A Mathematical Sociologist’s Tribute to Comte: Sociology as Science
Nobel Prize-winning elementary particle physicist Murray Gell-Mann once challenged his colleagues rhetorically,
“Imagine how hard physics would be if particles could think.”
by John Angle, Inequality Process Institute*
When I taught sociology, I introduced
sociology as a science-in-intention
although one that at present was not far
along as a mathematical science. I thus
affirmed Auguste Comte’s “positivist”
vision of sociology, a word he coined to
name a science of society like physics.
More generally I was affirming the agenda
of the Enlightenment to discover and
understand scientifically processes of the
natural world of which society is a part.
Benjamin Franklin, a leading contributor to
the Enlightenment, saw society as a subject
for science and engineering. He wrote in
1780 that he wished he had been born later
in time so he might see future scientific
marvels such as the levitation of masses,
life extension, and something beyond these
in difficulty: “O that ... Science were in
as fair a way of Improvement, that Men
would cease to be Wolves to one another,
and that human Beings would at length
learn ... Humanity.”
Positivism Unleashed?
Some sociologists share my enthusiasm
for Comte’s vision. I recognize, accept,
and value other approaches to sociology.
Positivism would be more attractive
if sociologists thought it would lead
to discoveries. Dubiousness about that
possibility is understandable. In several
decades, Comte’s vision of sociology as a
mathematical science will be two centuries
old. What would sociologists say to a student
who asks for an example of a success
of Comte’s positivist vision? There have
been successes, but little leaps to mind if
you are not a mathematical sociologist. So,
the comments of Bruce Keith, U.S. Military
Academy, in his December 2005 Footnotesarticle assessing sociology’s future are
understandable. He wrote, “I surmise that
sociology is more akin to a profession than
a science because I find no evidence that
members of our discipline have discovered
any law or principle that is applicable
temporally across social contexts.”
The length of the silence to Prof. Keith’s
year-old assertion reveals how Comte’s
vision has faded. To many sociologists it
may seem yesteryear’s future, a “monorail”
that never found a place in the present.
In 1988, New York Times culture critic
Richard Bernstein “panned” the sociology
on display at the ASA Annual Meeting
and then quoted a sociologist to the effect
that sociology will never be a science like
physics and those expecting it are fooling
themselves. Perhaps not entirely coincidental,
a few sociology programs were shut
down in years following.
Someone taking Prof. Keith’s point of
view might very well ask when Comte’s
vision of a science of society like physics
is going to arrive. Would it suffice if there
were a discovery of a process, describable
by a simple mathematical formula, operating
in all societies? It would be harder still
to ignore if that process impacts people,
and how they relate to each other, in ways
of interest to sociologists.
Unequal Math
I maintain that there is at least one
such discovery, known as the Inequality
Process (IP). This discovery mathematically
describes a universal process of competition
in human populations. Unlike popular
notions of Social Darwinism—which Vince
Lombardi’s “winning is the only thing”
characterization of football describes
well—in the simplest version of the
Inequality Process (IP), everyone loses as
often as they win. In the long term, those
who do best in this simplest IP are the
robust losers. The IP was abstracted from
G. Lenski’s (1966) speculation that the
more productive worker loses less in the
competition for wealth.
Economist Thomas Lux (2005) pointed
out to an international conference of econophysicists
that the findings about income
distribution presented in multiple papers
at the conference had been anticipated 20
years earlier in the first paper published
on the Inequality Process. “Econophysics”
and “sociophysics” are the extension of the
field of statistical mechanics in physics into
the social sciences. Statistical mechanics is
about how macro-level phenomena emerge
out of micro-level interactions between
particles in a large population of particles.
Essentially, its subject matter is what
sociologists call macro-micro theory. The
disciplinary line between sociology and
economics is institutionalized and an imaginary
but de facto barrier to those on either
side. The distinction between sociophysics
and econophysics is fluid and
nearly meaningless. Lux (2005) cited my
papers on the IP as evidence of his thesis
that econophysicists should not ignore
social scientists. In 2006, I published an
introductory review and extension of the
Inequality Process for econophysicists
in Physica A: Statistical Mechanics and Its
Applications (2006a; see draft at www.lisproject.org/publications).
Figures 1 and 2 give examples of
empirical patterns implied by the IP. In
statistical mechanical terms—the way
econophysicists see the IP—Figures 1 and
2 are a kind of condensation/crystallization
resulting from the “cooling” of competition
among people. The shapes of the
distribution of wage income as a function
of workers’ levels of education. In IP
terms, the shape difference between the
wage income distributions of the more
and less educated indicate the competition
experienced by the more educated is
“cooler.”
The Math of Bigotry
Because the IP models competition
among people, which, as urban sociologist
Robert E. Park knew, drives discrimination
and victimization, the IP provides
a solution to Franklin’s “wolves”
problem. The IP traces how individual
acts of victimization by a majority
against a minority result in exquisitely
detailed patterns in minority income
statistics, patterns never understood as
the consequence of such acts before the
IP. See the figure labeled “hill of hate”
in my paper (Angle, 1992) about the
distribution of personal income among
African-Americans. The IP offers hope
for reducing the intensity of interpersonal
competition along with techniques
(e.g., social insurance) to disincentivize
discrimination. The IP also explains why
social movements that thrive on bigotry
want to eliminate social insurance. In
the IP every human population “cooks”
with competition at some temperature.
