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Coping with Complexity April 1999 John J. Tyson Department of Biology Virginia Tech

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

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  1. Coping with Complexity April 1999 John J. Tyson Department of Biology Virginia Tech

  2. Biology is the science of living things in all their complexity

  3. “Hey! What’s this Drosophila melanogaster doing in my soup?”

  4. “To the death, Carlson! Hang on to the death!”

  5. April 26. After several months I now feel that these strange little rodents have finally accepted me as one of their own.

  6. “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

  7. What good is mathematics?

  8. Mathematics isa disciplined way of thinking... • about numbers • about shapes • about patterns … in space and time

  9. 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...

  10. The Golden Rectangle L W W L-W

  11. The GR is “self-similar”…expand by (1.618)4@ 6.854

  12. William Harvey, 1628An Anatomical Treatise of the Motion of the Heart and Blood Harvey’s conclusion: blood must circulate!

  13. 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

  14. Plague in Eyam, England, 1666 Susceptibles b = 0.14 per day g = 0.09 per day Infectives

  15. Basic reproductive rate For infection to spread, rate of new infection > rate of removal Ro = 1.6 for plague

  16. Can we stop the spread of infection by immunization?

  17. The Overcrowding Game... space mmmummm m = available u = occupied

  18. time space mmmummm mmumumm

  19. time space mmmummm mmumumm mummmum overcrowded

  20. time space mmmummm mmumumm mummmum umumumu

  21. u umu ummmu umumumu ummmmmmmu umummmmmumu ummmummmummmu umumumumumumumu ummmmmmmmmmmmmmmu umummmmmmmmmmmmmumu ummmummmmmmmmmmmummmu umumumummmmmmmmmumumumu ummmmmmmummmmmmmummmmmmmu umummmmmumummmmmumummmmmumu ummmummmummmummmummmummmummmu umumumumumumumumumumumumumumumu ummmmmmmmmmmmmmmmmmmmmmmmmmmmmmmu umummmmmmmmmmmmmmmmmmmmmmmmmmmmmumu ummmummmmmmmmmmmmmmmmmmmmmmmmmmmummmu umumumummmmmmmmmmmmmmmmmmmmmmmmmumumumu ummmmmmmummmmmmmmmmmmmmmmmmmmmmmummmmmmmu umummmmmumummmmmmmmmmmmmmmmmmmmmumummmmmumu ummmummmummmummmmmmmmmmmmmmmmmmmummmummmummmu umumumumumumumummmmmmmmmmmmmmmmmumumumumumumumu ummmmmmmmmmmmmmmummmmmmmmmmmmmmmummmmmmmmmmmmmmmu umummmmmmmmmmmmmumummmmmmmmmmmmmumummmmmmmmmmmmmumu ummmummmmmmmmmmmummmummmmmmmmmmmummmummmmmmmmmmmummmu umumumummmmmmmmmumumumummmmmmmmmumumumummmmmmmmmumumumu ummmmmmmummmmmmmummmmmmmummmmmmmummmmmmmummmmmmmummmmmmmu umummmmmumummmmmumummmmmumummmmmumummmmmumummmmmumummmmmumu ummmummmummmummmummmummmummmummmummmummmummmummmummmummmummmu umumumumumumumumumumumumumumumumumumumumumumumumumumumumumumumu Pascal’s Triangle

  22. Pascal’s Tree Bushes and Trees Arteries and Veins Bronchial tubes Self-similar, One-dimensional (lines)

  23. Olivia (mollusc)

  24. Hans Meinhardt, The Algorithmic Beauty of Sea Shells

  25. Cymbiola (pattern = Serpinski’s gasket)

  26. Serpinski’s Gasket

  27. Johnson Hall Human geometry is Euclidean Wild Carrot Life’s geometry is fractal P. Prusinkiewicz, Univ. Calgary

  28. 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

  29. Excitable medium... mmmmmmmmmmmmm mmmmmmmmmmmmm mmmmmmmmmmmmm mmmmmmummmmmm mmmmmmmmmmmmm mmmmmmmmmmmmm mmmmmmmmmmmmm m = resting u = excited z = refractory space space

  30. mmmmmmmmmmmmm mmmmmmmmmmmmm mmmmmmummmmmm mmmmmuzummmmm mmmmmmummmmmm mmmmmmmmmmmmm mmmmmmmmmmmmm

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