tbickler you can please stop
the disparagement? looking at post 39902 the 2 statements are different and have different meanings.
The word "that" in the first posting and the word "where" in the 2nd posting make the 2 statements different.
tbickler you can please stop
the disparagement? looking at post 39902 the 2 statements are different and have different meanings.
The word "that" in the first posting and the word "where" in the 2nd posting make the 2 statements different.
That is not an analogy.
Oh yes it is. There is not just a single proofing method in chess, as ell as several other sciences.
Squaring the circle is fairly easy, although not possible by using just classical geometry.
No, it isn't an analogy.
If there is no proof, then you can't know if the claim 'chess is a draw' is true or false.
I think chess is a draw. But I have no proof, and neither does anyone else.
Ever heard about probabilistic arguments (which is what ponz is doing here)?
Mathematical approaches to such arguments like, say, Drake's Equation? No?
tbickler you can please stop
the disparagement? looking at post 39902 the 2 statements are different and have different meanings.
The word "that" in the first posting and the word "where" in the 2nd posting make the 2 statements different.
You're going to have to post something that makes sense if you want a cogent reply.
If an engine dominates others then by definition the other ones are weaker -.-
On another note, I never said anything about engines not being able to get stronger.
That's crap and you know it. When Stockfish and Komodo have traded off titles, it's because they found slight improvements overall that seemed to work well against the other (of course, the developers obviously test heavily against their main rivals). It usually did not allow them to particularly crush the field any more or less than other seasons. This type of incremental leapfrogging is an indicator of "elbow room" in the improvement space, but the engine that gets tweaked is not leaps and bounds better than it's previous incarnation, nor its perennial competitors.
So your counterargument is to talk about engines that did not dominate each other? *slowly claps*
That is not an analogy.
Oh yes it is. There is not just a single proofing method in chess, as ell as several other sciences.
Squaring the circle is fairly easy, although not possible by using just classical geometry.
No, it isn't an analogy.
If there is no proof, then you can't know if the claim 'chess is a draw' is true or false.
I think chess is a draw. But I have no proof, and neither does anyone else.
Ever heard about probabilistic arguments (which is what ponz is doing here)?
Mathematical approaches to such arguments like, say, Drake's Equation? No?
Oh my dear pfren, if only it was that simple. I'll remind you that even if an event A has probability 0*, it doesn't imply such event is impossible.
*No ifs and buts, it is exactly 0.
If an engine dominates others then by definition the other ones are weaker -.-
On another note, I never said anything about engines not being able to get stronger.
That's crap and you know it. When Stockfish and Komodo have traded off titles, it's because they found slight improvements overall that seemed to work well against the other (of course, the developers obviously test heavily against their main rivals). It usually did not allow them to particularly crush the field any more or less than other seasons. This type of incremental leapfrogging is an indicator of "elbow room" in the improvement space, but the engine that gets tweaked is not leaps and bounds better than it's previous incarnation, nor its perennial competitors.
So your counterargument is to talk about engines that did not dominate each other? *slowly claps*
It's not my problem if you don't understand why that means something. But other people reading will get it. Some may agree, some may not, but they will grasp the distinction.
If an engine dominates others then by definition the other ones are weaker -.-
On another note, I never said anything about engines not being able to get stronger.
That's crap and you know it. When Stockfish and Komodo have traded off titles, it's because they found slight improvements overall that seemed to work well against the other (of course, the developers obviously test heavily against their main rivals). It usually did not allow them to particularly crush the field any more or less than other seasons. This type of incremental leapfrogging is an indicator of "elbow room" in the improvement space, but the engine that gets tweaked is not leaps and bounds better than it's previous incarnation, nor its perennial competitors.
So your counterargument is to talk about engines that did not dominate each other? *slowly claps*
It's not my problem if you don't understand why that means something. But other people reading will get it. Some may agree, some may not, but they will grasp the distinction.
So it was a strawman? Good then, keep arguing about things I didn't say.
Please, please, please stop continuing this ridiculous discussion. Chess is a draw with best play. The end. Move on!
Please, please, please stop continuing this ridiculous discussion. Chess is a draw with best play. The end. Move on!
Some people have time on their hands and a need to waste it.
These forums exist for that purpose. Fly fishing, of course, is a better way to waste time.
That is not an analogy.
Oh yes it is. There is not just a single proofing method in chess, as ell as several other sciences.
Squaring the circle is fairly easy, although not possible by using just classical geometry.
No, it isn't an analogy.
If there is no proof, then you can't know if the claim 'chess is a draw' is true or false.
I think chess is a draw. But I have no proof, and neither does anyone else.
Ever heard about probabilistic arguments (which is what ponz is doing here)?
Mathematical approaches to such arguments like, say, Drake's Equation? No?
Oh my dear pfren, if only it was that simple. I'll remind you that even if an event A has probability 0*, it doesn't imply such event is impossible.
*No ifs and buts, it is exactly 0.
Probability zero doesn't imply impossibility. It directly means impossibility. However, the proviso is that the factors in play have been correctly identified and evaluated. In a complex model, of course that is unlikely. Generally, mathematics that describes the real world is a complex model.
If it means it is an impossibility (it isn't) then it implies itself, it's a tautology, it's just p <=> p
On another note, my comment was purely mathematical so you can cut the "factors" and "models" technobable there.
I've been arguing consistently that chess is logically a draw and that therefore a mathematical proof is possible. I asked my son, who's a mathematician, and he thinks that a mathematical proof is difficult and perhaps impossible at the moment. I think it's potentially possible, because mathematics will progress to complex games theory. I think I know the outline of the method that will be used. But there's no point going into it too deeply. At various points in this amazingly convoluted thread, there have been what I would think are quite ludicrous arguments; such as that a forced win for black may be a solution. It should be obvious that is logically impossible but again, I could describe why but I couldn't formally prove it.
If I took a ten-minute walk in the Sahara through a sandstorm, do you think that I could prove that my nose would come into contact with at least one grain of sand? It may seem obvious that it would but can it be proven? I doubt it. That chess is a draw ultimately can be proven, however.
...or maybe you should just listen to your son .
The sandstorm analogy is off. I guess it could apply if sandstorm particle movements were all driven by players and the particle movements followed a set of rules. But the particles hitting you could be proven by particle density/your volume. You don't have to follow each particle in that particular case. But we're not trying to prove if a chess draw can "hit" you, or how often. We're trying to prove whether 1 or more set of positions in 10^46 possible positions is a forced win, in which case chess is solved and forced draw is not the result. So, if a particle of sand *can* hit you would be the closer analogy .
So it was a strawman? Good then, keep arguing about things I didn't say.
That doesn't follow from what I said.
You cannot keep straight what you posted even a short time ago. You misinterpreted my meaning, as well. I did not not say anything in the context of humans being better with engines (far too obvious to mention), I said it in the context of engines being better with human input.