Tagged: Infinity

Finite and Infinite Games

A game is defined by its rules. In a finite game, the rules are designed for the purpose to have a winner, therefore to end the game. In an infinite game, the purpose is to play the game, therefore continue to play.
You know what the game is by knowing the  rules. Rules in a finite game are the terms  by which the players agree who has won. Rules are valid because the players agree to them. There is no rule that require us to obey the rules. (Saul Kripke on Wittgenstein.)
In a finite game, the players have to agree who won. Since there is a clear end, there must also be a clear beginning. The boundaries for finite games are externally defined.
Players have to play freely, or else it is not a game. Whoever must play, cannot play. This is the only commonality between finite and infinite games.
Infinite games have no boundaries: time is created within the game itself. One cannot say how long an infinite game has been played because it generates its own time.

Mathematical Infinity

“There are two approaches to mathematical infinity. It can be seen as defining limiting cases that can never be realized or as existing in some philosophical sense. These mathematical approaches parallel approaches to meaning and value that I call absolutist and evolutionary. The absolutist sees ultimate meaning as something that exists most commonly in the form of an all powerful infinite God. The evolutionary sees life and all of a creation as an ever expanding journey with no ultimate or final goal. There is only the journey. There is no destination. This video argues for an evolutionary view in our sense of meaning and values and in our mathematical understanding. There is a deep connection between the two with profound implications for the evolution of consciousness and human destiny.” (Paul Budnik)