Columns | January 16, 2008 18:11

[lang_en]Order and chaos in chess[/lang_en][lang_nl]Orde en chaos in het schaakspel[/lang_nl]

[lang_nl]Wordt het schaakspel uiteindelijk door vaste regels en logica beheerst, of is het gewoon een ?¢‚ǨÀúrandom' spelletje? Een vergelijking met de wetenschap.

door Arne Moll [/lang_nl][lang_en]Is chess ultimately governed by fixed rules and logic, or is it just a 'random' game? A comparison with science.

by Arne [/lang_en]

[lang_nl]Enige tijd geleden schreef ik een artikel over de toekomst van schaakkennis. Ik ging in op de mogelijkheid dat computers, theoretisch gezien, ooit te weten kunnen komen wat de ultieme waarheid van de beginstelling is (wint wit met perfect spel? Is het remise? Zou het kunnen dat zwart gewonnen staat?), maar dat wij mensen dit misschien nooit zullen begrijpen omdat het buiten het menselijk begrip ligt, zoals quantummechanica buiten het menselijk begrip ligt (zelfs al heeft de mens uitgevonden dat quantummechanica echt is.)[/lang_nl][lang_en]Some time ago, I wrote an article about the future of chess knowledge. I considered the possibility that, theoretically speaking, computers can some day find out the ultimate truth of the initial position (is White winning with perfect play? Is it a draw? Could Black be winning?), but we humans may never understand it because it's beyond human comprehension, just like quantum physics is beyond human comprehension (even though humans have found out that quantum physics is real.)[/lang_en]

[lang_nl]Geloof in orde

Onlangs schreef de theoretisch natuurkundige en kosmoloog Paul Davies (tevens auteur van diverse populair-wetenschappelijke boeken) een provocerend opiniestuk in The New York Times, waardoor ik weer moest denken aan de vraag of we ooit enige ultieme waarheid in het schaakspel kunnen begrijpen. In zijn artikel verdedigt Davies het standpunt dat niet alleen religie, maar ook wetenschap op geloof gebaseerd is. Hij schrijft:

Alle wetenschap is gebaseerd op de aanname dat de natuur geordend is op een rationele en begrijpelijke wijze. Je zou geen wetenschapper kunnen zijn als je dacht dat het heelal een betekenisloze verzameling losse eindjes is die lukraak op elkaar gestapeld zijn.

davies

Door zich met wetenschap bezig te houden, beweert Davies, gaan wetenschappers impliciet uit van regels en patronen in het heelal. Ze veronderstellen een zekere logica, zelfs al die logica misschien ons begrip voor altijd te boven zal gaan. Dientengevolge is het geloof van de wetenschapper dat er orde is, want als er geen orde zou zijn, zou er alleen maar chaos zijn ?¢‚Ǩ‚Äú en wat zou het doel van wetenschap zijn als chaos niet getemd kan worden?

Natuurlijk riep Davies' artikel veel reacties op. Veel wetenschappers tekenden met klem bezwaar aan niet alleen tegen de claims van Davies, maar ook tegen de gedachte alleen al dat religie en wetenschap ook maar iets met elkaar te maken zouden hebben - zelfs als wetenschappers geloofden dat er duidelijke wetten in het heelal waren. Sterker nog, het bleek dat veel wetenschappers het helemaal niet nodig achten om te geloven in een geordend heelal. Bioloog P.Z. Myers schreef:

(...) Als we kijken naar de verschijning van een bepaald fenomeen moeten we erop voorbereid zijn dat het niet het gevolg is van een of andere geordende progressie ?¢‚Ǩ‚Äú misschien gebeurde het gewoon zo. (?¢‚Ǩ¬¶) Davies heeft misschien geloof in de wetenschap, maar ik niet. Ik neem het zoals het komt.

We hebben dus twee standpunten:

  • Er moet orde zijn, wat is de anders ?ɬºberhaupt het nut van proberen te achterhalen hoe dingen werken?
  • Het is een open vraag of er orde of chaos ten grondslag ligt aan de werkelijkheid, maar het zou niet moeten uitmaken zolang we nog kunnen uitvinden hoe dingen werken.

Een random spel?

