Reading difficulties again?
It says, "Chess will never be solved, here's why and what's @Optimissed's IQ and does he turn water into wine or the other way round and what did his family have for breakfast", does it?
Chess will never be solved, here's why
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Sep 30, 2022
0
#4363
MARattigan wrote:
Elroch wrote:
... Science, by contrast is a black box which takes in observations and generates and tests models which describe patterns in those observations. ...
Is that what Newton would be doing if by using the word "two" in the hypothetical statement I gave or would he be using mathematics?
I would say no, on the grounds that a caveman with no mathematics would understand the concept of an object and another object that was not the first object. It is a very basic structural concept, so you could be terribly pedantic and argue it is primeval mathematics. Mathematics is about the structure. So, when Newton's work involved arithmetic like addition or multiplication, he was (of course) using mathematics. More fundamentally, he did so when he said there was a scale of mass (and many other things) where quantities were associated with real numbers. The notion that there is a scale of mass and you can add masses is non-trivial use of mathematics.
This discussion brings to mind how huge a deal it was to do things like quantify physical quantities with numbers at first. We are so used to it, we forget that.
... you start with an intuitive notion of a mathematical object - eg the counting numbers - then you find some axioms that represent your intuition. ...
In the link I gave those axioms are just the logical axioms.
Principia is a work on constructing mathematics on a single foundation. Set theory and logic are typically used.
Then you are off to the races (as say Euclid was).
Only more or less if you read the Elements, but you'd hardly say it wasn't mathematics.
I didn't. I used it as a canonical example of mathematics
Not sure what you did to the format there...
llama36 wrote:
mikekalish wrote:
I always thought of science as "What humans know about the physical universe" and mathematics as the "Language we have devised to describe that knowledge". And to me, they are two very different things, even though they are closely related.
That's probably a very crude way of looking at it, and likely I'll be corrected....but go easy. I'm old.
It goes beyond that though. The fun thing about math is it could still be done even if this universe didn't exist. If nothing we know of existed, we couldn't talk about color or shape or time, etc. But all the math we know right now would still exist.
That's not the "fun" thing for me. The "fun" thing about math for me is how it describes the physical universe.
Sep 30, 2022
0
#4365
Elroch wrote:
Not sure what you did to the format there...
Don't ask me. I think the AI applied to the edit window has developed an evil consciousness of it's own.
NervesofButter wrote:
At 59 im healthier than most people i know. I am the only one i know that is not on any prescription medications. I bike ride to work. I go to the gym when i can. I have hobbies. I have a small group of friends that can tell me the truth, and we can be honest with each other. I too have grandchildren
Am I "rich" in the monetary sense? Not even close. But am I rich in things that truly matter? Absolutely.
I would not trade the aches and pains of growing older for the wisdom i have gained and where im at in life.
You're doing it right....staying active and staying connected.....and walking with "you-know-who"....that I'd probably get in trouble for mentioning here.
mikekalish wrote:
You're doing it right....staying active and staying connected.....and walking with "you-know-who"....that I'd probably get in trouble for mentioning here.
The mods have not been enforcing much of anything lately, so...
Sep 30, 2022
0
#4369
To revert to a previous topic
The co-evolution of physics and maths (Symmetry Magazine)
[couldn't have been in a better place]
I was an atheist for 50+ years, but that all changed in 2021.
Optimissed wrote:
Don't like her.
Sep 30, 2022
0
#4373
Boris is the only politician I've ever seen that has a bad hair day every day.
Sep 30, 2022
0
#4374
Optimissed wrote:
Don't like her.
Oh, I thought you meant your daughter in law. Didn't think of Liz Truss.
Back on topic after the spamming spree of the trolls.
The game-theoretic value of a game is the outcome when all participants play optimally.
Ultra-weakly solved means that the game-theoretic value of the initial position has been determined. There is massive evidence that Chess is a draw.
- Expert opinions of all World Champions.
- AlphaZero self play 97.7% draws at 1 min / move, more with more time,
even if stalemate is declared a win. - TCEC with imposed 50 slightly unbalanced openings to prevent all draws.
- Human World Championships and top tournaments.
