Chess and Physics in the classroom

by ChessBase
3/6/2017 – While comparisons between chess and mathematics and chess and science are not new, with greats such as Feynman elaborating, the article here is more than yet another comparison, it is an actual lesson that will appear in high school physics classes in Crete. Enjoy this excellent article by physicist Ioannis Halkias.

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By Ioannis Halkias

The great physicist and Nobel laureate Richard Feynman, often compared and likened physics to chess. This tendency of his could be an excellent starting point for the present analysis, if only it had not already been discussed in the following article published at ChessBase, "Feynman: Using chess to explain science". Therefore, I will simply proceed to mention some of the laws of physics that also apply to chess.

Law: Conservation of Energy

Let's begin by discussing one of the key properties in nature: Energy.

Feynman states:

…The law is called the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in the manifold changes which nature undergoes… it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same.

This applies to almost nothing else around us! Among the countless things that can be measured in nature (the leaves of a tree, the speed of a car, age, height, etc.), there are only 7 that remain the same regardless of time and space, energy being one of them. Consider how important it is to find something stable in a world where everything changes! In such a world where almost all figures increase or decrease, grow or diminish, we can have something we can trust; a number that will always be the same!

The pendulum constitutes a simple example of this:

Assume a bob is placed at point A. At the moment of release it has no speed (i.e. kinetic energy), but is the recipient of two forces: the force of gravity (dark red) and the tension force of the string (green). When a body is acted upon by certain forces, these forces provide it with the potential to do something – such as move – which is why, at point A, the bob has potential energy. Naturally, the bob then moves to point B, where it is noted that the two forces neutralize each other. Therefore, it no longer has any potential energy. Was that energy lost? Certainly not! At point A, the bob was motionless, but when it was released, it started accelerating, thus turning its initial potential energy into kinetic energy!

At this point, it would be interesting to examine how the energy conservation law is also applicable in chess. The only difference in chess is that Energy is called Advantage and the law is: The transformation of advantages.

Kramnik - Aronian

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Thanks to Pc4, White has a nice square on d5 to place a piece so: 18.Nd5 White's Knight looks great! . Nxd5 What? . 19.cxd5 What happened to our great square? We wanted to use it for a piece but only a humble pawn stands there. Wait, we now have the c6 square to place a piece! . Rc7 20.Rc6 Great! . Rxc6 What is goind on, there goes the other square as well! . 21.dxc6 Once again, only a pawn stands on our great square and this time we cannot even use the squares the pawn protects to place a piece -as we did before. But wait, this pawn is not a passed pawn and we may try to advance it and promote it! Let's try this: . Rc8 22.Rc1 e6 23.Bd2 Qc7 24.a4 d5 25.axb5 axb5 26.Qb4 Rb8 27.Qa3 Bd4 28.Qa6 Be5 29.f4 Bd6 30.Ba5 Qc8 31.Qa7 Ra8 32.Qb6 Rb8 33.Qd4 b4 34.c7 Ra8 ok We managed to advance the pawn but Black's Queen blocks it and there is no easy way to chase it away! But wait... Since the Black's pieces are buzy holding Pc7 back maybe we could attack elsewhere! Let's attack Pb4 which is weak! . 35.Qb6 Bf8 36.Bxb4 and White has won a pawn! The advantage of the great d5-square has transformed into material advantage. 1–0
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Kramnik,V-Aronian,L-1–02006A30Turin Olympiad

However, a question inevitably arises: if energy is conserved and remains constant without ever being lost or produced but only transformed into a different form, then how was everything we see and experience around us created? How was this energy created if nothing existed in the beginning? Who raised all these impressive mountains; who created the stars and the galaxies?

One theory suggests that perhaps this energy was never created! ... Or rather, it was created, but the total energy in the universe still remains zero! In nature, positive energy is always accompanied by negative energy. For example, it is still impossible to jump to the moon! The reason for this is because, the Earth has surrounded itself with negative energy which traps us in. In physics, we call such situations as bound states.

The exact same thing happens in a game of chess! The initial energy equals zero if we were to assume White has the positive energy while Black the negative. Consequently, in order for the white player to win (increased positive energy), the black player ought to commit an error (resulting in negative energy). Otherwise, no matter how well the white player plays, he will never be able to gain an advantage and win.

