@Elroch is usually correct. On occasion when somebody makes an accurate statement - he asserts about a somewhat different matter.
But that doesn't mean he's always off target.
Unfortunately - this could lead to situations where he rightly calls out a big error - but whoever isn't listening.
Which can happen anyway.
In math - whether the so-called 'pure' math or 'applied' math or statistical math ... whatever type of math it is - there are basics.
Foundations of mathematical processes.
Including about definitions and mathematical induction and logical assertions connected with mathematics.
One doesn't need two degrees or even one mathematics degree to both know about and grasp those basics.
But that doesn't mean the degrees Hurt. 
Point: those who don't catch on to the basics in math early on about the strictness and objectivity ...
well then everything they 'learn' afterwards or 'think they grasp' that is heavily mathematics-dependent may be distorted or continually eclipsed by the failure to catch on to the basics early.
Such situations are often insidious.
It would be like studying electricity having failed to catch on years previously to what amps and volts and watts are.
Something 'on the hard drive'.
The irony is that somebody with far less knowledge and experience may actually understand better.
They haven't made the mistakes yet and might never do so.
So they therefore cannot 'build on those mistakes'.
Chess will never be solved, here's why
Optimissed labels, so that weak and strong are not considered on a spectrum 
...
Weak solution = solved for one starting point
Strong solution = solved from any starting point
1) Inferences from weak solutions ... bad idea mathematically.
2) Depending - relying - premising ... on 'weak' solutions - also 'getting worse'.
3) Poorly-defined weak solutions - or total failure of definition -
further compounding the errors of 1) and 2).
But does this all mean 'weak solution' is always useless and irrelevant ?
No.
Plus - comparing 'weak solution' with what players actually do to make progress in the game - one might find more connections there than with 'strong solution'.
Players 'strongly solve' K+Q against K and K+R against K.
Some take some time to 'strongly solve' most K+P versus K.
Mostly done early in their chess development.
But for the most part - chess development and activity is 'weakly solve'.
Or only 'strongly solve' within short sequences or 'islands' within each 'ocean' of the game or type of position concerned.
"You may imagine Elroch tends to be right. That may be but it doesn't apply to things he doesn't understand."
But so often or most of the time - the converse.
Its that 'other' that doesn't understand - but thinks he does.
@Elroch often calls out some big mistakes. But whoever doesn't listen.
Its 'unfortunate'. But goes with the territory of forums like this.
Its similiar with @MARattigan and @btickler and @haiaku .
They're almost always right.
But that doesn't mean whoever is paying attention properly.
"Somebody" has been complaining for almost the entire forum that its 'getting nowhere'.
But almost always - instead mistakes are being exposed.
Whether mistakes within the subject matter or other kinds of mistakes.
Those mistakes are not to be blamed on @Elroch but rather - on whoever fails to take responsibility for his mistakes with or without blaming them on others. Apparently there are only two persons consistently doing so.
... Since the authorities who seem to be omniscient fail to mention a semi-strong process, they are in error. ...
And since the self appointed authority who does mention it doesn't define it, he's talking gibberish.
[snip]
The checkers proof consisted of solving 19 three-move openings, leading to a determination of the starting position’s value: a draw. Although there are roughly 300 three-move openings, over 100 are duplicates (move transpositions). The rest can be proven [not have been proven] to be irrelevant by an Alpha Beta search.
[snip]
This point may have been missed earlier. I continue to assert there is a genuine weak solution of checkers. It permits (game-theoretic) optimal play as black or white.
IMHO, there is only one possible interpretation of "can be proven" there - that they have been proven. It's just a matter of showing that the knowledge that arises about positions for the 19 openings imply the results for the others by showing there is always a transposition to some position dealt with in the 19 openings available. (So you never actually need the tablebase to solve all the other openings).
If the proofs were not available, such a claim would be outrageous - believing that there is a proof would have no more substance than guessing that checkers is a draw.
Gradually circling around back to 'cabal'. Accusing the forum.
Have seen the cycle before. 'shouldn't forget' something that is invalid in the first place. Pattern of unfounded premises.
Which can get even worse in things mathematical.
Usually - it means I don't read those posts.
But occasionally make an exception.
