The beauty of the mammalian vascular system

Julio Gil,Jesús Laborda,Javier Nubiala,Rafael Lahoz-Beltra,Miguel Gimeno

doi:10.1038/npre.2009.2976.1

Julio Gil, Jesús Laborda + Show 3 more

Open Access

https://doi.org/10.1038/npre.2009.2976.1

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Abstract

AbstractBeauty is a characteristic of objects that provides a perceptual experience of pleasure. In nature, aesthetic appreciation thereof has given rise to the mathematical search for good series (e.g. the Fibonacci series) and proportions (e.g. the Golden proportion) as important elements of beauty. In 1928 the mathematician George David Birkhoff introduced a formula for aesthetic measurement of an object. Birkhoff equation defines the aesthetic value as the amount of order divided by the complexity of the product. These two features can be measured easily in poetry, music, painting, architecture, etc. In the fine arts, it is the artist who manipulates both these features, but how does nature manage order and complexity in living organisms or their parts? Here we show how Birkhoff equation, applied to the mammalian vascular system of eight representative animals, results in new insights into the organization of the animal vascular system. We found that order and complexity are highly correlated in the mammalian vascular system (R^2^=0.9511). Accordingly, in nature both features are not independently managed in the manner of artists. We found significant differences among the Birkhoff aesthetic values in the mammalian arterial system, whereas no such differences exist in the venous system. We anticipate our approach to be useful in the study of morphogenesis and evolution of tree-like structures, employing the Birkhoff aesthetic value as a simple tool for conducting such studies.

Highlights

Aesthetic appreciation[1] of nature has always been a common attitude in poets, musicians, and artists, and this does not differ from the appreciation of beauty in naturalists and scientists
In the fine arts is the artist who manipulates both features of M, orderliness O and complexity C, but how does nature manage the order and complexity of a given structure? What is the aesthetic value of molecules, cells, tissues, organs, systems, or individuals? Here we show how Birkhoff’s equation can be applied in the physiological study of living organisms, for example, to obtain new insights into the organization of the animal vascular system
Limiting our study to mammals, we answered the following question: what is the aesthetic value of the circulatory system? To address this question, we selected the circulatory system of eight representative mammalians: dogs, cats, horses, pigs, cows, sheep, goats and humans

Summary

Introduction

Aesthetic appreciation[1] of nature has always been a common attitude in poets, musicians, and artists, and this does not differ from the appreciation of beauty in naturalists and scientists. In the 19th century the American mathematician George David Birkhoff[2] introduced an equation to measure levels of aesthetics M based on a ratio of order O and complexity C: M = O (1) C The original equation had an artistic aim, assigning a high Birkhoff aesthetic value to orderliness and a low one to complexity. Limiting our study to mammals, we answered the following question: what is the aesthetic value of the circulatory system?

Results

Conclusion