Kunnen we deze discussie toepassen op schaken? Gelooft u dat schaken uiteindelijk door vaste regels en logica wordt beheerst, of gelooft u dat het gewoon een ?¢‚ǨÀúrandom' spelletje is waar, om Myers te parafraseren, dingen ?¢‚ǨÀúgewoon zo zijn'?

Misschien kunnen we erachter komen. Om te beginnen is het misschien zo dat we de ultieme waarheid van de beginstelling nooit zullen kennen, maar we weten wel de ultieme waarheid van bepaalde basis eindspelen. Een paar wetmatigheden zijn er dus in elk geval wel. Deze feiten zijn natuurlijk ook door computers gecontroleerd. In bepaalde eindspelen weten we niet alleen of een stelling gewonnen of verloren is, maar we kunnen het winstplan ook begrijpen en deze kennis gebruiken om de winstvoering op het bord te brengen. Als je bijvoorbeeld de regels (formules) kent voor hoe je moet matzetten met koning en toren tegen koning alleen, kun je dit net zo snel en perfect als een computer.

Sommige eindspelen zijn natuurlijk ingewikkelder dan dit voorbeeld. Een goed voorbeeld is het theoretische eindspel dat Shirov op het bord kreeg tegen Karjakin in de recente World Cup: toren en loper versus twee paarden. Tim Krabb?ɬ© heeft al veel geschreven over dit fascinerende eindspel (en over dit onderwerp!), en in zijn dagboekaantekening van 16 december 2007 werpt hij de vraag op of mensen ooit zullen begrijpen wat computers al hebben berekend: hoe dit eindspel te winnen?

Krabb?ɬ© geeft twee diagrammen om te laten zien hoe moeilijk het zal zijn om de winstweg te begrijpen. Op een bepaald moment moet wit tweehonderd 'perfecte' zetten achter elkaar doen om de volgende stap te bereiken ?¢‚Ǩ‚Äú maar deze stap lijkt net zo willekeurig en onbegrijpelijk als iedere andere stelling in dit eindspel. Hoe kunnen we ooit begrijpen wat er gaande is? Heeft het zin om het te proberen?

Wat zou Paul Davies ons adviseren? Misschien zoiets: ?¢‚Ǩ?ìHet heeft alleen zin om dit eindspel te begrijpen als je gelooft dat aan de wortel van elke schaakstelling een bepaald logisch patroon of een formule ligt die we kunnen ontdekken, en die je naar de ultieme waarheid van een stelling leidt.?جø¬??

P.Z. Myers geeft misschien een heel ander antwoord: ?¢‚Ǩ?ìJe moet er rekening mee houden dat we nooit zullen kunnen begrijpen hoe deze stelling te winnen is, omdat het is slechts een willekeurige reeks zetten is, weet je. Ja, een computer kan het met extreme rekenkracht uitrekenen, maar dat is eigenlijk gewoon tellen ?¢‚Ǩ‚Äú er is geen elegante formule of iets dergelijks.?جø¬??

Zeker, we hebben vele praktische vuistregels in het schaken (?¢‚Ǩ?ìtorens horen op open lijnen, ontwikkel je stukken, etc.?جø¬??) maar aangezien deze niet altijd geldig zijn, zijn het geen echte formules, zoals E=mc^2 of V=(4/3)*pi*(r^3). Zijn zulke formules in principe mogelijk in het schaakspel, zelfs al zien ze er misschien volslagen anders uit? Is schaken uiteindelijk een spel van orde of een spel van chaos? Wat gelooft u?[/lang_nl][lang_en]Faith in order

Recently, the theoretical physicist and cosmologist Paul Davies (and author of various books on science) wrote a provocative OpEd piece in The New York Times, that made me think again of the question whether we can ever understand any ultimate truth in chess. In his article, Davies defends the view that not only religion, but science, too, relies on faith. He writes:

All science proceeds on the assumption that nature is ordered in a rational and intelligible way. You couldn't be a scientist if you thought the universe was a meaningless jumble of odds and ends haphazardly juxtaposed

davies

By doing science, Davies claims, scientists implicitly assume rules and patterns in the universe. They assume a certain kind of logic, even though this logic may forever be beyond our comprehension. Thus, the scientists' faith is that there is order, for if there weren't any order, there would only be chaos - and what would be the purpose of science if chaos could not be made orderly?