The point is that if the definition doesn't exist, a term is meaningless.
Emphasis seems necessary.
Correct. Especially in math - but in other contexts too.
But at least two people aren't catching on.
They probably won't.
But we'll continue to hear to the effect of 'better than all of you' from both of them.
I mentioned that you're the most able but that doesn't mean I think I could learn much from you. You're just as unfocussed as the rest, because you shouldn't need me to define it *again*. Indeed, if you could think for yourself, you wouldn't need it to be defined at all, because you'd be able to work it out. There's a reason it's a clique.
I don't see how there's any notion of a clique between people that don't interact outside of public thread posts, really.
That would imply a pre-existing relationship, but the common focal points for this theoretical clique historically would seem to be Tygxc and yourself, or more accurately, the ummm...steadfast and closely-held ideas you both post month in and month out. Maybe you have something in common...but I wouldn't call you two a partnership .
[snip]
The checkers proof consisted of solving 19 three-move openings, leading to a determination of the starting position’s value: a draw. Although there are roughly 300 three-move openings, over 100 are duplicates (move transpositions). The rest can be proven [not have been proven] to be irrelevant by an Alpha Beta search.
[snip]
This point may have been missed earlier. I continue to assert there is a genuine weak solution of checkers. It permits (game-theoretic) optimal play as black or white.
You could be right. Do you know which version of checkers has been weakly solved?
IMHO, there is only one possible interpretation of "can be proven" there - that they have been proven. It's just a matter of showing that the knowledge that arises about positions for the 19 openings imply the results for the others by showing there is always a transposition to some position dealt with in the 19 openings available. (So you never actually need the tablebase to solve all the other openings).
OK, but my point was that the first quote seems to suggest that applied to only about 100 of 300 openings.
If the proofs were not available, such a claim would be outrageous - believing that there is a proof would have no more substance than guessing that checkers is a draw.
I believe that in matches one of the 19 openings is preset. If so, an algorithm for drawing from each of those positions would be a weak solution of that game. It comes back to which game of checkers has been solved.
But having spent about a quarter of my working life debugging system problems I probably have a somewhat jaundiced view of the probability of a decades long computerised project involving vast amounts of data producing exact results at the end anyway.
Some op is sure to drop a crate of beer onto one of your tape cartridges at some point and sweep it silently into the bin.
With tablebases, for a given objective, it is, in principle, possible to produce completely independent versions - different people, languages, systems and check for a complete match at the end. With a weak solution two totally independent solutions may match nowhere at all, even if they're both correct, so verification would be a major problem.
For me to be convinced, I'd really like to see more details of the steps taken to eliminate errors than just "This site can't be reached".
"With a weak solution two totally independent solutions may match nowhere at all, even if they're both correct, so verification would be a major problem."
Which would happen to some extent anyway - with weak solutions.
Since strong solutions are only widely available up to 7 pieces onboard -
and it seems to be much agreed in the forum that chess isn't going to be 'strongly solved' in the foreseeable future - if ever -
the forum has been mostly about 'weak solutions'.
Candidate general definition of 'weak solution':
Any solution that isn't a strong one.
But that leaves a lot of range.
And many differing possible definitions of particular 'weak solutions'.
Different parties will want their 'weak solution' and its particular definition.
And to push it. As we've been seeing here.
I mentioned that you're the most able but that doesn't mean I think I could learn much from you. You're just as unfocussed as the rest, because you shouldn't need me to define it *again*. Indeed, if you could think for yourself, you wouldn't need it to be defined at all, because you'd be able to work it out. There's a reason it's a clique.
I don't see how there's any notion of a clique between people that don't interact outside of public thread posts, really.
That would imply a pre-existing relationship, but the common focal points for this theoretical clique historically would seem to be Tygxc and yourself, or more accurately, the ummm...steadfast and closely-held ideas you both post month in and month out. Maybe you have something in common...but I wouldn't call you two a partnership .
They Definitely have something in common. Intensely.
'Better than all of you' coming from each of them.
(while so far from the case)
From one of them - the 'better than' is asserted periodically.
But from the other - an intense instance of Explicitly.
"I am pretty sure I know more about mathematics than any of you, including the man with the 2 degrees."
