2625: Field Topology - Revision history

2.98.65.8: /* Explanation */ ...except that I messed it up, by a doubled-up key typo. ;)

2025-11-02T18:22:01Z

‎Explanation: ...except that I messed it up, by a doubled-up key typo. ;)

2.98.65.8: Neatening the provided link. (By several steps. Not [#], not [replacement text], not even {{template|what if}} (local) but {{template|What If}} (original)...

2025-11-02T18:20:59Z

Neatening the provided link. (By several steps. Not [#], not [replacement text], not even {{template|what if}} (local) but {{template|What If}} (original)...

217.65.132.37: Added citation

2025-11-02T17:13:59Z

Added citation

CalibansCreations: /* Explanation */

2024-10-15T07:52:57Z

‎Explanation

172.70.58.22: A misclick?

2024-10-04T19:01:55Z

A misclick?

141.101.98.203: /* Explanation */

2024-10-04T15:44:05Z

‎Explanation

172.71.242.188: Undo revision 340475 by 172.68.34.58 (talk) Already topologically explained. Hard to topologically re-explain in reverse.

2024-04-24T07:55:33Z

Undo revision 340475 by 172.68.34.58 (talk) Already topologically explained. Hard to topologically re-explain in reverse.

172.68.34.58: /* Explanation */

2024-04-24T00:38:15Z

‎Explanation

Xurkitree10: /* Transcript */

2023-04-20T06:40:11Z

‎Transcript

172.70.219.36: /* Explanation */

2022-11-01T16:57:35Z

‎Explanation

@@ Line 24: / Line 24: @@
 A basketball court has two hoops. {{w|Parallel bars}} can be thought of as two archways. Both have opportunities to pass through either (or both) structures, and so the material of the structures define a hole in the topological abstract of the playing 'space'.  Since we are told that these sports fields belong to the Topology Department - and are not necessarily generalized to all sports fields - we might assume that their "football" field is either for {{w|Rugby_union|rugby}} or for American football using H-shaped {{w|Goal (sports)|uprights}}.
-An {{w|Olympic-sized_swimming_pool|Olympic-sized swimming pool}} has ten lanes, and thus nine lane dividers which are fastened to the walls of the pool at each end, creating topological holes through the play area. Each hoop in {{w|croquet}} is similarly a hole through the space; while most versions of croquet use six hoops, nine hoops are used for "backyard croquet" which is played recreationally in the United States and Canada. The fact that the space in a swimming pool is {{What If|144||typically filled with water}} has been overlooked by the topology department.
+An {{w|Olympic-sized_swimming_pool|Olympic-sized swimming pool}} has ten lanes, and thus nine lane dividers which are fastened to the walls of the pool at each end, creating topological holes through the play area. Each hoop in {{w|croquet}} is similarly a hole through the space; while most versions of croquet use six hoops, nine hoops are used for "backyard croquet" which is played recreationally in the United States and Canada. The fact that the space in a swimming pool is {{What If|144|typically filled with water}} has been overlooked by the topology department.
 As mentioned in the title text, this last configuration is also {{w|homeomorphism|homeomorphic}} to a {{w|foosball}} table (with each rod sustaining the player figures above the table defining a hole) or a {{w|Skee-Ball}} lane (which is even more straightforward, as it is just a plane with several holes in which to throw balls). These "fields" don't actually have the same number of holes, but are apparently lumped together by the Topology Department as having "many" holes.

@@ Line 24: / Line 24: @@
 A basketball court has two hoops. {{w|Parallel bars}} can be thought of as two archways. Both have opportunities to pass through either (or both) structures, and so the material of the structures define a hole in the topological abstract of the playing 'space'.  Since we are told that these sports fields belong to the Topology Department - and are not necessarily generalized to all sports fields - we might assume that their "football" field is either for {{w|Rugby_union|rugby}} or for American football using H-shaped {{w|Goal (sports)|uprights}}.
-An {{w|Olympic-sized_swimming_pool|Olympic-sized swimming pool}} has ten lanes, and thus nine lane dividers which are fastened to the walls of the pool at each end, creating topological holes through the play area. Each hoop in {{w|croquet}} is similarly a hole through the space; while most versions of croquet use six hoops, nine hoops are used for "backyard croquet" which is played recreationally in the United States and Canada. The fact that the space in a swimming pool is typically filled with water[https://what-if.xkcd.com/144] has been overlooked by the topology department.
+An {{w|Olympic-sized_swimming_pool|Olympic-sized swimming pool}} has ten lanes, and thus nine lane dividers which are fastened to the walls of the pool at each end, creating topological holes through the play area. Each hoop in {{w|croquet}} is similarly a hole through the space; while most versions of croquet use six hoops, nine hoops are used for "backyard croquet" which is played recreationally in the United States and Canada. The fact that the space in a swimming pool is {{What If|144||typically filled with water}} has been overlooked by the topology department.
 As mentioned in the title text, this last configuration is also {{w|homeomorphism|homeomorphic}} to a {{w|foosball}} table (with each rod sustaining the player figures above the table defining a hole) or a {{w|Skee-Ball}} lane (which is even more straightforward, as it is just a plane with several holes in which to throw balls). These "fields" don't actually have the same number of holes, but are apparently lumped together by the Topology Department as having "many" holes.