Of course, Davies' article created a lot of responses. Many scientists objected heavily not only to the claims made by Davies, but also to the mere suggestion that religion and science should even be remotely similar - even if scientists believed there were fixed rules in the universe. In fact, it turned out that many scientists actually do not consider it necessary to have faith in an orderly universe. Biologist P.Z. Myers wrote:

(...) When looking at the appearance of some particular feature we have to be prepared for the possibility that it is not a consequence of some orderly progression?¢‚Ǩ‚Äùperhaps it just happened that way. (...) Maybe Davies has faith in science, but I don't. I take it as it comes.

So, we have two points of view now:

  • There must be order, otherwise what's the point of trying to figure things out in the first place?
  • It's an open question whether there's order or chaos at the basis of reality, but it shouldn't matter as long as there's still things to find out.

A random game?

Can we apply this discussion to chess? Do you believe that chess is ultimately governed by fixed rules and logic, or do you believe it's just a 'random' game where, to paraphrase Myers, things 'just happen that way'?

Perhaps we can find out. For starters, we may not know the ultimate truth of the initial position (yet), but we do know the ultimate truth of some basic endgames. Some rules, then, appear to be present. These truths have, of course, also been verified by computers. In some of these endgames we not only know whether a position is won or lost, but we can actually understand the winning plan and use this knowledge to execute it ourselves. For example, if you understand the rules (formulas) of how to mate with king and rook against a lone king, you can do it as smoothly and perfectly as any computer.

Of course, some endgames are more complex than this. A case in point is the theoretical endgame Shirov had against Karjakin in the recent World Cup: rook and bishop versus two knights. Tim Krabb?ɬ© has already written a lot about this fascinating endgame (and about this subject!), and in his diary entry of December 16, 2007, he raises the question whether humans will ever understand what computers have already calculated: how to win this endgame?

Krabb?ɬ© gives two diagrams to show how difficult it will be to understand the winning method. At some point White needs to play two hundred 'perfect' moves in a row to come to the next step - but this next step seems as random and unintelligble as any position in this endgame. How can we ever understand what's going on? Does it make sense to try?

What would Paul Davies advise us? Perhaps something like this: "It only makes sense to understand this endgame if you believe that at the core of any chess position there's some kind of logical pattern, a formula, that we can discover, and that will lead you to the ultimate truth of the position."

P.Z. Myers might give us an advise that's very different: "You should be prepared to find that we can never understand how to win this position, because, you know, it's just a random sequence of moves. Yes, a computer can calculate it through brute force, but that's just counting - there's no elegant formula or something."

Sure, we have many practical rules of thumb ("put rooks on an open file, develop your pieces, etc.") but because they don't always work, they're not real formulas, like E=mc^2 or V=(4/3)*pi*(r^3). Are such formulas in principe possible in chess, even though they may look entirely different? Is chess ultimately a game of order, or a game of chaos? What do you believe?[/lang_en]

Arne Moll's picture
Author: Arne Moll

Chess.com

Comments

Patzer's picture

I just wrote a long post, and deleted it by accident. This is the short version. Ron - you miss the fact that particles, clusters of particles. and atoms are analogies created to aid human understanding, the most fundamental processes detectable by science might lay on a much smaller scale than that. There is no randomness in chess, because the moves are defined by the rules, but chess is 'nearly infinite' and so the number of abstractions necessary to understand it completely means can be regarded as similar to science. The best players have a combination of opening theory, calculative ability, and ability to understand the abstract points of complex positions.

Rob's picture

One way to rephrase the problem is what would be the shortest program that could play perfect chess in every game? Counting memory used towards program length so a tablebase generator would not do. Obviously such a program would be many orders of magnitude shorter than a 32 piece tablebase but I suspect still way beyond human understanding.

For all of you who say chess is mathematically simple would you be able to generate such a program if you had the complete tablebase? Is there any way to do this except by hand? (i.e. looking at the positions, guesing the rules yourself then implementing them?)
What I mean is there a generalized way, given the rules of a finite game (including the winning condition), to generate type 2 rules even if not the simplest ones?
Has this been done for any simple games, or simplified chess positions?

These questions certainly don't seem trivial to me. Apart from their mathematical intrest they would have a 'practical' application: they could be used to find wins in certain endgames which may not be the shortest but easier for humans to understand.

