1 / 70

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!”.

Sophia
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

  31. mmmmmmmmmmmmm mmmmmmummmmmm mmmmmuzummmmm mmmmuzmzummmm mmmmmuzummmmm mmmmmmummmmmm mmmmmmmmmmmmm

  32. mmmmmmummmmmm mmmmmuzummmmm mmmmuzmzummmm mmmuzmmmzummm mmmmuzmzummmm mmmmmuzummmmm mmmmmmummmmmm

  33. mmmmmuzummmmm mmmmuzmzummmm mmmuzmmmzummm mmuzmmmmmzumm mmmuzmmmzummm mmmmuzmzummmm mmmmmuzummmmm

  34. mmmmuzmzummmm mmmuzmmmzummm mmuzmmmmmzumm muzmmmmmmmzum mmuzmmmmmzumm mmmuzmmmzummm mmmmuzmzummmm

  35. mmmuzmmmzummm mmuzmmmmmzumm muzmmmmmmmzum uzmmmmmmmmmzu muzmmmmmmmzum mmuzmmmmmzumm mmmuzmmmzummm

  36. mmuzmmmmmzumm muzmmmmmmmzum uzmmmmmmmmmzu zmmmmmmmmmmmz uzmmmmmmmmmzu muzmmmmmmmzum mmuzmmmmmzumm

  37. muzmmmmmmmzum uzmmmmmmmmmzu zmmmmmmmmmmmz mmmmmmmmmmmmm zmmmmmmmmmmmz uzmmmmmmmmmzu muzmmmmmmmzum

  38. uzmmmmmmmmmzu zmmmmmmmmmmmz mmmmmmmmmmmmm mmmmmmmmmmmmm mmmmmmmmmmmmm zmmmmmmmmmmmz uzmmmmmmmmmzu

  39. zmmmmmmmmmmmz mmmmmmmmmmmmm mmmmmmmmmmmmm mmmmmmmmmmmmm mmmmmmmmmmmmm mmmmmmmmmmmmm zmmmmmmmmmmmz

  40. mmmmmmmmmmmmm mmmmmmmmmmmmm mmmmmmmmmmmmm mmmmmmmmmmmmm mmmmmmmmmmmmm mmmmmmmmmmmmm mmmmmmmmmmmmm

  41. mmmmmmmmmmm mmmmmmmmmmm mmmmmmmmmmm mmmmmmmmmmm mmmmmmmmmmm mmmmmuuuuuu mmmmmzzzzzz mmmmmmmmmmm mmmmmmmmmmm mmmmmmmmmmm mmmmmmmmmmm

  42. mmmmmmmmmmm mmmmmmmmmmm mmmmmmmmmmm mmmmmmmmmmm mmmmmuuuuuu mmmmuzzzzzz mmmmmmmmmmm mmmmmmmmmmm mmmmmmmmmmm mmmmmmmmmmm mmmmmmmmmmm

More Related