Difference between revisions of "Talk:2625: Field Topology"

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* The general arena-wide area is a further superset (perhaps with no additional complications, i.e. exactly congruent) of the field-of-play(er) definition. For coin-operated table-top games (foosball/table-football) the path from each goal may (additionally to any on-top topological loop-disconnections) force passage of the ball underneath and out into the new-play insertion spot. So add a couple more (unidirectional) paths, at least. Or six for a coin-operated pool/etc table, and I assume the Skeeball (not something I'm familar with, at least by that name) is defined that way already...
 
* The general arena-wide area is a further superset (perhaps with no additional complications, i.e. exactly congruent) of the field-of-play(er) definition. For coin-operated table-top games (foosball/table-football) the path from each goal may (additionally to any on-top topological loop-disconnections) force passage of the ball underneath and out into the new-play insertion spot. So add a couple more (unidirectional) paths, at least. Or six for a coin-operated pool/etc table, and I assume the Skeeball (not something I'm familar with, at least by that name) is defined that way already...
 
Sorry, I found I needed to say a lot more than I thought I did, so the first point (and sub-points) went on a bit and I cut down what I might have said for the following points. I may come back to re-edit this. I've got a handy little table, in mind, but I'm not sure it'll work much better to summarise everything I've been cogitating about for most of today while away from the keyboard... [[Special:Contributions/172.70.162.5|172.70.162.5]] 15:57, 28 May 2022 (UTC)
 
Sorry, I found I needed to say a lot more than I thought I did, so the first point (and sub-points) went on a bit and I cut down what I might have said for the following points. I may come back to re-edit this. I've got a handy little table, in mind, but I'm not sure it'll work much better to summarise everything I've been cogitating about for most of today while away from the keyboard... [[Special:Contributions/172.70.162.5|172.70.162.5]] 15:57, 28 May 2022 (UTC)
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:The "hole" in the goalpost in American football is relevant for field goals, not touchdowns.

Revision as of 16:40, 28 May 2022

First 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? 172.69.68.88 12:58, 27 May 2022 (UTC)

I think it is because the goal posts extend into infinity and the topological definition of a hole: something you can draw a circle around that you cannot contract to a point. [the user placed a horizontal rule instead of a signature by accident.]
Well, you might still be able to call them holes. They would be if they were fully rectangles. --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. 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. 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'. 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.172.70.175.146 14:05, 27 May 2022 (UTC)
Speaking from a "football is soccer" nation (well, mostly, the exceptional subregions would argue that it's rugby) a soccer goal is typically not draggable around the field, but permanent (or a unit frame that has to be painstakingly hoisted out of the ground if you don't want them in your football stadium, when you repurpose it for other purposes) and it's only the optional net that gets added to the park's permanent goalposts for the official five-aside competition evening or day of the weekend. Draggable goalposts need a further level of intermediate organisation that goes beyond the typical "shipping container with windows cut in it (with shutters bolted over them) as a cheap changing room/officials' cabin" that might be found near the edge of the field but rarely even has as much as a corner flag left in them, between games".
I presume that US 'football' posts are considered holes because they are an infinitely-tall window (even though the delineating poles only reach so high) that is a meaningful slice (where the goal is, you have to loop around it in mutually different unsimplifiable paths to reach the other side), but then that should make for two holes per end, if you count getting a field-goal and then returning round the sides (or vice-versa) as another valid surface-path.
...but, yeah, I can imagine the problem of definition (and cultural famiarity) here is going to produce more problems even than the understanding of topology. One of the less internationally-accepted comics, this. 172.70.85.177 18:51, 27 May 2022 (UTC)
O_O . Randall is united-statesian, so football means the thing where you tackle each other and hold the ball in your hands. I've never been into football, and I've always seen it with two large goal posts with a horizontal bar between them. The hole is formed under the horizontal bar. When I played football in computer games, you had to get the ball over the horizontal bar. After this, I'll search the web to see if the horizontal bar still exists. Regarding soccer, there aren't two holes because the nets are closed at the back. You cannot pass through the field structure by going through a goal: you bump into the net the ball bounces off of when a goal is made. So, Randall is considering soccer fields topologically equivalent to a plane (ignoring all the holes in the netting). 172.70.114.229 14:58, 28 May 2022 (UTC)
I looked up the goal thing and found that what I was imagining are called H-frame or H-style goal posts. Not the norm; the have two posts instead of one. I'm a weirdo that I thought they were what was up. But Randall could have been thinking of H-frame goals. 172.70.230.63 15:04, 28 May 2022 (UTC)
Many high school and amateur football fields still use H-frame goals. The resulting space can be used as a goal in some other sports. That does raise the question of why they didn't just have one field with lots of holes, and just plug the ones up that aren't needed for the sport being played. 172.70.134.191 15:57, 28 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. 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... 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? 172.70.91.80 13:26, 27 May 2022 (UTC)

[1] 'Nine-wicket croquet, sometimes called "backyard croquet", is played mainly in Canada and the United States, and is the game most recreational players in those countries call simply "croquet".' (Wikipedia) 172.70.126.215 18:58, 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 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). 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.--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. Aramisuvla (talk) 16:03, 27 May 2022 (UTC)
Agreed. Soccer goals are shaped such that their bottoms connect smoothly to the ground in a single continuous piece. So they are topologically equivalent to the plane. This wouldn't be the case if not for the back part holding the net. That's unlike basketball hoops, which are actual holes. The holes in football must be referring to the H-shaped uprights that were standard until 1967 in professional leagues and are still seen in some high school fields and even a couple college fields. 172.70.131.128 03:08, 28 May 2022 (UTC)
EDIT: I should point out that the net actually has, like, hundreds of holes. But I think the net here is being treated as a continuous sheet. 172.70.126.215 03:10, 28 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.--Pere prlpz (talk) 14:18, 27 May 2022 (UTC)

