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I realize modern algebraic notation is fairly new but for as long as there have been recorded chess games, every square I think was referred to using two coordinates, in old descriptive notation a column named after a piece and a row which I think would always have been a number from 1 to 8. Come to think of it, the game of Go would have had no good way other than two integer coordinates to refer to the intersections on which stones were placed.

Is there any evidence that Descartes or earlier mathematicians had been inspired by recorded chess or Go games, perhaps even introducing their ideas using the game boards? Go and chess are of course ancient games and I know recorded chess games predate Descartes by centuries and assume that Go also was recorded long ago.

It seems not even hard to imagine that before Descartes someone noticed that the distance between two points on the Go or chess board could be calculated using coordinates.

EDIT: Regarding Go notation: As I understand it, a very cumbersome way to record Go games was/is in use until fairly recently or still which actually displays successive positions. I guess the value is, just recording the moves would be very hard to follow for all but the best players (I emphasize "guess" because I barely know the rules of Go) could follow a game using algebraic notation. But I suspect had coordinates been used 2000 years ago, something like Cartesian geometry would have been the almost inevitable result -- who knows what that would have meant for China combined with other advances? I realize this is speculation, of course.

releseabe
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    The point was not coordinates as such, but their adaptation to solving geometric problems. The latitude-longitude coordinates were used in geography and astronomy since Eratosthenes and Hipparchus, and did not influence geometry much, although Oresme did call his axes after them. Discrete grid of chess was even less relevant. Apollonius used some proto-coordinates in Conic Sections, and that was the main influence on Descartes, along with Vieta's conversion of geometric problems into equations with lengths. – Conifold Jan 23 '23 at 11:30
  • @Conifold: would using coordinates on a map of two locations to calculates the distance between them not be an example of them being used to solve a geometric problem? if so, did no one do something like this prior to Descartes? – releseabe Jan 23 '23 at 11:56
  • That is done with the Pythagorean theorem (or its spherical variant), and coordinates only clutter the view. Descartes had to demonstrate that he could solve problems previously intractable or greatly simplify/unify known solutions. – Conifold Jan 23 '23 at 12:08
  • On a map, why would you use the Pythagorean theorem? If u calculate the legs of the triangle lengths, why not just directly calculate the length of the hypotenuse? i am assuming they would simply use the scale of the map to multiple the length calculated directly. – releseabe Jan 23 '23 at 12:14
  • Do we have examples of recorded chess games from 1600 or before? That would be interesting to see, even if they had no influence on Descartes. – Gerald Edgar Jan 23 '23 at 12:56
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    See this post for details: originally Descartes used non-orthogonal coordinates. – Mauro ALLEGRANZA Jan 23 '23 at 13:52
  • @GeraldEdgar i believe blindfolded chess -- not literally blindfolded but played twixt two players for example on horseback is pretty old and so some sort of way of referring to the squares verbally must have existed. it is possible that each square was given its own name and so co-ords were not used but i sure doubt it. – releseabe Jan 23 '23 at 16:11
  • Question about early recorded chess games asked here: https://chess.stackexchange.com/q/41424/34098 – Gerald Edgar Jan 23 '23 at 17:17
  • @GeraldEdgar i feel that descriptive notation in chess is less likely to inspire coordinates than Go's notation although i do not know how games were recorded in ancient times -- while blindfold chess is 1000 years old, i have heard that even world class Go players do not play without sight of the board which makes sense somewhat although i am not sure what i heard is even correct. – releseabe Jan 23 '23 at 18:29
  • @GeraldEdgar i read that some play blindfold go. but given that even in chess blindfold play was still a novelty until the 19th century, i could see go not having been played this way until recently. but notation does not employ coordinates but rather diagrams. – releseabe Jan 23 '23 at 18:37
  • @MauroALLEGRANZA: Here in Oresme we find a largely (I sure had never heard of him prior to reading your post) unknown wizard of centuries ago. Thanks for this very illuminating information. – releseabe Jan 24 '23 at 08:20
  • It is a version of Cartesian coordinates, but about "early version", one has to check how old is the chess notation, really. – Alexandre Eremenko Jan 24 '23 at 15:06

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