Human mathematics

Human mathematics icon (s)
An equation overlay artisitic depiction of human mathematics: the application of mathematics to questions of human concern, such as how the mind operates, love, economics, morality, etc.
In science, human mathematics is the study or use of pure mathematics or mathematical theory applied to humans, human behavior, or problems, phenomena, or subjects in the humanities.

History
In circa 1845, Scottish mathematical physicist and engineer William Rankine penned "The Mathematician in Love".

In 1854, English mathematical philosopher George Boole (1815-1864) published his An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, in which he utilized Boolean logic to example human thought processing operations.

In 1881, Irish mathematical economist Francis Edgeworth published his Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences, the beginning of his long career in the subject, is said to be book was notoriously difficult to read, outlines a “tentative study” of the creative applications of mathematics to economic or moral issues. Edgeworth aruges that mathematical psychics, or rather ‘psychological mathematics’ (or mathematical psychology) in a modern sense, can be divided into pure and applied, wherein he attempts formulation on concepts such as a quantity of pleasure, principles of maximum energy, and a calculus of feeling, among others.

In circa 1972, American mathematical psychologist John Gottman applied mathematics to the study of marriage dynamics.

Strogatz
In 1986, American applied mathematician Steven Strogatz completed his PhD at Harvard in with a dissertation on the “The Mathematical Structure of the Human Sleep-wake Cycle”. [1]

Strogatz followed this up with the 1988 article “Love Affairs and Differential Equations”, wherein he does some of the first differential equation formulation for the equation of love and in which he explains how he teaches students about ordinary coupled differential equations using examples of variations of levels or ratios of love and hate, similar to the Gottman stability ratio, in Shakespeare-style Romeo and Juliet type relationships. [2] Much of Strogatz’ applied human mathematics logic is presented in his 2003 book Sync: the Emerging Science of Spontaneous Order, in which he attempts to explain things such as “synchronal or simultaneous flashing of fireflies”, why women roommates often find their menstrual cycles to sync, the triggering of riots, fads, and mass hysteria, to the synchronicity of the solar system in possible relation to dinosaur extinction, among other subjects. [3]
Strange Attractors (2008)
The 2008 book Strange Attractors, a collection of historical poems, over the last 4000-years, on the overlap of love and mathematics. [5]

In 2009, Strogatz published “Energy Landscape of Social Balance”, in which he and his colleagues, Seth Marvel and Jon Kleinberg, to take a stab at deriving a mathematical version of a "social energy landscape", the synopsis of which is: “the shifting of alliances and rivalries in a social group can be viewed as arising from an energy minimization process.” [4]

Other
In 2010, Spanish mathematical economist Jose-Manuel Rey published his “A Mathematical Model of Sentimental Dynamics Accounting for Marital Dissolution”, which builds on the work of John Gottman, to attempt to formulaically and graphically explain marital dissolution using a metaphorical version of the second law to indicate that “indicate that the feeling of attachment in a relationship ‘cools down’ (thermal word) as time evolves—unless energy in form of effort is supplied to keep things alive.”

See also
HM pioneers
The Mathematician in Love

References
1. Strogatz, Steven H. (1986). The Mathematical Structure of the Human Sleep-Wake Cycle. (PhD thesis, Harvard). Springer.
2. Strogatz, Steven H. (1988). "Love Affairs and Differential Equations", Mathematics Magazine, 61(1): 35.
3. Strogatz, Steven (2003). Sync: the Emerging Science of Spontaneous Order. Hyperion.
4. Marvel, Seth A., Strogatz, Steven H., and Kleinberg, Jon M. (2009). “Energy Landscape of Social Balance”, Physical Review Letters, PRL 103, 198701.
5. Glaz, Sarah and Growney, Joanne. (2008). Strange Attractors: Poems of Love and Mathematics (abs). AK Peters.

Further reading
● Porter, Theodore. (1981). “The Mathematics of Society: Variation and Error in Quetelet’s Statistics”, British Journal for the History of Science, 18: 51-69.
● Salmon, Nathan. (2005). Metaphysics, Mathematics, and Meaning (ch.13: “The Limits of Human Mathematics (2001)”, pgs. 243-). Oxford University Press.
● Grant, Philip C. (2008). The Mathematics of Human Motivation: Applying the Law of Escalating marginal Sacrifice: a Cost-benefit Framework for Understanding Determinants of Performance (abs). University Press of America.

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