I will make one short comment. There is a difference between the physical nature of the wave function as a sum over possibilities and the actuality of a measurement. One can believe in the actuality of all the possibilities. This is David Deutch’s contention. It is a matter of debate. There is no question that the wave function as a whole has physical meaning, but what has physical actuality is what can be measured. What has mathematical actuality is another matter. The highest orders of infinity have mathematical actuality.

> On Mar 28, 2016, at 9:45 AM, Bruno Marchal <marc...@ulb.ac.be> wrote: > > Dear Lou and Colleagues, > > > On 25 Mar 2016, at 19:51, Louis H Kauffman wrote: > >> Dear Karl, >> >> Thank you for this very considered letter. >> I would like to ask you about your entry >> >> "6. Quantum information. By keeping an exact accounting about which >> predictions are being fulfilled to which degree we see a self-organisation >> evolve on competing interpretations of a+b=c. Using the property of an >> element to belong to a cycle with cardinality n, we can use the negated form >> of not-belonging to different other cycles to transmit information. >> Information is a statement about something that is not the case. We can show >> the impossibility of a spatial arrangement of arguments of a sentence to >> cause impossibilities of coexistence of commutative arguments of the same >> sentence. “ >> >> My question: How is your comment about quantum information related to the >> orthodox minimal model for quantum information that we usually use? >> I will detail this model in the next paragraph. I do understand that your >> paragraph refers to the complementarity aspects of quantum information. The >> description below is a concise formulation of the entire quantum model. >> What is lacking for physics is the addition of the structure of observables >> and the relationship of the temporal evolution of the unitary transformation >> with the Hamiltonian (i.e. with formulations of physical energy). >> Lifted in this way from the particular physics, this description is minimal >> take on quantum theory that can be used in discussing its properties. >> >> Quantum Theory in a Nutshell >> 1. A state of a quantum system is a vector |psi> of unit length in a complex >> vector space H. H is a Hilbert space, but it can be finite dimensional. >> Convectors are denoted by <phi | so that <phi |psi> is a complex number and >> <psi |psi> is a positive real number. >> 2. A quantum process is a unitary transformation U: H ——> H. Unitary means >> that the U* = U^{-1} where U* denotes the conjugate transpose of U. >> 3. An observation projects the state to a subspace. The simplest and most >> useful form of this is to >> assume that H has an orthonormal basis { |e_1> ,|e_2>,…} that consists in >> all possible results of observations. >> Then observing |psi> results in |e_n> for some n with probability |<e_n | >> psi>|^2. >> Note that the Sum_{n} |<e_n | psi>|^2 = 1 since |psi> is a vector of unit >> length. >> >> This description shows that quantum theory is a dynamic sort of probability >> theory. The state vector |psi> is a superposition of all the possibilities >> for observation, with complex number coefficients. > > It seems to me that what is truly remarkable in quantum mechanics (without > collapse) is that the superposition are *not* superposition of possibilities, > but of actualities. If those where not actualities, we would not been able to > exploit the interference between parallel computations like we can do with a > quantum computer (but which is also already illustrated in the two slits > experiments). > > Then this confirms the "computationalist theory of everything", which is > given by any formalism, like Robinson Arithmetic (the rest is given by the > internal machine's phenomenology, like the one deducible from > incompleteness). Indeed, in that theory, the stable (predictible) observable > have to be given by a statistics on all computation going through our actual > state. This (retro-)predicts that the physical obeys to some quantum logic, > and it can be derived from some intensional nuance on the Gödel > self-referential provability predicate (like beweisbar('p') & > consistent('t')). > > In quantum mechanics without collapse of the wave during observation, the > axiom 3 is phenomenological, and with computationalism in the cognitive > science (the