Maarten S's picture

Being a mathematician and a chess player, I fully agree with bartleby.
The number of possibilities in chess is finite, so in principle it is possible to decide the best move in any given position.
At the same time, it is abundantly clear that this beyond the comprehension of humans, and beyond the capacities of any foreseeable non-quantum computer.

If chess has to be compared to some science, I would vote for biology. How a chess game develops is not determined by fixed rules, like an algorithm, or by pure chance, like quantum-mechanics. Rather, it is the consequence of a vague set of rules that the players to try to apply, inconsistently, sensitive to all kinds of disturbance and certainly not optimal. But let's rejoice in this, it's what makes chess a sport!

B's picture

"Cassia vs Garry Kasparov"

With a deep understanding of the consequences of each move, the way endgames are entered into would be different I imagine. Someone with perfect play would be in control of each phase of the game. Leading not into a chaotic position but into the opposite. The interesting thing about formula expressions is that they put the complex into the simplified. If there is hidden 'laws' governing the chess universe I would bet they would be simple and elegant.

Theo's picture

Schaken is zo 'perfect' (of heel benaderend aan perfectie) dat er zowel ORDER als CHAOS in zitten!
Volledige "orde" bestaat natuurlijk niet. Het is dan steeds een geordende vorm van "chaos"
Uiteindelijk en in essentie is alles natuurlijk Chaos. Enkel de mensheid ordent die zodanig dat het voor ons logisch en "orde" lijkt.
Dat is net zoiets als tijd en wiskunde. Natuurlijk 'klopt' de wiskunde voor ons...wij hebben die uitgevonden. En dus "doen we het kloppen"

Kortom: in schaken zit zowel orde als chaos, en het is duidelijk dat grote Meesters zoals Karpov de chaos beter kunnen 'ordenen' dan gewone stervelingen...

Alles is relatief. Volledige orde of volledige chaos bestaat trouwens niet. Dat zijn gewoon Utopische polen. Zoals zwart en wit. De 2 extremen. Niets neemt ooit zulke extremen aan. Het is telkens een dynamische gradatie tussen de 2 contrasterende statische tegenpolen.

Deze visie is natuurlijk ook subjectief en relatief.
Filosofische schaakgroeten,
Theo ;-)

Jit's picture

All chess games start in the same state. After 10 moves, it is impossible to predict the position. That seems to be chaotic. But the 'chaos' is in the minds of the players - when, if ever, a computer 'solves' chess, then in a game between two computers that had the solution, it would be a simple matter to predict the position after 10 moves.

Regarding endgames: I have heard that masters perform no better than a competent club player when the pieces are randomised (as in Fischer's chess), or in set problems. To me complex endgames approach randomness because their solutions are less likely - there are millions of ways to win a game when all the pieces are present, but not when you have B and Kt against King. Endgames can be highly complex in the sense that there are many possible moves at any point, of which only one may be correct. That move may be indirect, and therefore not obvious; at an early phase of the game, it could hardly be.

peter's picture

My contribution to the discussion is that certain types of endings will always be beyond human comprehension. At some point the tablebases will include positions with more pieces and pawns, and the specific strategies will involve consequences more than three hundred moves later, when for example a knight or rook promotion will be decisive.

I can also think of a different scenario: some types of endings can only be understood by completely forgetting about the official rules of chess and the 'human techniques', and it will be a game in itself to solve and describe certain winning strategies. Like the problem solving tournaments of nowadays. Mr Nunn's grand children will be the first to win these events.

hexag1's picture

before you take Paul Davies' view on science to heart, you might have a look at some of the criticism of that piece that came from the science community.
For example:

http://www.samharris.org/site/full_text/response-to-paul-c-davies/

DallasFuck's picture

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Bartleby's picture

Mathematically speaking, chess is boring, because there is a simple, yet lengthy process how to solve it.

The chaos lies not in the mathematics of chess, but in the fact that our brains, and computers, are just able to get a glimpse or two on how an ultimate answer may be achieved, but the answer itself is out of our reach for the foreseeable future.

We may make progress, if we get a better understanding on how concepts are formed.

nick's picture

In reality there is no randomness. The beginning of the universe set off a chain of energetic cause and effect that has branched into multi paradigms and systems beyond our limited primate brains.
Chaos theory shows us hidden structures in systems that appear completely random. The dripping of a tap. The rise and fall of the nile. Weather Systems. There is a pattern behind everything.
At this point that natural selection has spat us out ,our biological brains alone are too limited to understand NN vs BR endings. However technology is an extension of our physical brains and as technology grows exponentially, a new, more efficient version of evolution - that of 'memes' - is rapidly evolving our understanding of the universe and chess!
Who would have thought nano technology & gene therapy & space travel possible just 100 years ago.

