Karl
Dear Loet and Jerry,
let me comment on your interesting exchange:
you write:
one studies specific arrangements and configurations. (I mentioned graphs.)
However, the red herring emerges when these configurations are made the
subject of "information theory" (in contrast to "informatics") without
further reflection.
contribution:
In the Addition Table one sees specific arrangements and configurations.
There is no red herring in natural numbers.
you write:
the strength of Shannon's information theory is its grounding in
probability theory. This is more abstract and not field specific.
contribution:
The Order Theory (not, as was suggested, Category Theory)
The entire study needs a category theory construct.
that one can read off a Table of a+b=c has its grounding in axiomatic logic.
This is only one part of the map in category theory (arrow) you need the
object (set of variables maybe in this case) to complete the map.
And the bookkeeping laws of associations and identity take care of the
arrangements and configurations. The probability part is then taken care of
by the subobject classifier (truth value object) of a Topos.
That is even more basic - fundamental - than probability theory. Natural
numbers are even more abstract and less field specific than probability
theory.
This can be taken care of by the "limit" axiom of a Topos (quantity).
you write:
the specifics of the morphology and spatial arrangements have first to be
rewritten numerically (e.g., in terms of coordinates) before they can be
made a subject of analysis and calculation.
That's why one can use category theory.
Regards
Gavin
contribution:
The specifics of morphology and spatial arrangements have not first to be
rewritten numerically. They are alrady there as implications of a+b=c. One
only needs to do a few steps, namely:
1. create 136 additions (between 1+1=2 and 16+16=32)
2. create 9 aspects of the additions
(a,b,a+b,2b-a,b-a,3b-2a,2a-b.17-(a+b),3a-2b)
3. order /sort/ the 136 additions on two of the aspects
4. reorder /resort/ the additions into a distinct sorting order
5. use 2x3 and 2x2 sorting orders as spatial grids (Euclid coordinates)
6. observe the interdependence between morphology and spatial arrangements.
So, what you have asked for is already there for the doing of the exercise
of building the Addition Table.
Karl
2011/10/17 Loet Leydesdorff <l...@leydesdorff.net>
Dear Jerry,
Perhaps, we exchange at cross-purposes. I don't wish to deny that in
specific fields such as chemo-informatics or social-science informatics, one
studies specific arrangements and configurations. (I mentioned graphs.)
However, the red herring emerges when these configurations are made the
subject of "information theory" (in contrast to "informatics") without
further reflection.
It may be easiest to raise some questions:
1. What is the equivalent in chemo-informatics of a bit of information? Can
this be operationalized as a formula like Shannon's H?
2. Can one compute with this formula in fields other than chemistry? For
example, in economics; without using metaphors? ("As if")
I agree that each field has its own specific theories and nobody can forbid
to call these "informatics". However, the strength of Shannon's information
theory is its grounding in probability theory. This is more abstract and not
field specific. At that level, the specifics of the morphology and spatial
arrangements have first to be rewritten numerically (e.g., in terms of
coordinates) before they can be made a subject of analysis and calculation.
Best wishes,
Loet
-----Original Message-----
From: fis-boun...@listas.unizar.es [mailto:fis-boun...@listas.unizar.es] On
Behalf Of Jerry LR Chandler
Sent: Sunday, October 16, 2011 5:47 PM
To: fis@listas.unizar.es; fis@listas.unizar.es
Subject: [Fis] Chemo-informatics as the source of morphogenesis - both
practical and logical.
FIS, Loet, Joe:
This message is a response to Loet's notion that morphogenesis is a
red-herring.
Before my specific comments, I would like to acknowledge Michel for his
excellent introduction to the conceptualization of chemo-informatics as a
branch of information theory and engineering of chemical systems. The
motivation for the work of developing chemo-informatics come from various
sources, but, generally speaking, they are tied to the concept of DESIGN -
another term for morphogenesis.
Practical chemistry searches for ways to get a job done by finding ways to
use chemical knowledge to solve a problem. Often, this means testing a
range of different chemicals to see if the desired effects are obtained. In
the early history of chemistry, various natural sources of different sorts
of matter were empirically tested. Following the theoretical developments in
the late 18th and early 19th century, mathematical chemistry slowly
developed from the concepts introduced by John Dalton that all chemical
structures were ratios of small whole numbers composed from different
chemical elements. Given the large number of different sorts of chemical
elements and the unbounded number of combinatorial possibilities, the
chemical community gradually developed a system of mathematics which
captured the essential features of the information content of chemical
structures. The mathematical system is simple enough to be taught in high
school but the combinatorial 'explosion' of structures and properties is so
vast that a sub-discipline of 'chemo-informatics' was developed just to
study the interrelations between subsets of chemical structures and subsets
of chemical properties.
Chemo-informatics developed a separate form of information as Michel has
summarized. The form (ie, the morphology) of chemical information is iconic.
The atomic numbers, as icons, are combined to form chemical structures, the
basic mathematical objects of chemo-informatics. Chemo-informatics developed
a separate form of logic. The logic of chemo-informatics has both regular
components, such as those associated with mass (strictly additive) and
irregular components, such as those associated with electrical parity of
iconic representations of atomic numbers. For the electrical associations, a
separate method of relational addition was developed as a theory of valence
(from empirical observations). The later theory is closely akin to and the
precursor of mathematical category theory. The iconic representation of
atomic numbers is calculated in terms of graphs. Chemo-informatics can be
thought of as the logical precursor of both category theory and graph
theory. Charles S. Peirce, 1839-1914, laid the foundations for modern logic,
based on both chemistry (his term - existential graphs as forms of logic)
and Scholastic logic.
