A chess problem holds the key to human consciousness?

by Frederic Friedel
3/16/2017 – That, in fact, is what the newly founded Penrose Institute is suggesting. The founder, famous mathematician Sir Roger Penrose, has composed a problem devised "to defeat an artificially intelligent (AI) computer but be solvable for humans". The latter are asked to submit their solutions and share their reasoning. But the position itself and the logic behind the experiment is not compelling. Still, you may enjoy checking it with your chess engine.

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The story was broken by Sarah Knapton, Science Editor of The Telegraph, who put it up in her newspaper. In it she reported on the launch of the new Penrose Institute, founded by mathematics professor Sir Roger Penrose, who gained world-wide renown in 1988 by working out black hole singularities together with Stephen Hawking (the two received the Wolf Prize in Physics for that). I was unable to find the original chess artical on the Penrose Institute site, but Sarah Knapton quotes extensively from it:

The chess problem – originally drawn by Sir Roger – has been devised to defeat an artificially intelligent (AI) computer but be solvable for humans. The Penrose Institute scientists are inviting readers to work out how White can win, or force a stalemate, and then share their reasoning. The team then hopes to scan the brains of people with the quickest times, or interesting Eureka moments, to see if the genesis of human ‘insight’ or ‘intuition’ can be spotted in mind.

Can you solve the puzzle?

Scientists from the Penrose Institute want to hear from you if you've cracked it. They write:

The puzzle above may seem hopeless for White, with just a king and four pawns remaining, but it is possible to draw and even win. Scientists have constructed it in a way to confound a chess computer, which would normally consider that it is a win for Black. However an average chess-playing human should be able to see that a draw is possible.

A chess computer struggles because it looks like an impossible position, even though it is perfectly legal. The three bishops forces the computer to perform a massive search of possible positions that will rapidly expand to something that exceeds all the computational power on planet earth.

Humans attempting the problem are advised to find some peace and quiet and notice how the solution arises. Was there a flash of insight? Did you need to leave the puzzle for a while and come back to it? The main goal is to force a draw, although it is even possible to trick black into a blunder that might allow white to win.

The first person who can demonstrate the solution legally will receive a bonus prize. Both humans, computers and even quantum computers are invited to play the game and solutions should be emailed to puzzles@penroseinstitute.com.

Read the full Telegraph article here

The Telegraph report was picked up by a number of media outlets, like this one (in Mashable). There Lance Ulanoff writes:

It’s hard to imagine how the game got here—it's even harder to imagine what happens next, let alone a scenario in which four white pawns and a white king could play to a draw, or even win this game. Yet: scientists at the newly-formed Penrose Institute say it’s not only possible, but that human players see the solution almost instantly, while chess computers consistently fail to find the right move.

“We plugged it into Fritz, the standard practice computer for chess players, which did three-quarters of a billion calculations, 20 moves ahead," explained James Tagg Co-Founder and Director of the Penrose Institute, which was founded this week to understand human consciousness through physics. "It says that one side or the other wins. But," Tagg continued, "the answer that it gives is wrong."

True. Above is the calculation displayed by the oldest engine I have installed on my notebook. Fritz 13 scores the position as 31.72 pawns ahead for Black. On ChessBase India Sagar Shah checked it out with Houdini 5.01 Pro 64 bit, down to 34 ply in a four-line search. Result: 24.91 pawns ahead for Black.

It is true that chess engines will display high scores in favour of Black, due to the material advantage of a queen, two rooks, three bishops and a pawn. What they are saying is that Black has a huge material advantage, one that should result in a win (–+). And they will keep moving their bishops, displaying a high positive evaluation right until the 50-move rule approaches and they see there is no possibility of forcing a pawn move by White. Maybe some of our readers can play out the position and tell us when top engines see the futility of continuing to move and display an eval = 0.00.

Interestingly, when I remove two black bishops my ancient Fritz 13 sees the draw in mere seconds. If I remove just one bishop it does not come up with a 0.00 evaluation in a reasonable amount of time.

