Counting and optimization

Dear Colleagues:

This message responds to a number of posts (Heiner, John H., Pedro,
Karl, Christophe) over the past several weeks. In most cases I
include quotes from the author to help inform the readers of the
original issue of correspondence.

Heiner Benking post of Sun, 22 Sep 2002 09:55:26 +0200 (MET DST)
proposes to bridge ...
 the space between data and meaning by adding some work
done in the field of terminology research. This "zooming" into the space
between data and meaning is made clear at:
http://benking.de/Global-Change/Con-con.gif
more can be found at: CONCEPT AND CONTEXT MAPPING - TKE 1996 Vienna
http://www.ceptualinstitute.com/genre/benking/term/terminology.htm
and
http://benking.de/Global-Change/spatial-spacial.html

I do not understand how this sort of global classification solves the
problems of the information sciences. Subjective classifications are
difficult precisely because they require judgments that are
controversial. The usual approach to resolving such controversies is
to count. Perhaps Heiner would demonstrate how this "zooming in"
process approaches Karls commentary on counting.

  For example, Karl wrote on Tue, 24 Sep 2002 13:00:57 +0200 (MET DST)
"My contention --jumping to a theoretical science level-- is that we
have to let loose the conceptualizations transported by our way of
counting (1,2,3,...) because they carry in an implicit way of
thinking that does not agree with biological phenomena. The ideas
behind a basic assumption about the world that are implicit in
counting like 1,2,3,... seem to be:

-- all elements are alike in their basic unit (there is only one kind of basic
units),
-- the distance between elements is the same,
-- the increase from one element to the next is the same (the basic element),
-- there is no end in sight to this series,
-- there are no preferred sizes to elements,
-- there are no two basic kinds of elements that cooperate in the
generation of a new element."

To what extend can Heiner's classification meet the criteria of Karl?

Pedro wrote (within his doctrine of limitation, on Fri, 27 Sep 2002
14:46:01 +0200 (MET DST)

The neuronal information processing capabilities are built
exclusively upon cellular building blocks that continuously
instantiate their signaling abilities. The cellular use of electric
fields becomes a prolongation of the transgenerational processing of
genomes, both mapping into terribly different time scales, material
substrates and 'topological' processes the overall fitness of the
organism.

Karl prefers to relate to the issues raised by Pedro by iterating his
views on partitioning [Wed, 9 Oct 2002 14:32:27 +0200 (MET DST)]:

My hypothesis is that (his) { "his" refers to another reference, not
Pedro} type of simple partitional exercise, reminding a random walk,
may serve quite well for making sense of the interactions between the
atomic components (how neutrons, protons and electrons may add up to
compose the multi-dimensional atomic truth table).

Perhaps, Karl, you would clarify your ideas by demonstrating such a
truth table? Biological organization generates exponential
functions, not merely addition, does it not?

In response to my question,
<Does the concept of information depend on communication?
 John Holgate replies on Thu, 3 Oct 2002 09:42:36 +0200 (MET DST)
That's the big question, isn't it?
What we really need is a solid theory of 'agency' and mediated interaction.
(both Goranson and Fuchs come at agency from different angles in their papers).

Coeira's 'Mediated Agent Interaction' might be of interest
<http://www.coiera.com/papers/AIME-01.pdf>http://www.coiera.com/papers
/AIME-01.pdf
It looks at the contextual constraint of 'common ground' .
John: Thank you for the reference. This paper is well worth the
time. The author clearly distinguishes between the concept of
transmission and mere translation. This distinction deserves wider
attention, especially in relation to the meaning of information.
Shannon information is "freely" translatable among different computer
systems (no deep conceptual problems, but lots of practical technical
problems.)

Pedro follows the doctrine of limitations, recognizing the cost of
partitioning Fri, 4 Oct 2002 15:13:32 +0200 (MET DST)

"The biggest cost is related to the painful process of 'decomposing'
the big global problem into very small ones addressed towards a
population of thousands of 'limited' specialized scientists and
engineers."

In mathematics, a general formula for partitioning has been available
for several decades. I have never seen this formula for partitioning
cited by a biologist or a physician. Is this because the fundamental
problem of communication is not merely dividing the whole into the
sum of its parts?

Pedro continues:
Finally, the discussions we are having on a non-mechanistic
conceptualization of info, may have some intriguing connection with
that very social-cognitive problem --How sciences working as a
collective nervous system may throw 'anticipatory light' to overcome
the impending menaces upon our planetary survival? In other words, we
need to develop 'the art of socially playing with the Rubik cube of
knowledge'. Our knowledge system has devoted countless
scientific-philosophical energies to discussions on reductionism and
the like, an almost nothing to 'integrationism', 'perspectivism',
'limitation', etc. A mature info perspective (or science) could help,
and should help, to readdress the cognitive imbalance.

The metaphor of "the Rubik cube of knowledge" is delightful!

On a deeper level, Pedro brings to mind the extensive work of Herbert
Simon, The Sciences of the Artificial, etc. Simon introduces the
concept of "satisfactory and sufficient" in place of optimization.
The long history of "optimization" in engineering and mathematical
theory suggest that the term will bring substantial confusion if used
with respect to the dynamics of the CNS.

