Chess and Physics in the classroom

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.

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

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

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

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

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

Albert Einstein – Robert Oppenheimer

[Event "Princeton University"] [Site "?"] [Date "1933.??.??"] [Round "?"] [White "Einstein, Albert"] [Black "Oppenheimer, Robert"] [Result "1-0"] [PlyCount "47"] 1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4. Ba4 b5 5. Bb3 Nf6 6. O-O 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

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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benedictralph benedictralph 3/6/2017 09:20
Nice article for a change.
Nathanian Nathanian 3/6/2017 04:32
This is an excellent article. Ioannis did a great job. It should be taught in Euclidean geometry class as a supplementary lecture to broaden knowledge in high school or lower. That is why Minkowski Geometry often called Euclid's twin geometry. I fondly remember the supplementary notes by Bjohn Felsager in Copenhagen 2004.
Silverback Silverback 3/6/2017 05:24
I couldn't help but notice that the painting of Gary Kasparov was made by Carina Jørgensen, a good friend of mine. This painting has appeared on magazine covers, websites, and even on stamps in Africa without giving her any credit for her artistic abilities. Please update the article with a name credit.


A7fecd1676b88 A7fecd1676b88 3/6/2017 05:32
"The great physicist and Nobel laureate Richard Feynman, often compared and likened physics to chess"

No, he didn't..unless the words often and likened have acquired a new meaning.

What he did was use a game (in this case, chess) with known rules, to talk about finding the laws of the universe. It did not have to be chess. It could have been ANY game. Checkers could have been substituted, and with minimal changes to his anecdote or lecture, the physics could have been explained just as well.

Having read most of his works, in addition to owning his collected works and papers in various colloquia in my personal library, plus videos of his talks, I am quite happy to tell Ioannis Halkias he has no idea what he is talking about.
Nathanian Nathanian 3/6/2017 05:35
Silverback, You are correct. Only with this practice, ChessBase keeps its head high with proper journalism for all of us. Credit has to be given when credit due. The painting was beautiful, the 13th champion looked very dignified. Look at the deep eyes!
Kasparogers Kasparogers 3/6/2017 06:31
Chess is a meditation about time, matter and space (and their transformations in each others!)
pari95 pari95 3/6/2017 07:19
Very nice! Halkias is also correct about Feynman. He did used chess often as an example, much more often than other games at least... But to my understanding this is not an article about physicists but about Physics, and it's a great one I should add!
GordonE GordonE 3/6/2017 09:52
Creative and excellent article. I enjoyed every bit.

@ A7fecd1676b88
I hope you wiped twice after spurting that garbage! Horribilis commentary.
Peter B Peter B 3/7/2017 12:33
These are analogies, nothing more. There is no real connection to physics.
A7fecd1676b88 A7fecd1676b88 3/7/2017 01:31
@Peter B -- Correct!

In Feynman’s book “Surely You’re Joking Mr. Feynman!”, in the chapter titled “Meeeeeee!”, Feynman gave his opinion on these attempts to make analogies with physics – the analogies are meaningless. To wit, here is Feynman:

“Another time somebody gave a talk about poetry. He talked about the structure of the poem and the emotions that come with it; he divided everything up into certain kinds of classes. In the discussion that came afterwards, he said, “Isn’t that the same as in mathematics, Dr. Eisenhart?”

Dr. Eisenhart was the dean of the graduate school and a great professor of mathematics. He was also very clever. He said, “I’d like to know what Dick Feynman thinks about it in reference to theoretical physics.” He was always putting me on in this kind of situation.

I got up and said, “Yes, it’s very closely related. In theoretical physics, the analog of the word is the mathematical formula, the analog of the structure of the poem is the interrelationship of the theoretical bling-bling with the so-and-so”–and I went through the whole thing, making a perfect analogy. The speaker’s eyes were beaming with happiness. Then I said, “It seems to me that no matter what you say about poetry, I could find a way of making up an analog with any subject, just as I did for theoretical physics. I don’t consider such analogs meaningful.”
Nathanian Nathanian 3/7/2017 01:53
if you do chess engine or chess programming, use the Manhattan distance or taxi-cab distance., or Chebyshev distance. Please see:


The sentence is not in quote so It is not from Feynman, it is from the author. The word “likened” in that context is from another physicist Dave Goldberg in his book “The Universe in the Rearview mirror.” Please Google the following phrase: “The great twentieth century Nobel laureate Richard Feynman likened the physical world as a game of chess”. You will judge for yourself.