Ε=mc2 – Relativity

As one would expect, it is impossible to discuss energy without mentioning Einstein’s famous formula E=mc2! According to this, mass equals energy multiplied by a certain number... a very big number! ... And, not only is this number big, it is even squared, which indicates that mass can produce a huge amount of energy!

The aforementioned formula also applies in chess. Of course, in chess, as in physics – where nuclear reactors are needed to create the result described above – it is crucial that mass be offered in the right way and at the right time to obtain the maximum amount of energy. This method is called “sacrifice” or “combination” and can be equally impressive and imposing as a nuclear explosion!

Sacrifice in chess is reminiscent of certain phenomena observed in nature: after something is destroyed, the bodies left around it absorb some “extra” energy provided by it.

G. Kasparov – V. Topalov

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Here, Kasparov understanding that sacrificed mass radiates energy played: 24.Rxd4! giving a whole Rook away! . cxd4 25.Re7+ and not only that, he is now offering the second rook as well! Topalov, being aware of the Einstein's formula, as well, doesn't accept the offer. . Kb6 26.Qxd4+ this time a knight is given! . Kxa5 27.b4+ Ka4 28.Qc3 Threatening Qb3 checkmate! It is easy to see that the sacrificed material emited energy absorbed by the rest of white's pieces -Kasparov actually went on to win in great style! 1–0
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Kasparov,G2812Topalov,V27001–01999B07Hoogovens4

The space in which the bodies move plays a pivotal role in the theory of relativity! Let us examine the chess board within a physical framework:

Minkowski Geometry

In this picture, the white king intends to climb to the 8th line. Which route is shorter: the green or the yellow one? None! Counting the number of steps required, the two routes are the same, as, in both cases, the king will need to move seven steps ahead. It seems that in chess, the length of the side of the triangle is equal to the hypotenuse –a fact that would greatly displease Pythagoras!

This picture here presents one of the standard charts of introduction to Minkowski geometry. Let us suppose a light beam is emitted perpendicular to the ceiling inside a moving train. On the left, this light is portrayed as observed by a passenger of the train, while, on the right, the same light beam is portrayed as observed by someone standing on the street, who sees the train passing in front of them!

It is therefore obvious that chess and relativity share numerous similarities!

Speaking of relativity, it is also important to mention the deformation of shape-size

One of the most bizarre and funny ideas borne by relativity was the deformation of the bodies as they approach the speed of light. The faster a body moves the thinner it appears; in other words, running is a slimming activity! The deformation of the “size” of objects also exists in chess when fast attacks start occurring!

Jorge Szmetan – G. Garcia Gonzales

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Normal "size" of the pieces: . Knight= 3 pawns Bishop= About 3 pawns Rook= 5 pawns Queen= 9 pawns . Let's see, in a variation, if the size of pieces changes when approaching the speed of... lightning attack! . 19.Bxd5 Bxd5 20.Nxd5 exd5 So far we have: a knight=1 pawn . 21.e6+ f6 22.Qh5 and a Queen for nothing! . gxh5 23.gxf6+ Kh8 24.f7+ Qe5 25.Bxe5+ Bf6 26.Bxf6# 1–0
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Szmetan,J-Garcia Gonzales,G-1–01976B89Malaga

Color charge conservation

Similar to the law of energy conservation, there is another law dictating the conservation of color charge; one of the most recent laws discovered! It states that quarks inside a nucleus have “color” which must be conserved! We will not go into too much detail in regard to this law. It suffices to say that it also applies in chess!