- ICCF World Championship Finals: 136 games = 127 draws + 6 white wins + 3 black wins.
table base win claims of > 50 moves without capture or pawn move allowed but do not occur - A tempo in the initial position is worth 1/3 pawn. You cannot queen a tempo.
Weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition.
Strongly solved is being used for a game for which such a strategy has been determined for all legal positions. For Chess this means a 32-men table base with 10^44 positions.
Weakly solving Chess needs 10^17 relevant positions.
- Samples of the 10^44 legal positions or the 10^37 positions without promotion to pieces not previously captured cannot be reached by optimal play from both sides.
- Checkers needed 10^14 positions to weakly solve and Losing Chess 10^9.
- Connect Four has been solved with 9 knowledge rules.
- A strategy can be brute force, can be a set of rules, or a combination of both.
- An engine of 10^9 positions / s running for 17 s (or a desktop for 4.7 h) includes the table base exact move in its top w = 4 moves with 1 error in 10^20 positions.
- The average length of ICCF WC games is d = 39 moves.
- 1104 ICCF WC draws are perfect games with optimal play from both sides.
- An upper bound U assuming no transpositions is U = ( w^(d + 1) - 1) / (w - 1).
- A lower bound L assuming full transpositions is L = e^w, regardless of d.
- An estimate E is the geometric mean of the upper and lower bounds: E = sqrt (L * U).
Cloud engines can calculate a billion positions / s.
A year counts 365.25 d / a * 24 h / d * 3600 s / h = 31,557,600 s / a.
Thus 3 cloud engines can weakly solve Chess in 5 years.
Humans are necessary to restrict the calculation to relevant positions only.
GM Sveshnikov said:
'Give me five years, good assistants and the latest computers
- I will bring all openings to technical endgames and "close" chess.'
The 'give me' implies 3 million $
to hire 3 (ICCF) (grand)masters 40 h / week and rent 3 cloud engines 24 / 7 for 5 years.
tygxc wrote:
Back on topic after the spamming spree of the trolls.
The game-theoretic value of a game is the outcome when all participants play optimally.
Ultra-weakly solved means that the game-theoretic value of the initial position has been determined. There is massive evidence that for Chess it is a draw.
- Expert opinions of all World Champions
- AlphaZero self play 97.7% draws at 1 min / move, more with more time,
even if stalemate is declared a win - TCEC with imposed 50 slightly unbalanced openings to prevent all draws
- Human World Championships and top tournaments
- ICCF World Championship Finals: 136 games = 127 draws + 6 white wins + 3 black wins.
table base win claims of > 50 moves without capture or pawn move allowed but do not occur - A tempo in the initial position is worth 1/3 pawn. You cannot queen a tempo.
Weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition.
Strongly solved is being used for a game for which such a strategy has been determined for all legal positions. For Chess this means a 32-men table base with 10^44 positions.
Weakly solving Chess needs 10^17 relevant positions.
- Samples of the 10^44 legal positions or the 10^37 positions without promotion to pieces not previously captured cannot be reached by optimal play from both sides.
- Checkers needed 10^14 positions to weakly solve and Losing Chess 10^9
- Connect Four has been solved with 9 knowledge rules.
- A strategy can be brute force, can be a set of rules, or a combination of both.
- Width w = 4 candidates moves includes the table base exact move within the top 4 engine moves is an engine of 10^9 positions / s runs for 17 s (or a desktop for 4.7 h) with 1 error in 10^20 positions
- The average length of ICCF WC games is d = 39 moves
- 1104 ICCF WC draws are perfect games with optimal play from both sides
- An upper bound U assuming no transpositions is U = ( w^(d + 1) - 1) / (w - 1)
- A lower bound L assuming full transpositions is L = e^w, regardless of d
- An estimate E is the geometric mean of the upper and lower bounds: E = sqrt (L * U)
Cloud engines can calculate a billion positions / s
A year counts 365.25 d / a * 24 h / d * 3600 s / h = 31,557,600 s / a
Thus 3 cloud engines can weakly solve Chess in 5 years
Humans are necessary to restrict the calculation to relevant positions only
This is what GM Sveshnikov said:
'Give me five years, good assistants and the latest computers
- I will bring all openings to technical endgames and "close" chess.'
