Right-to-left Cartesian planes
April 18, 2024 5:37 PM Subscribe
Has there ever been a convention for a Cartesian-style plane read right-to-left?
René Descartes is acknowledged as the originator of the mathematical convention for planes of coordinates, with an (x,y) axis, read with positive x values to the right and negative values to the left. But he didn't invent algebra, nor geometry, nor algebra about geometry, and many of the mathematicians who preceded him read and wrote in scripts (Arabic, Persian, Hebrew) which are read right-to-left. So has there ever been a convention for geometrical planes read in this way?
René Descartes is acknowledged as the originator of the mathematical convention for planes of coordinates, with an (x,y) axis, read with positive x values to the right and negative values to the left. But he didn't invent algebra, nor geometry, nor algebra about geometry, and many of the mathematicians who preceded him read and wrote in scripts (Arabic, Persian, Hebrew) which are read right-to-left. So has there ever been a convention for geometrical planes read in this way?
English is read left-to-right, as are many European languages, including the romance and germanic languages. There has been some work in cognitive science dealing with representations of numerosity, and native speakers of Hebrew (a language written right-to-left) in Israel are also taught in elementary school with a number line, on which numbers increase in the right-to-left direction.
In electrophysiological research (ERPs, which are an EEG-like measure), negative voltage potential is often plotted up. The legend i've heard is that for neuronal single-unit activity, a voltage potential corresponding to a neuron firing would be plotted with positive up. That voltage in a single neuron firing measured within the cell relative to outside the cell would go in a positive direction. The induced currents generated outside the cell would flow in the reverse direction. So, the convention of plotting negative up (hand-wavy up is "activity") came from analogy to intracellular potentials and trying to keep "activity" from baseline pointed in the same direction.
For doctors, x-rays, CT and MRI images are often produced in "radiological orientation" where the patient's left is on the right side of the image.
For physicists, the direction that current flows is often taken to be the opposite direction that electrons travel-- "conventional current" is the flow of positive charge in a certain direction. Chemists will consider current as flowing in the same direction that electrons move, and their convention disagrees with the physicist's convention. Physicists also use "the right hand rule." Nothing special about the right hand-- a convention was chosen, and it has been adhered to. The rules work the same with the left hand, if everywhere a cross-product is taken, the order of inputs is flipped.
This idea of choosing a direction for the sake of convention comes up very often, and convention is the only think that keeps people in agreement.
posted by Maxwell_Smart at 7:08 PM on April 18
In electrophysiological research (ERPs, which are an EEG-like measure), negative voltage potential is often plotted up. The legend i've heard is that for neuronal single-unit activity, a voltage potential corresponding to a neuron firing would be plotted with positive up. That voltage in a single neuron firing measured within the cell relative to outside the cell would go in a positive direction. The induced currents generated outside the cell would flow in the reverse direction. So, the convention of plotting negative up (hand-wavy up is "activity") came from analogy to intracellular potentials and trying to keep "activity" from baseline pointed in the same direction.
For doctors, x-rays, CT and MRI images are often produced in "radiological orientation" where the patient's left is on the right side of the image.
For physicists, the direction that current flows is often taken to be the opposite direction that electrons travel-- "conventional current" is the flow of positive charge in a certain direction. Chemists will consider current as flowing in the same direction that electrons move, and their convention disagrees with the physicist's convention. Physicists also use "the right hand rule." Nothing special about the right hand-- a convention was chosen, and it has been adhered to. The rules work the same with the left hand, if everywhere a cross-product is taken, the order of inputs is flipped.
This idea of choosing a direction for the sake of convention comes up very often, and convention is the only think that keeps people in agreement.
posted by Maxwell_Smart at 7:08 PM on April 18
Clarification: Descartes didn't use an explicit y-axis, just a line along which variable quantities are measured: "The concept of using a pair of axes was introduced later, after Descartes' La Géométrie was translated into Latin in 1649, by Frans van Schooten and his students. " Moreover "Contrary to popular belief, Rene Descartes's original La Géométrie does not feature a number line, defined as we use it today, though it does use a coordinate system. In particular, Descartes's work does not contain specific numbers mapped onto lines, only abstract quantities." The ruled number line aspect is due to Wallis. So a lot of what we call the Cartesian plane is stuff that René didn't set up.
If you swap the signs or the labels of the axes on our modern cartesian plane, you get a left-handed co-ordinate system, which is used in lots of computer applications. They essentially put the origin at the top left of the view screen, and count positive x to the right and positive y downward. Which is the same as counting positive x to the left, if y increases upward. RenderMan uses a left-handed system, as does picotron. I'm sure there are lots of other modern examples related to computers.
This is all down to sign convention of course (on preview: as alluded above), and so there are examples related to that. E.g. in timelines it's common to see units of Ma, increase to the left and decrease to the right, like so. Perhaps unsatisfying, but at least a few cases of numbers getting bigger to the left/ being left-handed.
posted by SaltySalticid at 7:10 PM on April 18 [2 favorites]
If you swap the signs or the labels of the axes on our modern cartesian plane, you get a left-handed co-ordinate system, which is used in lots of computer applications. They essentially put the origin at the top left of the view screen, and count positive x to the right and positive y downward. Which is the same as counting positive x to the left, if y increases upward. RenderMan uses a left-handed system, as does picotron. I'm sure there are lots of other modern examples related to computers.
This is all down to sign convention of course (on preview: as alluded above), and so there are examples related to that. E.g. in timelines it's common to see units of Ma, increase to the left and decrease to the right, like so. Perhaps unsatisfying, but at least a few cases of numbers getting bigger to the left/ being left-handed.
posted by SaltySalticid at 7:10 PM on April 18 [2 favorites]
On your ordinary map, north (0 degrees) is up, and directions in degrees go clockwise. The geometry is like the usual math axes rotated over the 45 degree line.
Of course, lat/long lines are based on the sphere, so the geometry needs some sort of adjusment depending on distance and the need for accuracy.
posted by SemiSalt at 4:34 AM on April 19
Of course, lat/long lines are based on the sphere, so the geometry needs some sort of adjusment depending on distance and the need for accuracy.
posted by SemiSalt at 4:34 AM on April 19
In Minecraft, location coordinates increase from left to right, so that's not applicable, but they increase from up to down (north to south in the game), which drives me a little nuts every time I play. Mmmaybe not what you're looking for...
posted by bricoleur at 4:45 AM on April 19 [1 favorite]
posted by bricoleur at 4:45 AM on April 19 [1 favorite]
My GIS skills are very rusty, but there appear to be some map projected coordinate systems that use metre grids but use Westings (instead of Eastings) and Northings. One such system is Hjorsey 1955 / Lambert 1955 for Iceland.
Unfortunately, all the open-source geo libraries seem to have a huge problem with west-positive coordinates, so I can't confirm this is a real thing.
posted by scruss at 10:01 AM on April 19 [1 favorite]
Unfortunately, all the open-source geo libraries seem to have a huge problem with west-positive coordinates, so I can't confirm this is a real thing.
posted by scruss at 10:01 AM on April 19 [1 favorite]
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More directly related to your question, the convention for matrices is (row, column), which is the opposite of Cartesian coordinates, but not in the sense you're thinking of, I don't think.
posted by hoyland at 6:42 PM on April 18 [1 favorite]