A Theory of God and Everything

I happened upon this theory while reading a book by Stephen Wolfram called A New Kind of Science.

In A New Kind of Science Wolfram describes numerous observations about something called cellular automata. He uses his observations about cellular automata to put forward a theory about order in the universe.

Cellular automata are cells represented on a computer that evolve according to some simple rule. These cells are typically represented by colored squares. An example of a cellular automaton is rule 110. In this rule, a cell can be either black or white. The color of every cell is determined by the color of the cells diagonally above to the left, directly above, and diagonally above to the right. For example, if the cell diagonally above to the left is black, the cell directly above is white, and the cell diagonally above to the right is white, then the color of the dependent cell is white.

The complete set of rules is shown here:

When rule 110 is started with one black square and all the rest white, it produces this result:

On a larger scale, it produces this result:

It can be proven that rule 110 is what is called “Turing complete”. In other words, if rule 110 were begun with the proper settings, it could be used to solve any problem that can be solved by a computer. Theoretically, this means that if rule 110 were started with the correct initial setting on a large enough board it could represent any logical structure including our entire universe. Stephen Wolfram argues that our universe could be nothing more than the implementation of a rule as simple as rule 110.

While contemplating this concept, I realized a couple of obvious problems. First of all, in order for rule 110 to run at all, it must be supported by a complicated computing device. However, there are other more subtle problems. Who or what sets the initial conditions for the rule? Also, what forces the cells to continue to follow a particular rule and not decide to switch midway and follow some other rule? On a computer, a person sets the default state for a rule and the program forces the cells to follow it; but what about the universe? What is the universe’s default state and what forces the universe to keep following the same rule?

Then, I had this epiphany. What if the universe had no default state and there was nothing to make it follow any rule? It occurred to me that this model for the “beginning” of the universe was the only default state that could stand on its own without assuming some other supporting structure.

What would happen?

I then realized there may be something that is true regardless of the existence or order of anything. The obvious candidate was the three laws of Aristotelian logic:

1. A proposition that is true is true. A proposition that is false is false.
2. A proposition that is true is not false. A proposition that is false is not true.
3. A proposition must be either true or false. (the law of the excluded middle)

The last law, the law of the excluded middle, has a surprising consequence. To say that there are no undecided propositions is equivalent to saying that every possible proposition must be decided. But if there is nothing to decide them, what happens?

In mathematics, there is something called a choice function. Many proofs depend on the existence of a choice function that is capable of choosing one element from every set. The existence of such a function is referred to as the “Axiom of Choice”. What I propose is that this function does not merely exist in the theoretical sense, but that it actually exists. Moreover, this choice function is logically equivalent to the law of the excluded middle.

If we think of all the possibilities for how the universe could be structured as the domain set of a choice function, and the actual universe as the range, then there must exist a choice function that maps the first set into the latter.

To summarize, the law of the excluded middle says that every proposition is either true or false. However this implies, in turn, that every proposition is decided. The determinacy of every proposition implies the existence of a choice function that is capable of deciding. Hence, the law of the excluded middle is equivalent to the existence of a universal choice function.

Suppose there were more than one candidate for the choice function that is capable of performing this mapping? This would demand the existence of yet another choice function that is capable of choosing between every possible candidate. However, what if there was more than one choice function capable of choosing among possible candidates? We are led into an iterative process that generates a hierarchy of possible choice functions. This hierarchy of choice functions forms a lattice for which there must be a unique maximal element. In other words, there must be a supreme function that is master of all other choice functions with no other choice function that is master of it.

What characteristics does this supreme choice function have?

Part of the domain of this function must include every possible quality that we observe in the universe. The domain may contain other qualities, but everything we observe must be included. In order to choose, the function must have some characteristic that is roughly equivalent to “preference”. Since the function is capable of choosing qualities such as intelligence and consciousness, it makes sense that the function has something that is roughly equivalent to an “understanding” of intelligence and consciousness. If the function is capable of understanding these concepts, it might also be assumed to possess them. The function is omnipotent by definition.

Of course, this is the classical definition of God. There is no point in calling the choice function anything else. Hence, the law of the excluded middle is equivalent to the classical definition of God.

It must be observed at this point that this is not a religious insight. It is merely an application of Aristotelian logic to a basic problem. The inevitable outcome, the existence of a universal choice function, is just the result of following Aristotelian logic to its conclusion. As to the naming of this choice function, calling it anything but what it obviously is would be petty.

Many modern philosophers assume that the universe is physical and that the basis of the universe must be physics. Implicit in this model is the assumption that the universe is driven by cause and effect. However, these philosophers are never able to get around an obvious problem. What is it that supports their physics? What is it that generates their rule and forces the universe to follow it?

What I propose is that the basis of the universe is not physics, but logic. The universe is not driven by cause and effect. It is driven by propositions and their implied consequences. The universe is driven by truth.

Now, as to what exactly the aforementioned choice function has chosen and how it intends to follow up on those choices is another matter. All you have to do is look around and you will have a pretty good idea what has already been implemented. However, I plan to take this idea for how the universe was constructed and incorporate it into a complete explanation of what the universe is, how it works, and where it is headed.