Deep Simplicity - Chapter 4

From Chaos to Complexity

• Thermodynamics
• Closed system - poincare recurrence (time reversibility)
• Open system - irreversible arrow of time; dissipation of energy
• Lars Onsager - theory of reciprocal relations
• Temperature gradient produces concentration gradient (vice versa)
• Ilya Prigogine - dissipative system in linear regime doesn't end in (settle at) entropy, but when entropy (dissipation) is occurring slowest
• Linear: adult human beings
• Nonlinear: growth of fertilized egg
• Nonlinearity is most important when feedback is present
• System can only be held in an 'interesting' state away from equilibrium if it is dissipative and open to the outside environment, w/ an outside energy source (sun)
• Equilibrium is NOT interesting
• Chaos is NOT interesting
• Something in between is interesting (Order in the midst of Chaos)

• Gravity is the key to creating order
• Gravitational energy of any object that has mass is initially negative (potential energy)
• Initial states of objects infinitely far apart has 0 gravitational energy (Gmm/r^2)
• As they move closer, they gain kinetic energy (speed increases)
• Comes from gravitational field
• This leads to negative energy for the gravitational field
• How much for a given point mass?
• -MC^2 (exact opposite of mass energy)
• When gravitational energy is ignored (closed box), entropy results (uniformly spread gas)
• When it is not ignored (large clusters of gas & dust), gravity can create (pull) order and reduce entropy
• Due to negative energy of gravitational field
• Gravity ultimately determines direction of time

•  Alan Turing - tried to invent universal computer (Turing Machine)
• Read On Growth and Form as a kid (inspiration)
• Studied how structures emerge from a spherical, featureless egg cell
• Broken symmetry problem (convection)
• "Chemical Basis of Morphogenesis" - reversal of thermodynamics
• Catalysis - presence of chemical is autocataytic, inhibitive, or both
• B(inhibitor) must diffuse more quickly than A(catalyst), but not universal
• Runaway production of A = autocatalytic
• Pattern created is stable (even tho its not at 'equilibrium') - dynamic process
• As long as continual 'source' of new chemicals (catalysts) is present
• As long as there is a 'sink' where end-products are removed

• Belousov - concoted solution which continuously changes colors (confirmed Turing)
• 2nd law of thermo suggests that solution should eventually settle into even distribution
• Lotka (1910) - created formula for this type of chemical oscillation
• Bray (1921) - showed chemical reaction based on Lotka, using iodine + oxygen
• Volterra (1930's) - described changes in fish population as prey + predator numbers oscillate
• They all contradicted 2nd law of thermodynamics - results not well-received
• Zhabotinsky - reproduced Belousov reaction (BZ Reaction)
• By changing rate of chemical inputs + removal of waste products, one can create changes in the number of 'stable' state (chaos)
• "How Leopards Get Its Spots" - James Murray
• Animal skin development follows Turing Model (melanin)
• Small effects produce big changes
• Happens at embryo stage
• Development in embryo stage is tantamont to development
• Even w/ identical DNA