Dear FIS Colleagues,

1.      Are the facts complicated or is our interpretation of the facts

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

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

Happy First Full Moon After Spring Equinox to you all.


2016-03-24 19:31 GMT+01:00 Louis H Kauffman <>:

> 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 <>
> *Date: *Tue, 22 Mar 2016 17:56:06 -0500
> *To: *fis<>
> *Cc: *Pedro C. Marijuan<>
> *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 <
>> 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 <>
> 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 <
>>> 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:
>> 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 <
>>> 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)
>>> -------------------------------------------------
>>> _______________________________________________
>>> Fis mailing list
> _______________________________________________
> Fis mailing list
Fis mailing list

Reply via email to