explain xkcd - User contributions [en]

2625: Field Topology

2022-05-27T16:24:52Z

Aramisuvla: /* Explanation */ Add note about Gaelic football and Rugby.

{{comic
| number = 2625
| date = May 27, 2022
| title = Field Topology
| image = field_topology.png
| titletext = The combination croquet set/10-lane pool can also be used for some varieties of foosball and Skee-Ball.
}}

==Explanation==
{{incomplete|Created by a TOPOLOGIST MATHLETE - Please change this comment when editing this page. Do NOT delete this tag too soon.}}

This comic strip depicts a logical extreme of multi-use athletic facilities, in which sports are grouped by the topological equivalence of their fields (not to be confused with {{w|Field (mathematics)|mathematical fields}}, or the {{w|Fields Medal}} prize -- although successfully {{w|Straightedge and compass construction|constructing}} these fields might lead to medals of one kind or another being granted).

In topology, shapes which can be smoothly changed into one another, without making or closing cuts or holes, are equivalent{{Citation needed}}. {{w|Baseball}}, {{w|soccer}}, and {{w|tetherball}} are played on fields with no obstructions, so they are grouped ({{w|Group (mathematics)|heh!}}) into one continuous field without holes. Note that the goals on a soccer field do not create holes; because the goal posts are connected to the field with a net, altogether the goals and field are topologically equivalent to a plane. The same is true of ice hockey, as well.

{{w|Volleyball}} and {{w|badminton}} are played on a field split in two by a net, and the {{w|high jump}} has a bar that contestants jump over. The space bounded by the bottom of the net (or bar), the supporting poles and the ground can be considered as a hole, so their fields all have one "hole".

A basketball court has two holes, the nets. Parallel bars can be thought of as two rectangles and thus as two topographical "holes". A football field is a special case. Commonly, an American football field uses a "Y" shaped upright, which makes the field topologically equivalent to a plane. However, at lower levels of play (primary and secondary schools), sometimes the an "H" shaped upright is used, which creates a topological hole under the crossbar at both ends of the field. The comic might instead refer to Gaelic football or Rugby, both of which use "H" shaped goals and are called "football" in certain contexts.

The lane dividers in swimming create bounded holes on the 'playing surface' equivalent to the number of lanes minus one. And each hoop in croquet is a hole with one edge bounded by the playing surface.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

Four indistinct shapes with various numbers of holes in, with signs next to them

zero holes: "Baseball. Soccer. Tetherball."

one hole: "Volleyball. Badminton. High jump."

two holes: Basketball. Football. Parallel bars."

nine holes: "Olympic swimming. Croquet."

Image caption: "No one ever wants to use the topology department's athletic fields."

{{comic discussion}}

2625: Field Topology

2022-05-27T16:16:13Z

Aramisuvla: /* Explanation */ Change the explanation for football, taking into account H-shaped goal posts.

{{comic
| number = 2625
| date = May 27, 2022
| title = Field Topology
| image = field_topology.png
| titletext = The combination croquet set/10-lane pool can also be used for some varieties of foosball and Skee-Ball.
}}

==Explanation==
{{incomplete|Created by a TOPOLOGIST MATHLETE - Please change this comment when editing this page. Do NOT delete this tag too soon.}}

This comic strip depicts a logical extreme of multi-use athletic facilities, in which sports are grouped by the topological equivalence of their fields (not to be confused with {{w|Field (mathematics)|mathematical fields}}, or the {{w|Fields Medal}} prize -- although successfully {{w|Straightedge and compass construction|constructing}} these fields might lead to medals of one kind or another being granted).

In topology, shapes which can be smoothly changed into one another, without making or closing cuts or holes, are equivalent{{Citation needed}}. {{w|Baseball}}, {{w|soccer}}, and {{w|tetherball}} are played on fields with no obstructions, so they are grouped ({{w|Group (mathematics)|heh!}}) into one continuous field without holes. Note that the goals on a soccer field do not create holes; because the goal posts are connected to the field with a net, altogether the goals and field are topologically equivalent to a plane. The same is true of ice hockey, as well.

{{w|Volleyball}} and {{w|badminton}} are played on a field split in two by a net, and the {{w|high jump}} has a bar that contestants jump over. The space bounded by the bottom of the net (or bar), the supporting poles and the ground can be considered as a hole, so their fields all have one "hole".

