Social physics or sociophysics is a field of science which uses mathematical tools inspired by physics to understand the behavior of human crowds. In a modern commercial use, it can also refer to the analysis of social phenomena with big data.

Social physics is closely related to econophysics which uses physics methods to describe economics.


The earliest mentions of a concept of social physics began with the English philosopher Thomas Hobbes. In 1636, Hobbes traveled to Florence, Italy, and met the astronomer Galileo Galilei, of whom was well-known for his contributions to the sciences, namely, the ideas of motion.[1] It was here that Hobbes began to outline the idea of representing the "physical phenomena" of society in terms of the laws of motion.[1] In his treatise De Corpore, Hobbes sought to relate the movement of "material bodies"[2] to the mathematical terms of motion outlined by Galileo and similar scientists of the time period. Although there was no explicit mention of "social physics", the sentiment of examining society with scientific methods began before the first written mention of social physics.

Later, French social thinker Henri de Saint-Simon’s first book, the 1803 Lettres d’un Habitant de Geneve, introduced the idea of describing society using laws similar to those of the physical and biological sciences.[3] His student and collaborator was Auguste Comte, a French philosopher widely regarded as the founder of sociology, who first defined the term in an essay appearing in Le Producteur, a journal project by Saint-Simon.[3] Comte defined social physics as

Social physics is that science which occupies itself with social phenomena, considered in the same light as astronomical, physical, chemical, and physiological phenomena, that is to say as being subject to natural and invariable laws, the discovery of which is the special object of its researches.

After Saint-Simon and Comte, Belgian statistician Adolphe Quetelet, proposed that society be modeled using mathematical probability and social statistics. Quetelet's 1835 book, Essay on Social Physics: Man and the Development of his Faculties, outlines the project of a social physics characterized by measured variables that follow a normal distribution, and collected data about many such variables.[4] A frequently repeated anecdote is that when Comte discovered that Quetelet had appropriated the term 'social physics', he found it necessary to invent a new term 'sociologie' (sociology) because he disagreed with Quetelet's collection of statistics.

There have been several “generations” of social physicists.[5] The first generation began with Saint-Simon, Comte, and Quetelet, and ended with the late 1800s with historian Henry Adams. In the middle of the 20th century, researchers such as the American astrophysicist John Q. Stewart and Swedish geographer Reino Ajo,[6] who showed that the spatial distribution of social interactions could be described using gravity models. Physicists such as Arthur Iberall use a homeokinetics approach to study social systems as complex self-organizing systems.[7][8] For example, a homeokinetics analysis of society shows that one must account for flow variables such as the flow of energy, of materials, of action, reproduction rate, and value-in-exchange.[9] More recently there have been a large number of social science papers that use mathematics broadly similar to that of physics, and described as “computational social science”.[10]

In the late 1800s, Adams separated “human physics” into the subsets of social physics or social mechanics (sociology of interactions using physics-like mathematical tools)[11] and social thermodynamics or sociophysics, (sociology described using mathematical invariances similar to those in thermodynamics).[12] This dichotomy is roughly analogous to the difference between microeconomics and macroeconomics.


Ising model and voter dynamics

A 5x5 representational grid of an Ising model. Each space holds a spin and the red bars indicate communication between neighbors.
A 5x5 representational grid of an Ising model. Each space holds a spin and the red bars indicate communication between neighbors.

One of the most well-known examples in social physics is the relationship of the Ising model and the voting dynamics of a finite population. The Ising model, as a model of ferromagnetism, is represented by a grid of spaces, each of which is occupied by a spin (physics), numerically ±1. Mathematically, the final energy state of the system depends on the interactions of the spaces and their respective spins. For example, if two adjacent spaces share the same spin, the surrounding neighbors will begin to align,[13] and the system will eventually reach a state of consensus. In social physics, it has been observed that voter dynamics in a finite population obey the same mathematical properties of the Ising model. In the social physics model, each spin denotes an opinion, e.g. yes or no, and each space represents a "voter".[13] If two adjacent spaces (voters) share the same spin (opinion), their neighbors begin to align with their spin value; if two adjacent spaces do not share the same spin, then their neighbors remain the same.[14][15] Eventually, the remaining voters will reach a state of consensus as the "information flows outward".[15]

Example of social validation in the Sznajd model. If two neighbors agree (top), then their neighbors agree with them. If two neighbors disagree (bottom), their neighbors begin to disagree as well.
Example of social validation in the Sznajd model. If two neighbors agree (top), then their neighbors agree with them. If two neighbors disagree (bottom), their neighbors begin to disagree as well.

