An Inclination to Combinatorics, Law of Large Numbers, and the Central Limit Theorem in Resolving Tensions in Evidencing Micro- to Macro- Level Individual to Social Transformation

This had been drafted for a discussion post for SOC-310 on Social Theory at Washington State University. There are some minor edits for readability and extended citations for any wishing to dig deeper into well accepted themes.

This week’s focus on the structures of social theory, Dr. Horne and readings had communicated theory as explanation, built on observations and empirical study. Hechter and Horne (2009a) made the case for identification of important factors leading to social outcomes, explanations inclusive of causal relations and mechanisms, best explanations, empirical implications, spurious variables not influential of the dependent variables, and suggested that readers infer the causal relations and mechanisms in social theories. Hedström (2009) focused on causal mechanisms, surfaced questions as to the selection of material within which theories are constructed and distinguished statistical explanations from mechanism explanations. Constructing a frame of helpful reference for theorization, Hechter and Horne (2009b) provided the “Coleman Boat” construct in the making of sociological theories, borrowing from Coleman (1987, 1986).

What’s more fascinating is that Coleman’s (1986) paper addressed Parsons’ (1937) Theory of Social Action, a theory that Mills’ (1949) Sociological Imagination had “translated” parts of it, arguing the translation of “grand theory” warranted its simplified grounding. Now having read two references to Parsons, it is a bias to study, inviting further investigation. That said, this investigation will go in in parallel to the remainder of the course, and while it may infect or otherwise impinge on sociological study currently underway, it may offer greater utility in offering a bridge to other fields through a rich array of what appear to be research memos indexing outflows of sociological imagination. Abandoning or eliminating Parsons’ embedded, thick, description, while in some cases beneficial, in my case after having conferred with Dr. Horne, with respect to a sociology of science, itself, would abandon tremendous value in Parsons’ publishing of such a richly worded theory.

Apparently, Parsons’ (1937) attempt at a theory of action, had been followed by Coleman (1986), which had concerned a macro- to micro- level problem of European sociologists (p. 1321). A singular line stood out, “one of the most serious defects of a program of theory building and research based on such macro-level relations is data-inadequacy: At a macrosocial level, there is ordinarily too little variation, either in a single social system over time or among different social systems, to test the relation empirically” (pp. 1321–1322). According to Coleman and illustrated with his boat, the issue of Parsons, and others had been the empirical evidence of transformations from micro-individual levels to macro-social levels (pp. 1322–1323).

Without going through greater study of Coleman’s or Parsons’ works at this time (it’s too early to time with this course’s study), the Coleman boat’s preconceived structure for constructing social theory seems a solid Vygotskian (1978) scaffold to observe, construct/analyze, and communicate social theory of basic science to empower applied sciences in changing social order. Though I am interested in practicing a grounded theory perspective in sciences of social psychology, I can see the practicality and thoughtfulness of Colman’s construct. Digging deeper, Coleman’s attention to resolving issues concerning evidence of transformation seems intimately tied to effects/illusions of probability.

Personally, as the result of being informed of mathematical realities of the law of large numbers (Bernoulli, 1713), and the central limit theory (Moivre, 1733/1738; Laplace, 1812; Lyapunov, 1901; Pólya, 1920), it only makes sense that samples of samples of micro-individual behaviors lead to narrower standard deviations evidencing a certain macro-social behavioral set observed by micro-level researchers drawing on samples of samples in construction of social frames1. Now, this all goes without saying, that actions in response to observations from any member of society allows for one’s own theorization, valid or not, and this therein introduces Thomas theorem (Thomas & Thomas, 1928, p. 572) like effects of a recursive micro- to macro- aspect of combinatorics.

