Thursday, August 3, 2017

Shaking marbles in a jar as the simplest exposition of evolution, A.I., and economics

I am not using "entropy" in this article in a vague sense. I am talking about the entropy measured by physics equations.(see note if you're interested in the physics)

Executive Summary of the Physics
Physical evolution in its simplest form is shaking a jar of randomly-packed marbles in a gravitational field. In short, complex (but not completely random) 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 ones came in...all energy transfer is a sending of photons). Since entropy is a conserved quantity, the entropy inside the container is reduced. A reduction in entropy exhibits itself as a higher degree of order by becoming more densely packed, harder, and repeating patterns. The 2nd law is not "entropy always increases" (see good physics texts such the famous Feynman lectures on thermodynamics that mention this). "Always increases" is an engineering idealization for isolated systems. There is no isolated system in the universe thanks to black body radiation. Gravitational systems are emitting entropy "so that the Universe can expand" (or alternatively "as a result of the Universe expanding"), leaving a lower-entropy state behind. (more detail: The entropy of the Universe is constant on a co-moving volume basis and reducing on a constant-volume basis. This last statement is not speculation but I do not have a good reference. It is not required for the following, but provides the deepest explanation for the origin of life that I have.)

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 shaking them afterwards, starting first with hard shakes 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. The highest theoretical packing is 75%. The shaking can't be completely random and consistent because it will continually un-pack. Non-random shaking can be thought of as a "periodic" or "semi-periodic" force (or energy injection). For packing differently sized and shaped small objects there is a more complicated way that does the same basic thing: add heat while lowering pressure, then raise pressure as the heat drops, and then repeat, but lowering the temperature and pressure each time (see wiki's "Simulated annealing"). The heat checks 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
I'm not going to hardly mention the chemical bonds that are crucial to life other than to say 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 just as in gravity. They can react to form durable bonds that releases entropy and heat to the universe, leaving behind more durable arrangement with lower entropy. Getting into specific chemical bonds can and should be done, but for this post it would be like getting into the motivations of an employee in a company when I only want to discuss company-wide profit seeking that enables the employees to exist. Similarly, when getting into employees motiviations, we do not address the chemical reactions in his brain, nor the genes and environment that led to those reactions. But this outline is trying to show how the "environment" (the Sun, Moon, and Earth via thermodynamics and cosmology) resulted in those genes based on physics as opposed to some nebulous beliefs about "evolution".

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 discusses this). Its effect decreases with time as the moon get further away each year, in keeping with the jar analogy but I do not want to stress the "decreasing" part because it is not as important as simply not being random. 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). The Sun is more important via photosynthesis these days, but I have investigated the extent to which life initially capitalized on ("extracted") the low entropy created by the moon's initial placement. 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 the "heating" quality 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. I considered the parallel this has with law guiding individual free market transactions, but have rejected it. Law will be the jar within Earth's jar.

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 be possible if the moon had not churned the mantle enough to make more ore concentrations possible via volcanic activity? That non-random placement of mass is again a physically-measurable lower state of entropy that resulted from a lowing of the Earth's rotation via the moon.

I have cast it as an low-entropy injection from the Earth-moon system's volume increasing, but most of the lower entropy is coming from balancing the black body radiation (entropy) being emitted as a result of churning/heating caused by the Sun and slowing of the Earth's rotation.

The Sun affected molecules with periodic (daily) heating to enable them to form stronger bonds, a key ingredient for life (the success of "genes" is a combination of ability to spread quickly and last a long time via the really strong bonds of DNA crystals). I will not dive into chemistry because I think that is missing the forest for the trees. It is important to keep in mind genes have no force of their own. They are just enzymes. Future genes model on past genes. Crucial to efficient packing is that the next layer of marbles are guided by the lower levels, obviously copying their arrangement. In what sense is this not like genes? Obviously the marbles do not evolve diversity, but I'm only allowing one type of object into the jar to try to see the essence of physical evolution.

I should mention the Sun and rotation combine to cause a bulk periodic movement of mass like the moon, not just heating. A side effect of this causes charge potential energy gradients that result in lightening strikes which been theorized to be crucial for life. Those strikes are like sudden large "shakes of the jar" at the molecular and atomic layers.

I discussed this in more detail earlier this year, but the above section is more efficient and has new material to show more parallels.

Correlation to artificial intelligence
A large part of A.I. in finding the solution to complex problems is starting with random values in neural nets, Bayesian probabilities, and genetic algorithms. The marbles (in our brain) are the neural nodes, Bayesian nodes, or genes (well, not genes exactly). 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) and a gravity provided by the training data to find an efficient (low entropy) solution. The solution will show many patterns in the node weights, probabilities, or genes which is the marbles' repeatinng arrangement. 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. The final result is not a repeated pattern but it is the same(?) or less total entropy. It is more entropy on a per weight/probability/gene basis in an absolute sense, but the entropy per weight/probability/gene "per this system" is the same or less. Nodes in neural and Bayesian nets might be identical in an algorithmic sense (like the jar constraint) and change only their weighting factors (placement). In genetic algorithms, the genes would repeat and/or reduce in number. So the algorithm representing the jar is the set of rules of gene interaction rather than a description of the genes. The genes vary while the marbles do not. There is only 1 type of marble. To compress the marble packing to reduce the number of marbles in the jar, but to completely describe the pattern, only a few marbles are needed. A.I. seeks to find repeating patterns of marbles and normally compress into a single pattern. Fewer marbles are better if they are smart.

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 the amount of CPU power (FLOPS) and memory space that the algorithm can use. 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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