I believe one day we will all understand chess fully. Each game will be drawn, but we'll still love to play and watch the beauty of it unfold.

arne's picture

@Ron, you write: "computers are already showing that these ?¢‚ǨÀúRules?¢‚Ǩ‚Ñ¢ have many exceptions." Yes, in most situations this is true, but *not* in theoretical endgames. In the ending KR vs R, it's *always* the best idea to chase the enemy king to the edge and then to the corner. This is the type of "rule" that I have in mind: are such rules, in principe, also possible for middlegames and even openings? We don't know that yet, but that doesn't mean it's not possible.

@nick. "The beginning of the universe set off a chain of energetic cause and effect". If we would live in a universe governed by classical physics, that would be true. But we may not live in such a universe. Ours is a quantum universe, and there thing could be very different. (I'm not talking about the possible wave-functions of every particle in the universe, but about the problem of observation.) So, we don't *know* whether we live in a deterministic universe, and hence we don't know whether there's no real randomness. The same could be true for chess, and the point of my article was to stimulate thinking about this.

arne's picture

@hexag1: yes, but how's that different from what I already wrote about the responses Davies' article received?

arne's picture

@peter, I think you're right, but the fact that we'll probably never have a *holistic* understanding of chess, doesn't mean we can't understand (some) *individual* steps in the process of reaching the ultimate truth in certain positions. This is also Krabb?ɬ©'s point: can we ever make *any* progress in such complicated tablebase endings, or will it always seem *completely* random?

Ron's picture

Arne, your first set of rules are indeed Rules. Your second set is what we think are 'Rules' using our limited brains and 'understanding'. But I am convinced that there are no such 'Rules' in chess. Castling is a good move most of the time, but sometimes it is not. Sometimes an open line is a blessing, sometimes a curse. When is the bishop pair 'good' and when not? Yes we try to approximate, as good as we can, find 'Rules', but computers are already showing that these 'Rules' have many exceptions.
More fundamental question to you and the Forum here: what is chess? IS a game between two computers really chess? Or is it the game that we humans play (Donner's opinion), including our mistakes and emotions?

Ron's picture

Also consider The Hitchhiker Guide's answer to the Ultimate Question (42)! :-)

Merijn's picture

On me chess makes a very complicated, but not a chaotic impression. The questions (what) seem to be clear most of the time, just the answers (how) are impossible to calculate.

Logic 1: Mate ends the game, so the direct way to win the game is an attack on the king and mate.
Logic 2: The more central a piece is, the more options it has (compare Nh1 with Ne4). So the indirect way to win the game is to create more options for your pieces compared to the opponent?Ǭ¥s pieces.

I think as computers become more powerful all chess strategy comes down to "mate" and "the centre". It remains how...

Raptor's picture

Ah, thanks arne. But actually, I was just pointing that out and then went off in another direction. Anyway, yeah, I'd say the second set of rules was more in line with chaos theory. To the whole point of one line splitting into two, and those two splitting into two, and so on until you are left with a mess.... But in this case, it's moves. He does X, so you can do this or that, and each of those generating possible different counters to it.

If there was a perfect way to win a game, no matter what the other side did, then I think the problem would come up that both sides can't win, so one side must beat the other and therefor, a perfect counter to every move cannot exist. A best, you would be left with a draw and a game between two kings that continues into infinity, or at least as long as the board and the pieces last.

So a universal law or formula that governs chest and makes it so that you can't lose? No, I don't think such a thing exists, even with it existing beyond our understanding. Paradoxes aside. I think what we'll get is close enough and use it to make a computer that a human can't beat at chess and when it faces itself, it gets a draw, every time.

I expect chaos is in everything, even the rules, making it impossible to come to any formula that will tell you what to do next.

However, I will note, there is skill involved in chess, knowing when to play what, and I do see that implies some sort of rules or some sort of reasoning that certain moves are better than others.... Expect that whole chaos theory getting tossed in there. And it's not really randomness so much, as just having no knowledge of what the other person will do, of having too many possibilities and outcomes, of chaos itself. And it might really be that chess comes down to not having perfect moves, but having proportionally more moves that are most likely to result in a win than the other person. And there is no formula for something like that.

