By the way, I also plan to migrate the content from this site to the new one.

Although I was planning on giving more analogies, I think I'll just cut to the chase: I believe our entire universe is simply an evolutionary process defined by a few simple rules. I cannot tell you exactly what these rules are (in fact, I think that it is impossible to do so), but I have a feeling that this might not matter. If we built a computer simulation based upon rules that had the same "themes" (for lack of a better word), then we would observe another evolutionary process similar to our own. In short, we could construct another "universe", but the rules dictating this universe would not need to be anything at all like our own (example: the universe might lack any notion of geometry).

I believe that there are an unlimited number of "rule sets" that can produce an evolutionary process like our universe. However, I also believe that any "universe" governed by these rules must pass through the following stages (note: it might be possible to "bootstrap" a universe so that it bypasses one or more stages):

0. The Null Universe:
In this stage, all of the rules are in place governing the objects of the universe, but there are no objects. For us, this would be like having a universe that is completely devoid of physical particles and energy.

1. Atoms and The Creation of Simple Machines:
An uncountable number of "atoms" are injected into the null universe. The rules governing the universe cause the "atoms" to begin interacting with one another in a simple cause-and-effect manner. Transient structures, or "molecules", begin to appear as a result of these interactions. In many ways, these "molecules" are just like the simple atoms except that their behaviors are more intricate. In an abstract sense, these "atoms" and "molecules" are really nothing more than very simple machines.

2. Survival Techniques
Probabilistically speaking, we are much more likely to see smaller, simpler molecules than large, complex molecules. The reason for this is due to the recursive nature of molecular composition: a complex molecule always consists of a number of simpler components. For example, the automobile did not appear instantaneously: we first had to invent wheels, axles, gears, the internal-combustion engine, and the radiator (to name a few things). Likewise, a larger molecule does not arise instantly: it must be build progressively by recombining simpler molecules.

Let's suppose we have a universe with 4 types of atoms: A, B, C, and D. Furthermore, let's say that these atoms like to "connect" to one another to form linear chains. How likely would it be to find each of the following chains in our universe:

i) A
ii) AB
iii) AABABBAAABAACCCBCCDDCDCBDCACDBDADCBBDCADCBBBBCBADBCDADDCACDCCADCABDBDBCB

As long as atoms can exist in isolation (which may not be true in a given universe), the first chain is almost guaranteed to occur. Likewise, the second chain has a fairly high probability of occurrence. The last chain is much less likely to appear. Assuming that I counted correctly, there is a 1 in 4^72 chance that this chain would appear completely randomly (actually, the probability is really even lower than that since I was not accounting for a termination state). For those of you who aren't great at math, let's just say you'd be more likely to win the lottery, get struck by lightning, and become the president in the same day.

Fortunately for these molecules, their occurrence isn't entirely random. Every molecule is a state machine that interacts with the environment around it (ie, other molecules and atoms). A molecular structure can promote its existence at an arbitrary time t by using any of the following techniques:

a) Stability:
If a molecular structure happens to be nigh invulnerable, then it will be highly unlikely to disappear once it occurs. This is (probably) the simplest way to ensure a molecule's existence at any time.

b) Environmental Anticipation
Even if a molecule isn't invulnerable, it can at least be "smart" about what it does. If a molecule exhibits behaviors that steer it away from destructive forces, then it will be more likely to exist for longer periods of time. This means that we will be more likely to observe instances of the molecule at arbitrary times in the universe's evolution.

c) Productive Processes
So far, both of the techniques I mentioned promoted the existence of only a single molecular structure. A molecular structure is even more likely to occur if there exists a process that generates instances of the molecule. For example, a molecule might generate copies of itself as it moves through its environment. In other situations, there might exist external processes that generate a structure. Cars don't reproduce on their own, you know!

d) Resource Collection
This really does not directly promote the existence of a structure. If a molecule participates in a production process, then it would be useful if its natural behaviors encourage the gathering of necessary resources for the production.

As I already mentioned, it is incredibly unlikely for a complex molecular structure to occur unless it exhibits one or more of these specialized behaviors. This implies that as the universe ages, the complex molecules that DO exist will be very likely to exhibit one of more of these behaviors. In other words, the occurrence of such behaviors is actually PROBABLE for a sufficiently aged universe.

I'm going to wrap this entry up here for now. I really didn't expect things to get this long, and I don't think I'm even half way done! In my next entry, I'll discuss the complexity of internal and external behaviors, which should lead into a theory of intelligent processes. At some point, I'll follow that up with a discussion of emergent languages, and my predictions of the future stages of a universe's evolution.

My class's description ended there, but I knew the pattern had already progressed well beyond this stage. Humans began to group into tribes and clans. As time passed, these expanded to become small villages. Humans living within the villages began to specialize their trades to suit the needs of the village (in other words, the village began to compartmentalize in the same way that cells did). Roads of communication began to open between villages, and soon the villages were transformed into the components of larger countries. Needless to say, this progression did not stop here. Today, we have hundreds (thousands?) of countries with veins of rapid transportation and communication running in every direction. Humans are not the most evolved living creature on Earth, nor have they been for the last several thousand years. Cities, countries, and higher-order structures have been forming neural networks of consciousness right before our eyes.

I say neural networks of consciousness for a reason. Even at the atomic level, it is evident that there is a communication pattern. Atoms typically fluctuate between high and low energy states depending upon the conditions of the environment around them. On one hand, this could be seen as a completely chaotic system because so little can be said about the state of an atom over a long period of time. On the other hand, a large number of factors are in fact predetermined. For instance, atoms of similar structures tend to be clustered together (for example: people find deposits of copper and other metals. Sure, other compounds are mixed in, but the density of copper is relatively high compared to the other compounds). These properties place some constraints on how the energy can be transferred between adjacent atoms.

