2. What is the game?
3. The game is to define the rules of the game.
4. Mathematicians play the game by proposing new rules.
5. The goal of the game is to have your rule registered in the rulebook.
6. A rule is registered in the rulebook when, after lengthy plays (negotiations), a consensus is reached.
7. The ultimate goal is to have your new rule registered under your own name but you have to be an exceptional player for this to happen.
8. In addition to the rules of the game, mathematicians also play the game of defining boundaries and limits.
9. One important limit is the limit of analysis.
10. Analysis is the process of asking a series of questions.
11. But each answer creates new questions, so analysis is infinitely deep.
12. Mathematicians put a stop to the analytical questions by defining an artificial boundary; they then accept this defined boundary as the true boundary.
13. Mathematicians can accept a boundary they defined as the true boundary because they are players; in order to be a player you must accept to play by the rules.
14. For instance, there is an accepted limit on how much a mathematician can query the meaning of the word "infinity"; they must stop at the current limit set by Cantor.
15. Until Cantor's redefinition of infinity, mathematicians did not question its traditional definition.
16. Now, Cantor's definition is the new semantic bottom of infinity.
17. But in the future a new Cantor will reveal that the semantic bottom had not been reached yet.
18. Another example of conventional nature of mathematical boundaries: the boundaries of geometry set by Euclid were believed to be true boundaries until the 19th century when mathematicians realized that Euclid’s boundaries were conventional only; after this realizations mathematicians were able to define new geometries that were not bound by Euclid's definitions.
19. Mathematics has a characteristic mental construct that does not exist outside of the mathematical playground: the foolproof, absolute mathematical proof.
20. This type of absolute proof exists only in mathematics because mathematics is a game, that is, a closed system with its own rules and boundaries.
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The 5 characteristics of game according to Johan Huizinga [my comments in brackets]:
1. Play is free.
[Mathematics is free. Anyone can play mathematics without spending any money.]
2. Play is not “ordinary” or “real” life.
[Mathematics is not “ordinary” or “real life” because mathematics is a mental construct.
3. Play is distinct from “ordinary” life both as locally and duration.
[Mathematics is outside of space and time.]
4. Play creates order. Play demands order absolute and supreme.
[Mathematics creates order. This is the reason for the “unreasonable effectiveness of mathematics” in describing natural phenomena. Mathematical defines the chaotic world around us as orderly which brings meaning.
5. Play is connected with no material interest and no profit can be gained from it.
[Mathematics is connected with no material interest and no profit can be gained from it. Mathematicians consider the uselessness of mathematics its most important virtue.]
Notlar:
--- Johan Huizinga's Homo Ludens.
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