I suppose if you could read the mind of the other player then you'd never lose, but that still doesn't produce any kind of a formula.

george's picture

Are we mere pawns, or is everyone of us the king of his own game/life? I want to believe the latter, even though my life points to the former. In any case, I think we confuse chaos with what cannot be counted.

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Terrance's picture

The beauty in chess is that is played by two imperfect beings each of which has a possibility of winning. If chess was a systemetic game that had empirical rules that allowed white to win every single time it would be a very boring game.

arne's picture

It seems some people are confused by my use of the word 'rules'. So let me clarify this: there are two kinds of 'rules' in chess:
1. the rules of how the pieces go and who has to make a move, etc. for example: the rook can only go straight (never in a diagonal) etc.
2. the rules which makes one win games, for example: in the opening, one should try to castle and develop pieces, in the endgame one should try to activate the king, in the theoretical endgame of KR vs. K the lone king should be driven to the edge and then to the corner, etc.

In most of my article, I'm talking about the *second* kind of rules. So when people draw my attention to the fact that chess is a game goverened by man-made rules, of course this is true, but in principe it's only true for the *first* kind of rules, not for the second. The second kind of rules is discovered by experience and by evidence. My article is about the question whether a second kind of rule exists for the initial position of the game of chess, and whether there's a solution to the entire game of chess. I hope this clarifies some issues.

Raptor's picture

First off, chess is a man made game, while an interesting slimily, it is not the universe. We have set rules for it, which are established before the game is played. However, because of the way human minds work, because we are prone to mistakes, and because we are trying out wit one another and being forced to respond to certain moves, it throws in there the aspect of chaos, in which it is impossible to predict every move of the game before it has been played out. The only way you could do this is to know the minds of both players and how they would respond to what. And even that might change on a whim, because unlike computers, we are not grounded in making the moves which we are programmed to.

Chaos is one of those funny theories where things just flat out get strange. have a line that splits into two, and each of those into two, and eventually you'll reach chaos, but give it enough time to run and order will pop out of it, three lines, before returning to chaos.

The universe was not predestined or preprogrammed to do anything. Not to make Earth, not to make humans. There were no laws that were set into place before hand that says X has to happen. The universe was not ordered to make us... Everything in the universe ordered itself to that universe. The universe is not tuned to fit us, but we are tuned to fit the universe. So on and so forth.

There are some basic laws, that came into being after the universe started, things that direct the movement of other things, of partials and interactions, but there are always exceptions and always extreme cases where the rules get bent or broken. Rules on top of rules on top of rules, this, but not this, and sometimes this, but only if this. And there is a fair chance we won't ever get to the end of figuring out the full extent of all the rules.

However, that does not mean we should stop our study, as Davies suggests. Just because we may never understand fully, does not mean that it is a pointless search. There is things to be discovered along the way and it is impossible to say that in the future, we will never discover what it is.

Chaos is a wonderful thing and we see little hints of it here and there in life. Cars on a highway, the line at IHOP in the morning, a game of chess, and so on. But just because we think they are confusing or that the formulas are long and mess does not make it fruitless. Nor, does it make it a religion and Davies is a bigger fool for suggesting that scientists would ignore evidence if it suggested something else.

As a little side note, I really hate hearing that. That science must be a religion because science prescribes to certain things and doesn't think that another theory is valid because it goes against the original. Sorry people, that's not how it works.

B's picture

The starting position of the game is an ordered universe unto itself. It is able to be infinitely dissected and rearranged depending on what each side of the board chooses.
This is order leading to chaos?¢‚Ǩ¬¶leading back to order? It is possible that chess is both random and formulaic underlining what perfect play means, God only knows.

