“Then, too, although what I know is infinite, it is also true that what there is to know is infinite, and how can I be sure that both infinities are equal? The infinity of potential knowledge may be infinitely greater than the infinity of my actual knowledge. Here is a simple example: If I knew every one of the even integers, I would know an infinite number of items, and yet I would still not know a single odd integer.”
Murray said, “But the odd integers can be derived. If you divide every even integer in the entire infinite series by two, you will get another infinite series which will contain within it the infinite series of odd integers.”
The Voice said, “You have the idea. I am pleased. It will be your task to find other such ways, far more difficult ones, from the known to the not-yet-known. You have your memories. You will remember all the data you have ever collected or learned, or that you have or will deduce from that data. If necessary, you will be allowed to learn what additional data you will consider relevant to the problems you set yourself.”
Current mood: Thoughtful
Remainings of the above text, can be found
here
