is that I do not have a good understanding of S4Grz. Could you point me to papers on it that I might obtain online? > I think that this is > intentional since you are taking an explicit Platonic Idea stance in > the > Modelization of Plotinusian Statics. I appreciate that, but > understand that > unless we can derive change from changelessness within our > modelizing we are > doomed to eliminatism when it comes to our 1st and 3rd notions > temporal > transitivity, duration and causality. [BM] That's right, but the nice thing is that the first person notion automatically provides an internal dynamics. [SPK] Ummm, I am not so sure that is a correct statement of the relationship. From what I have been able to understand so far, the 1st person notion entails an internal dynamic because of its self-referencing maps. My point is that the mere existence of automorphisms or self-mappings alone is insufficient. We need a ground within which these would act; otherwise we just have the equivalent of a dust with no hope of interactions. > It is my contention that it is > impossible to derive change from changelessness, [BM] Even physicalists can accept this though. Many physicists don't believe in time. It emerges for local observers when embedded in the block-static reality. Of course we accept the (non trivial) ordering of the natural numbers, which can be seen as the Mother of all computational times. [SPK] So does this allow us to not consider the alternative? This is so frustrating, we have a beautiful way of deriving the appearance of changelessness from fundamental change, by using the notion of automorphisms within a wider context of morphism, and this is rejected out of hand? That is about the most irrational thinking that I can witness! The only explanation that I can think of for this is that the hope of an impersonal determinism that obtains from the block-static reality doctrine allows it adherents to avoid all notions of personal responsibility for their behaviors. As to the non-trivial ordering of numbers, it should be obvious that there does not exist a unique ordering over the class of possible 1st person experiences, or computational strings; the class is not equivalent to a simply connected space which is, essentially, what is required for a unique ordering to be possible. We see this in physics in the Foliation Problem of General Relativity and in differential topology. See: www.cmp.caltech.edu/~dannyc/papers/fpams.pdf.gz we are fooling ourselves if we think that time is just the ordering of natural numbers. Again, we can ignore this and retreat into pseudo-monorealism - that only I exist - and use that solipsism to conclude that any other alternative is just a diffeomorphism of one's own notion of the natural ordering. This might explain the irrational resistance to the reality of the implications of a finite speed of Light that we find in many people. I think that the notion of Person that Plotinus uses to consider his hypostases conceals this problem. By assuming personhood he is surreptitiously introducing the 1st person self-mapping. This is equivalent to assuming a fundamental Becoming grundladen within one's basic axioms. I recall a conversation that I have with a writer that was arguing that time did not exist. I pointed out that his model involved the computation of optimizations over infinite collections of interactions and how this was the mother of all NP-Complete problems and quoted to him his own words taken from a discussion of how computational intensive it was for him to obtain solutions to small examples of these optimizations on his physical desktop computer and was taken aback by his complete incomprehension of this point. One cannot consider that the mere existence of a solution to an infinite NP-Complete problem is sufficient grounds to argue that the computation itself need not ever occur, because that solution is not alone, it exists mixed up with all of the infinite number of alternatives and the physical act of running a machine is what manifests that One solution. The same argument applies to the Universal Dovetailer. Snip Kindest regards, Stephen -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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