I learn a lot from reading Brad DeLong or the economically-inclined folks at Crooked Timber, but I get special enjoyment from Marginal Revolution. (I’m actually not being sarcastic for once, in case it’s unclear.) Much like training in physics affects they way you view the physical world, training in economics affects the way you view — well, almost everything. All of life becomes an exercise in maximizing returns and minimizing costs, subject to constraints. Consider for example the Tennis Ball Problem.
How many tennis balls should you play with?
Let’s say you had many, many balls and you could open the cans for free and never run out. Opening a new can every four points (four balls fit in a can) would lead to a massive clean-up and carry problem at the end. Furthermore how much help is it having more balls? Once they hit the net you still have to deal with getting another ball into play. In other words, the real trick is to manage your stock well (read: aim for good volleys), not to just to speed up the flow of balls into the court.
Just one ball is not efficient, because when it falls out of play it is probably far from you. The greater the number of balls, the more likely at least one will be close.
Many problems in life, including those of dating, the number of children you should have, and optimal inventory management, resemble the tennis ball problem.
I do not know how to solve the tennis ball problem, but I feel that twelve balls is too many.
Those last two sentences just about sum it up, don’t they?
I sense a variational approach to the Tennis Ball problem coming on should be possible.
There would, of course, be an important caveat to this approach: If tf, the endpoint of the curve, corresponds to your opponent’s crotch, it is obvious that the optimal number of tennis balls required is one.
Twelve balls might not be too many if you are working extremely hard to improve your ground stroke.
Heh, balls. Hard. Stroke.
You need an astrophysicist here, clearly.
One ball is not enough.
It is obvious that 100 balls is too many.
Therefore, O(10) balls is about right…
If they come in quanta of 4, then 8 maybe not quite enough, and 16 is close to the magical factor of 2 where you worry about the detailed physics. So, 12 sounds about right.
Wait, did I just agree with an economist…
Oh, not it is ok. 16 is too many, 12, not so much. ‘Cause 8 is clearly ok, and 12 and 8 are within one standard deviation of 10 and indistinguishable in most realistic observational contexts.
the correct answer is 8
Proof that economists are even more out of touch with the real world than physicists: tennis balls come three to a can.
Birds have to solve ”economics” problems all the time, see here. 🙂
I am wondering how much of practicing economics has to do with beautiful mathematical models (game theory can be really cool), and how much it has to do with the ugly reality (politics etc.), probably a little bit of both…
I know an Economist who will proudly tell you that he doesn’t care at all about the real world – only the beautiful mathematics. Strangely, he still seems to have quite a bit of money.
And I know an academic Economist, who has clearly demonstrated that he doesn’t think much of the real world, who comes to Category Theory seminars.
Kea, LoL,
though I’m currently studying applications of Category theory to Quantum Mechanics. We physicists are not save from this kind of wanderings either… 😉
“I’m currently studying applications of Category theory to Quantum Mechanics.”
fh
Really? Great! What sort of thing? Intuitionistic approaches?
The inherent weakness in this discussion: Just one ball is not efficient, because when it falls out of play it is probably far from you. The greater the number of balls, the more likely at least one will be close.
We are asked to assume that one is too lazy to walk over and pick it up, although one is desiring to play tennis?? The greater the number of balls the more likely one is to get injured, twisting an ankle or knee, falling on the court, etc. And, while macho points out that the balls come three to a can, i never understood why? Maybe economists already solved that problem, now they are worrying about balls?
clearly this depends on singles/doubles, pocket size, ease of removal from pocket, prescence of ballboys, ball speeds(balls might die if the players are good enough), fence hight, match or practice, players tendency to hit the ball long or in the net, desire for specific pace of points(if player is out of shape they will want to spend more time getting balls), ect ect.
obviously this is an experimental question not a theoretical one.
spyder, it’s a matter of maximizing returns. The time you spend picking up balls is not spent playing tennis. Actually I’m not completely sure that the problem isn’t dominated by boundary conditions, and it wouldn’t be most efficient to use a different ball for each volley, picking up the whole bunch of them once you are done.
And I did think it was three to a can, but things could have changed since my younger or tennis-ball-lobbing days.
Kea,
nope at least not yet. At the moment it’s actually still quite close to proper physics. and I’m making my way to the definitions of TQFT, and applications to quantum computation. So it’s mostly closed compact/symmetric monoidial categories, quite basic really, I haven’t strayed to the intuionist/Topoi side of things yet.
Are you working on that? Do you have any pointers of interesting (from a physicists PoV) allees to stray to in that direction?
Hi fh
If you think symmetric monoidal categories are simple (and you are quite young, correct?) then you have a bright future ahead of you! Yes, I am working on intuitionistic approaches to quantum logic (well, actually, QG logic but I haven’t got that far yet). There is surprisingly little out there. If you google Coecke you will find the most interesting papers to date. Take your time.
Cheers
Kea
Thanks!
Coeckes paper with Abramsky on a categorial semantics for quantum protocols (I *love* the title) has been precisely what I have looked through the last week. And yes I’m young, but if symmetric monoidal categories seem simple to me it’s because John Baez writes about them (quant-ph/0404040 and on his webpage), and everything John Baez writes about seems simple 😉
Nevermind that due to your suggestion what is now Coeckes next paper on my reading list is actually called Kindergarten Quantum Mechanics. *g*
I didn’t see yet that this is related to intuionist approaches (which I know next to nothing about!) though, I’ll keep my eyes open, thanks!