Larsen –Spassky

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1.b3 In this game we will examine what "color strategy" is about: . another example 1.e4 White will play on the Kingside and light-squares c5 while Black will try play on the Queenside and dark squares. 2.Nf3 White doesn't want to give Black freedom on the dark squares and since he is a move ahead he has the luxury to try neutralize Black's initiative on the opposite colour, so he exchanges Black's pawn. 2.Nc3 in this case, white insists on his light-square strategy but this gives Black the time to establish himself on the dark-squares and the game becomes double-edge so Black starts having chances. . 1...e5 we already see that White will play on the Queenside and light-squares while Black will play on the queenside and dark-squares. . White controls the central d4-dark-square as well as the dark square f4. Black's queen already operates on dark-squares and Bf8 will soon contribute in the fight for dark-squares. . 2.Bb2 Nc6 another piece that can control dark-squares comes into the game. The bad thing about Nc6 is that in is not easy to contribute in the King-side assault so easily because of his short range powers. On the other hand, as soon as Bf8 develops to c5 it will pressure the dark-squares at the kingside no matter that he will be standing on the other side of the board. . 3.c4 Nf6 we can see that this knight for now pressures light-squares but as soon as we complete our development it can contribute in the dark-squared strategy after Nf6-g4. . Spassky follows Lasker's rule: In the opening develop your Knights before the Bishops because your opponent knows where the knights are going anyway, so by developing the Bishops later you don't give away to much information about your plans -because the bishops have many possibilities on where to develope. . The arrows, though might be confusing, will indicate how black's pieces can attack dark squares on the Kingside. . 4.Nf3 The problem with this piece is that it has influance on the dark squares so it restricts our strategy. What's more with Bb2 they are threatening our Pe5. . e4! When we have colour strategy we want to place our pawns on the opposite colour. So our pieces will not have obstacles on their movement along the colour that we control... So there was no reason for Spassky to protect it on the square that it was standing. Furthermore, this pawn advance chases away the piece that was fighting against our colour strategy and even better it will be exchanged for a piece that we had on the opposite side of the board and wasn't easy to contribute on the Kingside attack. Probably, it was better for White to play 4.g3 to avoid 4...e4. . 5.Nd4 Bc5 Developing a piece with a threat! . From now on with green light I mark the squares of our strategy (dark-squares on the Kingside) in white's camp and with red colour the squares of our strategy that have something to attack on them. . 6.Nxc6 6.e3? Bxd4 7.exd4 d5 and Black is winning 2-4 in development. . 6...dxc6 It seems to me that Spassky had already made his mind about 0-0-0 and takes away of the centre in order to strengthen his queenside against possible white's attacks. Similar strategy is followed by white in the Nc3 variation of the Petroff. . 7.e3 Bf5 Pe4 keeps white's pawns on dark squares and so it is usefull to overprotect this pawn. Bc8 could not have any other part in Black strategy exept exchanging himself for white's knight -because his knight can control dark-squares. . 8.Qc2 Qe7 Black is aiming for 0-0-0 and of course plays Qe7 to keep the queen operating on the dark squares. . 9.Be2?! L 0-0-0 10.f4?? This move weakens the dark squares even more, for example g3 is now defended only once. . Larsen gives this move "?" and Spassky supports that White surely has no advantage anymore. . Pa3 was Larsen's suggestion after the game, probably with the idea of Pb4 chasing away Bc5 that pressures the dark-squares. . Spassky gives another move with a similar idea -to my mind. He suggests Bxf6, to my view the point is that Nf6 will attack white's dark-squares on the Kingside but Bb2 cannot defend them. After all, White's strategy would be on the light-squares (if he had the time) so Bb2 is not usefull to him anyway. . Ng4! Immediately, after Black castle he strengthens his grip on the dark-squares. . From now on, with yellow I mark pieces that immediately target dark-squares. These are our useful pieces, the rest can either be improved or given away for a good purpose. Good purpose means exploring our dark-squared domination or material gains.. . 11.g3 Trying to put some resistance on the dark squares but white can exchange his forces that control dark squares for white's... Because trading is a good policy when ahead on material and Black is way ahead in material on the dark squares! . Just keep in mind that as we mentioned, in the first lesson in Attacking Strategy that in the attack pieces and pawns are the same. On this topic you can also see on youtube the video: Kasparov's Calculations - Mindboggling!!! (very instructive) . . It was too late for both 11.0-0 Qh4 12.h3 h5 L 13.hxg4 hxg4 . and 11.Bxg4 Qh4+ . you can observe that both moves fail because White's dark squares have been weakened. 11...h5 heading to h4 where it will be exchanged reducing white's defenders on the dark-squares. . another intresting variation was also 11...Rxd2 12.Nxd2 Nxe3 giving away on force attacking dark-squares for two defending them! As we said, pieces and pawns count the same in the attack! 13.Qc3 Rd8 . 12.h3 well, this is not realy a theat. The pawn was on h2 defending dark squares and is now about to be "exchanged" for a force that attacks dark squares so it is just one for one. . What is even more, after this "exchange" we give a knight and we "win" a rook! That is because Rh8 that is now not doing much will enter the game. This is a common strategy, for example many times when Black answers the Bg5 pin on Nf6 against his queen with Ph6, it is not incommon for white instead of retreating the bishop to play Ph4 with the same idea as here, giving a bishop to "win" a rook! . 12.Nc3 Rxd2! with the same idea as in the previous comment, giving one for two! . 12...h4! Spassky gives this move "!" but today it should be considered natural and would probably be played by any grandmaster. Even though it would still get an exclamation mark! . 13.hxg4 Spassky gives a similar to the game variation: 13.Bxg4 Bxg4 14.hxg4 hxg3 15.Rg1 Rh1! S 16.Rxh1 g2 17.Rg1 Qh4+ 18.Ke2 Qxg4+ 19.Ke1 Qg3+ 20.Ke2 Qf3+ 21.Ke1 Be7-+ once again the game is decided on the dark squares. 13...hxg3 okay so two for two have been exchanged and now white is ahead in material with five against two on the dark squares. . 14.Rg1 As mentioned in the comment on Black's 10th move "every piece that is not in yellow should be improved or given away for a good purpose. Good purpose means exploring our dark-squared domination or material gains". . Well, Rh8 is not in yellow! . Rh1! We have the same situation as in the comments on white's 12th move. Black gives a Rook to "win" a Queen... Partly because Qe7 was not in yellow either! . So Rh1 surved both pusposes "exploring the dark squares and material gains"! . 15.Rxh1 g2 16.Rf1 Qh4+ We now have all the pieces that can attack dark squares working and Black is not realy defending them. . In the next move Black resigned but it is intresting to notice that despite the fact that initially all Black's moves where focused on the dark squares some of the last moves where made on light-squares and some of them where attacking white's pieces on light-squares as well. Those where the moves 14, 15, 17 and 18 of the analysis -even the mate comes on light squares as you can see in the analysis. This is indeed common because if you dominate one colour then, it is like the squares vibrate and hit the squares next to them as well! So dominating one colour will help you win the other as well -but remember that you first want to dominate one of them. . After this comment you can understand the comment on the first move on why it is better for white in the Sicilian to play 2.Nf3 and 3.Pd4. . 17.Kd1 gxf1Q+ this is the end and White now resigned. . 18.Bxf1 Bxg4+ 19.Kc1 19.Be2 Qh1# The light squares have fallen as well! 19...Qe1+ 20.Qd1 Qxd1# No defence on light squares either! 0–1
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Larsen,B-Spassky,B-0–11970A01URS-World2.1

