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Can you simply translate the problemm to time then, it first takes half a second to get there, then 1/3 then 1/4... and since numbers are infinite, why does it reach it's target?
Because you are looking at just one segment of time. Say it takes one second to travel the whole distance - you look at the first half second, it went half distance, quarter second, it's now .75, eighth of a second, .875, etc. Eventually you'll get .99999999 of a second and 99.9999999% of the distance. But you are still limiting your view to a finite amount of time, which is an erroneous limit as simple observation will tell you that time does not stop as it approaches 1 second.
You can make any assumptions you want as long as it's just a math problem, but when you want to apply it to the real world, you have to base your assumptions on real-world observations. Sure I could design a math problem where gravity accelerates you AWAY from the surface of the Earth, however that's ignoring the actual observed and measurable effect of gravity.
To put it in chess terms... in Chessmaster GM Edition you can create a personality and edit their perceived values of a piece. You can make them value Queens at 0.50 - so two Queens are worth a single pawn! With that (erroneous) assumption in place by your computer opponent you can easily beat him even at his maximum calculation ability - he will gladly sack his Queen for one of your pawns and then simply not understand how you are beating him when he seems to be up material!
In this case, our medieval experimenter was operating under an erroneous assumption and couldn't comprehend why things were not working out the way he thought they should. And good thing he was only experimenting on a tree! :)
What you mention as the question, it was a real math problem:
What is the sum of 1/ n, when n goes to infinity? And it was proved by a middle age scientist that the sum diverges (infinity) :D
I did'nt know it was a math problemm, I got the story in a physics class in secondary school, the teacher told it the way I told it.
Last edited by Claude Carrier; Sunday, 9th September, 2012, 08:48 PM.
You can make any assumptions you want as long as it's just a math problem, but when you want to apply it to the real world, you have to base your assumptions on real-world observations.
Once upon a time in the middle ages, a scientist asked himself: if I were to lauch an arrow at that tree with my bow, it would first travel half the distance, then one third, then one 4th.....1/100000000 of the distance... but since numbers are infinite, then it will never reach it's target.
So he set up the experiment, he fired an arrow at the tree and incredibly, it reached it's target.
He never managed to explain why.
Again, it is not about drawing, it is allowed! Short or long draws, it does not matter. I am all for it and the shorter the better. There is no point in playing moves just to make believe. But these draws must be agreed during the game, not before. This is in the rules and even if it was not explicitly mentionned, it would still be against basic sport ethics.
Originally posted by Pierre Denommee
The answer has clearly be shown to be YES. Both the CFC Code of Ethics and the CFC Tournaments Rules, which are more specific, forbid prearranged games of any kind.
Prearranged draws and short draws are two different issues. For a prearranged draw, the criminal intention to fix the game result before it begins has to be proven. This is really hard.
Furthermore, even if there were no written rule against fixing a game result, the preface of the Laws of Chess states that The Laws assume that arbiters have the necessary competence, sound judgement and absolute objectivity. Any arbiter with competence, sound judgement and absolute objectivity would punished a fixed game if he has sufficient proof that the game has been fixed.
I just looked through this thread. Interesting topic (I mean pre-arranged games, not math task at the end of the thread).
I should agree that pre-arranged games in any sport (not only in chess) are against basic sport ethics. And as we can see above, they are forbidden by FIDE and by CFC rules. As well as by rules of any other sports.
However, these kind of pre-arranged games (draws) happen sometimes in sports where it would be much easier to avoid them. For example, famous "Nordic" 2:2 draw between Sweden and Denmark on the soccer World Cup in the last round of the round-robin. With this draw both Nordic teams successfully moved to the play-offs and kicked out Italy (by the way, this 2:2 draw did not give Italy any chance in their last group game - they would be out even if they would win their last game 100:0). Question: was this draw pre-arranged? Perhaps, there was not enough proof of that, and the result was confirmed by FIFA. And this was in a soccer game where at list 30 people should be involved to pre-arrange the result.
So, how could you imagine preventing it in chess? If two players want to make a draw, they will do it. If both players obey the rules and basic sport ethics, they may not pre-arrange the game in advance but just make the draw agreement after move one. That's why as per my opinion there are no chances to avoid this kind of situations in chess. Even changing the rules - like using "Bulgarian" rules - will not help too much. Chess is not soccer and not hockey where you can schedule the shutouts after the game to avoid a draw. There is no way to do it in chess in Swiss or round robin tournaments.
From the other side, I would like Jean and other respected chess players to answer, how would you act in this kind of situation? Let's say you need half a point in the last round to win the tournament, you are playing weaker player, and you are sure that he/she will accept a short draw if you would offer it. So, been an exemplary chess player, you should not contact your opponent before the game, and then immediately offer a draw after move one? Will this comply with the FIDE rules and basic chess ethics? Or the draw should be offered only after move 8? Or move 10? Or move 15?
Frankly, I do not see any difference. Unfortunately, rules are not working if you cannot enforce them...
Why would you ask someone to disclose potentially private information here?
You are obviously poorly educated in the scholarly sense (no understanding of grade 10 probability) and in the social sense. I hope you're banned soon.
There are some who believe that Zeno's paradox demonstrates that material substance does not, and cannot exist, and that therefore only mind or thinking substance exists, and that space therefore is ideal rather than real, that motion is an illusion and so forth. But much of the commentary in this thread would lead me to question the existence of thinking substance in the first place. :)
When neither player wants to win (risk losing), I would rather they didn't play. The rules could reasonably be changed to allow players to agree to a draw at the outset. This would be against the current culture, but there's no fundamental reason not to make it the rule.
It effectively happens anyway when the players choose to play a dull game and offer a short draw. Why waste the spectators' time and the players' time with a boring and irrelevant game? Keep the rubbish out of the databases. We might as well because there is little hope of proving collusion in these cases, and it often happens without collusion.
I would suggest using 3:1:0 scoring to encourage playing, but that's not necessary in most cases.
There are some who believe that Zeno's paradox demonstrates that material substance does not, and cannot exist, and that therefore only mind or thinking substance exists, and that space therefore is ideal rather than real, that motion is an illusion and so forth. But much of the commentary in this thread would lead me to question the existence of thinking substance in the first place. :)
I shot an arrow in the air; it landed I know not where. :D:D
From the other side, I would like Jean and other respected chess players to answer, how would you act in this kind of situation? Let's say you need half a point in the last round to win the tournament, you are playing weaker player, and you are sure that he/she will accept a short draw if you would offer it. So, been an exemplary chess player, you should not contact your opponent before the game, and then immediately offer a draw after move one? Will this comply with the FIDE rules and basic chess ethics? Or the draw should be offered only after move 8? Or move 10? Or move 15?
Frankly, I do not see any difference. Unfortunately, rules are not working if you cannot enforce them...
If I'm playing a weaker player in the tourney and all I need is a draw, I'd just offer a draw on any move in the opening since there's a high possibility that regardless what opening it is (petrov, sicilian dragon, a6 b5) he'll probably just take it. I know of players who even offer a draw after being up a pawn against a stronger player. It's not hard to draw.
If I'm playing a weaker player in the tourney and all I need is a draw, I'd just offer a draw on any move in the opening since there's a high possibility that regardless what opening it is (petrov, sicilian dragon, a6 b5) he'll probably just take it. I know of players who even offer a draw after being up a pawn against a stronger player. It's not hard to draw.
Thank you, Bindi, for the fair and straightforward answer.
But in this case, what all this thread is about? That's exactly what Bator did.
Even if (just if) when meeting Roman prior to the final game he would say something like "Hi, I am going to offer you a short draw" - I don't think that it should be a big deal.
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