On Tuesday, March 3, 2020 at 5:11:18 AM UTC-6, Bruno Marchal wrote: > > > On 2 Mar 2020, at 15:30, Philip Thrift <[email protected] <javascript:>> > wrote: > > > > On Monday, March 2, 2020 at 6:38:29 AM UTC-6, Bruno Marchal wrote: >> >> >> On 1 Mar 2020, at 19:11, Philip Thrift <[email protected]> wrote: >> >> >> In a stack-based language (e.g like a FORTH variant) world >> >> 2 + 2 >> >> results in 2 on top of the stack. >> >> push 2 >> push + (top of stack is combined with what's below, which is empty) >> push 2 >> (stack is 2 2) >> >> vs 2 2 + >> (stack sequence is 2, 2 2, 4) >> >> >> So, FORTH seems to confirm what I say, apparently. It is just that FORTH >> use a different language to say the same truth. It says 2 2 + instead of 2 >> + 2. That shows the importance in distinguish the language (conventional) >> from the truth (not conventional). >> >> I did not expect less from FORTH, one of the oldest and cutest universal >> number (aka Turing universal system) :) >> >> Bruno >> >> >> > One could also have a CHESS machine for chess moves. > > Chess notation: > http://www.chesscorner.com/tutorial/basic/notation/notate.htm > > example: > > 1. f4 e5 > 2. fxe5 d6 > 3. exd6 Bxd6 > 4. g3 Qg5 > 5. Nf3 Qxg3+ > 6. hxg3 Bxg3# > > Instead of an arithmetic game with symbols from [0,1,2,...9,+,-], it's a > chess game with some additional symbols. > > > This will not do, unless you modify the game of chess, and allow an non > bounded chessboard. In that case we can conceive a set of rules of games > making that Chess-game Turing universal, and then indeed, it will give the > same theology and the same physics than arithmetic. Again, elementary > arithmetic is simpler and better known. > > > > > That's all the TRUTH there is to it. The truth of the game. > > > > If you game or formal system is Turing universal, the truth is far beyond > what you can justify in any effective (where a proof is checkable) theory. > Any theory will only see a tiny part of the “whole truth”, even when the > “whole truth” is limited to the (3p) possible games. > > Bruno > > As I think I've posted here before, Hampkins has written on infinite chess:
http://jdh.hamkins.org/tag/infinite-chess/ Abstract. I shall give a general introduction to the theory of infinite games, using infinite chess — chess played on an infinite edgeless chessboard — as a central example. Since chess, when won, is won at a finite stage of play, infinite chess is an example of what is known technically as an open game, and such games admit the theory of transfinite ordinal game values. I shall exhibit several interesting positions in infinite chess with very high transfinite game values. The precise value of the omega one of chess is an open mathematical question. This talk will include some of the latest progress, which includes a position with game value ω^4. . But whether its the rules of Hampkins chess or Peano arithmetic, they can be encoded in Agda and run on a computer. @philipthrift -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/902e1dea-9cc9-4458-8d31-054eb9dfc08a%40googlegroups.com.
