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 > 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>:
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>
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 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 > 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> 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 > 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

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 > 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 (& 6818)
pcmarijuan.i...@aragon.es
http://sites.google.com/site/pedrocmarijuan/
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