assumption that there is a level of description of the brain > such that my consciousness would proceed through any such emulation of my > brain or body at that level or below) the whole "physical" is > phenomenological. > Physics becomes a statistics on our consistent sharable first person (plural) > experiences. With "our" referring to us = the universal numbers knowing that > they are universal (Peano Arithmetic, Zermelo Fraenkel Set Theory, viewed as > machine, are such numbers). > > An actuality is a possibility seen from inside, somehow, in this context or > theory (QM without collapse, or Computationalism). > > Personally, it seems that quantum mechanics, when we agree on the internal > phenomenological of actuality in the possibilities, confirms the most > startling, perhaps shocking, consequence of computationalism (digital > mechanism). Note that it does not make the physical itself computable a > priori. > > >> Via the absolute squares of these coefficients |psi. can be regarded as a >> probability distribution for the outcomes that correspond to each basis >> direction. Since the coefficients are complex numbers and the quantum >> processes preserve the total probability, one has room for complexity of >> interaction, phase, superposition, cancellation and so on. > > OK. > > Best, > > Bruno > > > > > > >> >> Best, >> Lou Kauffman >> >>> On Mar 25, 2016, at 10:22 AM, Karl Javorszky <karl.javors...@gmail.com >>> <mailto:karl.javors...@gmail.com>> wrote: >>> >>> Dear FIS Colleagues, >>> >>> 1. Are the facts complicated or is our interpretation of the facts >>> complicated? >>> >>> again, the discussion centres on interpretations of Nature. How do we >>> picture some processes of Nature – like, specifically, the workings of >>> genetics and biology generally -, and which explanational tools do we use >>> to consolidate our views of Nature. >>> >>> We assume that Nature is describable by our tools, which tools agree to our >>> concepts of consistent, logical, useful, true. We agree that basic working >>> principles of Nature must be simple, easy to understand and quite logical, >>> in fact self-evident, once one has understood them. >>> >>> We agree that what we want to observe are relations among appearances, and >>> that geometry, specifically topology will play a fundamental part in the >>> explanations which we seek. >>> >>> Now the next step is to reflect on what makes our current perceptions and >>> ideas about Nature so far off the right track, that we experience Nature to >>> be hard to understand, complicated and beyond our present capacity to >>> explain in a simple fashion. >>> >>> We cannot state that basic rules and laws Nature appears to obey are >>> circumstantial and complicated. We can only conclude that we, humans, are >>> making an interpretation complicated, although Nature by axiom works in the >>> most simple and logical fashion. >>> >>> 2. Back to basics >>> >>> The rule we want to understand is very simple and basic. It is only our >>> being used to not paying attention to small details which makes us believe >>> that the rule is complicated. Had we not insisted that generating c=a+b >>> from (a,b) is the most important way of dealing with (a,b) we could use >>> other aspects of (a,b) too. >>> >>> The addition makes use of the similarity property of object. Similarity >>> (and within it, the special case of symmetry) is such an important tool in >>> survival and reproduction that our neurology forces us to see it far more >>> important than dissimilarity. Culture reinforces this common sense approach >>> to (a,b). >>> >>> Nature herself, however, is not in a Darwinian competition, therefore she >>> does make use of other aspects of (a,b), next to a+b=c. Just for >>> illustration, let me mention b-a, b-2a, 2b-3a, a-2b, 2a-3b and more of this >>> kind. These are as valid properties of (a,b) as their sum, but have had >>> much less of stage time and employment so far. >>> >>> If we want to learn something new, why don’t we start with a+b=c, the >>> mother of all observations. Let us give it a try and believe it to be >>> possible that one can learn something new and clever and that it will be >>> useful. >>> >>> 3. Order >>> >>> We cannot dispute the fact that there is a quite exact and well-regulated >>> order behind genetics. So it is natural that we look deeper into the >>> concept of order. >>> >>> Order means that an element with known