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Wittgenstein on (Chess)-Rule following...
Anyone familiar with Wittgensteins arguements about rule following? Or, more specifically, the Kipkean version of them? Crudely put, Kripke makes an argument that the Sceptic could always argue that I don't follow the rule of addition at all when I solve the mathematical problem 57+46 but another rule alltogether. Namely, the rule of caddition, that states: "for every number lower than 60, use the rule of addition when cadding them, but for numbers higher than 60, use the rule of multiplication".
It would make no difference whether I follow the addition rule or the caddition rule when figuring out what the correct result of 57+46 is, since neither number is higher than 60.
And, the Sceptic is pointing out with a big smile, you can't object by saying that you _learned_ how to add in your early years, you _know_ how adding works. Because he will reply: "No, you didn't learn to add, you learned to cadd! You just didn't know! When you learned to cadd, you simply never got to numbers >60, so you just didn't realize!"
The sceptic gist of this kind of argument is simply, that rules "fluctuate", no rule is as fixed as we always would like it to be. Because, we can always hold, that we, in fact, never followed our rule, but instead the "crule", the rule that holds for all the past applications of our rule, but states some new condition for some specific future applications.
Anyway... I was reminded of this after I played a blitz game on the ICC against a computer. I timed out on him in an K+R vs K+N ending. I had the rook and the final result was draw, because he, having only a knight didn't have enough mating material.
I got curious and looked at the fide rules, and indeed: If you flag, you loose, unless your opponent has no means to mate you, even by the most cooperative play by your opponent. It explicitely does NOT say "in theoretically drawn positions".
But what if you flag having just reached the following position (no repetition yet): wt Ka1, bl pawn on a3, K on b3. The position is a dead draw as the king can't be driven out of the corner, but black does have enough material to be able to deliver mate (with white doing his utmost to help). Also, I suspect one can set up a helpmate with a knight against a rook?
So, is that in fact lost then???
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Given the wording...
..."unless the opponent has no means to mate you, even by the most cooperative play by your opponent", then, yes, the time out by K+R against K+N is lost. Let's set up a simple helpmate position: WKa1, WRh8, BKa3, BNb5, white to play: 1.Rh1 Nd4. 2.Rb1 Nc2#.
Some of the most misleading observations about chess involve what we learn about the powers of the pieces. Given the right conditions, for example, any piece can deliver mate unaided. Recall "Philidor's Legacy" in which the Knight delivers a smothered mate unaided. It isn't always easy to adjudicate whether a given set of conditions constitutes a draw, or, however hypothetically, a win...
However, reverting to the K+R vs K+N example, is it possible to set up a position in which mate can be forced? I pretty sure there isn't one. Ought the wording be amended accordingly to consider cooperative play short of allowing mate-in-one? No doubt you will have spotted already the fishhooks in this one!
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From the FIDE Handbook: "6.10 Except where Articles 5.1 or one of the Articles 5.2 (a), (b) and (c) apply, if a player does not complete the prescribed number of moves in the allotted time, the game is lost by the player. However, the game is drawn, if the position is such that the opponent cannot checkmate the player`s king by any possible series of legal moves, even with the most unskilled counterplay."
Article 5.1 and 5.2 deal with draw by 50-move rule etc.
So what does "most unskilled counterplay" mean :o))
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... The rule you are using is the rule you think you are using. In summing 57 and 46, one generally is using (and thinks is using) the rule of addition, even though the rule of caddition will yield the same answer. Indeed, suppose one were to visit a universe in which the rule of caddition were standard, and the rule of addition were unknown (and cWittgenstein hadn't been born yet). Then, faced with summing each pair of the series (10x+7) + (10[x-1]+6), for x=1,...,9, say, our traveller would use the rule of addition that he has been taught, until he was told that his method was incorrect once one of the numbers has exceeded 60. At no time was our traveller cadding without knowing it.
Your pal the Sceptic might genuinely be cadding as he says, but I'm sceptical...
But there is another kind of rule following that can be fun to shake up, because sometimes a good deal hinges upon one's response to the question.
