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 aboutwhich predictions are being fulfilled to which degree we see a self-organisation evolve on competing interpretations of a+b=c. Using theproperty of an element to belong to a cycle with cardinality n, wecan use the negated form of not-belonging to different other cyclesto transmit information. Information is a statement about somethingthat is not the case. We can show the impossibility of a spatialarrangement of arguments of a sentence to cause impossibilities ofcoexistence of commutative arguments of the same sentence. “My question: How is your comment about quantum information relatedto the orthodox minimal model for quantum information that weusually use?I will detail this model in the next paragraph. I do understand thatyour paragraph refers to the complementarity aspects of quantuminformation. The description below is a concise formulation of theentire quantum model.What is lacking for physics is the addition of the structure ofobservables and the relationship of the temporal evolution of theunitary transformation with the Hamiltonian (i.e. with formulationsof physical energy).Lifted in this way from the particular physics, this description isminimal take on quantum theory that can be used in discussing itsproperties.Quantum Theory in a Nutshell1. A state of a quantum system is a vector |psi> of unit length in acomplex vector space H. H is a Hilbert space, but it can be finitedimensional.Convectors are denoted by <phi | so that <phi |psi> is a complexnumber and <psi |psi> is a positive real number.2. A quantum process is a unitary transformation U: H ——> H. Unitarymeans that the U* = U^{-1} where U* denotes the conjugate transposeof U.3. An observation projects the state to a subspace. The simplest andmost useful form of this is toassume that H has an orthonormal basis { |e_1> ,|e_2>,…} thatconsists 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 ofunit length.This description shows that quantum theory is a dynamic sort ofprobability theory. The state vector |psi> is a superposition of allthe 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 regardedas a probability distribution for the outcomes that correspond toeach basis direction. Since the coefficients are complex numbers andthe quantum processes preserve the total probability, one has roomfor complexity of interaction, phase, superposition, cancellationand so on.

OK. Best, Bruno

Best, Lou KauffmanOn Mar 25, 2016, at 10:22 AM, Karl Javorszky <karl.javors...@gmail.com> wrote:Dear FIS Colleagues,1. Are the facts complicated or is our interpretation of thefacts complicated?again, the discussion centres on interpretations of Nature. How dowe picture some processes of Nature – like, specifically, theworkings of genetics and biology generally -, and whichexplanational tools do we use to consolidate our views of Nature.We assume that Nature is describable by our tools, which toolsagree to our concepts of consistent, logical, useful, true. Weagree that basic working principles of Nature must be simple, easyto understand and quite logical, in fact self-evident, once one hasunderstood them.We agree that what we want to observe are relations amongappearances, and that geometry, specifically topology will play afundamental part in the explanations which we seek.Now the next step is to reflect on what makes our currentperceptions and ideas about Nature so far off the right track, thatwe experience Nature to be hard to understand, complicated andbeyond our present capacity to explain in a simple fashion.We cannot state that basic rules and laws Nature appears to obeyare circumstantial and complicated. We can only conclude that we,humans, are making an interpretation complicated, although Natureby axiom works in the most simple and logical fashion.2. Back to basicsThe rule we want to understand is very simple and basic. It is onlyour being used to not paying attention to small details which makesus believe that the rule is complicated. Had we not insisted thatgenerating c=a+b from (a,b) is the most important way of dealingwith (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 animportant tool in survival and reproduction that our neurologyforces us to see it far more important than dissimilarity. Culturereinforces 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 employmentso 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 itto be possible that one can learn something new and clever and thatit will be useful.3. OrderWe cannot dispute the fact that there is a quite exact and well-regulated order behind genetics. So it is natural that we lookdeeper into the concept of order.Order means that an element with known properties is in a placewith known properties that match the same order, which establishedthe match. Order assigns a place to an element and an element to aplace.Doing an exercise