Contradictions in games?
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From: Robert Kaufman on 2 Aug 2010 06:58 Hi, It just occurred to me, that the whole business of a multivalued function collapsing to a single valued function after a choice doesn't sound like mathematics. In fact, it sounds more like quantum mechanics. One of my questions in this thread was exactly what's the difference between mathematics and games. They obviously share many features, but one thing mathematics does not share is the similarity of games to quantum physics. Are there other differences? Respectfully, Robert Kaufman
From: I.N. Galidakis on 2 Aug 2010 11:36 Robert Kaufman wrote: > Hi, > > It just occurred to me, that the whole business of a multivalued > function collapsing to a single valued function after a choice > doesn't sound like mathematics. In fact, it sounds more like > quantum mechanics. What you have in mind is not quite a "multivalued" function. It is an unordered list which gets a complete order via the Position-Evaluation function. The list consists of all possible (legal) moves in a given position and the PE function in every case picks the list element which maximizes the positional value. It is possible (for a poorly designed engine's PE function) to give the same value for two different elements of this list, in which case the corresponding PE function would indeed be "multivalued", but usually the resolution of good engines is such that different moves will always generate different numbers, therefore the maximum will be unique. > One of my questions in this thread was > exactly what's the difference between mathematics and games. Mathematics is a modelling language. A game is usually an algorithm which may or may not make use of some (or other) modelling language. [snip] > Respectfully, > > Robert Kaufman -- I.
From: Tim Little on 2 Aug 2010 21:45 On 2010-08-02, Robert Kaufman <Yearachmeel(a)verizon.net> wrote: > Thanks for your reply. Your example involving pawns was clear to me, > but how do you show that even in a game between inexperienced or > inattentive players two kings cannot check each other? If you mean players sufficiently inattentive to realise they are breaking the rules of chess, of course they can check each other. Next they might capture the king, keep playing, take a piece off the board for not jumping, and yell "king me!" when a pawn reaches the last rank. - Tim
From: Tim Little on 2 Aug 2010 22:00 On 2010-08-02, Ilmari Karonen <usenet2(a)vyznev.invalid> wrote: > Obviously, a move which, say, added a dozen kings to the table would > be guaranteed to raise eyebrows; but it would still be a possible > move, just not one allowed by the rules.) Obviously it is forbidden by the current official rules of chess, but I remember noting that the version one local school chess club used specified that a pawn may be promoted to any piece whatsoever. Consequently I had entertained the notion of promoting my pawn to a king of the opposite colour in checkmate. - Tim
From: Gerry Myerson on 3 Aug 2010 00:08
In article <87pqy2a03i.fsf(a)dialatheia.truth.invalid>, Aatu Koskensilta <aatu.koskensilta(a)uta.fi> wrote: > Robert Kaufman <Yearachmeel(a)verizon.net> writes: > > > I guess what all these replies have brought out is that there is a > > vast difference between mathematics and chess,but exactly what is the > > difference? > > What's the difference between mathematics and water polo? Mathematics minus water polo. Next? -- Gerry Myerson (gerry(a)maths.mq.edi.ai) (i -> u for email) |