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Many savants had the idea to use the chess game like a model for illustrating some concept of the Theoretical Physics. The universe is perceive like a wide game, analogous with Chess, played by the Gods. Then science consists to discover the rules. It's usually in this sense that is used the metaphor : Chess, familiar thing, is used to explain Physics, complex one. Sometimes this metaphor may reveal itself deep and accurate. This is at the honor of Chess, "Jeu des Rois, Roi des jeux". Unfortunately, this point of view is always frequently based on a positivist vision : the universe is an object and science studies its properties by using mathematical tools. Some people restrict the significance of this transposition, affiming laws of Chess aren't of a mathematical nature like those of the Physics. The positivist manner of seeing don't suit neither for science nor for chess. First of all, isn't evident laws of chess aren't of mathematical nature. Effectively a rule of the chess game is similar to an axiom in mathematics. For exemple, if you want to define a pawn, you have to specify its initial position, its way of moving etc... In other words a pawn is defines by its properties, exactly like a point, a straight line or a circle are defined by specifying their properties. Finally, the positivism, which beleived abolish the old idea of mathematical harmony of the world, is refuted because recent progress in theoretical physics. And this harmony is in the heart of the intelligibility of the world. In the same way, it's possible to wonder about the intelligibility of chess. But people may consider the reponse is obvious because this one is given, in a certain manner, "by construction". You may refute this argument considering that chess is understandable because this game depends of simple rules. But what exactly means "simple"? Simple to understand? But then, what means "understand"? In a certain sense mathematics is the only way to understand really. It seems to us we understand what is an electron when we learn it is represented by a little sphere, but we don't understand at all if somebody informs us that an electron is a density of probability, because this become mathematical. But a sphere was already mathematical. A cognitive function as fundamental as the recognition of symmetries is based on mathematics, the exact definition of symmetry uses the mathematical concept of group, which is defined in an axiomatc way in general. One shows in mechanics (traditional or relativistic) that the existence of real quantities like energy derives mathematically (thus a priori from the formal invariance of the laws of Physics. Howerver this invariance is itself a condition of prioriti of our understanding. Mathematics is more than one tool, more than the language of science, they are thez language of the physical world If the Chess game is understandable it is in fact rather than its rules are universal like mathematical laws. They specify the authorized moves in all possible positions, even in new positions. They have a "formal invariance" which is a "condition a priori of our understanding", exactly as in the case of theoretical physics. This argumentation is purely theoretical, but I don't beleive it useless. I am persuaded that to deeply like the Chess game, it's necessary to see there another think that only an entertainment stripped of significance.
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