Mathematics of love

mathematics of love
A humorous algebraic rendition of the mathematics of love by graphic designer Andrija Markovic. [6]
In human mathematics, the mathematics of love refers to the subject of applying mathematical formalism, such as ordinary differential equations, to the question of love, falling in love, or being in love, etc., or attempts to derive mathematical equations of love.

In 1988, American mathematician Steven Strogatz, in his article "Love Affairs and Differential Equations", discussed his unusual teaching approach to introducing students to the subject of systems of coupled ordinary differential equations, by formulating hypothetical differential equations to describe the love/hate ratio functions for the interactions between William Shakespeare's Romeo and Juliet. [1]

The 1994 experimental findings of American mathematical psychologist John Gottman on marriage stability, as captured in his famous Gottman stability ratio, i.e. that a 5/1 ratio of attraction-to-repulsion is what characterizes stable long term marriages, is sometimes referred to as the “mathematics of love”. In a 2004 interview, Gottman summarized his work as follows: [2]

“We were able to derive a set of nonlinear difference equations for marital interaction as well as physiology and perception. These equations provided parameters, that allowed us to predict, with over 90 percent accuracy, what was going to happen to a relationship over a three-year period. The main advantage of the math modeling was that using these parameters, we are not only be able to predict, but now understand what people are doing when they affected one another. And through the equations we were now really able to build theory. That theory allows us to understand how to intervene and how to change things. And how to know what it is we're affecting, and why the interventions are effective. This is the mathematics of love.”
Mathematics and Sex (2003)
The 2003 book Mathematics and Sex mathematician Clio Cresswell who outlines the mathematics of love and also a subject she calls “sexual mathematics”. [4]

In 1998, Italian mathematician Sergio Rinaldi published his “Laura and Petrarch: an Intriguing Case of Cyclical Love Dynamics”, in which he employs three ordinary differential equations to model the dynamics of love between Petrarch, a celebrated 14th century Italian poet, and Laura, a beautiful by married lady. [7]

In 2001, inspired by the 1994 version of the “love model” of Strogatz (Nonlinear Dynamics and Chaos), American physicist Clint Sprott gave a 36-slide presentation entitled “Mathematical Models of Love and Happiness”, at the Chaos and Complex Systems Seminar, Madison, Wisconsin, wherein he expanded on the Romeo Juliet model of linear differential equation love. [3] Sprott followed this up with the 2004 article Dynamical Models of Love”. [8]

In the 2003 book Mathematics and Sex, mentioning the previous work of Strogatz and Rinaldi, Australian mathematician Clio Cresswell outlines the subject of what she calls “sexual mathematics”, which she says is similar to sexual chemistry, albeit with mathematical focus. [4]

In 2004, American engineer Charles Hansen wrote a chapter on the mathematics of love, wherein, building on work of Pitirim Sorokin and Talcott Parsons, among others, he attempts to outline a “vectors model” of human action. [5]

See also
Thermodynamics of love
Chemistry of love
Physics of love

1. Strogatz, Steven H. (1988). "Love Affairs and Differential Equations", Mathematics Magazine, 61(1): 35.
2. The Mathematics of Love: A Talk with John Gottman (14 Apr 2004) –
3. Sprott, J. Clint. (2001). “Mathematical Models of Love and Happiness” (36 slide presentation), Presented to the Chaos and Complex Systems Seminar, Madison, Wisconsin, Feb 06.
Mathematics and Sex (equations)
A 2009 artistic rendition of Australian mathematician Clio Cresswell’s theory of the mathematics of love/sex, who claims singles can increase their chances of finding true love by rejecting at least 12 potential partners before settling down. [9]
4. Cresswell, Clio. (2003). Mathematics and Sex. Allen & Unwin.
5. (a) The Mathematics of Love (excerpts) –
(b) Hansen, Charles E. (2004). The Technology of Love, Volume 1 (mathematics of love, pgs. 467-512). Corsense Institute Inc.
6. (a) Mathematics of love (white background) –
(b) Mathematics of love (chalkboard version) –
7. Rinaldi, Sergio. (1996). “Laura and Petrarch: an Intriguing Case of Cyclical Love Dynamics”, working paper; in: SIAM Journal of Applied Mathematics (abs), 1998, 58: 1205, Aug.
8. Sprott, J.C. (2004). “Dynamical Models of Love, Nonlinear Dynamics, Psychology, and Life Sciences, 8(3), Jul.
9. Browne, Rachel. (2009). “The Mathematical Formula for Love”,, Aug 25.

Further reading
● Rinaldi, Sergio and Gragnani, Alessandra. (1996). “Love Dynamics Between Secure Individuals: A Modeling Approach”, working paper; in: Nonlinear Dynamics, Psychology, and Life Sciences (abs), 1998, 2(4): 283-301.
● Peterson, Ivars. (1998). “Love’s Dynamics”, MMA blog, Sep 07.
● Gottman, John M., Murray, James D., Swanson, Catherine, Tyson, Rebecca, and Swanson, Kristin R. (2005). The Mathematics of Marriage: Dynamic Nonlinear Models. MIT Press.
● LaRosa, Jennifer. (2003). “Love Dynamics: Using Differential Equations to Model Cases of Linear and Nonlinear Couples”, Senior thesis, Middlebury College, Dec.
● Payne, Burly. (c.2010). The Quantum Theory of Love (abs). Buryl’s Books.

● Clinton, George and Burrell, Kim. (2008). “Song: Mathematics of Love”, Shanachie Entertainment.
● Parcek, Peter. (2010). “Interview: The Mathematics of Love”, Alternative Root.

External links
Mathematical Models of Romance (laboratory 3, Math 315) – Middlebury College.

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