Immortal. Definitive. The Keeper. From page 108 here. Currently post #2150. Could be framed and Enshrined. Including without the '2 degrees part.' Has far-reaching implications.
Others have been pointing out his crass mistakes -
but he just keeps repeating them ...
revealing not just ineptitude - but Deficiency.
He would appear to be much younger than the 'other' though.
Is it tragic in a way ? There's a word ... 'pathos' I think it is.
Another word is 'poignant'.
Young. So much time ahead of him.
How could he have possibly got this way ?
The answer might lie in the effects of the internet.
And how some of those born into it might be extra vulnerable.
Ironic and Hilarious that the other one attacks him?
Some kind of jealousy perhaps.
Regarding the right to talk back to such persons -
we're to have a "The Emperor has no clothes" situation ?
I don't think so.
Fortunately - the website doesn't seem to be run that way.
[snip]
The checkers proof consisted of solving 19 three-move openings, leading to a determination of the starting position’s value: a draw. Although there are roughly 300 three-move openings, over 100 are duplicates (move transpositions). The rest can be proven [not have been proven] to be irrelevant by an Alpha Beta search.
[snip]
This point may have been missed earlier. I continue to assert there is a genuine weak solution of checkers. It permits (game-theoretic) optimal play as black or white.
IMHO, there is only one possible interpretation of "can be proven" there - that they have been proven. It's just a matter of showing that the knowledge that arises about positions for the 19 openings imply the results for the others by showing there is always a transposition to some position dealt with in the 19 openings available. (So you never actually need the tablebase to solve all the other openings).
If the proofs were not available, such a claim would be outrageous - believing that there is a proof would have no more substance than guessing that checkers is a draw.
Relationship of 'can be proven' to 'has been proven'
looks solid.
With 'has not been proven' also factored.
Chess has not been solved.
So there is no proof that it can be.
Is that the same as 'could be' ? No.
The number of possible chess positions is finite.
So its argued that chess could be solved. Hypothetically.
But 'can be' is different. Because its also not proven that there will be the resources and the needed time to get that job done.
Like - millions of years of time! Or trillions of years.
Anybody impartially looking at this thread would have a laugh. Not knowing each other socially is irrelevant. People form groups, even online. Whatever differences you have between each other, you all close ranks when you're faced with explanations you refuse to even try to understand. I'm not suggesting there's an ability to understand though. Basically no-one can think for themselves and everyone needs the support of the rest of the group.
Anyhow, all the best to you all. Every so often I've tried to explain my conception of how this can be resolved. It isn't from lack of trying on my part. Must be something you lack. Goodnight.
There's a much simpler explanation for what you are rationalizing here.
#2245
"I don't see how there's any notion of a clique between people that don't interact outside of public thread posts, really. That would imply a pre-existing relationship, but the common focal points for this theoretical clique historically would seem to be Tygxc and yourself, or more accurately, the ummm...steadfast and closely-held ideas you both post month in and month out."
MARatingen 860
Btickler 1559
Haiaku 1667
Playerafar 1709
Elroch 1779
Optimissed 1890
Tygxc 2044
What could that relationship be?
#2249
"He would appear to be much younger than the 'other' though."
Thank you for this compliment. You made my day.
#2245
"I don't see how there's any notion of a clique between people that don't interact outside of public thread posts, really. That would imply a pre-existing relationship, but the common focal points for this theoretical clique historically would seem to be Tygxc and yourself, or more accurately, the ummm...steadfast and closely-held ideas you both post month in and month out."
MARatingen 860
Btickler 1559
Haiaku 1667
Playerafar 1709
Elroch 1779
Optimissed 1890
Tygxc 2044
What could that relationship be?
I guess you forgot that Pfren, BlueEmu, and Llama...all of whom are rated significantly higher than you, also refuted your premise here and on other threads, so that "relationship" is not valid. See...this is why you can't seem to get where you want to go...selective myopia.
You are also using rapid ratings of human beings, and pretending they should have some meaningful impact on understanding how chess can be solved by engines or some future technology. They do not. There's a reason that AlphaZero, Deep Blue, etc. were created by developers who also happened to play chess, and not by GMs who happen to know how to write software. One set of skills is far more useful than the other in this arena. Your rating gives you not one ounce more credibility than you have ever had here, which is not much. Much the same way that you don't ask your horse how to win the Kentucky Derby.