properties is in a place with known >>> properties that match the same order, which established the match. Order >>> assigns a place to an element and an element to a place. >>> >>> Doing an exercise with some standard specimen of a+b=c, we see that we can >>> order the collection in differing ways, according to the order aspect we >>> use to establish a sequence among the elements. (If we sort our library on >>> title, we arrive at a different linear enumeration of the books compared to >>> one we arrive at if we sort the library on author.) >>> >>> The differing aspects of a+b=c impose differing orders on the collection of >>> statements a+b=c. These may well be contradictory among each other. >>> >>> The realm we enter here may appear unusual and complicated, because we had >>> not been getting used to deal with logical statements that are false, >>> irrelevant or contradictory. >>> >>> Nature herself, however, has not been listening to Wittgenstein, and keeps >>> on doing things about which we should not be talking, as our rules of >>> logical grammar do not present themselves easily to discussing false, >>> irrelevant or contradictory states of the world. And, since we have had >>> some progress in processing of data since the time of Wittgenstein, we are >>> now able, with the help of computers, to visualise the creation and the >>> consolidation of logical conflicts. By using computers, we may start to >>> talk about that, what is not the case. We may observe typical patterns of >>> conflict resolution, of logical compromises that allow contradictions to >>> exist, up to a point. >>> >>> 4. Cycles >>> >>> Here comes the solution: Nature does not act illogically, but, rather >>> elegantly, pushes off logical contradictions either into the future or into >>> the non-space. The mechanism is strikingly simple and self-evident. One >>> only has to generate a sequence and sort and resort it to observe the >>> existence of cycles. The concept is known in mathematics under the title of >>> “cyclic permutations”. We can use each element (a,b) as a data depository, >>> wherein we place symbols that are concurrently commutative and sequential. >>> The membership in a cycle is a symbol that is commutative for each of the >>> members of the cycle, but confers also a sequential attribute relating to >>> the sequence of place changes that are the essence of a cycle. We thus have >>> both commutative and sequenced symbols on elements of a set, which allows >>> utilising the extraordinarily helpful relation between the “now” and the >>> “past/future: not now”, illustrated in OEIS A242615. >>> >>> We use the cycles as basic units, not the “1” and its replicas. Order is a >>> prediction about where will be what, and by generating all possible orders, >>> we may generate a biggish table which contains all elements’ places under >>> each possible order. The reordering from one of the orders into a different >>> one of the orders happens by means of cycles. >>> >>> Among the cycles there are some which lend themselves easily to be used as >>> standard cycles. The standard cycles are simple implications, corollaries, >>> of a+b=c. >>> >>> 5. Geometry >>> >>> The standard cycles allow building rectangular spaces modi Descartes. The >>> geometry is strikingly subtle, elegant, logical and self-evident. The >>> attachment handles and their topology can be read off some tables which >>> detail which versions of a+b=c can coexist with which other versions of >>> a+b=c. This is indeed a combinatorics of geometry, based on properties of >>> natural numbers. >>> >>> 6. Quantum information >>> >>> By keeping an exact accounting about which predictions are being fulfilled >>> to which degree we see a self-organisation evolve on competing >>> interpretations of a+b=c. Using the property of an element to belong to a >>> cycle with cardinality n, we can use the negated form of not-belonging to >>> different other cycles to transmit information. Information is a statement >>> about something that is not the case. We can show the impossibility of a >>> spatial arrangement of arguments of a sentence to cause impossibilities of >>> coexistence of commutative arguments of the same sentence. >>> >>> 7. Summary >>> >>> The natural numbers are ready and waiting for the user to read results out >>> of their multitude. The task is for the human to be willing to look at >>> patterns that evolve as the order concept assigns places to elements. The >>> patterns made visible by reordering instances of a+b=c appear to be >>> modelling ways Nature does business in a simple, easy and self-evident >>> fashion. >>> >>> >>> Happy First Full Moon After Spring Equinox to you all. >>> >>> Karl >>> >>> >>> 2016-03-24 19:31 GMT+01:00 Louis H Kauffman <kauff...