In response to my question:
> Can you provide an example of an MGS that produces meaningless
> information?
>
Christophe responds on Wed, 9 Oct 2002 22:58:03 +0200 (MET DST):
It is the purpose of a MGS to produce a meaningful information
that will allow action implementation for the satisfaction of the
constraint S of the MGS. So it is not in the function of a MGS to
produce meaningless information.
It is to be noted also that action implementation can take place
only in locations where the constraint S exists.
We can call these locations "Domain of Efficiency S". So a
meaningful (S) information can be efficient (S) or not, depending
if it is located in the Domain of Efficiency S or not.
In brief, a MGS produces only meaningful information, but these
meanings can be efficient or not. (if you want to know more on
this, see I.3 in http://www.theory-meaning.fr.st/).

The cultural difference between engineering and biology emerges in
this response. In the "Sciences of the Artificial", human ingenuity
construct systems that are then put into motion. Biological systems
simply run on internal sources of motion; the constraints are the
organism itself. Ultimately, the "information" suffices for either
life or death. Should the notion of "constraints" be viewed as a
physical metaphor for biology and medicine?

In response to my question:

"Karl: Is chemical and biochemical counting sufficiently complex to
>address your concerns about the nature of counting in FIS? Is
>correspondence with chemical counting a necessity for biological
>counting?"

Karl responds (Wed, 9 Oct 2002 14:32:27 +0200 (MET DST))
In my opinion, the entries in the periodic table of elements by
Mendeleiev can well be regarded as entries into a multi-dimensional
truth table. Now, which kind is the truth question to which these
answers yield always .t. (true)?

We presently have reason to assume that there exist about 104
distinguishable kinds of logical .t. values, which are to be splitted
up into some several hundred varieties, as each entry may have from 1
up to some dozen of equivalent forms (what the physicists call
"isotopes"). The roughly 100 main archetypes of logical truths are
subject to a manifold of logical relations. (there are some that
cannot be present both at the same time--but it is another separate
discussion).

The entries into the above truth table have an intrinsic ordering
principle which does not adhere strictly to their "weight". This
would be like saying that some subsets are similar to each other
irrespective of their cardinality. Also, their building grammar
appears to start at integer values of n=2i**2, with i = 1,2,3,... One
may want to look into the generating function:

Function m(n); local integer tmp, first, len, zero, m; tmp = int(sqrt(n/2));
first = 2*tmp**2; len = 4*tmp + 2; zero = if(n-first < len/2, first + tmp,
first + len/2 + tmp); m = n - zero; return(m).
which gives one a "long" periodicity starting off at values of n=2i**2, with
half-periodicities included.

Truth tables can be constructed for logical propositions and for
first order logic and for higher order logics. I do not understand
the reason for focusing on the concept of logical truth table in this
context. Chemistry and biology are experimental sciences; only
limited abstraction is possible. How does one relate the truth table
values of chemical propositions to communication? The experimental
observations of chemical compounds are constructions from the
elements, *not* partitioning of the elements.

Karl, while I agree that generating functions are critical to
mathematics, how does one move from the mathematical concept of a
generating function to communication? Do you intend that the "psuedo
- code" you include in your message should be given meaning in terms
of chemical structures, such a neural transmitters?

The following paragraphs:
In drawing-of-samples it helps to add to the Gauss distribution the
Euler distribution which is hugely asymmetric. In my opinion, the
Euler distribution is far more important than the Gauss one. With it,
one finds a
extremely useful connection between "size-of-set", "number-of-chunks"
and "size-of-chunk". (And of course also the other two ways around,
too.) The Euler distribution is very simple and elegant, although
shamefully neglected. Just chart the number of partitions into k
summands for each n (1 graph per each number, k horizontally, f
vertically) and then integrate with n -> inf.

Then, to speculate on whether there is a material 'constant' of which
these logical chemical archetypes are built up (the second question
we are trying to answer), one needs to generate the .2. set of
partitions. Those for which sum(m(ni))=m(n). On these, one may start
adding pairwise: those that fall down where .3. holds true, these
converge. One does not know whether the left or the right
half-periodicity is the right one and they differ ever so slightly.
My hypothesis is that his type of simple partitional exercise,
reminding a random walk, may serve quite well for making sense of the
interactions between the atomic components (how neutrons, protons and
electrons may add up to compose the multi-dimensional atomic truth
table).

are not understandable to me. The system under discussion, the
domain of discourse is not stated as it relates to communication. I
suspect that the basic presupposition is that communication is merely
a statistical abstraction. How does one read the notation: .2. and
.3. with respect to conjunctions and disjunctions of propositions or
first order statements? Is the discourse related to marketing
consumer products? Biochemically, biological communication
demonstrates both specificity and sensitivity. The issues of
Gaussian vs Eulerian distributions seldom arises.

This post is rather long. Individual respondents may hope to find
some relationships among my ordering of the responses.

Cheers to All

Jerry
Received on Sat Oct 19 22:42:22 2002