Let us conclude with a chess game played in Princeton many years ago, by two great physicists:

Albert Einstein – Robert Oppenheimer

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1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Ba4 b5 5.Bb3 Nf6 6.0-0 Nxe4 7.Re1 d5 8.a4 b4 9.d3 Nc5 10.Nxe5 Ne7 11.Qf3 f6 12.Qh5+ g6 13.Nxg6 hxg6 14.Qxh8 Nxb3 15.cxb3 Qd6 16.Bh6 Kd7 17.Bxf8 Bb7 18.Qg7 Re8 19.Nd2 c5 20.Rad1 a5 21.Nc4 dxc4 22.dxc4 Qxd1 23.Rxd1+ Kc8 24.Bxe7 1–0
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Einstein,A-Oppenheimer,R-1–01933Princeton University

Physics and chess have always been – and still remain – my two greatest loves, even if, at times, I cheat on them both! What attracts me the most is the mystery that hides underneath their veil. I hope this short analysis succeeded in showcasing a few of the reasons why they have captured my heart!

About the author

Ioannis Halkias is a physicist with a wide range of academic interests, from physics and mathematics to politics and philosophy. As a kid he had shown talent and love for natural sciences and thus entered the physics department at the University of Crete where he is now working on physics and on the mathematics of finance. His hobbies mainly revolve around sports, music – and chess. He also served as a Green Beret Corporal in the Greek Special Forces.


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