What is the next number in the series, 0,1,2,3,4...? Most people would say 5, following the most obvious looking 'rule'. Suppose I say that it is 106 (or 0, or pi, or -47, or 3i+8)? I'd be marked wrong, probably with some derisive comments thrown in. But I'm merely following a rule that involves substituting for x in a polynomial of the form ax^5 + bx^4 +cx^3 +dx^2 + ex. To find what the coefficients, a to e are, is a simple (though tedious) matter of simultaneous equations [The usually accepted 'rule' is indeed a fairly trivial case: Coefficients a to d are zero, e=1].
Sorry - couldn't resist - but the thinking involved is (I think) relevant to my earlier response, and to alberlie's endgame question. Here's one to vex you! It is known that K+2N can not force a win against a lone K. But we can set up a helpmate position (bearing in mind the 'cooperative play' gag): WKf1, BKh3, BNe5, BNf5, White to play: 1.Kg1 Nf3+ 2.Kh1 Ng3# So if Black's time is short, White can play on in a theoretical draw, avoiding the corners, knowing that he is the only one with genuine winning chances!! Truly chess is an astonishing game...
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...sounds pretty arbitrary to me. I've seen some spectacular suicide mates by beginning players, so the 'hiding in the corner' method displayed in the 2-Knight ending in my last post is not at all implausible. So the possible clue in 'counterplay', implying attempted resistance at least, doesn't seem to supply an answer.
On the other hand, it doesn't really imply cooperation either (though the final effect can be remarkably similar!). About 20 tears ago I lost on time (against a future IM) in a position in which I had Q,B and 4P vs 2P. Both enemy pawns were blocked by mine, and isolated at that. Given time, I would have had actively to assist my opponent in order to lose that game: in this particular game, it would have been no easy matter to free up the pawns to advance! This goes beyond, in my view, merely 'unskilled counterplay', but genuinely cooperative, not to say suicidal, play.
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Kasparov was the "victim" of such a situation as you describe, when he took an IQ test years ago where after some of his "errors" were published. (not sure but think he was about 170 btw). One he missed was a number sequence of the type you demonstrate, but in an invalid format. (I found that many numbers could be plugged in to be 'next' [simply using algebra aor various groupings.] Even as you are suggesting.) Usually on such tests, each number will bear a relationship to those preceding it, especially that which it immediately follows. But in this case, their "correct" answer had to group the numbers into pairs. EG 1&2, 3&4, 5& ? ....
And all the first of the paired #'s bore a relationship to each other, and all the 2nd of the pairs related to each other, but not to the first half of its own pair ... if I recall correctly. (It has been over 15 years). Obviously if one is allowed to split and group at will, you can put in pretty much anything and come up with a justification. It was not a kosher question. Which leads me to wonder if it was not a standardized test, but maybe some kind of short take home deal.
Anyway, just an F.Y.I. there. Hope it's at least 47.23% accurate after all this time!? :)
Another matter of rules comes to mind. In one FIDE tmt there was a dispute among some GM's. And Player 1 got a ruling against player #2, but it was very unpopular with a lot of the players. Which brought up the matter of player #3 later making a claim vs player #1 in their game, and uttering the immortal words
* * * * * * *
... 'He wants to live by the Rules, let him die by the Rules!'
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
Or something close to that. Now it is bothering me trying to think who was involved. I believe it may have been GM R. Huebner who was player #3. Probably in the 1980's. Does anyone know better who the involved players were? In any case, It was a spicy little tournament, it seems!
I may bring up some more in the talent vs bread thread.
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I'm pretty sure that "the opponent cannot checkmate the player`s king by any possible series of legal moves, even with the most unskilled counterplay" includes suicidal moves. You would have to agree that someone moving randomly is giving unskilled counterplay. And so if one series of legal moves against this random mover leads to mate, then you can't claim a draw.
Think about it this way: if you play moves that help your opponent, that would be unskilled.
In your situation, knowing that there isn't enough time to win (unless there was a possible mating sequence that you didn't have time for), I'd sac my queen and bishop for his pawns if possible. As long as he has only a king, there's no way for him to win, so it'd be a draw.