The 'give me' implies 3 million $
to hire 3 (ICCF) (grand)masters 40 h / week and rent 3 cloud engines 24 / 7 for 5 years
1. Inconclusive. Imperfect play.
2. Inconclusive. Imperfect play.
3. Not to prevent all draws, because that was not happening, but to make games more exciting and add more decisive outcomes, yes.
4. Inconclusive. Imperfect play.
5. Lol, do your math again.
6. Tempo and piece valuations are derived from imperfect play.
Notice a theme?
- 10^17 has no support save for one crackpot theoretician.
- Sveshnikov made an offhand claim in an interview to impress lay people.
@5749
2. AlphaZero approaches perfect play with more time / move.
3. On TCEC:
"Statistics of the previous two superfinals show that a Leela book exit of +0.30 or lower is an almost 100% certain draw."
https://www.chessdom.com/jeroen-noomen-and-gm-matthew-sadler-announce-tcec-s21-superfinal-book-cooperation/
Of the 50 imposed openings, 19 worked as intended: a win and a draw,
22 led to two draws, 9 are busted and led to a win and a loss.
5. The math again:
136 games = 127 draws + 6 white wins + 3 black wins
https://www.iccf.com/event?id=66745
First assume Chess a white, or black win.
Try to fit a Poisson distribution of errors / game with 127 / 136 probability of an odd number of errors. It is impossible. Thus Chess is no white or black win.
Then assume Chess is a draw.
Fit a Poisson distribution of errors / game with 9 / 136 probability of an odd number of errors.
It is possible with average of 1 error per 14 games. It leads to 99.7% certainty that the 127 draws are perfect games with optimal play from both sides.
Oct 1, 2022
0
#4378
tygxc wrote:
Back on topic after the spamming spree of the trolls.
...
Back on topic would be you showing your calculation of the theoretical result and error rates in my games I posted. I think we were all waiting for that. Here they are again.
Once you've done that we can stop discussing your proposal.
It doesn't work.
You don't have to wait for my KRPPvKRP runs. Your calculation should work for any material.
You just said.
5. The math again:
136 games = 127 draws + 6 white wins + 3 black wins
https://www.iccf.com/event?id=66745
First assume Chess a white, or black win.
Try to fit a Poisson distribution of errors / game with 127 / 136 probability of an odd number of errors. It is impossible. Thus Chess is no white or black win.
Then assume Chess is a draw.
Fit a Poisson distribution of errors / game with 9 / 136 probability of an odd number of errors.
It is possible with average of 1 error per 14 games. It leads to 99.7% certainty that the 127 draws are perfect games with optimal play from both sides.
Instead of applying it to a bunch of ICCF games where they give up in the middle of nowhere and guessing, try applying the same calculation to the games I posted where we have exact information.
What should be the result of the starting position and how many errors are there in those games? We're all dying to know.
Then everyone can really start discussing the topic. You've had the longest spamming spree of anyone ever.
@5751
"You don't have to wait for my KRPPvKRP runs."
++ I wait for your runs. My calculation works for 32 to 8 men. 7 men is a good verification point.
7 men or less are strongly solved in the 7-men endgame table base.
As for your 7-men position: white is lost, so this cannot result from optimal play by both sides.
Engine: Ba5.
1 Table base: Qc1+, Engine: Qc1+ Ka2
2 Table base: Bc4+, Engine: Bc4+ Nb3
3 Table base: Qg5, Engine: Qg5 Rh1+
4 Table base: Ke2, Engine: Ke2 Re1+
5 Table base: Kf3, Engine: Kf3 Bb4
6 Table base: Qd5, Engine: Qd5 Rb1
7 Table base: Kg4, Engine: Kg4 Ka3
8 Table base: Qf3, Engine: Qf3 Rb2
9 Table base: Be6 / Kh5, Engine: Qd3 Ka4, but 50-moves rule does not apply, still OK
10 Table base: Qf3, Engine Qf3 Nd4
11 Table base: Qd1+, Engine: Qd1+ Nb3
12 Table base: Be6, Engine: Be6 Bc5
13 Table base: Qd3, Engine: Qd3 Bb4
The top 1 engine move agrees with the table base even for this not relevant position.
It's real to me. Completely. I have no doubt that we can alter the world with our minds. None at all.
My continued existence belies your powers
.