Thursday, August 3, 2017

Shaking marbles in a jar as a bare-bones model of evolution, A.I., and economics

"...that we give off heat is not accidental, but essential. For this is precisely the manner in which we dispose of the surplus entropy we continually produce in our physical life process. This seems to suggest that the higher temperature of the warm-blooded animal includes the advantage of enabling it to get rid of its entropy at a quicker rate, so that it can afford a more intense life process. ... [But] the parallelism between body temperature and 'intensity of life', which I believe to exist, may have to be accounted for more directly by van't Hoff’s law: the higher temperature itself speeds up the chemical reactions involved in living."      
- Erwin Schrodinger, What is Life?
Physical evolution in its simplest form is shaking a jar of randomly-packed marbles in a gravitational field. In short, cyclic energy injected into a "closed thermodynamic system" results in entropy being released to the universe as black body radiation (more low-energy photons go out than high-energy photons came in, keeping a constant internal energy balance). Since entropy is a conserved quantity, the entropy inside the container is reduced (a feature of closed thermodynamic systems but not for "isolated" systems). A reduction in entropy exhibits itself as a higher degree of order by becoming more densely packed, harder, and repeating patterns.

The physics of shaking marbles in a jar
When you randomly and slowly place marbles in a jar they will pack with about 56% fill ratio, leaving 44% space. If you shake them afterwards, starting first with hard and then softer shakes, they will pack with > 63%. The harder shakes allow for the bottom layer to form first. The softer shakes allow the higher levels to settle without upsetting the lower levels. This is what the moon has done to Earth: it was initially a lot closer and is getting further away each year. The highest theoretical packing is 75%. Random forces in shaking do not have this effect. Non-random shaking can be thought of as a "periodic" or "semi-periodic" force (or energy injection). For packing differently sized and shaped particles much higher packing can be achieved by adding heat while lowering pressure, then raise pressure as the heat drops, and then repeat, but lowering the temperature and pressure each time (see "Simulated annealing"). The heat checks particle-orientation options while the pressure that follows secures and compacts the solutions. The pressure is a force like gravity. The heat is the shaking.

Chemical bonds
The reduction in entropy in the products of life can be measured via molar aka specific entropy. There exists in chemistry potential energy gradients due to charges that causes atoms and molecules to acquire lower-entropy states due to sticking better than previous arrangements, very much like the previous sections's packing.  Again, the excess entropy is released to the universe. The cycle of seasons (surface temperature variation) caused by the collision that created the moon and the moon itself cause a shaking of the atoms and molecules that assists the discovery of the "tighter packings". A side effect of the moon and seasons is more lightning strikes, ocean vents, tides, and ore concentrations, all of which are lower-entropy events that are believed to have assisted the development of life.

Correlation between the jar and life on Earth
The Sun, moon, and Earth's rotation are the initial source of non-random energy coming into the biosphere. The "non-random" (low entropy) placement of the moon's mass away from the Earth has been crucial for life's development (Isaac Asimov once discussed this). Its effect has decreased with time as the moon has gotten further away each year. The effect of the moon is apparent to NASA's life-hunters: the most promising places seem to involve an external gravitational force periodically affecting a celestial body (usually moons close to a planet). Water is important as it helps atoms and molecules find lower-entropy arrangements as in the marbles being somewhat "fluid" in a jar.  The Sun is more important via photosynthesis these days, but  life probably initially capitalized on (or extracted?) the low entropy accident of the moon's initial placement, and axis tilt. I calculated in a previous post that today the Sun is providing 150x more energy than the yearly loss in Earth's rotational energy due to the moon, but at the beginning of life, the moon was >3x closer with >9x more gravitational effect, and the Earth was turning a lot faster. My calculation (from available data) indicated the moon provided about 20% of what the Sun was providing. This is a "mass moving" quality of energy rather than simple "heating" provided by the Sun. The combination may have been crucial: periodic heating was a "periodic shaking" at the molecular level while the "mass moving" shaking provided a larger-scale directional force to where the resulting molecules would go. There might be a parallel here with government providing a macro-scale container and forcing function to individual micro "high-energy" (thermal agitation) market transactions.