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...quite right, as I hoped to convey when remarking on beginners' play. I recall a past opponent in a R+4P vs B+5P ending, his K in check from my rook, walked into a mate in 2, when his only available alternative gave him plenty to play for. So a 'no progress' rule must allow for cooperative play by the opponent.
As for your allusion to my game, you are right there, too, but the fact was that I finally achieved a material plus - the fruits of a long-sustained attack and a plausible but dire slip by my opponent - with less than a minute remaining on the clock to play the remainder of my game. It was just not enough to clear out the remaining material, and the position was such that a quick mate didn't seem to be on the cards.
Has anyone spotted my mistake in my 14:26 post? Don't you hate it when an idea sneaks into your mind without your noticing, until you realise you've said something dumb? Of course White can't win the WK vs BK, BN, BN ending. But he can lose it if he times out! So it is in Black's interest to play on (for 50 moves, of course), since can not lose the game, but can win it on a timeout!
An interesting puzzle [1&2, 3&4, 5&...] Depending on how the question was worded, I know I would waste time in an IQ test trying to choose between 6 and 8. They look equally likely for mine (leaving aside the infinity of other possibilities). Rules are based on experience of consistent patterns. It's an inductive process. There isn't enough here to establish a consistent pattern because we are dealing with pairs of numbers, not the numbers as individuals. So 6 or 8 or any other number would be a guess... I guess...
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Sorry about that. The actual numbers were different. I was just using 1 to denote the first number, 2 denotes the second number, etc. There answer turned out to be a three or four digit numeral i think. But I have no idea what the preceding were.
But I know you see what I mean there.
Even with that bad example using those numbers, one might say also that the first of pair relation ship is # Plus Two. And say the second of pair numbers relationship to each other is also Plus Two. Or could be # Squared instead. Or # Times Two. Or ... perhaps not ad infinitum. But close enough !
A bogus question. That's why I find it hard to believe it was Standardized.
(Tho I dont think Kasparov's outcome would necessarily have been terribly inaccurate. They say Fischer was 180. Who really knows, when such supposedly confidential results are bandied about. But both do seem within possiblity to me. I dont believe such extreme numbers of generalized intellegence are prerequisite to GM level play tho. To my mind, training, memory, concentration and perhaps a certain creativity are much more important to that end !?)
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The FIDE Rule . . .
. . . assumes worst-possible play. Hence, only K vs. K or K + N vs. K, K + B vs. K, and K + B vs. K + SAME SQUARE B and the like are technically "insufficient mating material." Therefore, when playing under those rules in such cases as R vs. N, you should force or claim your draw BEFORE your flag falls (for example, by sacrificing your R). HOWEVER, the rules for sudden death play ("quick play") allow one to make a claim for a draw on the basis that the position cannot be won "by normal means" when under 2 minutes on the clock. Again, though you must make the claim BEFORE the flag falls. Many federations (e.g. USCF) have similar provisions for such "insufficient losing chances" positions for sudden death time controls.
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This is proving to be fun!
...Craig, you have put your finger on the problem with IQ tests. Here's one I ran across many aeons ago: Which is the odd one out: (a) courage, (b) leave, (c) measles, (d) steamer? For the purposes of measuring anything, this question is also bogus - meaningless.
I rather like the 'insufficient losing chances' notion despite its somewhat arbitrary nature. On that ground, I might have claimed the draw with a reasonable expectation of its being granted, provided I lodged the claim before the flag fell. I presume that the draw could still be granted if the flag did fall whilst the claim was under consideration?
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The clock is stopped . . .
. . . while the claim is considered. Per FIDE, the arbiter can also have the game continue while observing and the arbiter may then intervene at ANY time (including after the flag falls for either player) to declare the game drawn. My preference as an arbiter and player is the option given in the US of putting a game with a UNCERTAIN claim (not the R vs. N if the ROOK player makes a claim or the Q-up game where the QUEEN player makes a claim--those claims should obviously be granted) on a 5 second time delay clock and see whether it IS a simple draw for the player (e.g. keeping the opposition in K + P vs. K when the player with the P keeps moving the K around hoping for a flag fall before 3 time rep or stalemate).