Today, the practice of chemistry is a practice of mathematics, a practice of
relational calculations on numbers. Organic chemical analysis and chemical
synthesis, including all molecular biological structures, are based on proof
theory. The notion of "proof of structure" in an exact notion that
establishes an exact graphical relationship between Dalton's 'ratio of small
whole numbers' and the iconic forms of chemical structures.
Chemo-informatics is closely associated with bio-informatics. A substantial
portion of bioinformatics consists of counting possible chemical forms or
closely related forms that differ in sequences. Bio-informatics can be
thought of as "engineering" extension of the potential for simple
combinatorics (graphs) of atomic numbers to generate sequences of subgraphs.
Again, the "combinatorial explosion" rears it head. Each potential sequence
has its own unique form. The morphogenesis of spatial forms of matter is
studied by the several methodologies, such as x-ray diffraction patterns.
One example with which I have had several years of experience with is the
development of a drug for epilepsy. On average, between 1,000 and 10,000
different unique structures were examined for each drug that eventually made
it to market. Chemo-informatics and biological assays and clinical trials
were all critical components of the process. All three sorts of empirical
studies were necessary to identify a useful medicine. The morphological form
of the isomers are critical components of matching of 'drug' to a
'receptor'.
I bring this example to the discussion to illustrate the application of
chemo-informatics as a practical way of sending messages to the human body.
Such messages, contained within a mathematically-defined iconic form, are
intimately interrelated to bio-informatics, the expression of forms of
genetic information.
Thus, Loet, I can not concur with your following assertions.
>
> It seems to me that the issue of "morphology" and its evolution is a red
herring in a discussion about information theory. A shape (e.g., a network)
can be described as a graph or also numerically.
1. Please provide a reference for the assertion that the conformation of
protein structures can be calculated from the chemical graph of the protein.
2. Are you mixing continuous and discrete concepts?
> This numerical description can easily be evaluated in terms of information
theory. Information theory, also offers options to develop measures for the
evolution over time (such as, Kullback-Leibler divergence, cf. Theil
(1972).)
>
> As formalisms from information theory can be applied to any system of
substantive communication, they can also be applied on system of formal
communication, such as sets of coordinates.
3. Metabolic networks are chemo-informatic message networks, generated from
biochemical - genetic information. Are you excluding metabolic networks as
systems of substantive communication?
4. ditto for mental networks?
>
> Best wishes,
> Loet
Loet, your point of view, from my perspective, is based on a generalized
inductive argument on formalisms. If a generalized inductive argument for
chemo-informatics existed, there would be no need for the particular
inductive logic used to construct chemical forms - for the morphogenesis of
chemical conformations from atomic numbers.
At the abstract logical root, the difference between chemo-informatics and
Shannon informatics lies in the empirical basis of induction. The
generalized inductive argument of Shannon encodes all messages as numbers
and then encodes the numbers into electrical signals. Message transmission
in Shannon theory relies on several generalized inductions related to
electrical properties of matter. The decoding of such messages inverts the
order of the encoding, regenerating the original message.
Chemo-informatics lacks any generalized encoding. (Dalton's law would not
be an essential part of chemo-informatics if such a generalized encoding
existed.) Chemo-informatics is based on the logic of the identity of
matter. This concept of identity of a labeled bipartite graph, the basic
object of chemo-informatics is not the concept of identity as used in
Shannon information.
A simple example of the mathematical distinction between chemo-informatics
and Shannon informatics is crystal clear.
The arithmetic operation of multiplication is integral to Shannon
informatics.
The arithmetic operation of multiplication on the atomic numbers generates
nonsense - if one multiples 2 (helium) by 3 (lithium), one does not get 6
(carbon).
The fundamental logical distinction that Dalton introduced over one hundred
years ago was a new form of inductive mathematics. The development of the
chemical sciences and molecular biology and personalized medicine follows
from this form of inductive logic. C. S. Peirce developed a framework for
relational logic from the recognition that a thing can be a source of
representation and that the method of representation is the source of the
form, the source of the message. Chemo-informatics follows Peirce in the
sense that it is necessary to distinguish among the symbol for networks of
atomic numbers, the indexes for molecules and the iconic representations of
the forms of molecules.
The physical basis of chemical logic is now well understood in terms of the
international system of units. Each atomic number is a different electrical
electrical category. Conjoining two different electrical objects creates a
new electrical object, a new category. Conjoining N different atomic
numbers (a molecular formula) creates the combinatorial explosions, often
loosely referred to as the isomer problems. The same N atomic numbers can
be combined into N' (N' >>> N) iconic forms. Each of the N' iconic forms has
the same mass and the same electrical particles, but each has different
identity as a consequence of the arrangements of the parts of the whole. The
alternative ways of connecting numbers into graphs lies at the heart of the
chemo-informatics challenge.
Robert Rosen recognized that a profound difference existed between "natural
systems" and formal systems. He postulated that different forms of
representation were needed. Rosen's theory, unfortunately, completely
excluded chemo-informatics from consideration, he chose to place his logical
analysis of biology on thermodynamic considerations. As a consequence, no
path from Rosen's system of thought to chemo-informatics has been, to the
best of my knowledge, found. The differences in the notion of artificial
addition and natural addition of numbers make such a path from Rosen's
conjectures to chemo-informatics appear impossible.
In summary: Chemo-informatics differs from Shannon informatics as the
natural atomic numbers differ from artificial numbers abstracted from the
properties of the integers. (By artificial numbers I am referring to the
generalized inductive abstractions of irrational, imaginary, and
transcendental objects associated with the continuum of the real number
line.)
Cheers
Jerry
(Footnote: Greetings to all my friends on the list. I have moved to
Minnesota and been in reclusion for several months, completing the logic of
the perplex number system. From my reclusion, I am optimistic about a
springtime eclosion. :-) :-) :-) )
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