So, a heated debate started over whether input really exists since the equals sign is a case of identity. For instance, x^2 = 16. x could either be 4 or -4, but both sides of the equation (both expressions) are really only expressing the same thing... the value: 16. One wouldn't normally think that this "x^2" has anything necessarily to do with 4 or -4 or (2+1+1) or (14-18)... but it has everything to do with the value:16. So if 16 is true, (14-18) is not necessarily true. Now, (14-18)^2 is... but this is the same as saying 16. Nor is 16 "made of 4" as it is not "made of -4". Well, if that seems obvious, it isn't so obvious when we consider what started the heated debate. We were discussing cellular automata, such as "http://www.bitstorm.org/gameoflife/" [Broken]", and I expressed an intuition I was having that in the game of life, the prior states did not exist. The states that are generated are "pure functions" of the previous state, and I argued that it is as though we are watching a math problem being solved... prior states are really just a complication of some form of output. So, theoretically (and this is true), multiple states can be skipped with better rules applied to the game, as with simplification in mathematics. Eventually this went on to talk about the nature of logic, time, equality... it was very broad, but I wanted to hear what you'd think. So, what do you think? Do you think that when I give the expression "3+2+1" I am expressing one value or multiple values?