Tuesday, March 22, 2005

I just thought of something rather interesting regarding Turing machines and God :
well, actually, I've been thinking about it for a long time, and have some interesting facts for you all regarding the Universe from a computational standpoint.

But first:

1. The question of whether or not God exists is not Turing-solvable ... i.e. we cannot truly prove or disprove God's existence from a scientific perspective. Ever.

2. Regardless, We can still conjecture certain properties of God and/or the Universe based on either of the two assumptions of God's existence.

3. In fact, I have many such conjectures; the majority of which I shall release at togehter (at a later date), and continue to add on incrementally, but not now. For now, I leave this interesting tidbit:

Read the note if you're either unsure of what a Turing Machine is, or if you believe the human brain is not a Turing Machine. Otherwise, skip down to the good stuff.

Quick note before I begin: I must aid setting the record straight: Turing Machines are NOT machines per se - they are computational models. They are just descriptions of one particular class of computational measurement, and in fact, they are at the very top of the heirarchy in regards to computational power -- the most beautiful and spectacular model of which is the human being.
In other words, to suggest a human is not a Turing Machine is actually ludicrous and self-insulting, since a Turing Machine (TM) is considered a TM if and only if it can simulate the operation of any other full TM or TM code (where the "code" is an algorithm ... what's an algorithm? A cooking recipe is a perfect example, as are directions to get from one place to another, any set of instructions, or list of daily chores, etc.)
In short, the classification of the Turing Machine in the mathematical sense is obviously broad: we sometimes lose sight of the usefulness unless we confine our related discussions to specific sub-classes. This lays the foundation for the ideas organized below. You should now at least have a basic understanding of Turing Machines. (If not, just google-search for Turing Machines)

Now we may begin:

We have two possibilites: God(and/or similar being(s)) exists, or God does not. We shall explore the ramifications of both possibilites. Let us start by assuming that the first possibility is true:

If God exists, then regardless of the fact that God's existence cannot be verified or refuted, our standard definition of God easily fits the computational model of a Turing Machine. At the same time, God would then contain an extension to the standard model that allows recognition of all possible Turing Machines. (Most likely something even more exotic than the Quantum Turing Machine) What's more, it's easily possible that God's processing scope extends far beyond that of a Turing Machine, for it's obvious that if God were a standard model, then God could not conceivably create a contradictory event such as an attempt to lift a rock that was created specifically to be unliftable by God.

But then, if God is not Turing-recognizeable as we assume from our standard description of God (since the mind of man might not be fit to understand the wisdom of God), then not only would there exist other computational models of "higher order" that encompass and extend the model of a Turing Machine, but simply by the nature of a Turing Machine, none of these models of computation could be directly/ completely understood, detected, or simulated by any normal Turing Machine, and thus they are all infathomable (!but not completely!) by mankind ! (And actually, to some extent, the topic of how much (if any) must a person know about an object before they can consider themselves able to simulate its output is arguable (yet unsolvable, once again, as-predicted)

This description of our Deity-in-question does allow such a process as parodoxical actions to occur: the reasoning here is that God and/or similar beings who also may or may not believe in/ know for sure / question the belief of God made the underlying framework of our reality. Our notions of computation and Turing Machines is based on our perceptions of the environment in which we interact. Thus, if logical structures exist beyond these perceptions, we may not be able to directly perceive them. If you feel so inclined, this can be considered a nonscientific generalization of Heisenberg's Uncertainty Principle.

More will come later.

I've already taken away too much time from my studies.

Good night.
At last ! I have found the mathematician's Amazon.com !
MAA online ! Go there !

Whew ... long time, no post. I have two midterms in two days (yes, they're a few weeks late - why don't you go and tell that to my professors? I'm sure they'll listen with open ears ;-P )

After sharing horror stories about evil past-professors (Fall registration is near), some fellow students and I derived the following academic life lesson:
"Some people should not be teachers, and some teachers should not be people" :-)