@uic.edu >>> <mailto:kauff...@uic.edu>>: >>> Sorry Louis, but try again, please, for your address was wrong in the >>> list!!!! --Pedro >>> (I have just discovered, in a trip pause) >>> BlackBerry de movistar, allí donde estés está tu oficin@ >>> From: Louis H Kauffman <lou...@gmail.com <mailto:lou...@gmail.com>> >>> Date: Tue, 22 Mar 2016 17:56:06 -0500 >>> To: fis<fis@listas.unizar.es <mailto:fis@listas.unizar.es>> >>> Cc: Pedro C. Marijuan<pcmarijuan.i...@aragon.es >>> <mailto:pcmarijuan.i...@aragon.es>> >>> Subject: Re: [Fis] SYMMETRY & _ On BioLogic >>> >>> Dear Plamen, >>> It is possible. We are looking here at Pivar and his colleagues working >>> with the possibilities of materials. It is similar to how people in origami >>> have explored the possibilities of producing forms by folding paper. >>> If we can make hypotheses on how topological geometric forms should develop >>> in a way that is resonant with biology, then we can explore these in a >>> systematic way. An example is indeed the use of knot theory to study DNA >>> recombination. We have a partial model of the topological aspect of >>> recombination, and we can explore this by using rope models and the >>> abstract apparatus of corresponding topological models. Something similar >>> might be possible for developmental biology. >>>> On Mar 17, 2016, at 2:45 AM, Dr. Plamen L. Simeonov >>>> <plamen.l.simeo...@gmail.com <mailto:plamen.l.simeo...@gmail.com>> wrote: >>>> >>>> Dear Lou and Colleagues, >>>> >>>> yes, I agree: an artistic approach can be very fruitful. This is like what >>>> Stuart Kauffman says about speaking with metaphors. At some point our >>>> mathematical descriptive tools do not have sufficient expressional power >>>> to grasp more global general insights and we reach out to the domains of >>>> narration, music and visualisation for help. And this is the point where >>>> this effort of reflection upon a subject begins to generate and develop >>>> new expressional forms of mathematics (logics, algebras, geometries). I >>>> think that you and Ralph Abraham noted this in your contributions about >>>> the mystic of mathematics in the 2015 JPBMB special issue. Therefore I ask >>>> here, if we all feel that there is some grain of imaginative truth in the >>>> works of Pivar and team, what piece of mathematics does it needs to become >>>> a serious theory. Spencer-Brown did also have similar flashy insights in >>>> the beginning, but he needed 20+ years to abstract them into a substantial >>>> book and theory. This is what also other mathematicians do. They are >>>> providing complete works. Modern artists and futurists are shooting fast >>>> and then moving to the next “inspiration”, often without “marketing” the >>>> earlier idea. And then they are often disappointed that they were not >>>> understood by their contemporaries. The lack of They are often arrogant >>>> and do not care about the opinion of others like we do in our FIS forum. >>>> But they often have some “oracle” messages. So, my question to you and the >>>> others here is: Is there a way that we, scientists, can build a solid >>>> theory on the base of others' artistic insights? Do you think you can help >>>> here as an expert in topology and logic to fill the formalisation gaps in >>>> Pivar’s approach and develop something foundational. All this would take >>>> time and I am not sure if such artists like Pivar would be ready to >>>> participate a scientific-humanitarian discourse, because we know that most >>>> of these talents as extremely egocentric and ignorant and we cannot change >>>> this. What do you think? >>>> >>>> Best, >>>> >>>> Plamen >>>> >>>> >>>> >>>> >>>> On Thu, Mar 17, 2016 at 8:09 AM, Louis H Kauffman <lou...@gmail.com >>>> <mailto:lou...