I think you mean that the paper says checkers has not been strongly solved. Strategies for optimal play from the opening position are complete. This only meant about 10^14 calculations (so certainly not the full 10^20 positions). The 10 piece endgame tablebase for the solution has 39 trillion positions, which is between 10^13 and 10^14 positions.
I was referring to the comments:
(a)
The fact that the game wasn’t solved for every possible position and then tucked away in a database doesn’t seem to bother him. ”Well, the checkers players would love it, because [then] you’ve got this oracle that can tell them everything—answer every single unanswered question in the game of checkers,” he says. ”But first of all, I don’t have the patience to do it. And second of all, I don’t have the technology to do it.” Even with the best data-compression techniques, Schaeffer says, the amount of storage required to solve all possible positions of checkers would exceed even the capacity of the world’s biggest supercomputers with tens of petabytes (1015) of storage by an order of magnitude. That puts it—at the earliest—at least a decade away.
This refers to a strong solution - "all possible positions".
Yes it does.
The question remains - is there a database for the weak solution of the positions he analysed or did he bin the actual moves for that?
He seems to have been interested mainly in an ultra weak solution witness:
Even if an error has crept into the calculations, it likely does not change the final result. Assume a position that is 40 ply away from the start is incorrect. The probability that this erroneous result can propagate up 40 ply and change the value for the game of checkers is vanishingly small
from https://www.researchgate.net/publication/231216842_Checkers_Is_Solved
If he doesn't count an error as changing the solution unless it changes the value of the game, that implies the intention is an ultra weak solution.
The paper also says:
The computer proof is online at www.cs.ualberta.ca/~chinook
so I could try that, but what I get is first:
then when I click on "checkers solution"
Not designed to inspire confidence. Can you locate said database or details of the proof?
So for me the question remains open. There are a fair number of things I would want to clarify.
The first would be what game exactly do they claim to have solved?
When I look up "checkers rules" online, I get two flavours corresponding to the basic rules game of chess and the competition rules game of chess. The first is unlimited; the second has a 40 move rule and a 3-fold repetition rule.
There is no mention of which version is solved in either the above link or the link https://webdocs.cs.ualberta.ca/~jonathan/publications/ai_publications/checksolved.pdf posted by @tygxc earlier.
and
(b)
Schaeffer’s proof solved checkers for 19 different openings, all of which end in draws. There are 300 total tournament openings, but many of these were determined to either be mirrors of other positions or altogether irrelevant to the proof because they lead to positions common to other openings.
Both mirrors and transpositions are fine - they are dealt with.
or from https://www.researchgate.net/publication/231216842_Checkers_Is_Solved
The checkers proof consisted of solving 19 three-move openings, leading to a determination of the starting position’s value: a draw. Although there are roughly 300 three-move openings, over 100 are duplicates (move transpositions). The rest can be proven [not have been proven] to be irrelevant by an Alpha Beta search.
So that's it: a complete opening strategy leading to the the tablebase - i.e. a weak solution.
That would be it if any of his 19 3-move openings had turned out to be a win, but they didn't.
Therefore he has to consider all the rest of the 300.
I have no problem with discounting mirrors and transpositions but:
The quotes:
Although there are roughly 300 three-move openings, over 100 are duplicates (move transpositions). The rest can be proven to be irrelevant by an Alpha-Beta search. (https://www.researchgate.net/publication/231216842_Checkers_Is_Solved)
and
Schaeffer’s proof solved checkers for 19 different openings, all of which end in draws. There are 300 total tournament openings, but many of these were determined to either be mirrors of other positions or altogether irrelevant to the proof because they lead to positions common to other openings. (https://webdocs.cs.ualberta.ca/~jonathan/publications/ai_publications/checksolved.pdf)
suggest that 180 openings have yet to be analysed. Note the phrase, " can be proven", rather than, "have been proven" in the first quote - and no mention of how an Alpha-Beta search would lead to a proof (the process is not normally reliable).
For the moment I remain unconvinced.