Desperation drives the competition.
The “hotter” the temperature, the more
predatory (cf Franklin) people are relative
to one another, the more like Social
Darwinism the competition becomes. In
a paper for last year’s American Physical
Society meetings, Kotz (2006) pointed
out that the IP would have predicted the
upsurge of prejudice and discrimination
in eastern Europe as the welfare systems
there were dismantled in the late 1980s
and 1990s. In the IP, participation in a
discriminatory coalition is an attempt to
transfer “heat” to the coalition’s victims.
The “hill of hate” figure in Angle
(1992) shows that the IP implies what is
called in statistical mechanics a “phase
transition” (like the melting of ice as its
temperature rises past 0 degrees Celsius),
a nonlinear increase in the incentive to
form a discriminatory coalition as the
“temperature” of competition rises. In IP
terms, a discriminatory coalition is something
like a convection cell in a fluid.
The difference between qualitative
insight into desperation and interpersonal
competition described via a temperature
metaphor on the one hand and
the IP on the other is that the IP relates
the metaphor to observed quantitative
patterns in data on income and wealth.
The IP also implies some principles of
economics never before understood as
joint implications of a single mathematical
model (Angle, 2006b). That is, in the
IP there is no divide between sociophysics
and econophysics. If a student asks
what sociology would be like if it were
a mathematical science, consider that
it might be like statistical mechanics in
physics and that the Inequality Process
might be a starting point. There are short
descriptions of the IP in Tim Liao, et al.’s
The SAGE Encyclopedia of Social Science
Research Methods (Sage, 2003) and Kleiber
and Kotz’s Statistical Size Distributions in
Economics and Actuarial Sciences. (Readers
can network about the interface between
sociology and sociophysics by joining the
ASA’s Mathematical Sociology Section.)
Some economists, such as Lux,
Univer-sity of Kiel (Germany), have
crossed the disciplinary divide between
economics and econophysics to the
enrichment of both. Sociologists
have been invited by professors B. K.
Chakrabarti and A. Chatterjee, conference
organizers, to attend this year’s
Econophys-Kolkata III (see www.saha.ac.in/cmp/econophys3.cmp). Lux
spoke at Econophys-Kolkata I at the Saha
Institute of Nuclear Physics in India.
Statistical physicists bring powerful
mathematical tools to Comte’s positivist
program, but they may need help with
moving beyond ad hoc modifications of
canonical models of statistical mechanics.
There is a potential for collaborations
between sociologists and interdisciplinary
physicists in pursuing Comte’s vision
based on complementary skills. There
is no difference in meaning between
sociophysics as used today by statistical
physicists and sociology as coined by
Comte almost two centuries ago.
For more information on how interdisciplinary
physicists have incorporated
the IP into their research since 2005, do
a search at www.google.com on “John
Angle” and physics, or email me at
angle@inequalityprocess.org.
* * *
References
Angle, J. 1992. “The Inequality Process and
the Distribution of Income to Blacks and
Whites.” Journal of Mathematical Sociology 17:77-98.
———. 2006a “The Inequality Process as a
Wealth Maximizing Algorithm.” Physica
A: Statistical Mechanics and Its Applications 367:388-414.
———. 2006b. “A Comment on Gallegati et
al.’s “Worrying Trends in Econophysics.”
In The Econophysics of Stocks and Other
Markets: The Proceedings of the Econophys
Kolkata II Conference, A. Chatterjee and B.
K. Chakrabarti (Eds.), February. Milan:
Springer.
Bernstein, R. 1988. “Sociology Branches Out
But Is Left in Splinters.” New York Times,
August 30.
Keith, B. 2005. “A Century of Motion:
Disciplinary Culture and Organizational
Drift in American Sociology.” Footnotes December, 33(9):6.
Kleiber, C. and S. Kotz. (2003). Statistical Size
Distributions in Economics and Actuarial
Science. New York: Wiley.
Kotz, S. 2006. “Reflection on Econophysics by
a Statistician.” Paper presented to March
2006 Meeting of the American Physical
Society. Abstract is online at meetings.aps.org/Meeting/MAR06/Event/39240.
Lenski, G. 1966. Power and Privilege. New York:
McGraw-Hill.
Liao, T., et al. (Eds.), The SAGE Encyclopedia
of Social Science Research Methods. Thousand
Oaks, CA: Sage.
Lux, T. 2005. “Emergent Statistical Wealth
Distributions in Simple Monetary Exchange
Models: A Critical Review.” Pp. 51-60
in Econophysics of Wealth Distributions,
A. Chatterjee, S. Yarlagadda, and B. K.
Chakrabarti (Eds.), September. Milan:
Springer.
* The Inequality Process Institute is an alias
for John Angle, private scholar.
* * *
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