### Re: [Fis] SYMMETRY & _ On BioLogic

```Dear Folks,

I am sending this again, just the quantum part, with typos removed.

Best,
Lou

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.
Dual vectors are denoted by  is a complex number and
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.
Unitarity preserves the length of vectors.

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 ||^2.
Note that the Sum_{n} ||^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.
Via the absolute squares of these coefficients, |psi> can be regarded as a
probability distribution for the outcomes that correspond to each basis
element.
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.

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```

### Re: [Fis] Fis Digest, Vol 24, Issue 20

```Fis Digest Vol 24, Issue 20.
RE: Lou Kauffman's,
"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."

ME: In my upcoming section of the discussion, I shall present a new kind of
information supported by organism regulatory systems, which is based on
instabilities.

At the heart of an instability is a catastrophe of the kind demonstrated by
Rene Thom in his work of catastrophe theory (La Theorie des Catastrophes)
developed in his famous book, 'Structural Stability and Morphogenesis'.

Organism loci of control in complexity biology are centred on critical
instabilities, either due to feedback instabilities, or to critical points
in switching processes regarded as phase transitions - though there may be
an equivalence between these two.

The catastrophes in the differential topology of switching processes permit
regulatory cytokines to exert symmetry breaking in specific ways supported
by the catastrophe in question. Embryogenesis exhibits a number of such
symmetry breaking, morphogenetic processes, all of which can be modelled by
appropriate catastrophes.

The place to look for such catastrophes is in the epigenetic networks
controlling gene expression. Simple gene expression cannot give rise to
structure, as any topologist will tell you. It is only through Thomian
catastrophes within epigenetic networks that morphogenesis becomes
possible, and (to quote Lou) "topological geometric forms develop."

Denis Noble of 'Music of Life' fame, has clearly stated as one of his
'Principles of Systems Biology', "There is no Genetic Program". The
response from complexity biology is that, "It is an Epigenetic Program".
What controls the genesis of form is completely different from the genesis
of proteins and their folding, fascinating as that topic surely is (as we
have heard).

On 25 March 2016 at 00:01,  wrote:

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> Today's Topics:
>
>1. Re: SYMMETRY & _ On BioLogic (Louis H Kauffman)
>2. Re: SYMMETRY & _ On BioLogic (Louis H Kauffman)
>
>
> --
>
> Message: 1
> Date: Thu, 24 Mar 2016 11:42:08 -0500
> From: Louis H Kauffman
> To: fis
> Subject: Re: [Fis] SYMMETRY & _ On BioLogic
> Message-ID:
> Content-Type: text/plain; charset="utf-8"
>
> list --Pedro
> (I have just discovered, in a trip pause)
> BlackBerry de movistar, all? donde est?s est? 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 <
> 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 ```

### Re: [Fis] SYMMETRY & _ On BioLogic

```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,

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 ```