But now we come to the humans, who can indeed work things out in a flash: the position is extremely contrived, and so the first thing you do is work out that Black has no legal moves except with his bishops. All White needs to do to defend the position is not to capture a black rook and not move the c6-pawn. He simply moves his king around, mainly on the white squares, and lets Black make pointless bishop moves. Absolutely nothing can go wrong. Once again we ask the owner of very old chess engines to check whether any of them will capture a rook, in order to reduce the material disadvantage slightly – but in the process lose the game.

On the other hand the contention that "it is even possible to trick Black into a blunder that might allow White to win" seems extremely far-fetched. Black would need to move his bishops out of the way, while White advances his king to protect the c-pawn, which then promotes (e.g. 1.Kf3 Be1 2.Ke4 Bc1 3.Kd5 Ba1 4.Ke6 Bec3 5.c7 Kb7 6.Kd7 Bf4 7.c8=Q#), but that is not White tricking Black, it is some kind of pointless helpmate.

Anyway, it is trivially easy for White to hold the draw, and the Penrose Institute will probably receive hundreds of correct solutions submitted by average chess players. The scientists say they are interested in the thought process that lead people to the solution – a sudden moment of genius, or the result of days of consternation? "If we find out how humans differ from computers, then it could have profound sociological implications," Penrose told The Telegraph. Really?

There are much more elegant positions and more profound examples that show the difference between human and computer thinking. Back in March 1992 I published the following study in a computer magazine, as a challenge for any machine to get it right:

[Event "La Strategie / CSS 3/92-29"] [Site "?"] [Date "1912.??.??"] [Round "?"] [White "Rudolph, W."] [Black "White to play and draw"] [Result "1/2-1/2"] [SetUp "1"] [FEN "3B4/1r2p3/r2p1p2/bkp1P1p1/1p1P1PPp/p1P1K2P/PPB5/8 w - - 0 1"] [PlyCount "11"] [EventDate "1912.??.??"] 1. Ba4+ $1 Kxa4 (1... Kc4 2. Bb3+ Kb5 3. Ba4+ Kc4 $11) 2. b3+ Kb5 3. c4+ Kc6 4. d5+ Kd7 5. e6+ Kxd8 6. f5 1/2-1/2

You probably know that you can switch on an engine on our JavaScript board (and move pieces to analyse). You can maximize the replayer, auto-play, flip the board and even change the piece style in the bar below the board. At the bottom of the notation window on the right there are buttons for editing (delete, promote, cut lines, unannotate, undo, redo) save, play out the position against Fritz. Hovering the mouse over any button will show you its function.

Fritz & co. display an eight-pawn disadvantage for White. The correct first move is to sacrifice even more material, which is the only way to secure a draw. This is a much more relevant test, as chess engines, playing the white side, will actually select the wrong strategy and lose the game. In the Penrose position computers with "think that White is losing", but they will hold the draw without any problem (I say this without having tested older engines and trying to entice them into capturing a rook and losing the game).

This little recreational pastime of taking the mickey out of chess playing computers has a long history, which will be told at a later stage. I must admit: it is getting harder and harder as these thing get stronger and stronger.


Topics chess problem

Editor-in-Chief of the ChessBase News Page. Studied Philosophy and Linguistics at the University of Hamburg and Oxford, graduating with a thesis on speech act theory and moral language. He started a university career but switched to science journalism, producing documentaries for German TV. In 1986 he co-founded ChessBase.
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saivishwesh saivishwesh 3/16/2017 05:17
i don't think white can ever force a stalemate let alone a checkmate...how will white force a stalemate if black places one of his bishop on c7 and keeps moving the g3 bishop between h2 and g3...??
cythlord cythlord 3/16/2017 05:05
The proof of a legal position is trivial: black needs six captures and white has no pieces left. By all means it is a stupid problem. Here's a sample game: [Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "*"]
[PlyCount "118"]

