Editing 2735: Coordinate Plane Closure

{{comic
| number    = 2735
| date      = February 8, 2023
| title     = Coordinate Plane Closure
| image     = coordinate_plane_closure_2x.png
| imagesize = 271x376px
| noexpand  = true
| titletext = 3D graphs that don't contact the plane in the closure area may proceed as scheduled, but be alert for possible collisions with 2D graph lines that reach the hole and unexpectedly enter 3D space.
}}

==Explanation==
This comic is a "Math Notice," which is presumably a warning or reminder for mathematicians or others who interact with the field of mathematics, in a similar way to how a "Travel Notice" may prewarn drivers of planned road closures for repairs (or [https://www.cameroncountytx.gov/spacex/ rocketry]). It also has similarities to that of a {{w|Notice to mariners}} or {{w|NOTAM|air missions}}, where nautical or aeronautical navigation might be impinged by an area (or volume) that should be kept clear from in the near future, and to notices from websites or software providers about planned maintenance, which alert users about upcoming outages. Specifically, this notice advises those who are using the coordinate plane to avoid drawing any graphs in the area with a hole until the damage is patched or fixed.

The joke may have been inspired as a response to the {{w|2023 China balloon incident}}, which occurred a few days earlier. This had occasioned one of the largest temporary flight restrictions, with a closed airspace as a response, in U.S. history. 

{{w|Coordinate planes}} are used in math for drawing graphs. The joke here is that a small section has been "closed for maintenance," likening the concept of a coordinate plane to an actual physical platform used by math, which is therefore vulnerable to damage such as is shown in the comic. In reality, the coordinate plane cannot be damaged as it is not a tangible thing.{{citation needed}}

Closure in mathematics can be a term relating to sets, specifically operations on sets, and a coordinate plane is a particular set of numbers.  A set is closed under an operation if all the "answers" to the operation are also in the set.  The coordinate plane is said to be closed under vector addition for example - adding together any two coordinates produces another coordinate in the plane.  Many functions and operators may be said to have closure on the real plane, and this comic may be a pun on that term. However, if there actually is a hole in the plane, then suddenly the plane will no longer exhibit closure. 

Also related to closure is the {{w|closure problem}}. Put simply, the closure problem is to find the highest or lowest weight of a closure in certain types of graphs. This comic may also be talking about the closure problem, as it talks about a hole in the graph, and to minimise it would be referring to the closure problem.
 
Closure can also be used in another sense, relating to the topology of a set; roughly speaking, a description of what parts of the set are "close" to others. In this sense, if one takes the closure of a plane with a hole, the result is indeed an intact plane, provided the hole is sufficiently (infinitesimally) small.

The title text notes that 3D graphs that cross the relevant x and y coordinates, but with non-zero z coordinates whilst in that zone, should be fine, since the hole only exists in the plane where z = 0. However, if they pass close - i.e. the z coordinate is small in this region - they should be wary of two dimensional graph lines suddenly becoming three-dimensional and interfering with them. This could be because they have intentionally entered three-dimensional space to avoid the closure, or possibly they have inadvertently been 'launched' above/below the plane by the torn and warped edges of the surface. Or they simply fell into the hole, thus entering 3D space. This is similar to warnings to road traffic in open lanes being warned of traffic merging from lanes that have been closed due to works or any other general warning of increased congestion upon a parallel route used as a diversion.

The concept of 2D objects suddenly entering 3D space — in a way that creates interesting drama and conflict — is the subject of a book, Flatland, that Randall has referenced repeatedly, such as in [[721: Flatland]].

==Transcript==
:[A coordinate graph is shown with both axes unlabeled but with two labeled ticks. In the middle of the shown area of the graph there is a hole torn in the white "fabric" of the graph's plane.  It has jagged edges and lines runs away from the hole in all directions. The area visible through the hole is covered in thin gray lines, and the edges of the hole cast shadows onto the surface below. Two points are marked on the graph at coordinates (X,Y) of (1.5, 1) and (2, 1.5). These two dots marks two of the corners of a square drawn with gray dotted lines, The square completely surrounds the hole. Above the graph there is a very large heading, with black danger triangles with exclamation marks in them, on either side of the heading. Below this there are three lines of text. And below the graph there are four more lines of text.]
:<big>! Math Notice !</big>
:The coordinate plane will be closed Thursday between (1.5, 1) and (2, 1.5) to repair a hole.
:Labels on Y-axis ticks: 1 2
:Labels on X-axis ticks: 1 2
:If your graph uses this area, please postpone drawing until Friday or transform it to different coordinates.

{{comic discussion}}

[[Category:Charts]]
[[Category:Math]]
[[Category:Flatland]]