Since the topic of spherical cows came up in the comments to the previous post, I'll use that as an excuse to retell two old jokes.
* * *
There was a civil servant. (Wait, it gets better.) He set out to research ways of improving milk production. He hired three teams: one led by a physicist, one by an engineer, and one by a mathematician. (He had an excuse; his office was out of monies earmarked for biologist-hiring, so he had to improvise.)
Six months and much paperwork passed; and the civil servant called the three into his office to hear how their particular experiments had succeeded.
First came the physicist. He reported a 20% increase in milk production; he had fed the cows raw chemical elements in the exact combination that milk is made of; and milk production had gone up 20%. Unfortunately, 20% of the cows had died, making this an exercise in running in place.
Hearing this, the mathematician sniggered.
Second, the engineer told her results. At her farm, the milk production had gone up 50%, thanks to a revolutionary new cow-exercising obstacle course and a milking machine made of surplus jet engine parts. (Thanks to one of them, anyway.) Unfortunately, 50% of the cows had been lost in jet engine-related mishaps; though in addition to milk, the farm now also produced bottled cow. Still, overall, the civil servant judged this as running in place.
Hearing this, the mathematician smirked.
Finally, the mathematician came in, and turned at the blackboard, and raised a piece of chalk --- only to be interrupted by an inquiry for the increase in milk production.
"Oh, an increase of 300%", the mathematician mumbled, and drew on the blackboard.
The physicist made an incredulous noise. The engineer choked. The civil servant expressed cautious approval.
And the mathematician said: "However, I did lose 300% of the provided cows."
* * *
I know, the canonical endquote is, "Ah yes, my method was very simple. Let us assume all cows are identical spheres of constant density..." --- but what's the fun in telling the joke you expect?
Oh, and the mathematician is naturally smirking not because she's smug and doing better; indeed, she's doing something horribly wrong; but she's amused because 80% times 120% and 50% times 150% are both less than 100%.
Now, the second joke.
* * *
A pair of physicists got into trouble, as physicists usually do. This time they got into a balloon, and went flying; there rose a great amount of mist, and obscured their view; there rose a greatly variable wind, and confused their senses of direction and location; and soon, drifting along at altitude, location and velocity unknown, they were forced to yell towards the sound of an accordion they heard rising from far below.
"Hello!" they cried. "Help! Please tell us where we are!"
After a while, a faint voice answered: "You're in a balloon!"
At this, one of the physicists pulled a cord, and the balloon collapsed; as the other howled in terror, they plunged downwards --- and with desperate steering just barely fell, with a great though safe splash, into the lake that was just next to their university's math department.
"Why", the second physicist, the terror-stricken one, gasped, "you lunatic! You could have killed us! What if it had been the Tall Spiky Biology Building below us!"
"Relax", the first physicist said, "it was perfectly safe. I knew a mathematician answered us, and the time of day being the working hours, she was at the department, right next to this lake."
"Why, how did you know she was a mathematician?"
"Perfectly simple. The answer she gave us was absolutely, indubitably, irrefutably true... and absolutely useless."