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The Math and Biology of Beauty: Averages and Symmetry

Aesthetic judgements of physical attractiveness – beauty – are not arbitrary. Scientific studies show that they are are related to biology and healthy, which is often manifested as facial symmetry.

In physical attractiveness studies, “averageness” describes the physical beauty that results from averaging the facial features of people of the same gender and approximately the same age. This is often called the “averageness-effect.”

Studies use photographic overlays of human faces, in which images are morphed together.

The term “average” here is a mathematical definition = arithmetic mean, = the sum of a collection of numbers divided by the count of numbers in the collection.

It turns out that an averaged face is not unremarkable, but is, in fact, quite good looking.

Averageness Face Beauty

Image from Koinophilia and human facial attractiveness, Aishwariya Iyengar et al.

Koinophilia and human facial attractiveness, April 2015, Volume 20, Issue 4, pp 311–319

Nor is averageness typical in the sense of common or frequently occurring in the population, though it appears familiar, and is typical in the sense that it is a good example of a face that is representative of the category of faces.

The evolutionary explanation for averageness is koinophilia: animals seek mates with average features, because extreme or uncommon features indicate disadvantageous mutations.


FaceResearch.org – Make Your Own Average


Note (1) Grammer, K.; Thornhill, R. (October 1994). “Human (Homo sapiens) facial attractiveness and sexual selection: the role of symmetry and averageness”. Journal of Comparative Psychology. 108 (3): 233–42. doi:10.1037/0735-7036.108.3.233. PMID 7924253. Retrieved 4 May 2019.

Rhodes, Gillian; Zebrowitz, Leslie A. (2002). Facial Attractiveness: Evolutionary, Cognitive, and Social Perspectives. Ablex. ISBN 978-1-56750-636-5.

Jones, B. C., Little, A. C., Tiddeman, B. P., Burt, D. M., & Perrett, D. I. (2001). Facial symmetry and judgements of apparent health Support for a “‘ good genes ’” explanation of the attractiveness – symmetry relationship, 22, 417–429.

Alison Pearce Stevens writes “Research shows that people with more symmetrical faces don’t just look nice. They also tend to be healthier than asymmetrical people. Genes provide the instructions for how a cell is to perform. All people have the same number of genes. But people with more average faces tend to have a greater diversity in the genes they are born with. And that, research has shown, can lead to a stronger immune system and better health.” What makes a pretty face? Science News for Students

Medical Daily: The Science Of Attraction: Men Perceive Women With Average, Youthful Facial Features As Beautiful


Iglesias-Julios M, Munoz-Reyes JA, Pita M et al. Facial Features: What Women Perceive as Attractive and What Men Consider Attractive. PLoS ONE. 2015.

Farmer H, McKay R, Tsakiris M. Trust in Me: Trustworthy Others Are Seen as More Physically Similar to the Self. Psychological Science. 2013.

Coetzee V, Keckp S, Kivleniece I et al. Facial attractiveness is related to women’s cortisol and body fat, but not with immune responsiveness. Biology Letters. 2013.

Emmy Noether

Amalie Emmy Noether (1882 – 1935) was a German mathematician known for her landmark contributions to abstract algebra and theoretical physics. She was described by Pavel Alexandrov, Albert Einstein, Hermann Weyl, and Norbert Wiener as the most important woman in the history of mathematics. In physics, Noether’s theorem explains the connection between symmetry and conservation laws.

Amalie Emmy Noether symmetry


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In her short life, mathematician Emmy Noether changed the face of physics. ScienceNews.Org