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In an answer to a programming question, I included the following:

The default behavior of [library function in question that displays an image] is to put the origin of the coordinate system in the upper left corner. This is different from plotting scientific data, such as two entities $x$ and $y$ against each other, where the origin, i.e. the point corresponding to the coordinate $(0,0)$, is in the lower left corner, with the (positive) $x$-axis extending to the right and the (positive) $y$-axis extending towards the top.

The latter is just scientific convention, though one that goes back centuries. Arguably (albeit near impossible to back up with historical evidence), the $x$-axis is traditionally aligned left-to-right because that's how text is written in many languages, while the $y$-axis is oriented towards the top as that's how people intuit an increase — much like the elevation of terrain.

It goes on to explain how that is different when plotting images. To be clear, my question here is not relevant to my original answer. The point of the above was to make the technical aspects more relatable. It was solely added for context.

I am curious, however, if "near impossible to back up with historical evidence" is in fact true. Or if there's any historical evidence that would contradict my statement.

I have read the history section in the Wikipedia article on the Cartesian coordinate system (though I do not currently have access to the references cited therein) as well as the question and answers regarding the Cartesian coordinate system in Newton's work here on this site.

Historically, what is the reason for the modern scientific convention that the horizontal plot axis is oriented left-to-right and the vertical plot axis bottom-to-top?

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    $\begingroup$ For the left to right orientation of $x$ axis, MY HUMBLE OPINION is : Western wirting is l-to-r. $\endgroup$ – Mauro ALLEGRANZA Aug 1 at 6:44
  • $\begingroup$ It would be interesting to know whether classical Arabic mathematicians saw the number line from right to left. As far as I can tell (see this image) today they have a l-r number line. $\endgroup$ – Chrystomath Aug 1 at 10:05
  • $\begingroup$ Maybe related to most people being right-handed. $\endgroup$ – Carl Witthoft Aug 1 at 12:33
  • $\begingroup$ @CarlWitthoft: Right-handedness is however prevalent among populations world-wide, including those that write from right to left. $\endgroup$ – John Hennig Aug 1 at 13:35
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    $\begingroup$ There is an old English tradition to orient the y-axis down. It goes back to Newton's times at least. But I've seen a 20 century British course of mathematical physics where the y-axis is oriented downwards. This makes the coordinate system oriented in the opposite way to the standard one and leads to the sign switch in some formulas. If I remember correctly the authors were Jeffreys and Swirles. $\endgroup$ – Alexandre Eremenko Aug 1 at 19:04
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From the description in Wikipedia it seems that graphs in the modern scientific sense were used by Nichole Oreseme (1323-1382), with the modern conventions about axis orientation. The Mactutor article on him asserts he invented graphing in the modern sense.

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  • $\begingroup$ Thanks a lot for your answer. I've (also) upvoted it, but am hesitant to outright accept it just yet. So as to not discourage further input. Though I do think this is good, or… as good as it gets, in terms of historical record. $\endgroup$ – John Hennig Aug 5 at 17:15
  • $\begingroup$ If the MacTutor article is correct and "it is possible that Descartes was influenced by Oresme's work", that would indeed be acceptable proof (I think) for the historical lineage of the convention. (The "reason" for the axes orientation then being: none in particular, just what Oresme chose.) The reference for the claim appears to be that book by Marshall Clagett. However, I don't have access to it. I have read a review of it, Grant 1972. But while it has convincing figures in it, it doesn't mention Descartes. $\endgroup$ – John Hennig Aug 5 at 17:16
  • $\begingroup$ @JohnHennig I'm on a trip and can't check what Clagett says. But in general (1) I tend to trust Mactutor more than Wikipedia, and (2) I trust Clagett more than both of them. $\endgroup$ – kimchi lover Aug 6 at 2:55

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