with some standard specimen of a+b=c, we see thatwe can order the collection in differing ways, according to theorder aspect we use to establish a sequence among the elements. (Ifwe sort our library on title, we arrive at a different linearenumeration of the books compared to one we arrive at if we sortthe library on author.)The differing aspects of a+b=c impose differing orders on thecollection of statements a+b=c. These may well be contradictoryamong each other.The realm we enter here may appear unusual and complicated, becausewe had not been getting used to deal with logical statements thatare 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, asour rules of logical grammar do not present themselves easily todiscussing false, irrelevant or contradictory states of the world.And, since we have had some progress in processing of data sincethe time of Wittgenstein, we are now able, with the help ofcomputers, to visualise the creation and the consolidation oflogical conflicts. By using computers, we may start to talk aboutthat, what is not the case. We may observe typical patterns ofconflict resolution, of logical compromises that allowcontradictions to exist, up to a point.4. CyclesHere comes the solution: Nature does not act illogically, but,rather elegantly, pushes off logical contradictions either into thefuture or into the non-space. The mechanism is strikingly simpleand self-evident. One only has to generate a sequence and sort andresort it to observe the existence of cycles. The concept is knownin mathematics under the title of “cyclic permutations”. We can useeach element (a,b) as a data depository, wherein we place symbolsthat are concurrently commutative and sequential. The membership ina cycle is a symbol that is commutative for each of the members ofthe cycle, but confers also a sequential attribute relating to thesequence of place changes that are the essence of a cycle. We thushave both commutative and sequenced symbols on elements of a set,which allows utilising the extraordinarily helpful relation betweenthe “now” and the “past/future: not now”, illustrated in OEISA242615.We use the cycles as basic units, not the “1” and its replicas.Order is a prediction about where will be what, and by generatingall possible orders, we may generate a biggish table which containsall elements’ places under each possible order. The reordering fromone of the orders into a different one of the orders happens bymeans of cycles.Among the cycles there are some which lend themselves easily to beused as standard cycles. The standard cycles are simpleimplications, corollaries, of a+b=c.5. GeometryThe standard cycles allow building rectangular spaces modiDescartes. The geometry is strikingly subtle, elegant, logical andself-evident. The attachment handles and their topology can be readoff some tables which detail which versions of a+b=c can coexistwith which other versions of a+b=c. This is indeed a combinatoricsof geometry, based on properties of natural numbers.6. Quantum informationBy keeping an exact accounting about which predictions are beingfulfilled to which degree we see a self-organisation evolve oncompeting interpretations of a+b=c. Using the property of anelement to belong to a cycle with cardinality n, we can use thenegated form of not-belonging to different other cycles to transmitinformation. Information is a statement about something that is notthe case. We can show the impossibility of a spatial arrangement ofarguments of a sentence to cause impossibilities of coexistence ofcommutative arguments of the same sentence.7. SummaryThe natural numbers are ready and waiting for the user to readresults out of their multitude. The task is for the human to bewilling to look at patterns that evolve as the order conceptassigns places to elements. The patterns made visible by reorderinginstances of a+b=c appear to be modelling ways Nature does businessin 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>:Sorry Louis, but try again, please, for your address was wrong inthe 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> Date: Tue, 22 Mar 2016 17:56:06 -0500 To: fis<fis@listas.unizar.es> Cc: Pedro C. Marijuan<pcmarijuan.i...@aragon.es> Subject: Re: [Fis] SYMMETRY & _ On BioLogic Dear Plamen,It is possible. We are looking here at Pivar and his colleaguesworking with the possibilities of materials. It is similar to howpeople in origami have explored the possibilities of producingforms by folding paper.If we can make hypotheses on how topological geometric forms shoulddevelop in a way that is resonant with biology, then we can explorethese in a systematic way. An example is indeed the use of knottheory to study DNA recombination. We have a partial model of thetopological aspect of recombination, and we can explore this byusing rope models and the abstract apparatus of correspondingtopological models. Something similar might be possible fordevelopmental biology.On Mar 17, 2016, at 2:45 AM, Dr. Plamen L. Simeonov <plamen.l.simeo...