The Sznajd model is an extension of the Ising model and is classified as an econophysics model. It emphasizes the alignment of the neighboring spins in a phenomenon called "social validation".[16] It follows the same properties as the Ising model and is extended to observe the patterns of opinion dynamics as a whole, rather than focusing on just voter dynamics.  

Potts model and cultural dynamics

The Potts model is a generalization of the Ising model and has been used to examine the concept of cultural dissemination as described by American political scientist Robert Axelrod. Axelrod's model of cultural dissemination states that individuals who share cultural characteristics are more likely to interact with each other, thus increasing the number of overlapping characteristics and expanding their interaction network.[17] The Potts model has the caveat that each spin can hold multiple values, unlike the Ising model that could only hold one value.[18][19][20] Each spin, then, represents an individual's "cultural characteristics... [or] in Axelrod’s words, 'the set of individual attributes that are subject to social influence'".[20] It is observed that, using the mathematical properties of the Potts model, neighbors whose cultural characteristics overlap tend to interact more frequently than with unlike neighbors, thus leading to a self-organizing grouping of similar characteristics.[19][18] Simulations done on the Potts model both show Axelrod's model of cultural dissemination agrees with the Potts model as an Ising-class model.[19]

Recent work

In modern use “social physics” refers to using “big data” analysis and the mathematical laws to understand the behavior of human crowds.[21] The core idea is that data about human activity (e.g., phone call records, credit card purchases, taxi rides, web activity) contain mathematical patterns that are characteristic of how social interactions spread and converge. These mathematical invariances can then serve as a filter for analysis of behavior changes and for detecting emerging behavioral patterns.[22]

Recent books about social physics include MIT Professor Alex Pentland’s book Social Physics[23] or Nature editor Mark Buchanan’s book The Social Atom.[24] Popular reading about sociophysics include English physicist Philip Ball’s Why Society is a Complex Matter,[25] Dirk Helbing's The Automation of Society is next or American physicist Laszlo Barabasi’s book Linked.[26]


