# Introduction to Non-Genetic Darwinism/Complexity Theory

 Development status: this resource is experimental in nature.
 Type classification: this is a lesson resource.

## Complexity Theory

Although Complexity Theory is usually an advanced topic in computer science, recently it has become important to understand just why things are organized the way they are. As such it impinges on Physics, and may change the way we look at self-organization.

## AIMS

1. To introduce the idea of complexity as a way of storing energy
2. To introduce A New Kind of Science, and the Class 4 Automata
3. To introduce the idea of emergence as precipitation of order
4. To link emergence with the Energy/Entropy Balance
5. To show how Darwinism is just a special case of emergence
6. To promote the idea that other forms of emergence often echo Darwinism

### The Energy Theory of Complexity

Einstein stated the basic law of conversion of mass into energy as E=MC2 What this means is that matter is a special form of energy. The Energy theory of Complexity takes things one step further, and says that all forms of complexity are really just forms of energy that are protected from entropic reduction by the high dimensionality of space.

When energy is high enough, it is chaotic, but as Entropy increases, energy is drained away and some of it gets caught in the dimensional structure of space precipitating out into forms of order. As energy continues to drain, the energy needed to maintain a particular structure of space, sometimes gets drained away, and releases the energy that was stored in that spatial structure back into the environment increasing the local energy levels temporarily, and reducing the order to smaller more stable energy/spatial structures. Thus the same level of Entropy at different levels of energy can either form new order, or reduce order to simpler structures.

When energy is increased in a system, first the energy causes larger structures to form, and then it makes the space more chaotic as the energy/entropy balance increases. If energy keeps increasing, Entropy begins increasing to compensate, and order begins to precipitate out again.

When energy is decreased in a system, first the energy flows away from spatial structures, weakening them until they break apart into smaller spatial structures, releasing energy, which if released in enough quantity makes the system more chaotic, until entropy again begins to precipitate out order at a smaller spatial structure.

### A New Kind of Science

Without getting too deep into his "Principle of Computational Equivalency" Stephen Wolfram's book, [1]A New Kind of Scienceoffers insights that are especially interesting to this discussion, In that it mentions Cellular Automata experiments of Class 4 complexity, that indicate that order and chaos might alternate in an incremental system.

#### Cellular Automata and the Discovery of Oscillating Order/Chaos systems

The idea that Order and Chaos alternate in an incremental system, flies in the face of our understanding of Entropy as a breaking down of complexity, and fits our energy/entropy balance model. However, to counter our reluctance to accept this concept, we must notice that the order of our universe is strangely inconsistent, and that the second law on which we base our understanding of Entropy, is limited to systems that start and stop at an equilibrium state, and doesn't adequately describe the state where energy is being increased or decreased within the system. If we can accept that assertion, then we need to look no closer than to our periodic table to see that order is not always consistent.

You would think that the atomic weight of an atom would go up in regular increments, but as you get further and further into the periodic table, the increments get further and further apart, and the order seems to break down into large gaps where elements that were once predicted, were not found. Some of this can be explained by radioactive decay but in some cases the gaps are there simply because the elements were never created. Perhaps order is not as simple as we would like to think.

If order is not as simple as we would like to think, then perhaps Entropy is not as simple as we would like to think especially in that area where we assume that the natural cooling effect of entropy is to break things down into simpler components. In fact, Cellular automata that have a decremental input pattern also have a tendency to break up into alternating order and chaos patterns. The fact that you can generate order in a system that is cooling, seems counter intuitive with our former understanding of entropy.

### The Big Bounce

Perhaps what we are seeing in the larger universe, is not only evidence for a Universe that is older than we thought, but evidence of an oscillating system within the Universe where periods of chaos alternate with periods of order, where the entropy state when it increases does not always result in breakdown into simpler elements, but sometimes results in the precipitation of order out of chaos. It might not be exactly the big bounce that the current Quantum Gravity scientists are working on, but it might be something a little less universal where elements are formed by the energies involved, and then recombine into molecules as a result of entropy, before they cool enough to break up again into smaller components.

#### Cyclical Entropy

One possible interpretation is that the reason for this oscillation in the precipitation of order, has to do with the local energy/entropy balance. In this interpretation it is thought that energy perturbs the system making it more dynamic, and Entropy cools the system making it more ordered. The idea is that the oscillation we observe has to do with the Entropy/Energy balance. At first when energy is added to a system it becomes more dynamic and may break up into chaos. However, as it cools, the energy entropy balance shifts slightly towards entropy, and order begins to precipitate out of the chaos. As cooling continues, the entropy rate increases again, increasing the rate of precipitation out of chaos, and order grows. Then when cooling reaches a certain level, it begins to overcome the energy, and break down the system into smaller elements, which in turn release energy into the system, causing the system to break down into dynamism again and become more chaotic. On the other side of the coin, when a system is incremental instead of decremental, we see a gradual increase in energy over time, and Entropy cooling just results in a sort of stair stepped curve called a power curve, where cooling balances energy input for a while, and thus the energy/entropy balance remains the same, then when energy increases enough there is chaos while the energy creates more dynamism until entropy catches up and causes the curve to plateau out again.

What is important is that as the Universe gets larger, the amount of entropy available increases which increases the amount of energy that is needed to overcome it, and so the expansion of the Universe is part of the reason for the power curve existing. In this interpretation the precipitation of order is a result of the Energy/Entropy balance, not Entropy alone, and so the reason why Entropy as a breaking down of order doesn't make sense is because we are misattributing the effects of the Energy/Entropy balance to Entropy alone.

