Sunshine And Delight

This morning, I was happy because the sun was shining. But why do I say "I'm happier whenever the sun is shining" instead of "I'm less happy whenever the sun is hidden"? Is the first more optimistic becauase it describes happiness, or the second because it ascribes happiness the default state?

Water clocks puzzle

Puzzle: I have two identical cylindrical lemonade bottles I punched small holes into the sides of, just above the bottom¹. I find that when I fill them each with water the first empties in 225 seconds and the second more quickly in 75 seconds. Without any other form of measurement, how do I use them to time 25 seconds?

Q. That's just one of those hourglass/numerology puzzles. If one hourglass empties in time p minutes, and the second in time q, then calculate p^-1 mod q, and you know pp^-1=1 (mod q) so pp^-1=1+nq. Run glass Q n times and glass P p^-1 times; when the first has finished you have exactly one minute before the second does.
A. If you think that's easy, try it.

Q. It's a trick, isn't it.
A. Probably.

Q. Tilt one of the bottles...
A. If you like. They *are* cylindrical, so you *can* halve the amount of water by tilting them until the water only just covers the base, if you think it'll help.

Q. I could use a...
A. No other equipment is necessary. You can use additional vessels of unknown size if you want to.

Q. How quickly did you solve it?
A. Actually, I made the puzzle up myself last night.

Q. Are you sure your solution works?
A. I may be mistaken. In which case I apologise, and promise to feel very embarassed.

Q. Do I need to use much maths for this?
A. Some. Nothing not taught at A-level IIRC.

Q. Can I find a different solution?
A. I don't think so, but try; it might be better.

[-1] That's not a footnote, that means 'inverse of p'
[1] Really.

Ship of Fools

I was browsing old message boards[1]. Is there anything more frustrating than when you find a six-month-old comment you want to reply to, but it isn't important enough to email or resurrect the thread...?

Someone's inner pedant objected to describing Jesus' crucifiction as him being "hung". Surely "men are hanged, dead meat is hung" is an approximation: doesn't "hung" refer to excecution by suspension specifically by the neck? I wouldn't have extended it to other suspension excecutions, especially if the suspension were not the primary cause of death.

As another morbid aside, Merriam-Webster has to say of hanging: "transitive verb: to suspend by the neck until dead esp. as a form of execution". I can't help but wonder what non-excecution ways there are to hang someone by the neck until dead? Accidents?

[1] Robhu linked to Ship of Fools Funniest and most offensive religious jokes competition, some of which are quite good. For instance:

A man ran through a crowded train looking very agitated, calling out, "Is there a Catholic priest on board?"

When he got no reply, he ran back up the train shouting, "Is there an Anglican priest on board?" Still no reply.

By now becoming more desparate, he ran down the train shouting, "Is there a Rabbi on board?"

Eventually, a gentleman stood up and said, "Can I be of any assistance, my friend? I'm a Methodist minister."

The man looked at him and said, "No, you're no bloody good. I need a corkscrew!"

Not that that's been methsoc's stereotype, I don't think :)

And in fact, before I realised I couldn't reply, I signed up. I've been officially sucked in to shipmateyness :)