RE: What is infinity and does it exist?
Your monkey on a typewriter analogy reminds me of the junkyard tornado as it relates to the teleological argument for God, of whole I believe is the only one which possesses infinity being eternal in nature. I don't believe such applies to the universe as it seems problematic considering entropy (unless you believe the universe to be an open system of which I would ask how you arrived at that conclusion.)
I do concur that granted an infinite amount of time certainly every permutation of characters would be cycled; therefore, our simian Shakespeare may have produced every known work of literature even the Holy Bible ONLY if it were if the keystrokes exhausted every conceivable combination.
The problem is what if the monkey instead of typing a diversity of characters and combinations instead opted to just type "Ooh ooh ah ah!" for all eternity. My doubt is in the nature of literature possessing intelligibility just as genetic information. If the process by which the monkey types results in every combination of character, I believe it is possible. The process must traverse every possible combination. Likewise, I don't believe a junkyard tornado would produce a Boeing 747 as I would not think there would be enough diversity in the process. Look forward to other thoughts. I noted the comment above had a similar objection albeit framed differenty (and probably more concisely).
The main point is that if there is a probability greater than zero of something happening, it must happen, in an infinite universe, even if the probability is inconceivably small. This is why the teleological argument for God is not valid. Something as complex as the eye or brain must evolve, in an infinite universe. Unimaginable periods of time are involved as well as inconceivably small probabilities. Besides, it seems obvious to me that the observational data is miraculous and doesn't conflict with the theory of intelligent design, despite how some people (scientists and theologians) may interpret it.
As for the monkey only ever typing "Ooh u ah AHH!" If the probability is greater than zero, it must happen, in an infinite universe.
Thanks for the thoughtful comment.
Sorry, I forgot to mention. I believe there exists one additional requirement for information that possesses intelligibility and that is a mind. Under my construct, that mind is the Divine Mind. I will add that I am not an evidentiary apologist and I will explain why and hope you will consider the propositions thereof.
I believe that man knows intuitively that there are things that exist in reality that require a Creator if you will as we see His "invisible attributes" in the wonder that is universe. I am glad that we agree that there is some type of intelligence behind the data and also the expression of dissent of interpretations of data that preclude that possibility.
I will say this when we consider in using natural evidences and observation as a "proof" for God's existence or otherwise, I believe we are subject a kind of divine determinism that predisposes us to arriving at starkly different conclusions regarding God's existence. Why is this so? I believe the reason is theological in nature ultimately.
The Scriptures speak of God decreeing a "strong delusion" to be sent to those that believe not in the gospel of Christ's death being imputed as the sole righteousness. I believe He has caused (through deterministic causality with a metaphysical/supernatural component as well) to believe/trust/intellectually assent in the gospel to include the mechanism by which one is converted.(predestination).
We can kind of think of this as akin to a program with various function. God has set x number of programs to be assigned the function BelieveTheGospelOfGrace() to these programs at the moment all requisite propositions exist in the mind of the one being converted. God invokes the function and the source code is encrypted with Christ's righteous death (Romans 6- baptized in His death). In IT, there is a thing called a CRC check (cyclic redundancy check) which essentially verifies the integrity of the data using a hash value. In the end, our program will be inspected. Those without the appropriate hash value will be discarded. Those with the hash value will inherit immortality not because of their source but because of the encryption/hash value God provided. This may be tangential to your OP but wanted you to know where I was coming from and peradventure God will add the "function" to your code as well as I believe He has mine.
You have a very interesting perspective. To be clear, I never actually said that I believe in intelligent design, only that the scientific data doesn't conflict with the theory.
I think many scientists would disagree that "man knows intuitively that there are things that exist in reality that require a Creator if you will as we see His 'invisible attributes' in the wonder that is universe." Of course, their disagreement doesn't mean you are wrong. This is where the argument of random mutation over billions of years would come up. However, once again an interpretation is involved of what randomness is. While I am willing to entertain the possibility that random mutations and natural selection doesn't require an active intelligence, I wonder about the source of it all. Again, to be clear, I am not a believer.
I like your analogy with computer programs.