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Do you know examples of application of mathematics in psychology besides statistical data processing?

For example, do there exist mathematical models of addiction to Internet sites?

jokersobak
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    I think almost all (if not all) applications of math in a social science involves statistics, Since the things in this world is highly imperfect and subjective, especially those that has to do with people's irrationality, – a point in Standard Students Jan 18 '16 at 01:59
  • @WeiYang May social research be phenomenological? Is it possible to describe some thought processes, for instance, by differential equations? – jokersobak Jan 18 '16 at 03:27
  • it's possible, conceivable that at some point in the future, we will be able to link every thought to some observable processes, thus be able to determine the thoughts with a list of rules (equations). But at the current stage, it is still only a philosophical debate on whether brain = machine – a point in Standard Students Jan 18 '16 at 04:13
  • (A philosophical sidenote: I think the term "thought process" is misleading as it gives the picture that thoughts are continuous. But this is highly debatable, philosophically (and I think there are some psychology research on this). In case you want to read about this, look for David Hume's idea on thoughts and self) – a point in Standard Students Jan 18 '16 at 04:40
  • @WeiYang I think that's no matter whether brain = machine or if thoughts are continuous. For example, gases and liquids consist of a finite number of molecules but can be considered as continuous media and modelled by differential equations. One may propose a description of the human mind involving a set of equations for various neurons. But can one use some macroscopic variables and reduce the model to a few equations? For instance, there are phenomenological models of the population growth (e.g., by Sergey Kapitsa) which include simple equations and describe the population well. – jokersobak Feb 17 '16 at 11:39

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The mathematician Ulf Grenander wrote a book where he applied his General Pattern Theory to propose a mathematical model of generation of train of thoughts.

This is an example of application of mathematics to higher cognition.

The model can be tuned to model abnormal psychological disorders characterized for example by obsessional thoughts.

The book is a good read and you have Matlab code to play with.

References :

Grenander, U. (2012). A calculus of ideas: a mathematical study of human thought. World Scientific.

Grenander, Ulf. General pattern theory: A mathematical study of regular structures Oxford mathematical monographs. Oxford University Press: Clarendon, 1993.

Code of the model : http://www.dam.brown.edu/ptg/REPORTS/mind07.zip

brgal
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Actually there are a few models using a different approach.

Have a look at Abelson 1967 and more recently

Agent-Based Modeling: A New Approach for Theory Building in Social Psychology Eliot R. Smith and Frederica R. Conrey Pers Soc Psychol Rev 2007; 11; 87 DOI: 10.1177/1088868306294789

I published also some models, see e.g.

Dal Forno A., & Merlone, U., (2013). Nonlinear dynamics in work groups with Bion's basic assumptions. Nonlinear Dynamics, Psychology, and Life Sciences, Vol.17, No.2, April, pp.295-315.

Ugo Merlone
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