Dear Lou,

Thanks for the invitation to elaborate on the concept of quantum and how it
connects to Wittgenstein’s taboo words and information.

We may have problems understanding the concept of a quantum because the
idea appears to be non-expressible by rational, logical speech. The grammar
of logical sentences creates constraints on what can be said intelligibly
(as Wittgenstein has pointed out). We can discuss the present King of
France (even if there is no such thing there, in Russell’s example) because
the grammar allows us to speak of places and things. The essence of
rational speech is that it is consistent. We cannot speak exactly of things
that may or may not be there, that may or not may have properties.
Specifically, we cannot speak of *unique, individual *concepts, which we
cannot contrast to such other concepts which we know.

Let me show you what the natural numbers offer as a possible definition of
such a concept that is transcending some logical categories.

a)      Preparation

We do an accounting exercise on some numbers. (For some numerical reasons,
it is best to speak of a collection that has 16 distinguishing categories
on two kinds of objects: that is, we have *(a,b) *appearing as tuplets *(1,1),
(1,2), (2,2), (1,3), (2,3), (3,3), (1,4), (2,4), …, (16,16),* that is
altogether 136 elements of a set.) These we sort on some aspects. Then we
re-sort them into a different sorting order, based on some different
aspects of *(a,b). * What we register is the properties of the cycle each
element in included in during a reorder.

b)     Action

We pick 1,2,3,… of the elements and discuss if, and if yes, in which and
how many altogether, cycles these elements can be included while
contemporaneous. Contemporaneous means “free of logical contradictions, is
the case, consistent, assigning a place to an element” in spoken language,
in the deictic language of numbers and tables it means that there is an
empty cell in a White or True Table we can write this element into.

We also mark in a separate Dark, Black or Negative Table (like a Bad Bank
or a No-Fly List) all those cycles that are presently not playable, because
of the element(s) being included in a cycle that cannot run concurrently
with those that are in the Black Table.

For the sake of accounting completeness, we also create a Grey Table, our
Basic Table of Ignorance, wherein are initially included all cycles,
wherefrom we move cycles either to the Possible or to the Not Possible

As we pick an element, we assign it a place. At first, it is irrelevant,
which order we assume to be the case. As we progress, the presence of
elements will have generated a series of facts and/or assumptions which
restrict the ways of either how we can place the element or how we can
choose the order we wish to maintain. One may be reminded of variants of
Go, Sudoku or the like.

c)      Evaluation

We can formulate our observations in an assertive, but as well also in a
negating way of describing the same state of the word. We can observe that
the element *e *is on place *p *in order *o*, but as well we can observe
that this deviates from order *not-o*, where either element e would be on
place *not-p*, or on place *p* would be an element *not-e*. As at least
elements *e* and *not-e* are numerically comparable (we know the extent of
difference between *(3,4)* and *(5,7)*), so there is hope that this and the
linear distance differences between places *p* and *not-p* allow
constructing a measure for the distance between orders *o* and *not-o*.

The contents of the Grey and Dark Tables are as descriptive of what we have
done as the contents of our Positive Registry of Actions. We not only do
talk about what Wittgenstein has said one should better leave alone, but we
split the background to that what we talk about, that what is the case,
into one part that is definitely false and one part, that which is simply
unknown. That what Wittgenstein has delineated as the background to
rational speech is now – thanks to computers – accessible. We propose to
use the name “information” for a logical statement which details facts that
are not the case, belong to the background in Wittgenstein’s sense.
Information is a description of the background to that what is the case.

d)     Unit of what

Now we arrive at what an accountant would term the minimal accounting unit.
The concept may well be called a quantum by people outside the accounting
world. In the tables, one may point to an increased degree of exactitude
which one arrives at having picked the *i-th *element. What this minimal
degree of increased exactitude refers to exactly, appears not that easy to
put in spoken words of a rational language. We do not restrict its meaning
to what is the case, but also may refer to something that is now more not
the case than before, and specifically we cannot say whether this increased
exactitude refers to a linear, spatial or material or temporal (mis-)
match. The general idea of a match (or its mirror experience, the
mis-match) or a Zero (in case we refer to the contents of the Gray Table)
may well be what is targeted by speakers who use the word quantum. That the
concept is not easy to catch appears to root in its referring to a mixture
of observations that refer to consistent, but also to non-consistent

e)     Vectors, agglomerations and directions

By using the standard reorders, one can build two Euclid spaces. These can
be merged into one Newton space with the axes *(a+b), (a-2b), (b-2a) *for *z,
y, x. *The cycles create a web which is very much directed and oriented.

Within this web, spatial geometry and topology is of paramount importance.
The picture is, however, overlaid by two additional planes, created by
standard reorders, that transcend the spaces created by the rectangular
axes of standard reorders. It may be a wild guess to suggest the words
“electro-magnetic” to be used while describing the effects these two planes

Influenced or not by the two extra planes, the general tendency of cycles
in space is to attribute density unevenly along their paths. There appear
agglomeration points in space, where the probability that on this spot
material exists continuously contemporaneously is higher than elsewhere.

These assemblies can be visualised as traffic jams that appear out of the
general density of material on paths and of the non-uniform speeds of the
vehicles that are in convoys. There appear a few hundred of such
agglomeration types, which we call *logical archetypes. *They are referred
to usually as chemical elements and their isotopes. Some of them cannot
exist contemporaneously, but some do.

The coexistence of some logical archetypes imposes constraints on which
other entities may be in existence and how these share the space. This is a
Lego/Tetris type arrangement, very much in molecular geometry.

I sincerely believe that the tautomat, the model of which has been
presented to FIS during the last few years, here reintroduced as a skeleton
on which one may demonstrate concepts, is a powerful and versatile tool to
discuss questions relating to order in Nature, and offers a deictic
definition for a concept of a minimal unit. The minimal unit can also have
the form of a negation of a logical state of affairs. This usage of the
concept of the minimal unit, namely to refer to something that is not the
case, is what was meant under “quantum information”.


2016-03-24 20:37 GMT+01:00 Louis H Kauffman <>:

> ------------------------------
> *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
Fis mailing list

Reply via email to