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The Importance of Being Peripheral John D. Barrow

The Importance of Being Peripheral John D. Barrow. Land Economy. Queen Dido’s Problem. Wiggliness. Isoperimetric Theorems. Maximum area is enclosed by a circle (Perimeter) 2  4   Area (2 r) 2 = 4   r 2 Maximum volume is enclosed by a sphere (Area) 3  36   (vol) 2

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The Importance of Being Peripheral John D. Barrow

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  1. The Importance of Being Peripheral John D. Barrow

  2. LandEconomy

  3. Queen Dido’s Problem

  4. Wiggliness

  5. Isoperimetric Theorems Maximum area is enclosed by a circle (Perimeter)2 4  Area (2r)2 = 4r2 Maximum volume is enclosed by a sphere (Area)3  36 (vol)2 (4r2)3 = 36 (4r3/3)2

  6. When Small Boundaries Are Best Keeping warm Avoiding detection

  7. Chilling Out Heat generation  volume  L3 Heat loss  surface  L2 Heating/Cooling  L Is there a biggest possible computer?

  8. Be big if you live at the North Pole

  9. Huddles and Herds Keeping warm

  10. Avoid being on the edge of the herd

  11. Trans-Atlantic Convoys Avoiding submarines Minimise perimeter or periscope image size

  12. One big one or many small ones?

  13. Sticking Together Is the best policy Split A into A/2 + A/2 Perimeter of single A convoy is 2A Perimeter of 2A/2 convoys is 22½A And is Bigger by 2 = 1.41..

  14. Fish-balling is bad for the group!

  15. Division leads to more boundary  cut

  16. area A area 2A area 4A Likelihood of explosion Is increasing 

  17. Fire Storms Ignition of dust produces explosive spread of fire

  18. Global Dimming? • Sunlight scattering off atmospheric pollutants • depends on surface area • more pollutants  more particles •  smaller droplets • relatively more surface area •  more back-reflection of sunlight  cooler Earth • 2-3% per decade in N lats • 1 deg C rise in USA 3 days after 9/11

  19. When Large Boundaries are Best Keeping cool Being seen Soaking up moisture Getting nutrients Dissolving fast

  20. Cooking Times Heat diffusing through a cooking turkey Time  area  (size)2  (weight)2/3 because weight  density  (size)3 N2 steps to random walk a straight line distance of N step-lengths T/t=k2T so T/t  T/d2andd2  t

  21. How big can your boundary get ? Leads to as big a boundary as you wish for the same finite area

  22. Numberof segments of length d needed to cover the coastline N(d) = M/dD D = 1.25 for the west coast of Britain D = 1.13 for the Australian coast D = 1.02 for the South African coast

  23. Fractals A recipe for maximising surface Copy the same pattern over and over again on all scales Trees Flowers Human lungs Metabolic systems Jackson Pollock paintings

  24. Romanesque Broccoli

  25. Lungs small mass andvolume but large surface interface

  26. Fractalsdamp vibrations Lungs and coastlines What is its length? Fractal coastlines damp down waves and reduce erosion very efficiently

  27. Universal metabolism Metabolic rate vs (mass)3/4 Kleiber’s Law

  28. Puzzling ??? Rate = Heat loss  area  L2 Mass  L3 So Metabolic rate  (Mass)2/3 Not  (Mass)3/4

  29. Model as a fractal network in D dims that transports nutrients while minimising the energy lost by dissipation Rate  (Mass)(D-1)/D Rate  (Mass)3/4 Fractal filling of 3 dims makes its information content like 4 dimensions

  30. Black Holes R = 2GM/c2 Area = 4R2  M2 Density  1/M2

  31. Black Holes Are Black Bodies They obey the Laws of Thermodynamics Thermal evaporation of energy with entropy given by the area and temperature by surface gravity (g)

  32. The 2nd Law of black-hole mechanics The total black hole area can never decrease The 2nd Law of thermodynamics Entropy can never decrease SBH Area  M2 Information content  SBH

  33. Is there a universal ‘holographic’ principle? The maximum information content of a region is determined by its surface area ??? S  (Area)/4 = SBH

  34. The edge of something to look into?

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