As the moon gets further away, the entropy of the Earth-moon system is increasing due to a volume increase. The Earth's rotation rate is slowing, giving some energy to the moon in order for it to get further away, but a much larger percent is used to churn the air, seas, and mantle via the moon's gravity. To what extent were an excess of ocean vents present (where the oldest known life fossils have been found) due to the moon churning the mantle? The second oldest place fossilized life has been found is in bays with ocean tidal zones, which is more obviously assisted by the moon. To what extent would our massive economic machine not have been possible if the moon had not churned the mantle enough to make more low-entropy ore concentrations possible via volcanic activity?  Most commodity production that is crucial to our economics depends massively on concentrations of things like metal ores and good soil.

DNA is a very low entropy crystal that lasts a long time, as should be expected form the thermodynamics of Earth described above. It is important to keep in mind genes have no force of their own. They are just enzymes. Only energy gradients can move them and help them to make copies. The copies are in some sense lower entropy (a "copy" is almost by definition lower entropy). Certainly DNA crystals are lower entropy than a random arrangement of those same atoms and molecules in soil and air. This requires tapping into an external source of low entropy (for a given temperature and pressure). My thesis here is that the moon and seasons have been re-injecting lower entropy and thereby made life more pervasive.

If there had not been a collision that created the moon, the Earth would have still been rotating (giving a daily cycle of temperature changes and resulting air current "forces") and water, so it's far from clear the moon was a necessary condition.

Correlation to artificial intelligence
A large part of A.I. in finding solutions to complex problems is starting with random values in neural nets, Bayesian probabilities, and genetic algorithms. The "marbles" are the neural nodes, Bayesian nodes, or genes. You typically start with random values and give the program computational energy (shaking) for the nodes or genes to request CPU time and memory (energy) while they are under a system-wide A.I. algorithmic constraint (the jar). The "shaking" has to be periodic (low entropy), not random. A good parallel in A.I. is competing against a copy of itself in games.  Non-efficient solutions will show many patterns in the node weights, probabilities, or genes. The patterns may be eliminated for condensing the node weights, probabilities, and genes into a smaller set of nodes that is more random on a per weight/probability/gene basis. This is like taking marbles out of the jar which is less entropy by a factor of roughly equal to N2/N1 (this is exact if it's a specific molar entropy) and it allows a smaller jar which is also less entropy by a factor described at the note at the bottom.

Correlation to economics
The A.I. must have some sort of direct, implied, or unnoticed limited-quantity currency that corresponds to the amount of CPU time (FLOPS) and memory that is available, if there is a limit on them. The currency is the energy being transmitted from the jar (the algorithm constraints) to each marble (the weight/probability change or gene replication). The CPU time and memory are kinetic and potential energies. The hardware itself is a potential energy. The currency quantity corresponds to computing quantity. If the hardware increases then the currency can be expanded by the algorithm (the government) to keep constant value so that nothing else in the algorithm needs to change. This is like increasing the level of shaking: the currency is the amount of energy being transferred from marble to marble from the jar. The energy comes from the governing jar or A.I via the permission granted by possession of the currency and eventually goes back to it (taxes). In my jar there is no currency I can point to except the energy itself. Although the energy coming in and size of the jar may not change, the entropy of the system gets smaller as it gets more efficient. The lower entropy means better command, control, and strength that is typically used to increase the incoming energy, the "size of the jar", and the number of "marbles". If the allowable nodes or genes are increased, then the value of the currency per node or gene decreases by that same proportion if the hardware has not improved because they will have to compete to get the same computer time and memory. So the currency quantity needs to decrease if the currency should represent the same amount of FLOPs and byte space.

In other words, for contracts to remain valid, the currency quantity should change in proportion to the energy per person that is under the system's control.

Physics note: All other things being equal, the entropy increase of the moon getting further away is S=S2-S1 where S1=a*[ln(b*V1) + c] where V is the volume of the Earth-moon system and a, b, and c are constants. There is rotational energy decrease and gravitational energy increase, but these are internal energies that do not change the kinetic energy of the system (that could have affected the entropy) because the Earth's temperature is about a constant. But those lost energies do emit a lot of entropy away from the system as waste heat. As another example important to the following: harder materials have lower entropy due to the atoms having fewer places per volume that they can occupy. Specifically, for a single harmonic oscillator (in a solid) S=k*ln(kT/hf + 1) where f is frequency of the oscillations which is higher for stronger bonds.

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