A basketball court has two holes, the nets. Parallel bars can be thought of as two rectangles and thus as two topographical "holes". A football field is a special case. Commonly, an American football field uses a "Y" shaped upright, which makes the field topologically equivalent to a plane. However, at lower levels of play (primary and secondary schools), sometimes the an "H" shaped upright is used, which creates a topological hole under the crossbar at both ends of the field.

The lane dividers in swimming create bounded holes on the 'playing surface' equivalent to the number of lanes minus one. And each hoop in croquet is a hole with one edge bounded by the playing surface.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

Four indistinct shapes with various numbers of holes in, with signs next to them

zero holes: "Baseball. Soccer. Tetherball."

one hole: "Volleyball. Badminton. High jump."

two holes: Basketball. Football. Parallel bars."

nine holes: "Olympic swimming. Croquet."

Image caption: "No one ever wants to use the topology department's athletic fields."

{{comic discussion}}

2625: Field Topology

2022-05-27T16:11:52Z

Aramisuvla: /* Explanation */ Correct the explanation for why soccer goals don't alter the topology of the soccer field.

{{comic
| number = 2625
| date = May 27, 2022
| title = Field Topology
| image = field_topology.png
| titletext = The combination croquet set/10-lane pool can also be used for some varieties of foosball and Skee-Ball.
}}

==Explanation==
{{incomplete|Created by a TOPOLOGIST MATHLETE - Please change this comment when editing this page. Do NOT delete this tag too soon.}}

This comic strip depicts a logical extreme of multi-use athletic facilities, in which sports are grouped by the topological equivalence of their fields (not to be confused with {{w|Field (mathematics)|mathematical fields}}, or the {{w|Fields Medal}} prize -- although successfully {{w|Straightedge and compass construction|constructing}} these fields might lead to medals of one kind or another being granted).

In topology, shapes which can be smoothly changed into one another, without making or closing cuts or holes, are equivalent{{Citation needed}}. {{w|Baseball}}, {{w|soccer}}, and {{w|tetherball}} are played on fields with no obstructions, so they are grouped ({{w|Group (mathematics)|heh!}}) into one continuous field without holes. Note that the goals on a soccer field do not create holes; because the goal posts are connected to the field with a net, altogether the goals and field are topologically equivalent to a plane. The same is true of ice hockey, as well.

{{w|Volleyball}} and {{w|badminton}} are played on a field split in two by a net, and the {{w|high jump}} has a bar that contestants jump over. The space bounded by the bottom of the net (or bar), the supporting poles and the ground can be considered as a hole, so their fields all have one "hole".

A basketball court has two holes , the nets. A football field has two end zones, thus creating a 'hole' at either end of the playing surface. Parallel bars can be thought of as two rectangles and thus as two topographical "holes".

The lane dividers in swimming create bounded holes on the 'playing surface' equivalent to the number of lanes minus one. And each hoop in croquet is a hole with one edge bounded by the playing surface.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

Four indistinct shapes with various numbers of holes in, with signs next to them

zero holes: "Baseball. Soccer. Tetherball."

one hole: "Volleyball. Badminton. High jump."

two holes: Basketball. Football. Parallel bars."

nine holes: "Olympic swimming. Croquet."

Image caption: "No one ever wants to use the topology department's athletic fields."

{{comic discussion}}

Talk:2625: Field Topology

2022-05-27T16:03:22Z

Aramisuvla:

First [[Special:Contributions/172.70.86.64|172.70.86.64]] 12:50, 27 May 2022 (UTC)

Why is football on the two-hole field? Where are the holes? I don't think the goal posts in American football introduce any since they're not closed. Maybe it's soccer? [[Special:Contributions/172.69.68.88|172.69.68.88]] 12:58, 27 May 2022 (UTC)

:Well, you might still be able to call them holes. They would be if they were fully rectangles. --[[User:BlackBeret|BlackBeret]] ([[User talk:BlackBeret|talk]]) 12:59, 27 May 2022 (UTC)

: Gridiron football's field contains two areas (the endzones) that can be thought of as not being part of the "normal" field of play, for lack of a better way of saying that pre-coffee. Association football likewise has the areas within the nets. [[User:Noëlle|Noëlle]] ([[User talk:Noëlle|talk]]) 13:05, 27 May 2022 (UTC)