In response to the thoughts above, and in meeting with Dr. Horne, a personal quest to greaten abilities in mathematical ability has been driven further. At one time, I had lived by two insights: (a) learn math last, and (b) learn math in secret. It appears that now, there is enough of a sampling of social phenomena, though convenience sampled, to reflect on and learn math to such a degree to provide evidence of social phenomena inferenced for greater rigor. Through this course, now motivated further (hats off), in assisting with psychological motivation, as informed by theories of motivation, that I shall learn more of this combinatorics, abstract mathematics, and quantum statistical mechanics, in order to provide assistance in combination with a deep interest in these matters of social and individual space (cough), across time (cough), with respect to matters of allocations of energy and matter (cough), and geometric, linear, non-linear, continuous, and discontinuous of layers of probability (cough). 

Dr. Horne had said in a call that sociologists lean more toward empirical, and Dr. Carrie Lane from the psychology department had expressed that sociology would be a requirement for social psychology. To that end, there is a deep and abiding appreciation for the works of many, and the entire field of sociology, for this effort is a long and sometimes, as evidenced in history of references provided, occasionally lacking recognition or support until after one’s death. This is acceptable, though, I’d hope, avoidable. That said, this is a matter of socioeconomic, sociocultural, and sociopsychological realities that maybe, just maybe, theories of sociology may assist in overcoming. 

In short, I am left in awe, and this awe individually percolates socially—now off the stove and into the cup, to share, and share alike, though quite frankly, I enjoy a good French press.


1 For more detail on social frames use here, see Goffman (1974) and Bateson (1955/1972). These considerations are well placed for knowledge-graph collision with Csikszentmihalyi’s (1975) launch into studies of flow.


Bateson, G. (1972). A theory of play and fantasy. In G. Bateson (Ed.), Steps to an ecology of mind (pp. 177–193). (Original work published 1955)

Bernoulli, J. (1713). Pars quarta: Usum & applicationem praecedentis doctrinae in civilibus, moralibus & oeconomicis. In J. Bernoulli, Ars conjectandi (Sheynin, O., Trans; pp. 210–239). Impensis Thurnisiorum Fratum.

Coleman, J. S. (1987). Microfoundations and Macrosocial Behavior. In J. C. Alexander, B. Giesen, R. Münch, & N. J. Smelser (Eds.), The micro-macro link (pp. 153–173). University of California Press.

Coleman, J. S. (1986). Social theory, social research, and a theory of action. American Journal of Sociology, 91(6), 1309–1335. 

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Goffman, E. (1974). Frame analysis: An essay on the organization of experience. Harvard University Press.

Hechter, M., & Horne, C. (2009). Theory is explanation. In M. Hechter & C. Horne (Eds.), Theories of social order (2nd ed.; pp. 7–11). Stanford Social Sciences.

Hechter, M., & Horne, C. (2009). Motives and mechanisms. In M. Hechter & C. Horne (Eds.), Theories of social order (2nd ed.; pp. 17–22). Stanford Social Sciences.

Hedström, P. (2009). Dissecting the social. In M. Hechter & C. Horne (Eds.), Theories of social order (2nd ed.; pp. 12–16). Stanford Social Sciences.

Laplace, P. S. (1812). Théorie analytique des probabilités. Ve. Courcier.

Lyapunov, A. M. (1901). Une proposition generale du calcul des probabilities. Comptes Rendus, 132(13), 814–815.

Mills, C. W. (1959). The sociological imagination. Oxford University Press.

Moivre, A. (1738). A method of approximating the sum of the terms of the binomial (a+b)n expanded into a series, from whence are deduced from practical rules, to estimate the degree of assent which is to be given to experiments. In A. Moivre, The Doctrine of Chances: Or, a method of calculating the probabilities of events at play (pp. 235–243). (Original work published 1733)

Parsons, T. (1937). The structure of social action. McGraw-Hill. 

Pólya, G. (1920). Über den zentralen grenzwertsatz der wahrscheinlichkeitsrechnung und das momentenproblem. Mathematische Zeitschrift8(3), 171–181.

Thomas, W. I., &. Thomas, D. S. (1928). The child in America: Behavior problems and programs. Knopf.

Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Harvard University Press.