@gmail.com>> wrote: >>>> Dear Plamen, >>>> I do not know why Gel-Mann supported this. It is interesting to me anyway. >>>> It is primarily an artistic endeavor but is based on some ideas of visual >>>> development of complex forms from simpler forms. >>>> Some of these stories may have a grain of truth. The sort of thing I do >>>> and others do is much more conservative (even what D’Arcy Thompson did is >>>> much more conservative). We look for simple patterns that definitely seem >>>> to occur in complex situations and we abstract them and work with them on >>>> their own grounds, and with regard to how these patterns work in a complex >>>> system. An artistic approach can be very fruitful. >>>> Best, >>>> Lou >>>> >>>>> On Mar 16, 2016, at 9:43 AM, Dr. Plamen L. Simeonov >>>>> <plamen.l.simeo...@gmail.com <mailto:plamen.l.simeo...@gmail.com>> wrote: >>>>> >>>>> Dear Lou, Pedro and Colleagues, >>>>> >>>>> I have another somewhat provoking question about the "constructive" role >>>>> of topology in morphogenesis. What do you think about the somewhat >>>>> artistic, but scientifically VERY controversial theory about the origin >>>>> and development of life forms based on physical forces from classical >>>>> mechanics and topology only, thus ignoring all of genetics, Darwinism and >>>>> Creationism: >>>>> >>>>> http://www.ilasol.org.il/ILASOL/uploads/files/Pivar_ILASOL-2010.pdf >>>>> <http://www.ilasol.org.il/ILASOL/uploads/files/Pivar_ILASOL-2010.pdf> >>>>> >>>>> What part of this can be regarded as science at all, and If there is >>>>> something missing what is it? Why did a person like Murray Gel-Mann >>>>> support this? >>>>> >>>>> >>>>> Best >>>>> >>>>> Plamen >>>>> >>>>> ____________________________________________________________ >>>>> >>>>> >>>>> On Tue, Mar 15, 2016 at 12:00 PM, Pedro C. Marijuan >>>>> <pcmarijuan.i...@aragon.es <mailto:pcmarijuan.i...@aragon.es>> wrote: >>>>> Louis, a very simple question: in your model of self-replication, when >>>>> you enter the environment, could it mean something else than just >>>>> providing the raw stuff for reproduction? It would be great if related to >>>>> successive cycles one could include emergent topological (say >>>>> geometrical-mechanical) properties. For instance, once you have divided >>>>> three times the initial egg-cell, you would encounter three symmetry axes >>>>> that would co-define the future axes of animal >>>>> development--dorsal/ventral, anterior/posterior, lateral/medial. Another >>>>> matter would be about the timing of complexity, whether mere repetition >>>>> of cycles could generate or not sufficient functional diversity such as >>>>> Plamen was inquiring in the case of molecular clocks (nope in my >>>>> opinion). best--Pedro >>>>> >>>>> >>>>> -- >>>>> ------------------------------------------------- >>>>> Pedro C. Marijuán >>>>> Grupo de Bioinformación / Bioinformation Group >>>>> Instituto Aragonés de Ciencias de la Salud >>>>> Centro de Investigación Biomédica de Aragón (CIBA) >>>>> Avda. San Juan Bosco, 13, planta X >>>>> 50009 Zaragoza, Spain >>>>> Tfno. +34 976 71 3526 <tel:%2B34%20976%2071%203526> (& 6818) >>>>> pcmarijuan.i...@aragon.es <mailto:pcmarijuan.i...@aragon.es> >>>>> http://sites.google.com/site/pedrocmarijuan/ >>>>> <http://sites.google.com/site/pedrocmarijuan/> >>>>> ------------------------------------------------- >>>>> >>>>> _______________________________________________ >>>>> Fis mailing list >>>>> Fis@listas.unizar.es <mailto:Fis@listas.unizar.es> >>>>> http://listas.unizar.es/cgi-bin/mailman/listinfo/fis >>>>> <http://listas.unizar.es/cgi-bin/mailman/listinfo/fis> >>>>> >>>> >>>> >>> >>> >>> _______________________________________________ >>> Fis mailing list >>> Fis@listas.unizar.es <mailto:Fis@listas.unizar.es> >>> http://listas.unizar.es/cgi-bin/mailman/listinfo/fis >>> <http://listas.unizar.es/cgi-bin/mailman/listinfo/fis> >>> >>> >>> _______________________________________________ >>> Fis mailing list >>> Fis@listas.unizar.es <mailto:Fis@listas.unizar.es> >>> http://listas.unizar.es/cgi-bin/mailman/listinfo/fis >>> <http://listas.unizar.es/cgi-bin/mailman/listinfo/fis> >> >> _______________________________________________ >> Fis mailing list >> Fis@listas.unizar.es <mailto:Fis@listas.unizar.es> >> http://listas.unizar.es/cgi-bin/mailman/listinfo/fis >> <http://listas.unizar.es/cgi-bin/mailman/listinfo/fis> > > http://iridia.ulb.ac.be/~marchal/ <http://iridia.ulb.ac.be/~marchal/> > > > > _______________________________________________ > Fis mailing list > Fis@listas.unizar.es <mailto:Fis@listas.unizar.es> > http://listas.unizar.es/cgi-bin/mailman/listinfo/fis > <http://listas.unizar.es/cgi-bin/mailman/listinfo/fis>

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