: My immediate thoughts were also that football (soccer) and football (gridiron) are the same, or indeed the other way round. In both cases the closed hole (assuming not a Y-like vertical holder, but H-like as per rugby football) plays no more or less topological part. Threading through the hole from behind has no relevence in either, and in fact defining it as a region that is 'a special enclosed gap with meaning' (which doesn't really matter in the topology sense, just like golf would be a topologically hole-less surface and as a coffee-cup's inside 'dimple' doesn't count, just its handle-hole that makes it equivalent to a doughnut) actually counts for something in association football. [[Special:Contributions/172.70.162.155|172.70.162.155]] 13:32, 27 May 2022 (UTC)

:: It's not the space bounded by the goal that is the 'hole' - it's the goal post itself (or in the case of the high jump, it's the bar, not the space under it). The reason soccer doesn't have 'holes' where the goals are is that they're positioned on the edge of the playable area - you can't play around the bars, because as soon as you cross the goal line you're out of play. And it doesn't matter whether it's a Y-shaped or H-shaped goal - topologically, they both form one continuous 'hole'. [[Special:Contributions/172.70.91.80|172.70.91.80]] 13:37, 27 May 2022 (UTC)

::: I don't think that's the reason why soccer doesn't have holes. The goalposts in football are also outside the playable area, and so are the poles in volleyball. I think soccer is listed as zero-holes because soccer goals are typically not fixed to the field, and are instead separate objects that can be dragged around and removed from the field. On the other hand, the same is true of volleyball and badminton nets (and those nets contain many holes!) so the comic seems a bit inconsistent.[[Special:Contributions/172.70.175.146|172.70.175.146]] 14:05, 27 May 2022 (UTC)

Tetherball, in many variants, does contain an obstruction -- the pole, which you're not allowed to touch. The Topology Department is getting tired of having to switch out the fields. [[User:Noëlle|Noëlle]] ([[User talk:Noëlle|talk]]) 13:05, 27 May 2022 (UTC)
:But you can surely jump over it, so it's topologically the same as a zero-height pole... [[Special:Contributions/172.70.162.155|172.70.162.155]] 13:32, 27 May 2022 (UTC)

Croquet has six hoops and a peg. How does that make for nine holes? Is it including the opponents' two balls as holes? And if so, why aren't opposing players counted as holes in the other sports? [[Special:Contributions/172.70.91.80|172.70.91.80]] 13:26, 27 May 2022 (UTC)

American football goals are Y-shaped. Rugby goals are H-shaped. Did... did Randall get those confused? Also, I fail to see how basketball and American football get two, croquet gets a bunch, but soccer gets zero. Aren't soccer goals (in-game at least) basically the same shape as croquet wickets, just waaaay bigger? Granted, I don't know anything about topology and I came to this wiki specifically cuz I'm dumb, so I'd love if someone could splain this all for me ;) --mezimm [[Special:Contributions/172.69.69.170|172.69.69.170]] 13:37, 27 May 2022 (UTC)
:The soccer goal has a net, so the ball can't go through it. Topologically it's just a wall (Randall seems to be ignoring all the tiny holes in netting, presumaby because they're smaller than the balls so they're insignificant to the sports). [[User:Barmar|Barmar]] ([[User talk:Barmar|talk]]) 14:10, 27 May 2022 (UTC)
::I agree with that explanation - the net is the only thing that makes the soccer field not to have holes. It should be included in the comic explanation.
::The hole for the volleyball only makes sense taking in account that the bottom of the net doesn't reach the floor, although this space is not used in the game.--[[User:Pere prlpz|Pere prlpz]] ([[User talk:Pere prlpz|talk]]) 14:18, 27 May 2022 (UTC)
::I agree about soccer; the explanation should be that soccer goals (with net) are topologically part of the plane. The same is true of ice hockey, even though you can travel "around" the net, it is topologically part of the field with no holes. As for (American) football, the topology only makes sense for H-shaped goals, which are more often seen on primary/secondary play fields than in higher level play. [[User:Aramisuvla|Aramisuvla]] ([[User talk:Aramisuvla|talk]]) 16:03, 27 May 2022 (UTC)

The group link pointing to group (mathematics) doesn't bear any relation with the sentence or the comic. I would remove the link.--[[User:Pere prlpz|Pere prlpz]] ([[User talk:Pere prlpz|talk]]) 14:18, 27 May 2022 (UTC)