jp wrote: ↑Fri Sep 04, 2020 12:55 am
That is unquestionably the whole point of the paper. Just read the abstract!
The only possibility (which is what towforce apparently thinks now) is that the paper has a fatal mistake in it. Of course, any human proof has a non-zero probability of having an error, but no sensible punter would bet money on this one having a fatal error IMO.
It is not just Paul asserting the fatal flaw. He has brought evidence for the fatal flaw "there's actually no proof in there that in complex positions, it's impossible for rules to exist which can tell you quickly whether the game is won or not."
It should be easy to disprove his evidence with the relevant page number quote. Do you have the relevant page number? ( I should point out that the paper is beyond me)
Evidence?
Paul claims :
(1)That in order for the paper to prove its thesis it would have to show that it is impossible for rules to exist which can tell you quickly whether the game is won or not.
(2) The paper does not do that.
Without going into how likely or unlikely are the existence of such rules are Paul's claims wrong ?
duncan wrote: ↑Thu Sep 03, 2020 1:20 pmI have not been following this discussion properly but have you posted about why you believe we will very likely solve chess in the future with these new emergent patterns, if that is your claim?
I cannot give you a straight answer, so I'll answer in parts and try to keep those parts understandable:
* some chess positions (and in particular, my intuition tells me, relationships between pieces) and their evaluations will be mapped into multidimensional space
* I will use an algorithm I am building to fit a polynomial that is good in the machine learning sense (accuracy de-emphasised (hence ranges for evaluation scores rather than exact numbers), simplicity emphasised - lowest degree and smallest number of terms possible)
* hopefully, some of the positions will then be able to be discarded without lowering the standard of the resulting EF
* hopefully, the resulting EF will evaluate some positions well
* where it evaluates a position badly, new position/evaluation data will be added to strengthen it there
* repeat
IMO, there are two reasons to be hopeful:
1. my intuition tells me that the size of the polynomial will grow less quickly than the number of data rows (if the polynomial grows exponentially with extra data rows, that will be very disappointing)
2. my experience with CBR tells me that the number of data rows needed is likely to be lower than most people are expecting. In CBR, the number of cases needed to make a good system is almost always a lot lower than people expect, and my intuition tells me that there are similarities with what I am doing here
The ultimate achievement would be, to put it simply, to look at the polynomial, spot where it is converging to, and hence write an EF that evaluates all chess positions correctly. A way to go to get to that point!
Thanks for your explanation.
Are you planning to respond to Chris's Linear evaluations with tic-tac-toe, thread?
duncan wrote: ↑Fri Sep 04, 2020 11:43 am
Do you accept or not that in order for the paper to prove its thesis it would have to show that it is impossible for rules to exist which can tell you quickly whether the game is won or not?
The proof does not have to talk about the non-existence of quick rules.
Thinking it does is getting things backwards. It needs to prove the claimed result by any valid mathematical argument. If it does that, then the result proves the non-existence of quick rules.
jp wrote: ↑Fri Sep 04, 2020 2:22 pmThe proof does not have to talk about the non-existence of quick rules.
Thinking it does is getting things backwards. It needs to prove the claimed result by any valid mathematical argument. If it does that, then the result proves the non-existence of quick rules.
Not the reverse.
So where's the part of the report that proves that? Where is there even a single sentence in the report that shows ANYTHING apart from the existence of positions in which the number of moves to checkmate increases exponentially in n on an n*n board?
Given that we know of the existence of rules to determine whether there's a win in some chess positions, the report therefore does not prove that which it claims to prove.
Writing is the antidote to confusion.
It's not "how smart you are", it's "how are you smart".
Your brain doesn't work the way you want, so train it!
towforce wrote: ↑Fri Sep 04, 2020 2:52 pm
... the report therefore does not prove that which it claims to prove.
Yes, it does (or at least no one has found any error in it).
It is not claiming that there are zero easy positions. It is claiming that there exist hard positions.
So if people want to find quick rules that apply to a strict subset of all positions, they can go ahead and hope. They just should not hope that those quick rules will apply to all positions.
towforce wrote: ↑Fri Sep 04, 2020 2:52 pm
... the report therefore does not prove that which it claims to prove.
Yes, it does (or at least no one has found any error in it).
It is not claiming that there are zero easy positions. It is claiming that there exist hard positions.
So if people want to find quick rules that apply to a strict subset of all positions, they can go ahead and hope. They just should not hope that those quick rules will apply to all positions.
There are chess positions in which there are a large number of moves to the checkmate, but for which a rule can be written to determine whether the position is winning or not. That disproves the (assumed, not stated in the report) idea that there is a linear relationship between the number of moves to checkmate and the amount of processing needed to determine that the position is winning.
Writing is the antidote to confusion.
It's not "how smart you are", it's "how are you smart".
Your brain doesn't work the way you want, so train it!
syzygy wrote: ↑Fri Sep 04, 2020 11:32 pm
If would be surprising if towforce were not able to square the circle. I encourage him to take a couple of years to try.
If you don't add the restrictions of "using only compass and straightedge" it's quite easy.
However, "squaring the circle" is generally taken to be the euclidean challenge.
Too bad someone proved it impossible. I gave it a go when I was a teenager, with predictable consequences.
Taking ideas is not a vice, it is a virtue. We have another word for this. It is called learning.
But sharing ideas is an even greater virtue. We have another word for this. It is called teaching.
Taking ideas is not a vice, it is a virtue. We have another word for this. It is called learning.
But sharing ideas is an even greater virtue. We have another word for this. It is called teaching.
towforce wrote: ↑Fri Sep 04, 2020 4:42 pm
There are chess positions in which there are a large number of moves to the checkmate, but for which a rule can be written to determine whether the position is winning or not. That disproves the (assumed, not stated in the report) idea that there is a linear relationship between the number of moves to checkmate and the amount of processing needed to determine that the position is winning.
No, that is incorrect. You are misunderstanding the paper.
There is nothing in the paper related to or assuming some "linear relationship".
The paper uses a standard TCS proof technique. If you are not familiar with this technique, it might be confusing to you.
