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"I get it. You don't want us cycling between a ladder and a chute for eternity."

"Ack! It's 'forever', not 'eternity'! Get it right! You know how much that annoys me when you mix those up."

"Sorry. Uh, I forgot. What is the difference between forever and eternity again?"

"Look, I told you a dozen times! Forever is in principle algorithmic. Eternity isn't."

"Oh yeah.. I forget what that means.."

"Keiichi, I already explained this. I swear, the high altitude must be making you stupid or something. Okay, let's go over it again. Forever is in principle algorithmic. It means that there exists, at least in theory, some kind of generating function or description for it. For example, you can express the set of factorials of all non-negative integers like this, written in the functional computer language Haskell:

fac 0 = 1
fac n = n * fac (n - 1)

"The set of factorials is infinite, but there exists a well-formed algorithm that describes how to generate them. A more complex example is the set of prime numbers. For example, here is a function to generate an arbitrarily long list of prime numbers, also written in Haskell:

primesTo m = 2 : sieve [2..]
where
sieve (p:xs) = p : sieve [x | x - xs, rem x p /= 0]

"Now, there is no easy way to predict whether any given really big number happens to be in this set. In fact, it is the hardness of the factorization of large numbers that is the foundation for the computer encryption algorithms that you find on the World Wide Web [SSL and TLS]. When you purchase something from Amazon with your credit card, or when you transfer money from your Fidelity bank account, your computer is actually using the factorization of a large number into two large primes to encrypt your account information.

"So now let us move up to a more abstract level. Let's define the set S of all Haskell programs that return the answer '1'. Here is the question: Is there a generating function for S that can be described using Haskell itself? In other words, can you write an algorithm written in Haskell, like the ones shown above, that will generate the set of all such Haskell programs?

"The answer is no. In the lingo of computability theory, it is undecidable. According to Gödel you could say that the Haskell programming language is 'incomplete', in the sense that it cannot express all expressible truth statements (members of S) within that logical system. So it is 'imperfect' in that sense. Yeah, I know this is easily provable using the Halting Problem, but bear with me here. The point is, any such sufficiently complex system that can be described using finite symbology is by necessity either incomplete or inconsistent. That is a direct consequence of Gödel's Incompleteness Theorem: That no such logical system can be both completely consistent (internally perfect) and can find and prove all its truth statements within that system (is complete). Such a system cannot possibly exist."

Keiichi said, "In other words, it is flawed."

"Yeah. Now let us move up to a really ambitious logical system. Remember when I described to you the Standard Model of particle physics, the so-called 'Theory of Everything'? The TOE?"

"Uh, yeah.."

"If you recall, the Standard Model describes the dynamical behavior of the fundamental particles of the physical universe within a quantum mechanical system whose gauge symmetry can be expressed as a function of the Lagrangian, L."

"In other words, it's a model. A system."

"Yes. And so in principle it can be generated algorithmically, although as a practical matter that's actually infeasible."

"Okay."

"So now, here is the big question: Is this model perfect? In the Gödelian sense?"

"It's a finite description, so no, it is not."

"Correct. So could you conclude that, in that sense, that the design of the physical universe is flawed?"

"Sure. In the sense that the quantum states are based on the operation of that finite TOE model. Okay, fine. But I still don't see what you are driving at."

"Don't you see, Keiichi? One of the big arguments against the existence of God is that His creation is flawed. God is perfect, the argument goes, but his creation is imperfect. Creation is messed up. And so atheists claim that this apparent contradiction refutes the existence of perfect God."

"Ah, I see. But we just established that a perfect creation is impossible to create."

"Bingo! Yay! I love it when you get clever." She playfully approached him to tousle his hair, but he jumped back before she could do it.

"Hey, don't muss up my hair! You know I hate that."

"Feh, like your hair can get any more mussed up than it already is. You never comb it."

"Just don't touch it. Anyway, I think I get what you are saying."

"The point is, God's creation is flawed by necessity. It is not His fault, it just is. By logical necessity. It is intrinsically flawed due to its nature of being described by finite rules."

"Got it."

"Now let's get really ambitious. God is perfect. So tell me, Keiichi, how would you describe God then?"

"You can't."

"And why not?"

"Uhm.."

"Before you answer, think carefully about the little thought experiment that we just did."

Keiichi thought hard. "Hmm.. the nature of God cannot be described by any finite logical system."

"Hooray! You got it! You win a kewpie doll! This is what we mean when we say God is eternal."

"In other words, God is literally indescribable."

"Correct. When we call something 'eternal', what we mean is that it cannot be described in finite symbols. Now you are ready to understand the distinction between 'forever' and 'eternal'. An entity that is eternal is something that cannot be conceived using finite terms. This is why Gödel cannot capture God within his nasty logic trap. Because to capture Him that way Gödel needs to first come up with a symbol that fully describes Him, and there isn't one.

"Is that why Jews are so reluctant speak God's name aloud?"

"I like to think so. You see, in a certain sense one can argue that God has no name. For he literally cannot be named by any symbol. More specifically, His conception cannot be labeled or captured in any finite set of symbols that fully describes Him."

Keiichi said, "I am rather amazed that I actually understood that."

"Heh, good boy. I admit these are rather deep concepts, but I think they are important."

"Is that what we are approaching as we climb up?"

"Yeah, I think so. I have a sneaking suspicion that the place where Big Sis dwells is actually eternal."

"Wow.."

[ Excerpt from After Ragnarok, Chapter 37. ]