Hi,
I modified and expanded the *structural hierarchy* discussed in
[biosemiotics:8854] to include 4 more levels -- biosphere, the earth,
galaxy, and the Universe as shown *Figure 1* below.
(1) The *structural hierarchy* consists of 9 levels, numbered 1 through 9,
each, except perhaps Level 6, having more than one members or examples
belonging to it as shown in the parenthesis.
(2) Each level can be identified as a *type* and the members belonging to
it as its *tokens*. Hence all the items in the network can be symbolically
represented as T_i or as T_i,j, where i is the level and j is the number
identifying the members belonging to the i^th level.
(3) The symbol, "A ---> B", can be read as "A is a part of B" and hence
Figure 1 can be called "*compositional hierarchy*" [1].
(4) Each level constitutes a "subsumption hierarchy" [1], since what is
inside a parenthesis can be viewed as "*a kind of*" something", the
"something" being the name of the level, e.g., Atom, Molecule, Cell, etc.
That is, "Oxygen is a kind of Atom", "Hydrogen is a kind of Atom,"
"Nitrogen is a kind of Atom.", etc. Using the symbols defined in (2), we
can more succinctly write, "T_i,j is *a kind of* T_i".
(5) Each level is associated with a unique "discipline" (see the terms in
bold letters), and this "discipline", I suggest, can be identified with
what is called "*functors*"in category theory [2, 3], since it provides the
connection among the "structure-preserving mappings" or "*morphisms*" that
in turn connect the members belonging to a given discipline.
(6) If the the category-theoretical assignments assumed in (5) are correct,
there are 8 (if Level 6 is excluded) or 9 (if not) *functors* in the
structural hierarchy shown in Figure 1. The *structure-preserving mapping*
that connects one functor to another is known as a *natural transformation*
[2, 4].
(7) I postulate that the natural transformation connecting the 8 or 9
functors in Figure 1 is *organization *(i.e., the arrangement of particles
or symbols in space and time).
(8) Finally, according to the *Gnergy Principle of Organization* (GPO) [5,
6, 7], all organizations in the Universe, including both biotic and abiotic
systems, have two complementary aspects -- *informational* (or formal) and
*energetic* (or material) aspects. In other words, if GPO is true, no
organization of matter in the Universe would be possible without the
*energy* dissipation driving the performance of the work of organizing and
the *information* to guide the work, since any work without being guided by
appropriate control information would inevitably lead to "*disorganized*"
complexity [8].
9. * Universe *(our Universe, other universes;
*Cosmology*)
^
|
|
8. *Galaxy* (Milky Way, other galaxies; '*Galaxology*
')
^
|
|
7. * Planet *(Earth, other planets; *Planetology*)
^
|
|
6. *Biosphere* (unique ?; *Ecology*)
^
|
|
5. *Societies* (ants, bees, humans, . . . ; *Sociology*)
^
|
|
4. * Brains* (bees, apes, humans, . . .; *Psychology*)
^
|
|
3. *Cells* (bacteria, yeast, white blood cells, . . .;
*Biology*)
^
|
|
2. *Molecules* (water, sugar, DNA, hemoglobin, . . .;
*Chemistry*)
^
|
|
1. *Atoms* (hydrogen, oxygen, nitrogen, . . .; *Physics*)
*Figure 1.* Nine levels of material ORGANIZATION with associated EMERGENT
properties.
Reproduced and modified from [biosemiotics:8854].
If you have any comments or questions, let me know.
With all the best.
Sung
--
Sungchul Ji, Ph.D.
Associate Professor of Pharmacology and Toxicology
Department of Pharmacology and Toxicology
Ernest Mario School of Pharmacy
Rutgers University
Piscataway, N.J. 08855
732-445-4701
www.conformon.net
*References:*
[1] Salthe, S. N. (20xx). Hierarchical Structures. *Axiomathes* Where
Science Meets Philosophy* 22*:355-383.
[2] Spivak, D. I. (2013). Category Theory for Scientists.
http://math.mit.edu/~dspivak/teaching/sp13/CT4S--static.pdf
[3] Brown, R. and Porter, T. (20xx). Category Theory: an abstract
setting for analogy and comparison.
http://pages.bangor.ac.uk/~mas010/Analogy-and-Comparison.pdf
[4] Natural Transformation.
https://en.wikipedia.org/wiki/Natural_transformation
[5] Ji, S. (1991). Biocybernetics: A Machine Theory of Biology,*
in* *Molecular
Theories of *
*Cell Life and Death, *S. Ji (ed.), Rutgers University Press, New
Brunswick, pp. 1-237.
[6] Ji, S. (2004). Semiotics of Life: A Unified Theory of Molecular
Machines, Cells, the
Mind, Peircean Signs, and the Universe Based on the Principle of
Information-Energy Complementarity,
in: Reports, Research Group on Mathematical
*Linguistics, XVII Tarragona Seminar on Formal Syntax and Semantics,*Rovira
i Virgili University, Tarragona, Spain, April 23-27, 2003. Available at
http://grammars.grlmc.com/GRLMC/reports/ or at http://www.conformon.net
under Publications >
Proceedings and Abstracts.
[7] Ji, S. (2012). Complementarity.
<http://www.conformon.net/wp-content/uploads/2012/08/Excerpts_Chapters_2_complementarity_08192012.pdf>
In:
*Molecular Theory of the Living Cell: Concepts, Molecular Mechanisms, **and
Biomedical Applications.* Springer, New York. Section 2.3, pp. 24-50.
PDF at http://www.conformon.net
[8] Weaver, W. (1948). Science and Complexity. *Am. Scientist*.
*36*:536.
Down loaded from
http://people.physics.anu.edu.au/~tas110/Teaching/Lectures/L1/Material/WEAVER1947.pdf
on 9/12/2015.
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