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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