My mathematical - logical side has been reawakened by learning "Set" - a wonderful game of matching and seeing patterns.
My mind drifted to chess and how hard it is to program chess because, with the current limitations of computers, you COULD program every combination of moves or write a program to consider every combination, but it would take too long and be too large. So you have to make shortcuts and define strategies for the computer. Also, you have to give the computer an opening strategy or game plan because the probabilities of winning on the first 2 or 3 moves are all just about equal.
This same problem is encountered with language. You COULD program a computer to learn all the different combinations of words, but that would be unwieldy and you'd spend 99% of the time eliminating grammatically absurd combinations. So you have to give it a game plan or a thought to express, and then strategies, or a grammar. A thought that is expressed through words ordered and defined by a grammar is a sentence. A game plan that is executed through moves ordered by strategies is a victory.
Theoretically, we could come up with a computer that evaluates the best decision at every moment (even the opening move) that is practically infallible. Similarly, we could craft a machine that speaks perfect English given enough time.
The question is, do we find humanity in this? Are any new ideas "offered" by the computer? Just because it knows every combination, does that make it smart?
This is the heart of the field of artificial intelligence, and as I see it, intelligence. If someone can work, write or speak perfectly, does that make them intelligent?
And if the answer is no, then does that mean that someone who does NOT speak perfectly can be intelligent? It doesn't logically follow, but I nonetheless support this case.
Even defining a grammar as any word selection that results in transmission of a thought, the grammar is still boundless. There's no limit to the word choices to express a thought, and therefore there's no limit on the grammar. The intelligence is not found in the medium, it's found in the object, or the listener.
Essentially what I'm saying is that it doesn't matter if my words transmit the thought if my point gets across.
Peace
John