Still, nothing has even been said about the fact that atoms tend to cluster into common molecular structures. At this point, the transfer of energy is no longer the only form of communication. The physical structure and characteristics of the group now seem to contain some form of "information energy" that is reminiscent of a memory or perhaps a promise of functionality. In other words, the molecule is no longer the victim of simple cause-and-effect relations. Placing the molecule in the correct environment can trigger a predetermined chain of events (not just a single communication transfer!) that is much like a recipe for a particular procedure.

I have much more to say on this topic, but it's getting late and I need to go to work in the morning. I'll try to add more tomorrow.

Anyway, I wanted to talk about the curriculum here at Case Western a little bit. In particular, I'm becoming more and more disappointed with the computer science program here as time goes on. Many of the students here fail to realize that there is a difference between computer science and software engineering. Software engineering is about building solutions to problems that may arise in industry. A software engineer really is not concerned with how the tools they use are implemented or what is really going on under the hood; rather, they are interested in how the tools used to develop a user application.

In contrast, a computer scientist really is not concerned with the development of a single application. The closest computer science should come to application development is in the design of flexible libraries (which in turn are used by software engineers). A they should focus on the mathematical theory of computation and not "quickly patching an application so it can get out of the door by the deadline." Thus, a computer scientist does not care about creating a solution; he or she only cares about creating the optimal solution to a problem, or at least a novel solution that is an improvement over the current methods. Furthermore, a real computer scientist should understand what a computer is really capable of doing. Any good computer scientist understands that the order in which operations are performed has a huge impact on the accuracy (numerical stability, conditioning, etc). Once again, it is not just a question of whether or not the job "gets done;" it is a matter of whether or not the result is as accurate as it can be.

Many of the faculty here at Case realize that this difference exists between computer science and software engineering. Many of them try to teach computer science, but it is difficult to teach it to a classroom of people who are expecting to be taught software engineering. I've had a number of classes (databases, operating systems, etc) where the instructor began the semester trying to teach computer science. However, once the entire class (with the exception of a few math majors) failed the first exam, the curriculum noticeably changed to a "here's how to get the job done" mentality. Thanks, but I already know how to get the job done. I came here to learn how to push a computer to its limit and, theoretically, how to push it beyond the limit.

A couple of minutes later, I pulled into my driveway and shut off the car. What was that song they were playing as I was leaving the party? As I fumbled for my house keys, I tried to think of a few lyrics that I could google to grab a title. Once inside my house, I walked to the computer and opened DC++ to begin searching for the mystery song that was stuck inside my head.

A light passed down the street in front of my house. The police right drove past a robbery in progress.

There are 3 operations in Euclidean construction:
1. Drawing a line between two points
2. Given the points A and B, drawing a circle centered at A with a radius extending to B.
3. Drawing the points of intersection between lines and circles.

Although these operations seem general enough to allow you to build any polygonal figure, one can prove mathematically that there exist certain figures that cannot be constructed. An example of this is a 7-sided polygon.

If one extends the rules, then certain constructions become trivial. For example, there exists no method to trisect arbitrary angles; however, as soon as one allows for distances to be measured, the construction becomes possible.

Here's where the philosophy part enters in. Suppose there is an omnipotent being named Bob with the ability to do anything. You tell this being to construct a 7-sided figure using only the rules of Euclidean construction. After a cloud of magic, Bob hands you the figure and poofs off into a wisp of smoke.

But wait a minute. You have already proven that it is impossible to construct a 7-sided figure in a finite number of steps. This leaves 3 possibilities:
1. Bob used some method that you didn't think of
2. Bob cheated
3. Bob works really really (infinitely) fast

Well, case 1 is already out of the question. The proof of nonconstructibility is an existance proof that demonstrates that no possible method exists. Case 3 is a possibility, although it somehow seems that performing an infinite number of steps in a finite amount of time is cheating. Thus, it only leaves case 2.

Uh oh. Something just went wrong. It appears that a set of 3 simple rules has suddenly become more powerful than an omnipotent being. At least, that was my first thought. After a while, though, I was able to reconcile what I observed with what I wanted to believe. I mean, an omnipotent being would be able to perform an infinite number of moves in a finite number of time, so case 3 really wasn't a contradiction. Besides, I've already shown that the construction becomes possible as soon as you add additional rules. Maybe these rules were just a meaningless curiousity, much like the statement "This statement is false".

Unfortunately, I soon thought of another example that I could not repair. Imagine that you have a rod with 5 flexible henges in it:

------*------*------*------*------*------

You want to bend this rod at the hinges to shape it into a tetrahedron (ie, the shape where every side is a triangle). After fiddling with it for a little while, you start to start to look around online for the solution.

In fact, the problem is impossible, and there are several ways to prove it. The most convincing argument, however, is probably the fact that you can iterate through every possible arrangements of the rod until you have exhausted all possibilities. In every case, you will be left with at least 1 segment of the rod that cannot reach its necessary location.

Now suppose you ask Bob to perform this task. He hands you a tetrahedron and again vanishes. This time, you're not convinced though. Any idiot could break the rod apart and glue it into a tetrahedron; you want to see how he actually did it.

But in this case, it is impossible for Bob to show you. Every possible solution terminates after a finite set of moves, so he cannot pull the whole "infinite-move" trick.

So which is more powerful? God, or the rules that God imposes?