@@ Line 24: / Line 24: @@
 A basketball court has two hoops. {{w|Parallel bars}} can be thought of as two archways. Both have opportunities to pass through either (or both) structures, and so the material of the structures define a hole in the topological abstract of the playing 'space'.  Since we are told that these sports fields belong to the Topology Department - and are not necessarily generalized to all sports fields - we might assume that their "football" field is either for {{w|Rugby_union|rugby}} or for American football using H-shaped {{w|Goal (sports)|uprights}}.
-An {{w|Olympic-sized_swimming_pool|Olympic-sized swimming pool}} has ten lanes, and thus nine lane dividers which are fastened to the walls of the pool at each end, creating topological holes through the play area. Each hoop in {{w|croquet}} is similarly a hole through the space; while most versions of croquet use six hoops, nine hoops are used for "backyard croquet" which is played recreationally in the United States and Canada. The fact that the space in a swimming pool is typically filled with water{{citation needed}} has been overlooked by the topology department.
+An {{w|Olympic-sized_swimming_pool|Olympic-sized swimming pool}} has ten lanes, and thus nine lane dividers which are fastened to the walls of the pool at each end, creating topological holes through the play area. Each hoop in {{w|croquet}} is similarly a hole through the space; while most versions of croquet use six hoops, nine hoops are used for "backyard croquet" which is played recreationally in the United States and Canada. The fact that the space in a swimming pool is typically filled with water[https://what-if.xkcd.com/144] has been overlooked by the topology department.
 As mentioned in the title text, this last configuration is also {{w|homeomorphism|homeomorphic}} to a {{w|foosball}} table (with each rod sustaining the player figures above the table defining a hole) or a {{w|Skee-Ball}} lane (which is even more straightforward, as it is just a plane with several holes in which to throw balls). These "fields" don't actually have the same number of holes, but are apparently lumped together by the Topology Department as having "many" holes.

@@ Line 28: / Line 28: @@
 As mentioned in the title text, this last configuration is also {{w|homeomorphism|homeomorphic}} to a {{w|foosball}} table (with each rod sustaining the player figures above the table defining a hole) or a {{w|Skee-Ball}} lane (which is even more straightforward, as it is just a plane with several holes in which to throw balls). These "fields" don't actually have the same number of holes, but are apparently lumped together by the Topology Department as having "many" holes.
-Unfortunately, the Topology Department does not seem to have a field for {{w|hurdling}} events.
+<s>Un</s>fortunately, the Topology Department does not seem to have a field for {{w|hurdling}} events.
 ==Transcript==

@@ Line 7: / Line 7: @@
 }}
-<nowiki>Insert non-formatted text here</nowiki>==Explanation==
+==Explanation==
 Field Topology is [https://encyclopediaofmath.org/wiki/Topological_field a subject in mathematics], but in this comic, Randall is instead examining the topology of playing fields used for various sports. The comic strip depicts a situation in which the common practice of multi-use athletic facilities has been organized by the "topology department" and constructed to be shared by all sports whose normal playing fields are {{w|topology|topologically equivalent}}. One key assumption in topology is that you can ignore the specificities of shape, size and material of the objects concerned. This presents an amusing contrast as the "equivalent" topology department playing fields are actually not very appropriate for the activities listed in the comic, as the standard positioning, size and shape of hoops, nets and bars and the material of the field itself are not equivalent to the real playing fields used for those activities.

