The Importance of Being Peripheral

John D. Barrow

Land Economy

Queen Didos Problem

Wiggliness

Maximum area is enclosed by a circle(Perimeter)2 4 Area(2r)2 = 4 r2Maximum volume is enclosed by a sphere(Area)3 36 (vol)2(4r2)3 = 36 (4r3/3)2Isoperimetric Theorems

When Small Boundaries Are BestKeeping warmAvoiding detection

Chilling OutHeat generation volume L3Heat loss surface L2Heating/Cooling LIs there a biggest possible computer?

Be big if you live at the North Pole

Huddles and HerdsKeeping warm

Avoid being on the edge of the herd

Trans-Atlantic Convoys Avoiding submarines

Minimise perimeter or periscope image size

One big one or many small ones?

Sticking TogetherIs the best policySplit A into A/2 + A/2Perimeter of single A convoy is 2APerimeter of 2A/2 convoys is22AAnd isBigger by 2 = 1.41..

Fish-balling is bad for the group!

Division leads to more boundarycut

area A area 2A area 4A Likelihood of explosionIs increasing

Fire StormsIgnition of dust produces explosive spread of fire

Global Dimming?Sunlight scattering off atmospheric pollutants depends on surface areamore pollutants more particles smaller droplets relatively more surface area more back-reflection of sunlight cooler Earth2-3% per decade in N lats1 deg C rise in USA 3 days after 9/11

When Large Boundaries are BestKeeping coolBeing seenSoaking up moistureGetting nutrientsDissolving fast

Cooking Times

Heat diffusing through a cooking turkeyTime area (size)2 (weight)2/3because weight density (size)3N2 steps to random walk a straight line distance of N step-lengthsT/t=k2T so T/t T/d2 and d2 t

How big can your boundary get ?

Leads to as big a boundary as you wish for the same finite area

Number of segments of length d needed to cover the coastlineN(d) = M/dDD = 1.25 for the west coast of BritainD = 1.13 for the Australian coastD = 1.02 for the South African coast

FractalsA recipe for maximising surfaceCopy the same pattern over and over again on all scalesTreesFlowersHuman lungsMetabolic systemsJackson Pollock paintings

Romanesque Broccoli

Lungs

small mass and volume but large surface interface

Fractals damp vibrationsLungs and coastlines

What is its length?Fractal coastlines damp down waves and reduce erosion very efficiently

Universal metabolism Metabolic rate vs (mass)3/4Kleibers Law

Puzzling ??? Rate = Heat loss area L2Mass L3So Metabolic rate (Mass)2/3Not (Mass)3/4

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

Black Holes

R = 2GM/c2Area = 4R2 M2Density 1/M2

Black Holes Are Black BodiesThey obey the Laws of ThermodynamicsThermal evaporation of energy with entropy given by the areaand temperature by surface gravity (g)

The 2nd Law of black-hole mechanicsThe total black hole area can never decreaseThe 2nd Law of thermodynamicsEntropy can never decreaseSBH Area M2Information content SBH

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

The edge of something to look into?

The Heat Death of the UniverseStotal grows

butSmax grows fasterStimeSmaxStotal

StimeSmaxStotalUniverse accelerates

The Importance of Being Peripheral*John D. Barrow

A fractal simulation

Cauliflower