Another comment, Minkowski spaces are finite Banach spaces in general. It is a prelude 4-dimension to special relativity. The 4 dim is timelike. I still think the article will make people think of those things: chess, physics, and math…
A7fecd1676b88 A7fecd1676b88 3/7/2017 03:03
@Nathanian -- I gather English is not your native let me clarify some things for you.

Just because the words Minkowski and Spaces are used together does not mean you are talking about the Minkowski spacetime of relativity.
Google and wikipedia are not going to help you. You actually have to understand the subject.

Thus, if you wish to define "Minkowski Spaces" as finite Banach Spaces, then so knowing that Minkowski Spacetime of relativity is not such a space, and "Minkowski Spaces" are not a prelude to special relativity. Since you evidently know what a Banach Space is, you must know what a norm is. There is no norm on Minkowski spacetime in the sense of Banach spaces. You should be able to verify this yourself.
Nathanian Nathanian 3/7/2017 07:21
Minkowski space = R1,n. It is n + 1 dimensional space with a new dot product:

⟨(v0,v1,...,vn),(w0,w1,...,wn)⟩=−v0w0 +v1w1 +···+vnwn.

The Minkowski inner product satisfies the following properties:

η ( a u + v , w ) = a η ( u , w ) + η ( v , w ) , ∀ u , v ∈ M , ∀ a ∈ R (linearity in first slot)
η ( u , v ) = η ( v , u ) (symmetry)
η ( u , v ) = 0 ∀ v ∈ M ⇒ u = 0 (non-degeneracy)

Then we have backward triangle inequality instead of <=, we use >= and backward inequality.

In Minkowski spacetime, we have "backward" Pythagorean Theorem |c|2 = |a|2−|b|2

Can generalize now Minkowski spacetimes are finite backward Banach spaces? This is another topic.

Thank you @A7fecd1676b88 and @Ioannis!. We always need referees in any work.
Ty Riprock Ty Riprock 3/7/2017 08:34
Emanuel Lasker was a friend and colleague of Einstein's, held a Ph.D. in Mathematics as well as one in Philosophy, and was present for several of the early parlor debates between Einstein and Bohr. Asked years later how much he understood of what they discussed, Lasker hesitated, then replied, "I understand a good deal more of it than Albert does of chess!"
ngn ngn 3/7/2017 03:07
Agree with Peter B. Some clever analogies, admittedly. But no real connection.

Also, the game Einstein vs Oppenheimer is very likely a fake.
pari95 pari95 3/7/2017 03:47
An article is not enough to teach physics or chess but I like the similarities. I think those ideas could be used as an introduction to physics lessons not scaring the kids away!
Nathanian Nathanian 3/7/2017 03:49
Botvinnik always encouraged his pupils to publish their analysis. Wait until 5 more years, I finish a Ph.D. in Mathematics and Deep Learning.I will have more novelty in both fields.

(continued) @A7fecd1676b88, @Ioannis, and et al It turns out the Minkowski space R1,3 is the model for spacelike in special relativity.i.e. timelike, lightlike, spacelike. I enjoy the discussion. Thank you.
okfine90 okfine90 3/8/2017 07:43
Albert Einstein is one of the greatest minds in the history. He has a special place in this Universe. In general, Chess cannot be compared with how physicists think. In Physics(actually in science) it's NOT ONLY intuition(we all know that humans cannot think without intuition) . But in physics you have an additional challenge. You need to have equations to tell the truth(e.g E=mc2). For example Einstein did not predict ONLY by intuition/judgement that Gravity slows time(General Relativity topic) and stop there(still it would have been much more brilliant in the world, so strange it is, but it happens and GPS systems have to consider that) . In fact he had his General Relativity equations ready even before the solar eclipse experiment. So Maths came first and then the experimental result!!!. Another example is Quantum Mechanics which is considered as the greatest intellectual achievement of human mind(and one can easily sense that after reading about it, so counter intuitive! it is yet the most powerful tool ) . So again these are not just intuitive thoughts. You have to have Maths behind it(one more example, Higgs boson detected in lab recently but predicated long before) to tell the ultimate truth(generalization) or else it has no meaning. And now after 100 years we see a Gravitational Wave detected in LAB due to collision between two black holes. And Gravitational waves were predicted by Einstein(obviously there is Maths behind it). Chess is a sport. It needs same skills as other sports-although it is a mind sport and needs some other skills. But Chess cannot surely teach Maths/Physics. The thinking process and goals of scientific thinking are totally different than chess thinking(chess as a sport not AI). We live in an internet age and are actually fortunate to have lots of stunning ,beautiful visual tutorials/films to teach physics(imagine those boring dead lectures 30 years before).