Follow-through

As far as I know, in all racquet sports players are told to follow-through: to continue the racquet swing after the ball or shuttle have left the racquet. But of course the ball or shuttle doesn’t care what the racquet is doing at that point. So what’s the point of follow-through? The usual story is this: by aiming to follow-through, one hits the ball or shuttle better. If one weren’t trying to follow-through, the swing’s direction would be wrong or the swing might slow down.

This is interesting action-theoretically. The follow-through appears pointless, because the agent’s interest is in what happens before the follow-through, the impact’s having the right physical properties, and yet there is surely no backwards causation here. But there not appear to be an effective way to reliably secure these physical properties of the impact except by trying for the follow-through. So the follow-through itself is pointless, but one’s aiming at or trying for the follow-through very much has a point. And here the order of causality is respected: one swings aiming at the follow-through, which causes an impact with the right physical properties, and the swing then continues on to the “pointless” follow-through.

Clearly the follow-through is intended—it’s consciously planned, aimed at, etc. But it need not be a means to anything one cares about in the game (though, of course, in some cases it can be a means to impressing the spectators or intimidating an opponent). But is it an end? It seems pointless as an end!

Yet it seems that whatever is intended is intended as a means or an end. One might reject this principle, taking follow-through to be a counterexample.

Another move is this. We actually have a normative power to make something be an end. And then it becomes genuinely worth pursuing, because we have adopted it as an end. So the player first exercises the normative power to make follow-through be an end, and then pursues that end as an end.

But there is a problem here. For even if there is a “success value” in accomplishing a self-set goal, the strength of the reasons for pursuing the follow-through is also proportioned to facts independent of this exercise of normative power. Rather, the reasons for pursuing the follow-through will include the internal and external goods of victory (winning as such, prizes, adulation, etc.), and these are independent of one’s setting follow-through as one’s goal.

Maybe we should say this. Even if all intentional action is end-directed, there are two kinds of reasons for an action: the reasons that come from the value of the end and the reasons that come from the value of the pursuit of that end. In the case of follow-through, there may be a fairly trivial success value in the follow-through—a success value that comes from one’s exercise of normative power in adopting the follow-through as one’s end—but that success value provides only fairly trivial reasons. However, there can be significantly non-trivial reasons for one’s pursuing that end, reasons independent of that end.

Canadian doubles

Since the shutdowns of the spring, I’ve been playing more tennis, with my son and with graduate students. Sometimes you end up having three people wanting to play tennis, though, and what do you do?

The canned solution is Canadian doubles where you have two people on one side and one on the other, you get two points for winning on the singles side and one for winning on doubles, you rotate the players counterclockwise between games, and you end at some fixed number of points, say 11, by a lead of two. And the singles court is used on the singles side while the doubles court is used on the doubles side.

This is a good game: alternating between being a single playing facing off against two and playing as part of a team is fun. However, we noticed two difficulties. First, the standard rotation scheme has the result that each time one serves, one faces the same person. That reduces the variation. A fix of this is to depart from the counterclockwise rotation. A more serious problem is that towards the end of a match, when playing on the double side, one can have a perverse desire to lose the game. For imagine that your partner has 10 points, you have 8, and the third player has less than 8. Then if your side wins, your partner reaches 11 and wins the match. But if your side loses, you may still have a chance to win the match later. This can sap motivation.

Also missing from the standard Canadian doubles is that in the interest of trying all combinations, it would be nice to have the chance to be a singles server and a singles receiver in the same match.

So, after a number of iterations, here is improved Canadian doubles (I am Canadian, by the way). Instead of playing to a fixed score, you play three rounds of six games. Highest score wins. Ties are possible. You can end early if you can see that the number of games left is insufficient to change the ranking between the players.

The first and third rounds have serving from the doubles side. The second round has serving from the singles side. In each round, positions rotate in such a way that each of the six arrangements occurs once. Moreover, the positions are so arranged as to minimize the same player “being on the spot” too many times in a row. Thus, no one serves twice in a row or is in singles twice in a row, and we rule out the tiring sequence of singles, then serving, then singles again. I generated the sequences with a brute force python script.

Round 1: Service from doubles side

Server	Partner	Receiver
B	C	A
C	A	B
A	B	C
C	B	A
A	C	B
B	A	A

Round 2: Service from singles side

Server	Receiver-Deuce	Receiver-Ad
A	C	B
C	A	B
A	B	C
B	A	C
C	B	A
B	C	A

Round 3: Service from doubles side

Server	Partner	Receiver
C	B	A
B	A	C
A	C	B
B	C	A
A	B	C
C	A	B

Racquet sports

With the gym shut down, my teenage son and I have been exploring the world of racquet sports, including some more obscure ones. We love badminton, but we’ve been having too much wind (and pretty much any wind is too much for semi-serious badminton), so we also got a crossminton set. That was fun, though after the recent storms the wind is too high even for crossminton. Tennis has also worked for us, and is much more wind-tolerant, but I can't do it as often due to the danger of injury. We sometimes play ping pong on our kitchen table, but the table is a bit too small for a really good game (and the kitchen a bit too small for a larger table).

I also made wooden paddles for Goodminton / Jazzminton for light play with our seven-year-old. Sadly, it’s harder than advertised, at least for her, but I have been enjoying solo play, rallying with myself, one paddle in each hand. They could easily have been cut by hand, but I used my CNC router. The build instructions, with links to stl and svg files, are here.