Bike light

I also think I fixed by bike light, which had been nagging me for ages. I don't know that I'm ahead on things I should have done, but it's always good to make steady progress.

Thanks to alex for the best suggestion, of using tinfoil. But in the end, when I actually examined the innards in detail, I discovered the problem was not, as I supposed, that the batteries slipped sideways off the contacts. Rather than they are held in place at one end by a conducting plate, and the other, by a conducting springy tongue, and when you cycle over a bump, the battery moves laterally, temporarily compressing the insufficiently springy tongue, and momentarily losing contact with the plate.

As I'd thought, it would actually have worked better if there was a physical on-off switch, rather than an electronic one. The electronic solution is conveniently extensible, if you want to let the same button cycle through flashing modes, etc. However, the physical on-off switch would have had the advantage of remembering its state after a temporary power outage. Which shouldn't matter, but made the whole system just a little more fragile.

Fortuitously, having identified the problem, it was eminently susceptible to the most trivial of solutions. I inserted a little bit of folded paper behind each tongue, and lo, it had much less give, and the battery has no tendency to move in it's slot. It stayed on even when I tapped it, but I didn't feel confident calling it fixed until I'd ridden it an it kept working, which it now has.

ETA: Although come to think of it, that can't be the whole story, because it didn't used to just turn off: when it was tapped, it would sometimes cycle between "bright" and "faded" and "off". Anyway, the same solution seems to have cleared that up too.

Uncountable infinities in Magic

Update, someone else raised a very similar question on a message board. Indeed, using much the same technique I suggested, and I had found that link once before, but forgotten about it.

Page 1
Page 2

On page 1, someone asks a rules question that's a particularly apposite example of uncountable rules:

* The defender has generated an infinite number of small blocking creatures
* (Using a combo which involves mana burning down to a negative infinite amount of life!)
* The attacker has a spell which will win the game if any creature is unblocked
* The attacker uses two Nacatl War Pride, which when it attacks copies itself for each defending creature
* And turns both Nacatl War Pride into creatures that also are doubling season ("whenever a counter is put into play, instead put twice that many into play", although I think only the first one is relevant). Thus the second one puts an infinite number of creatures into play, to which an infinite number of doubling effects apply
* And asks "Will there be any unblocked attacking creatures?"

It's a particularly good example, because the cardinality is exactly relevant: the defender is exactly trying to make a bijection between blocking creatures and attacking creatures, and the attacker wants to know if there will always be an excess attacking creature.

On the second page someone proposes an explicit bijection (or rather, absence of a bijection).
I think this is functionally equivalent to my example.