Ron's picture

My position is that there are two levels of 'reality'.
The first one (level 1) is the 'material' level so in terms of physics, this is the level of the particles, clusters of particles etc. On this level everything is governed by the mindless processes that are governed by the physical laws. In chess terms, this level is the level of the chess rules.
The second level (level 2) is what we experience as 'human understanding'. We 'see' structures and consciously 'understand' that these are trees, stars, animals, human beings. Also we (try to) 'understand' how the laws of nature work and describe those in mathematical terms. In chess terms, on this level we 'understand' chess, how to mate the king in a R+K against K endgame, how to play against the IQP etc.
Now if you are still with me: computers play 'chess' on level 1. Maybe some day they could play the game perfectly, blindly following the rules of the game ending in a forced draw or a forced win for either color. No 'understanding' is required at all on this level for the computer to play a perfect game.
Now level 2. Could humans on level 2 'understand' the perfect game played on level 1? I would say, very unlikely. Even the table base 5 piece rook endgames are extremely hard to 'understand' (see Dr Nunn's excellent book). We would just have to accept that white mates in 535 moves with perfect play by black. Nevertheless there is no randomness at all in a perfect chess game. It is fully determined, starting from the initial position, by the rules of the game and the goal to mate the enemy King.

On the level of the universe, this 'understanding' will be flat impossible. No matter what brilliant concepts we have invented to describe the laws of nature, with quantum mechanics, relativity, string theory etc: these are only crude human approximations of reality.
Fortunately, on our level 2, we can still experience the human feeling of beauty by looking at the equation e to the power of i times pi = -1, or by playing the endgame Kramnik - Eljanov, Wijk aan Zee 2008.

forest's picture

Interestingly Nigel Short commented on the new generation computer watching at Nepo's game. Nepo broke every rule (grabbing 3 pawns, did not develop, moved all his kingpawns up and castled kingside aftwards); ony engines would be positive about this, but humanly the position is impossible to defend afterwards!

Thomas S's picture

If I may say, the problem in your article is that you consider maths as the "language of truth", so to speak. As you quote in your examples, "E=MC?Ǭ?" and such should be the purest expression of "order".
But as a matter of fact, modern epistemology has revealed that our science entirely relies on different paradigms, or, as we would say "chesswise", on different patterns. In other terms, we now know that a lot of the most precise works in nowaday's physics or mathematics only "function" in this or this paradigm - but that a change of paradigm would make most of this work entirely irrelevant. For example, to put it in a simle way quanta physics is, to some extent, incompatible with thermodynamic, but both helps us to understand various aspects of our reality : they become most helpful tools.
Now with chess, I think we find ourselves in more or less the same scheme of thinking : I think there is no ultimate truth from the starting position, but that we may one day reach the ultimate truth of different patterns, each pattern forming a completely independant system from another.

So, to answer your question, wouldn't chess be a game in which our rationality feeds on chaos to achieve its goals ?

Maarten's picture

Interessant artikel!
Allereerst denk ik dat Paul Davies gewoon een goed punt heeft omdat in elk wetenschappelijk systeem aannames worden gedaan die niet door dat systeem formeel kunnen worden bewezen. Dus als Myers zegt dat hij iets aanneemt zoals het komt, berust dit al gelijk op een aantal aannames (dat er iets is, dat hij iets waarneemt, dat hij daar waarde aan kan toekennen etc.). Bij religie is het aantal en het belang van onbewijsbare aannames veel groter dan bij de meeste vormen van wetenschap, maar dat beide berusten op een hoeveelheid aannames lijkt mij evident.

Ik denk dat je de orde in de natuur (die soms met zeer elegante formules te beschrijven is) niet direct kunt toepassen op een menselijk spel, dat uiteindelijk berust op berekeningen en 'vooruitdenken'. Het menselijk inzicht hierbij is beperkt, dus zal er een grens zijn aan het begrijpen van systemen en oplossingen van bijvoorbeeld eindspelen. De computer daarentegen zal door brute rekenkracht van steeds ingewikkelder wordende systemen de perfecte afloop kunnen bepalen, maar van begrijpen is dan mijns inziens geen sprake.

arne's picture

@Raf, I have received comments like this before, but I think it misses the point. Of course it wasn't my intention to write a scientific article with 100% correct methodology. Rather, in my article I simply wanted to express some of my ideas about the issue of order and choas in chess, and explore the possibility that we can learn something about how to study and think about about chess from the way we study and think about the universe. And from the way leading scientists are thinking about these issues. So in fact, the possible difference between the finiteness of the universe and chess might actually emphasize the point I was trying to make, rather than refute it. I like to think of the comparison between chess and the universe not as a scientific concept, but as a possibly useful analogy to study some of the questions I described.

Raf's picture

I doubt whether it is methodologically correct to compare a finite system like chess to an infinite system like the universe.

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