@gmail.com> wrote:Dear Lou and Colleagues,yes, I agree: an artistic approach can be very fruitful. This islike what Stuart Kauffman says about speaking with metaphors. Atsome point our mathematical descriptive tools do not havesufficient expressional power to grasp more global generalinsights and we reach out to the domains of narration, music andvisualisation for help. And this is the point where this effort ofreflection upon a subject begins to generate and develop newexpressional forms of mathematics (logics, algebras, geometries).I think that you and Ralph Abraham noted this in yourcontributions about the mystic of mathematics in the 2015 JPBMBspecial issue. Therefore I ask here, if we all feel that there issome grain of imaginative truth in the works of Pivar and team,what piece of mathematics does it needs to become a serioustheory. Spencer-Brown did also have similar flashy insights in thebeginning, but he needed 20+ years to abstract them into asubstantial book and theory. This is what also othermathematicians do. They are providing complete works. Modernartists and futurists are shooting fast and then moving to thenext “inspiration”, often without “marketing” the earlier idea.And then they are often disappointed that they were not understoodby their contemporaries. The lack of They are often arrogant anddo not care about the opinion of others like we do in our FISforum. But they often have some “oracle” messages. So, my questionto 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 logicto fill the formalisation gaps in Pivar’s approach and developsomething foundational. All this would take time and I am not sureif such artists like Pivar would be ready to participate ascientific-humanitarian discourse, because we know that most ofthese talents as extremely egocentric and ignorant and we cannotchange this. What do you think?Best, PlamenOn Thu, Mar 17, 2016 at 8:09 AM, Louis H Kauffman<lou...@gmail.com> wrote:Dear Plamen,I do not know why Gel-Mann supported this. It is interesting to meanyway. It is primarily an artistic endeavor but is based on someideas of visual development of complex forms from simpler forms.Some of these stories may have a grain of truth. The sort of thingI do and others do is much more conservative (even what D’ArcyThompson did is much more conservative). We look for simplepatterns that definitely seem to occur in complex situations andwe abstract them and work with them on their own grounds, and withregard to how these patterns work in a complex system. An artisticapproach can be very fruitful.Best, LouOn Mar 16, 2016, at 9:43 AM, Dr. Plamen L. Simeonov <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 youthink about the somewhat artistic, but scientifically VERYcontroversial theory about the origin and development of lifeforms based on physical forces from classical mechanics andtopology only, thus ignoring all of genetics, Darwinism andCreationism:http://www.ilasol.org.il/ILASOL/uploads/files/Pivar_ILASOL-2010.pdfWhat part of this can be regarded as science at all, and If thereis 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> wrote:Louis, a very simple question: in your model of self-replication,when you enter the environment, could it mean something else thanjust providing the raw stuff for reproduction? It would be greatif related to successive cycles one could include emergenttopological (say geometrical-mechanical) properties. Forinstance, once you have divided three times the initial egg-cell,you would encounter three symmetry axes that would co-define thefuture axes of animal development--dorsal/ventral, anterior/posterior, lateral/medial. Another matter would be about thetiming of complexity, whether mere repetition of cycles couldgenerate or not sufficient functional diversity such as Plamenwas inquiring in the case of molecular clocks (nope in myopinion). 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 (& 6818) pcmarijuan.i...@aragon.es http://sites.google.com/site/pedrocmarijuan/ ------------------------------------------------- _______________________________________________ Fis mailing list Fis@listas.unizar.es http://listas.unizar.es/cgi-bin/mailman/listinfo/fis_______________________________________________ Fis mailing list Fis@listas.unizar.es http://listas.unizar.es/cgi-bin/mailman/listinfo/fis _______________________________________________ Fis mailing list Fis@listas.unizar.es http://listas.unizar.es/cgi-bin/mailman/listinfo/fis_______________________________________________ Fis mailing list Fis@listas.unizar.es http://listas.unizar.es/cgi-bin/mailman/listinfo/fis

http://iridia.ulb.ac.be/~marchal/

_______________________________________________ Fis mailing list Fis@listas.unizar.es http://listas.unizar.es/cgi-bin/mailman/listinfo/fis