The joke seems important to me because their no consideration of the word 'field' being a math pun, and it raises the idea in readers. 162.158.79.74 15:11, 28 May 2022 (UTC)

In rugby (both League and Union) the goalposts are within the field of play: significant game activity takes place behind them. This is not the case with soccer. I have no clue what difference this makes topologically. [[Special:Contributions/|]] ([[User talk:|talk]]) (please sign your comments with ~~~~)

I've been thinking about this classification system, and can't quite work out the baseline for it. I think we're supposed to assume that the whole 3d manifold is represented in a 2d 'field', or at least any path through the air flattened to an arbitrarily thin surface 'bulge' during topological rationalisation. But there are several possible field-of-play definitions we can be using...

  • A single valid 'play' or traversal
    • For ball-sports (or indeed other play-objects) this could be where the item can travel. But in this case I think almost 'all' codes of football are Type 1 (first of the topologies) as almost every football code deals with both 'goal' and 'endzone' (where valid) as the same as a hole (dimple) in golf... It goes into it and it might as well come out of it again, there's no continuation of play 'through the defined' space, and so the topological hole (the barrier defined the scoring membrane's edge) never comes into play.
      Unlike in Gridiron, where a touchdown doesn't even need the 'ball' to touch the ground, rugby (league and/or union, and possibly further derivatives) requires this and a player can fail to score a Try if (s)he passes bodily over the line but is unable to plant the ball (not allowed to throw/drop it) and I'd have to check what happens if the defending player(s) keeping them sufficiently off the ground (assuming that's done in an allowable fashion) returns the intended scorer back over the line via a circuitous route around /back-through the suspended goal-mouth (above the cross-bar, between the verticals)... They keep changing those kinds of technical rules, so I can't be sure of the current technicalities involved.
      Likewise, a volleyball or shuttlecock that passes under the net-top-edge is out of play, so it is really a Type 1 under this definition. (Might as well be a solid barrier, floor-to-top-height, rather than a thin bar or a partial net.)
      The basketball case is interesting. Although a dunk ends the play of the ball, I'm not sure if the path of a ball up through the hoop does not. In that circumstance I could believe it is a Type 3 case, but if that's a game-stopping thing then Type 1.
      Croquet is indeed a varying number of paths through (I think) an unordered set of holes, or at least nothing to say that they can be taken out of order (or 'un-passed-through'), and you can't necessarily restrict a 'play' to one shot at a time if certain conditions allow you to play on, so dodging in and around all scoring zones defined by the hoops gives you something like.
    • For player/competitor/participant movement, similarly passing under the bar is not valid for the High Jump.
      I don't think there's anything to stop such transitions upon the Parallel Bars, but it is much more a feature of the Uneven Parallel Bars, whereas from what I've seen of the sport, the even-variety tends to be topologically used much as the pommel-horse.
      Players of football (American variations certainly, rugby of course, proper football if you don't bother with the nets) are not restricted from passing through the scoring area (either way) on a circuitous path that may be off the field of play but isn't off the field of players.
      For the Olympic Swimming, I'm not suring porpoising over and under the lane-delineations is a thing, so I would have said that (under this definition), it should be a number of entirely disconnected Type 1 'zones', with no valid movement between them at all.
      So far as I'm aware, there are no rules for/against croquet players passing through hoops (intentionally or perhaps because they severely annoyed an opponent) so maybe that stands in this case, too. Ditto for basketball, if hoisted. Although in both cases it may prevent the balls passing through immediately afterwards, without game-stoppage to resolve the issue.
  • If it's a game's-worth of play, then the status of the basket in basketball (unlike the pocket in snooker/pool/some-versions-of-billards) might be defined by the topological-hole-that-is-the-physical-hole's-edge, rather than treat it as the old basket-with-bottom from which the precusor to the net-ring almost immediately evolved. And the same could be said about the suspended scoring-hole (whether supported as Y-post or an H-post, the lower limb(s) are merely physical necessities that play little part in the gameplay specifics except as a general hazard to avoid, it is the crossbar and verticals-to-infinity (and the infinity itself) that is the gap through which a circular path cannot be rationalised back to a point). For most of the rest (including the participant-paths, with there being nothing to stop the traversal of a footballer of whatever stripe jumping the cross-bar, but that may only mean something in the topology of some variations, as far as the game is concerned...) it seems meaningless. Even in an Aussie Rules field with four 'posts' per end, and probably more interest in whether jumping onto an opposing player is against the rules or indeed an entirely legitimate and expected tactic.
  • The general arena-wide area is a further superset (perhaps with no additional complications, i.e. exactly congruent) of the field-of-play(er) definition. For coin-operated table-top games (foosball/table-football) the path from each goal may (additionally to any on-top topological loop-disconnections) force passage of the ball underneath and out into the new-play insertion spot. So add a couple more (unidirectional) paths, at least. Or six for a coin-operated pool/etc table, and I assume the Skeeball (not something I'm familar with, at least by that name) is defined that way already...

Sorry, I found I needed to say a lot more than I thought I did, so the first point (and sub-points) went on a bit and I cut down what I might have said for the following points. I may come back to re-edit this. I've got a handy little table, in mind, but I'm not sure it'll work much better to summarise everything I've been cogitating about for most of today while away from the keyboard... 172.70.162.5 15:57, 28 May 2022 (UTC)

The "hole" in the goalpost in American football is relevant for field goals, not touchdowns.