#### The Power Curve and the precipitation of order

If this theory is correct, then we would expect the power curve to have longer and longer plateaus as the amount of entropy increases, and it takes more and more energy to create the dynamism that causes the next band of chaos to form. Further we would expect that our universe would be made up of elements that had atomic or molecular weights that fell further and further apart on the periodic table, and that we would have aggregation of galaxies that is more prevalent than was originally thought.

There is one major problem with this theory, and that is that it flies in the face of the first law of thermodynamics that energy can be neither created nor destroyed. If energy can't be created, where is all this energy needed to create the new plateaus on the power curve coming from?

#### Conservation of Order in an Incremental System

If the energy theory of complexity is correct, then in an incremental system, smaller structures will form first, and energy will combine those structures until it gets high enough to become chaotic. After a while Entropy will begin to catch up with energy again, and larger structures will form. The Energy/Entropy balance will result in a power curve where precipitation of order happens at gradually increasing energy levels, and as a result the complexity of the elements the system is made up of will increase, but earlier forms of complexity will be conserved as long as they did not break down into smaller components

#### Conservation of Order in a Decrementing System

As the Energy/Entropy balance shifts closer to the Entropic side, either through entropic cooling, or through energy flow from one system to another, The most energetic states tend to be more sensitive to further cooling. This seems related to the force that drives energy flow from one place to another. The higher the voltage of a wire, the more insulation is needed to keep the electricity from arcing over to another wire of lower potential. This is probably why radioactive isotopes break down faster than stable isotopes. Elements were formed in the high-energy states of the early universe, and as such, unless they are quite stable, they break down when molecules made of the same elements wont. This is probably because the molecule is already more entropic than the element itself.

## Evolution, as the emergence of order in an incremental Biological system

I once joked, that I exist simply as an opportunity to increase the partial pressure of long-chain molecules in the Universe. If we see complexity as simply a method of cooling the Universe by sequestering energy in complex arrangements, then, perhaps a more radical interpretation is possible, Life exists, simply to sequester more energy, than is possible with normal entropic mechanisms. It is perhaps less stable than the combination of two chemicals into a molecule, but more stable than fire. If this is true, then at the heart of Evolution we might find the same mechanism as was first used to create the elements, and then the molecules on which biology is based.

#### Chemistry, how Entropy actually helps combine chemicals

It takes time for an Atomic Bond to form. When two chemicals are first mixed together, it takes longer for them to combine, than once they have started combining. Energetic systems are more uncertain at the Atomic level, than cooler systems, and the result is that the energy of the atoms banging off each other may be too great for Atomic Bonds to form. This means that while it is good to have a hot temperature when you are breaking atomic bonds and separating reagents, it is good to have a cooler temperature when you are combining them, or letting them precipitate out as crystals.

No two chemicals will combine, if the result is a higher Energy/Entropy balance. Unless the ambient temperature of the solution is high enough to contribute the extra energy. And if the Energy/Entropy balance is too low, the result will either freeze or break into smaller parts. but when the Energy/Entropy balance is correct, chemicals combine better, than at other times. As a result it is often necessary to combine chemicals at a particular temperature for best combination.

#### The Energy Death of the Universe is Running Late

The Red shift suggests the Universe is still expanding, the complexity of the Universe indicates that it has not reached anywhere near the state of Energy/Entropy balance where it becomes uniformly uninteresting, as a result, we can say, that it looks like the Energy Death of the Universe is running late. We see no evidence of it even beginning to happen other than the local effects of entropy.

### Darwinism as a description of the principle by which order emerges and is conserved

It is my contention, that Darwinism is more than just the definition of a biological and genetic tendency to form species, it is a biological and genetic example of a more basic principle, the principle of Self-Organization or Self-Ordering, and that that principle, can be seen wherever the Energy/Entropy balance approaches the balance range needed for the precipitation of order out of chaos. Life promotes an energy/entropy balance that in turn promotes the precipitation of order out of chaos, but doesn't allow the energy levels to drop low enough to promote breaking apart into smaller structures.

#### Can Darwinism be applied to systems other than biological systems?

If this last statement is true, then Undoubtedly, YES, Darwinism can be applied to other systems that are non-biological in nature. Because it is in effect a system that promotes the precipitation of order out of chaos, and as long as there is enough energy for chaos to exist, other forms of precipitation that do not involve biology will also exist.

#### The Edge of Chaos

Recently some scientists have noted that Evolution seems to promote the stabilization of systems that balance almost halfway between order and chaos. Called the Edge of Chaos, this theory suggests that there might be an equilibrium state that balances energy and entropy. If so we can assume that the equilibrium will respond to new energy by oscillating back and forth between chaotic and ordered states. Evolution might therefore merely be an expression of the power curve that follows from the existence of such an equilibrium state in an incremental universe.

Assignment:

• If the energy of the universe increases, does Entropy increase or decrease? and The Energy/Entropy balance?
• If entropy increases in the Universe and energy is constant, does the Energy/Entropy Balance increase or decrease?
• Look at the Periodic Table of Atoms if you can find one that has more than just the atomic number at the top of each element, and usually near the bottom you will find the atomic weight. Look at the intervals between weights, do they trend to take longer between each element? Are they consistent, or are there gaps? Why do you think this is?
• Consider putting two chemicals into a solution, and getting a third chemical back out, do you think that the chemicals magically combined or did they need some self-organization to combine? Is Energy/Entropy balance, a reasonable explanation?
• Now that you have heard an explanation of why non-genetic Darwinism might exist, in an energy complexity theory Universe do you think that it does exist, or not? Write an essay on this question.
• Consider the Edge of Chaos theory, and the concept of an energy/entropy equilibrium. What would the effect of that equilibrium be on the second law of thermodynamics? Would this make life an exception to the rule, or simply an extension of the rule?
1. A New Kind of Science, Stephen Wolfram, Wolfram Media, 2002 ISBN 157955088, 9781579550080

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