  1. ^ a b Robertson, George Croom (1911). "Hobbes, Thomas" . Encyclopædia Britannica. 13 (11th ed.). pp. 545–552.
  2. ^ Duncan, Stewart (2021), "Thomas Hobbes", in Zalta, Edward N. (ed.), The Stanford Encyclopedia of Philosophy (Spring 2021 ed.), Metaphysics Research Lab, Stanford University, retrieved 2021-02-24
  3. ^ a b Iggers, Georg G. (1959). "Further Remarks about Early Uses of the Term "Social Science"". Journal of the History of Ideas. 20 (3): 433–436. doi:10.2307/2708121. JSTOR 2708121.
  4. ^ Quetelet, Adolphe (1835). Sur l'homme et le Développement de ses Facultés, ou Essai de Physique Sociale [Essay on Social Physics: Man and the Development of his Faculties] (in French). 1–2. Paris: Imprimeur-Libraire.
  5. ^ Iberall, Arthur (1984) [Presented at Annual Conference of the International Society for the Comparative Study of Civilizations (ISCSC), Syracuse, May 1980]. "Contributions to a Physical Science for the Study of Civilizations". Journal of Social and Biological Structures. 7 (3): 259–283. doi:10.1016/S0140-1750(84)80037-8.
  6. ^ Ajo, Reino (1953). Contributions to "Social Physics": a Programme Sketch with Special Regard to National Planning. Royal University of Lund.
  7. ^ Iberall, A (1985). "Outlining social physics for modern societies - locating culture, economics, and politics: The Enlightenment reconsidered". Proc Natl Acad Sci USA. 82 (17): 5582–84. Bibcode:1985PNAS...82.5582I. doi:10.1073/pnas.82.17.5582. PMC 390594. PMID 16593594.
  8. ^ Iberall, A; Hassler, F; Soodak, H; Wilkinson, D (2000). "Invitation to an Enterprise: From Physics to World History to Civilizations' Study". Comparative Civilization Review. 42: 4–22.
  9. ^ Iberall, Arthur S. (2016), Homeokinetics: The Basics, Medfield, MA: Strong Voices Publishing, ISBN 978-0-990-53614-7
  10. ^ Lazer, D., Pentland, A., et al Science 2010
  11. ^ Ball, Phillip (2002) [A talk presented at ‘Horizons in Complex Systems’ Messina, Sicily, Italy, 2001]. "The physical modelling of society: a historical perspective" (PDF). Physica A. 314 (1–4): 1–14. Bibcode:2002PhyA..314....1B. doi:10.1016/s0378-4371(02)01042-7.
  12. ^ Wilson, Alan (2005). "Notes on Some Concepts in Social Physics". Regional Science. 22 (1): 159–193. doi:10.1111/j.1435-5597.1969.tb01460.x.
  13. ^ a b Moulick, R. (2020-12-24). "The Ising Model And Social Dynamics". European Journal of Molecular & Clinical Medicine. 7 (7): 3835.
  14. ^ Moulick, R. (2020-12-24). "The Ising Model And Social Dynamics". European Journal of Molecular & Clinical Medicine. 7 (7): 3834–3836.
  15. ^ a b Sznajd-Weron, Katarzyna (2005-03-31). "Sznajd model and its applications". Acta Physica Polonica B. 36 (8): 2537. arXiv:physics/0503239. Bibcode:2005AcPPB..36.2537S.
  16. ^ Castellano, Claudio; Fortunato, Santo; Loreto, Vittorio (2009-05-11). "Statistical physics of social dynamics". Reviews of Modern Physics. 81 (2): 591–646. arXiv:0710.3256. Bibcode:2009RvMP...81..591C. doi:10.1103/RevModPhys.81.591. S2CID 118376889.
  17. ^ Axelrod, Robert (2016-07-01). "The Dissemination of Culture: A Model with Local Convergence and Global Polarization". Journal of Conflict Resolution. 41 (2): 203–226. doi:10.1177/0022002797041002001. S2CID 54639070.
  18. ^ a b Klemm, Konstantin; Eguíluz, Víctor M.; Toral, Raúl; Miguel, Maxi San (2003-04-15). "Global culture: A noise-induced transition in finite systems". Physical Review E. 67 (4): 045101. arXiv:cond-mat/0205188. Bibcode:2003PhRvE..67d5101K. doi:10.1103/PhysRevE.67.045101. hdl:10261/15315. PMID 12786417. S2CID 6976248.
  19. ^ a b c Gandica, Y.; Medina, E.; Bonalde, I. (2013-12-15). "A thermodynamic counterpart of the Axelrod model of social influence: The one-dimensional case". Physica A: Statistical Mechanics and Its Applications. 392 (24): 6561–6570. arXiv:1208.4381. Bibcode:2013PhyA..392.6561G. doi:10.1016/j.physa.2013.08.033. hdl:10316/27254. ISSN 0378-4371. S2CID 17918682.
  20. ^ a b Mihăilescu, Luca Mircea. "Simulation of Potts Model on a Dynamically Rewired Network". Cite journal requires |journal= (help)
  21. ^ GEORGE, Gerard; HAAS, Martine R.; PENTLAND, Alex (2014). "Big Data and Management: From the Editors". Academy of Management Journal. 57 (2): 321–326. doi:10.5465/amj.2014.4002.
  22. ^ "Predictive Analytics".
  23. ^ Pentland, Alex (2014). Social Physics: How Good Ideas Spread—the Lessons from a New Science. Penguin.
  24. ^ Buchanan, Mark (2007). The Social Atom - why the Rich get Richer, Cheaters get Caught, and Your Neighbor Usually Looks Like You. Bloomsbury USA. pp. x–xi. ISBN 9781596917316.
  25. ^ Ball, Philip (2012). Why Society is a Complex Matter: Meeting Twenty-First Century Challenges with a New Kind of Science. Springer.
  26. ^ Barabási, Albert-László (2002). Linked: The New Science of Networks. Perseus Books Group.