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Coping with Complexity April 1999 John J. Tyson Department of Biology Virginia Tech. Biology is the science of living things in all their complexity. “Hey! What’s this Drosophila melanogaster doing in my soup?”. “To the death, Carlson! Hang on to the death!”.
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Coping with Complexity April 1999 John J. Tyson Department of Biology Virginia Tech
Biology is the science of living things in all their complexity
“Hey! What’s this Drosophila melanogaster doing in my soup?”
April 26. After several months I now feel that these strange little rodents have finally accepted me as one of their own.
“If there is an equation for a curve like a bell, there must be an equation for one like a bluebell, and if a bluebell, why not a rose? Do we believe nature is written in numbers?” Thomasina, in Tom Stoppard’s play, Arcadia
Mathematics isa disciplined way of thinking... • about numbers • about shapes • about patterns … in space and time
Why the Disconnect? • Until recently the complexity of most biological problems was too great for the mathematical tools available. • Now we have the tools, but we don’t speak a common language. • My purpose is to open a serious dialog between mathematicians and biologists...
The Golden Rectangle L W W L-W
William Harvey, 1628An Anatomical Treatise of the Motion of the Heart and Blood Harvey’s conclusion: blood must circulate!
Kermack & McKendrick, 1927Infectious Diseases S = fraction of population that is susceptible I = fraction of population that is infectious dI/dt= b S I - g I
Plague in Eyam, England, 1666 Susceptibles b = 0.14 per day g = 0.09 per day Infectives
Basic reproductive rate For infection to spread, rate of new infection > rate of removal Ro = 1.6 for plague
The Overcrowding Game... space mmmummm m = available u = occupied
time space mmmummm mmumumm
time space mmmummm mmumumm mummmum overcrowded
time space mmmummm mmumumm mummmum umumumu
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Pascal’s Tree Bushes and Trees Arteries and Veins Bronchial tubes Self-similar, One-dimensional (lines)
Olivia (mollusc)
Johnson Hall Human geometry is Euclidean Wild Carrot Life’s geometry is fractal P. Prusinkiewicz, Univ. Calgary
Fractional dimension??? By this time everyone had learned how careful you have to be when dealing with numbers. E.B. White The Trumpet of the Swan
Excitable medium... mmmmmmmmmmmmm mmmmmmmmmmmmm mmmmmmmmmmmmm mmmmmmummmmmm mmmmmmmmmmmmm mmmmmmmmmmmmm mmmmmmmmmmmmm m = resting u = excited z = refractory space space
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