1. Nf3 b6 2. b3 c5 3. Ba3 d6 4. Bb4 cxb4 5. Na3 bxa3 6. c4 g5 7. Qc2 g4 8. Qf5
g3 9. Qc5 dxc5 10. Nd4 Nc6 11. Nc2 Ne5 12. Nb4 cxb4 13. d4 Nf3+ 14. gxf3 g2 15.
Kd2 g1=B 16. h4 Bb7 17. Rh3 Nf6 18. Rg3 Ng8 19. Rg6 Nh6 20. Rd6 exd6 21. Rc1
Ng8 22. Rc3 Qe7 23. Re3 Kd8 24. Re5 Bc6 25. Rd5 Kc8 26. Re5 Kb7 27. Rd5 Ka6 28.
Re5 h5 29. Re4 Rh6 30. Re3 Rg6 31. Kd1 Rg5 32. Kd2 Ra5 33. Kd1 Ra4 34. Kd2 Rc8
35. Kd1 Bb7 36. Kd2 Qe5 37. Kd1 Qa5 38. Kd2 Rc5 39. Kd1 Rb5 40. Re5 f5 41. Rc5
dxc5 42. d5 Bc6 43. dxc6 Nf6 44. e4 Nxe4 45. fxe4 fxe4 46. f3 exf3 47. Be2
fxe2+ 48. Kc2 e1=B 49. Kd3 Bxh4 50. Ke4 Bg3 51. Kf5 Bh4 52. Kg6 Bg3 53. Kxh5
Bh4 54. Kg4 Bg3 55. Kf3 Bf4 56. Ke2 Bgh2 57. Kd1 B8d6 58. Ke1 Bhg3+ 59. Ke2
Bde5 *

I struggle with even the most basic of retro problems, but this one was so easy I'm not sure it even qualifies as a retro problem.
pmousavi pmousavi 3/16/2017 05:02
"You insist that there is something a machine cannot do. If you will tell me precisely what it is that a
machine cannot do, then I can always make a machine which will do just that!" Jon Von Neumann
Frederic Frederic 3/16/2017 02:44
@benedictralph: you nailed a point that I could have made: chess playing computers are not programmed to deal with such problems since the corresponding positions NEVER occur -- in normal games, as opposed to very abstruse artificially constructed positions, that are presented for pure entertainment. To get a program to consider completely locked positions would indeed be quite easy, but in the end it would probably not add a point of playing strength in regular games. Well, maybe a few, but they would be cancelled by the time spent checking every position for blockages.
PEB216 PEB216 3/16/2017 02:41
A fascinating problem if we accept the challenge posed in the third paragraph of this article: ". . . workout how White can win, or force a stalemate." I couldn't see a win for White (not strictly true), but I did see the possibility for a "stalemate," although, unfortunately, it doesn't work. Here is my idea: Place the White King on c8 and the White Pawn on c7. With the threat Kb8 (with the idea Ka8 followed by c8(Q) and mate). If, after Kb8, Black responds with Bxc7+, then Ka8. Now White threatens a "stalemate" (if Black cooperates!) as follows: b3xa4, Qxa4; c4xb5+, Qxb5?? (of course, this is a blunder; the right move is Kxb5) stalemate. If Black plays Bxc7 (when the White King is still on c8), then play continues as previously: b3xa4, Qxa4; c4xb5+ Qxb5?? (Kxb5 is the correct move) stalemate.
sagitta sagitta 3/16/2017 12:21
This is shockingly stupid for a maths professor - I would guess that anyone rated above 1000 would see that it is a draw in a second or two
benedictralph benedictralph 3/16/2017 10:16
A computer could easily be programmed to solve *this type* of problem, if need be. Just like it can be programmed to do any number of other specific things. The problem "proves" nothing except that most chess programs are not coded in the right way to solve it. Indeed they are coded to play strong chess and this usually comes at the expense of dealing with "exotic" positions that are virtually impossible to occur in a real game.
deepestgreen deepestgreen 3/16/2017 10:08
presumably those that created this problem aren't really chess players. its so obvious, there isn't any thought process required.
Tom Box Tom Box 3/16/2017 09:08
For the Rudolph problem, Stockfish does not follow the line given above but recommends 1..b3. One of the simplest positions that shows a chess engine does not 'understand' but only calculates is a board divided by a wall of pawns of both colour with a king on one side and king and queen on the other. A child immediately sees that the separation is total and the 'superior' side's extra queen is meaningless, while the engine sees the position as winning for the side with the queen.