# Did René Descartes develop the Cartesian coordinate system by watching a fly on the ceiling?

René Descartes was a French man who lived in the 1600s. When he was a child, he was often sick, so the teachers at his boarding school let him stay in bed until noon. He went on staying in bed until noon for almost all his life. While in bed, Descartes thought about math and philosophy.

One day, Descartes noticed a fly crawling around on the ceiling. He watched the fly for a long time. He wanted to know how to tell someone else where the fly was. Finally he realized that he could describe the position of the fly by its distance from the walls of the room. When he got out of bed, Descartes wrote down what he had discovered. Then he tried describing the positions of points, the same way he described the position of the fly. Descartes had invented the coordinate plane! In fact, the coordinate plane is sometimes called the Cartesian plane, in his honor.

This website, quoted above, claims that René Descartes created his coordinate system by watching a fly on his bedroom ceiling while sick in bed. I've found the same claim on several other sites, including this one and this one which says "legend has it." This claim seems a bit absurd, as this website and this website place Descartes between ages 8 and 18 at the time of his discovery. The closest thing I've found to a reputable source is this page from Southern Arkansas University.

Is there an academic source confirming or disconfirming this claim?

• The Cartesian coordinate system seems to be attributed to Descartes, but coordinate systems predated him; for example, latitude/longitude goes back to at least 300BC, such that coordinate systems were clearly understood thousands of years before he was born. So, what exactly are these sources claiming that he invented?
– Nat
Commented Nov 20, 2017 at 22:25
• @Nat I think it's a bit clearer now that I've edited. I think they're referring to the Cartesian coordinate system you linked to, which defines all points in space by their distance from a fixed center point on each axis of whatever dimension of space is being referred to. I hadn't considered other coordinate systems when writing my question. Commented Nov 20, 2017 at 22:32
• I think the interesting part of the question is not whether Descartes was the first use such coordinates. But whether the fly story is true, or only made up many years later... Is that fly similar to the apple that fell on Newton's head in later fanciful retellings? Commented Nov 21, 2017 at 3:22
• In terms of constructing a focused, on-topic question, you've nailed it; this question's well-constructed. I'm mostly just trying to figure out how we can answer the question. The complication's that these claims have several layers of half-truths stacked on-top of each other. So, on one hand, we could in principle say, "No, the claim's false; that's not how any of this works.", but I think that such a simplistic response would itself be a half-truth, plus we'd lose out on the opportunity to fact-check the fuller story.
– Nat
Commented Nov 21, 2017 at 5:40
• For example, to mention the Newton's-apple thing as a well-known analog, part of that claim is that an apple hit Newton on the head one day. And presumably we could fact-check that, and it may-or-may-not appear to be true. But that's only a small part of the claim; even if that's true, did that apple affect Newton's work? And if so, then can that work be described as "discovering gravity"? And if so, can the effect on Newton's work be described as instantaneous, or did it merely kick off a chain of thoughts that led him to have certain thoughts about gravity?
– Nat
Commented Nov 21, 2017 at 5:45

The book Descartes: A Very Short Introduction (which at 100 pages vastly exceed most on-line biographies of him) only has this to say on the matter

Readers who are familiar with representing solutions to equations by using X and Y axes to plot coordinates are acquainted with techniques that, if not invented by Descartes, were developed and applied by him in novel ways in his Geometry.

I read implicit in that the doubt of the discovery story. No mention of a fly in the book.

The SEP page on Descartes is even a bit more adamant:

It should be noted, however, that as groundbreaking as this work may have been, contrary to the claims of many, nowhere in the Geometry is a “Cartesian Coordinate System” ever developed (that is, the x-y coordinate system taught to today's students of algebra), nor is he the originator of other mathematical concepts that bear his name, for example, the “Cartesian Product”

The 400-page Cambridge Companion to Descartes covers in some detail the Geometry. Basically, Descartes used two non-orthogonal coordinates to solve Papus' four-line locus problem. Actually, more or less the same info can be found freely on-line e.g. here. But nowhere in the Companion is it claimed that Descartes invented the Cartesian coordinates, nor is there a fly story mentioned. Also a MAA paper that is probably the best free write-up on this I found, says that in Descartes' Geometry "We do not see Cartesian coordinates."

• I would be interested in how far back the "fly" story goes. Commented Nov 21, 2017 at 15:46