Editing 1230: Polar/Cartesian

{{comic
| number    = 1230
| date      = June 26, 2013
| title     = Polar/Cartesian
| image     = polar_cartesian.png
| titletext = Protip: Any two-axis graph can be re-labeled 'coordinates of the ants crawling across my screen as a function of time'.
}}

==Explanation==
This comic plays upon the difference between reading a {{w|polar coordinate system|polar coordinate plot}} and the more common {{w|Cartesian coordinate system|Cartesian coordinate plot}}.

The graph purports to show the certainty in the viewers mind that it is a clockwise polar plot, as a function of time.

If seen as a Cartesian plot, the y (vertical) axis represents 'certainty' while the x (horizontal) axis represents 'time'. Each point on the plot is represented by two coordinates, the x-value and the y-value. As time increases, we move to the right and see the initial certainty of 50% decreases gradually to zero. That is, after a certain amount of time, we are certain that it is NOT a polar plot.

In a polar plot, each point on the plot is also located by two values, but in this case they are the radius (the distance from the origin) and the angle between the radius and an arbitrary starting line.  Here, the radius represents 'certainty' and the angle to the vertical represents 'time'. In this view, we see that as time increases (as we move clockwise around the plot) the initial certainty (the same 50%) now ''increases'' to a final value of 100%. That is, after a certain amount of time, we are certain that it IS a polar plot.

The intended joke seems to be that the graph is an exercise in confirmation bias. Whichever type you initially hypothesize is correct, that view will be confirmed by investigation. This is because the two different views are both correct - the graph can equally be considered a Cartesian or polar plot. This is somewhat counter-intuitive.

Throughout the graph, the sum of the two probabilities is 100%, i.e. (polar-observer's certainty that the graph is polar) + (Cartesian-observer's certainty that the graph is polar) = 100%. The shape of the graph appears to be (in clockwise polar form) r(t)=100/(1+cos(t)).

If the reader is open-minded, they would never reach certainty (0% / 100% depending on how you read the graph) because there isn't enough information to clearly decide either way.

The title text is a joke that if you are unsure how to label any two-axis (two-dimensional) graph, you can just say it represents the 'coordinates of the ants crawling across my screen as a function of time', and nobody could then argue with your data. "Hey, that's the path they walked!"

==Transcript==
:[Caption above the panel:]
:Certainty that this is a clockwise polar plot, not a Cartesian one, as a function of time:
:[There is a graph. The Y axis is marked out from 0% to 100%. The X axis is unmarked. A red line starts at 50% and traces out a roughly parabolic trend downwards along the X axis.]

==Trivia==
*It may also be a reference to the story of {{w|René Descartes|Descartes}}' discovery of the {{w|Cartesian coordinate system|cartesian plane}}, when he realized that he could pinpoint the location of bugs on his ceiling using numbers.

{{comic discussion}}
[[Category:Comics with color]]
[[Category:Math]]
[[Category:Line graphs]]
[[Category:Protip]]
[[Category:Self-reference]]
[[Category:Ants]]