Known Unknowns 201 Rule 1: If] have no glyph in front of a symbol I can assume there is an invisible Y there. Rule 2: If I have a positive letter (or a letter with no symbol in front of it) I can put a F in front of it and put it on the other side of the > Rule 3: I can swap the ¥ and symbols of all the symbols in my equation if I do it to all of them. The proof in symbols > & is the same as ¥ VY > ¥ &. (rule 1) Y Y > & is the same as AS > BY (rule 2 twice) B&> AY is the same as 8 > Y (rule 3) Any collection of symbols will do. The symbols have no meaning in themselves other than the meaning we have given them. A tribe in the Amazon jungle could demonstrate a proof without knowing any mathematics. All I need say is, “Hey, I want to play a game with you. Can anyone make this into that, in the fewest possible steps, while obeying these rules?” But, is it true we can ignore the meaning behind the symbols. Does it matter that we were talking of numbers rather than spears, counters, or crocodiles? If we look at the marathon winning analogy again, we know the nature of a game is important. In a running race we can interpret holding hands to mean the two athletes are treated as one, the existing rules can then be applied as normal and the pair become a single winner. But, in tennis, there would be a problem. I wouldn't want to come on court and find I’m playing against two opponents! On consideration though Id be happy if they had to hold hands while they played so that they constituted a single player. When we examine the actual circumstances, we can add a rule and show the rule works, but we have to see something about the specific sport that makes the rule fair and workable. Hilbert was convinced mathematical truth is not like this and that proofs follow from the rulebook without any knowledge of the circumstances, i.e., the sport being played or any other analogous thing. He was to be proven wrong by Kurt Godel. HOUSE_OVERSIGHT_015891