Do Animals Have a Math Instinct?

Deborah Von der Lage

June 16, 2010

Bees as Mathematicians

Bees have chosen the perfect shape for their honeycombs –the hexagon.

The area of a hexagon is greater than

that of a triangle or square if the apothem –the height of a triangle within the hexagon is the same.

p= perimeter

A=x² =¼p A=½ x ⅓p x ⅓p x √3 /2 A= =½ x √3 /2 x ⅙p x p .0625p² < .048p² < .072p²

x

p. 173 in Agnesi to Zeno – Over 100 Vignettes from the History of Math by Sanderson Smith

Dogs and Calculus

“Elvis is doing calculus in the sense that he somehow knows how to find the minimum time to get to the ball," Pennings a mathematician at Hope College says.

If the ball is thrown from point A to point B alongthe shores of the Lake Michigan, Elvis will always enter the water at Point D. The shortest distance.

“It's a Math World for Animals” by Emily Sohn

B

D CA

Elvis poses with the equipment used to measure how well he does his math.Tim Pennings

Animal Coat PatternsTigers, Leopards and Zebras

Proto-types of Patterns of Animal Tails Source: J.D. Murray, Mathematical Biology

Simulations of Animal Coat Patterns Source: J.D. Murray, Mathematical Biology

“Humans have long had a fascination with the coat patterns of animals. Alan Turing was

the first to articulate an explanation of how the patterns of animals like leopards, jaguars and zebras are determined. Turing asserted that the patterns can arise as a result of instabilities in the diffusion of morphogenetic chemicals in the animals' skins during the embryonic stage of development.Let C be the vector of morphogen concentrations. The vector equation giving the spatial and temporal dynamics of morphogen concentrations is:

∂C/∂t = F(C) + D∇2C

where F(C) is a nonlinear vector function and D is diagonal matrix. “

A low threshold for turning pigment ON A high threshold for turning pigment ON© 1997-2009, Millennium Mathematics Project, University of Cambridge.

Navigators

Ahmed

Dead reckoning

Tunisian desert

Lobster

GPS

Bird

Migration

Bats

Echolocation

Owl

Triangulation

Monarch Butterflies

Directional

Number Sense in Babies

Karen Wynn, researcher at the Infant Cognitive Center at Yale University, did studies involving an infant’s sense of number. The test has been repeated world wide with similar results. The babies will recognize that the number of puppets changes after watching two , two, two, two and then one. Videos record eye movement and focus. Theyalso tried the reverse – one, one, one,then two.

Math Instinct or Natural Instinct???

You Decide –(like created or discovered)

• Beavers building a dam

• Spiders spinning a web

• Cockroach locomotion

• Horses moving – walk, trot, canter, or gallop

• Human movement – walk, jog, run, sprint

• Fish swimming

• Salmon migration

Why I Choose this question and it’s application in class.

The article in the class text book on bees caught my attention. My father started three bee hives last summer. I thought the research would help me carry on a more informed conversation with him.

When signing up for my topic, I was directed to the book, ”Math Instinct” by Keith Devlin. The book was an excellent starting source.

The knowledge can be used to give interest to various topics throughout the year. Another set of “Stories” to engage the students in math.

Bibliography

• It's a Math World for AnimalsEmily Sohn

• coat patterns in leopards

http://www.sjsu.edu/faculty/watkins/murray.htm

• Math and the brain

http://mathaware.org/mam/07/mathinbrain.pdf

http://www.mathematicalbrain.com/pdf/MALECTURE.PDF

• language and the brain

life patterns

http://www.math.com/students/wonders/life/life.html

• James D. Murray, Mathematical Biology, 2nd Corrected Edition, Springer, 1993.

• J.D. Murray and M. R. Myerscough, "Pigmentation Pattern Formation on Snakes," Journal of Theoretical Biology, vol. 149 (1991), pp. 339-360.

• J.D. Murray, "Parameter Space for Turing Instability in Reaction Diffusion Mechanisms: A Comparison of Models," Journal of Theoretical Biology, vol. 98 (1982), pp. 143-163.

• brain research

http://www.mathematicalbrain.com/pdf/MALECTURE.PDF

• Dogs and calculus

http://www.sciencenewsforkids.org/articles/20031008/Feature1.asp

• © 1997-2009, Millennium Mathematics Project, University of Cambridge.

• The Amazing Ahmed

http://www.maa.org/devlin/devlin_12_04.html

• p. 173 in Agnesi to Zeno – Over 100 Vignettes from the History of Math by Sanderson Smith

Primary Starting point source -

• The Math Instinct – Why You’re a Mathematical Genius (along with Lobster, Birds, Cats and Dogs) by Keith Devlin

• “Alan Turing is considered to be one of the most brilliant mathematicians of the last century. He helped crack the German Enigma code during the Second World War and laid the foundations for the digital computer. His only foray into mathematical biology produced a paper so insightful that it is still regularly cited today, over 50 years since it was published. “

• Babies in math

• http://tibormachan.rationalreview.com/tag/paul-bloom-karen-wynn/