@@ Line 16: / Line 16: @@
 When describing a negative space, such as the space around an archway, the 'hole' would be the material of the arch itself. This is because a loop formed by a ring around any part of the arch material can only be shortened to a finite length, not to a point; the 'hole' is the arch-shaped obstruction which forces the existence of these loops. A {{w|basketball}} hoop connected to the ground forms a similar obstruction with a loop through it, so the space around the hoop contains an equivalent hole. In this comic the topology department has analysed the spaces where various sports are played by the number of such obstructions in the playing area. Each space depicted in the comic is then signposted with the sports which are played on a field with that number of holes.
-{{w|Baseball}}, {{w|tetherball}} and {{w|soccer}} are played on fields which are continuous in three-dimensional space. This means it is possible to traverse any path around or over any of the structures defining the field, while there are no obstructions which can be traversed through in a loop around them. The goals on a soccer field presumably do not create holes because the goalposts and crossbar are connected to the field by the net; Randall apparently considers these to form continuous surfaces which do not allow loops through them, or possibly he has mixed up football and soccer in this comic.
+{{w|Baseball}}, {{w|tetherball}} and {{w|soccer}} are played on fields which are continuous in three-dimensional space. This means it is possible to traverse any path around or over any of the structures defining the field, while there are no obstructions which can be traversed through in a loop around them. The goals on a soccer field presumably do not create holes because the goalposts and crossbar are connected to the field by the net; Randall apparently considers these to form continuous surfaces which do not allow loops through them.
 {{w|Volleyball}} and {{w|badminton}} are played using a net suspended from poles, and the {{w|high jump}} has a bar that contestants jump over. The structure formed by the net or bar and the supporting poles can be considered to be a "hole" through the playing field, as a path over and under the net/bar forming a loop cannot be contracted to a single point, so their playing fields in the comic all have one "hole".

← Older revision		Revision as of 06:40, 20 April 2023
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	==Transcript==		==Transcript==
−	~~{{incomplete transcript\|Do NOT delete this tag too soon.}}~~
−
	:[A row of four signs, each held up by two posts, followed by a row of four rounded lozenge shapes, one for each sign. The signs and lozenge shapes are shaded as if three-dimensional objects, all being flattish with a small third dimension; the four lozenge shapes each have one pair of sides horizontal and the other pair at a slight angle from vertical, denoting a horizontal plane perpendicular to the signs extending "out" towards the viewer, which places each shape "in front" of its sign. All but the first lozenge shape have various numbers of ellipses within the shape - ovoids shaded to denote holes piercing through the objects.]		:[A row of four signs, each held up by two posts, followed by a row of four rounded lozenge shapes, one for each sign. The signs and lozenge shapes are shaded as if three-dimensional objects, all being flattish with a small third dimension; the four lozenge shapes each have one pair of sides horizontal and the other pair at a slight angle from vertical, denoting a horizontal plane perpendicular to the signs extending "out" towards the viewer, which places each shape "in front" of its sign. All but the first lozenge shape have various numbers of ellipses within the shape - ovoids shaded to denote holes piercing through the objects.]

← Older revision		Revision as of 16:57, 1 November 2022
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	==Explanation==		==Explanation==
−	{{incomplete\|Created by A NEGATIVE SPACE WEDGIE THROUGH THE HANDLE OF A COFFEE MUG. Please make sure the topological holes through the playing space have been corrected for each sport, and edit for clarity. And maybe move the mathematical fields/Fields Medal diversion to a footnote regarding the title. And could someone please keep track of the linguistic differences between "ellipse", "ellipses", and "ellipsis"? Do NOT delete this tag too soon.}}
−
	Field Topology is [https://encyclopediaofmath.org/wiki/Topological_field a subject in mathematics], but in this comic, Randall is instead examining the topology of playing fields used for various sports. The comic strip depicts a situation in which the common practice of multi-use athletic facilities has been organized by the "topology department" and constructed to be shared by all sports whose normal playing fields are {{w\|topology\|topologically equivalent}}. One key assumption in topology is that you can ignore the specificities of shape, size and material of the objects concerned. This presents an amusing contrast as the "equivalent" topology department playing fields are actually not very appropriate for the activities listed in the comic, as the standard positioning, size and shape of hoops, nets and bars and the material of the field itself are not equivalent to the real playing fields used for those activities.		Field Topology is [https://encyclopediaofmath.org/wiki/Topological_field a subject in mathematics], but in this comic, Randall is instead examining the topology of playing fields used for various sports. The comic strip depicts a situation in which the common practice of multi-use athletic facilities has been organized by the "topology department" and constructed to be shared by all sports whose normal playing fields are {{w\|topology\|topologically equivalent}}. One key assumption in topology is that you can ignore the specificities of shape, size and material of the objects concerned. This presents an amusing contrast as the "equivalent" topology department playing fields are actually not very appropriate for the activities listed in the comic, as the standard positioning, size and shape of hoops, nets and bars and the material of the field itself are not equivalent to the real playing fields used for those activities.