The blog's been slow. I've been off writing real mathematics, thinking for and preparing for the class I'm teaching this summer, and so on. But I'm still here!
And while I'm here, you should read Chad Orzel on the faulty thermodynamics of children's stories. In the story of Goldilocks and the three bears, one would expect that the papa bear is the largest, then the mama bear, and then the baby bear. Furthermore, you'd think that the larger the bear, the larger the bowl of porridge, and the slower it should cool off. But it doesn't seem to work that way! Read the comments come up with some interesting explanations.
Exercise for the scientifically-inclined reader: comment on the physical implications of the Three Little Pigs.
Exercise for the not-so-scientifically-inclined reader: what's with all the animals coming in threes?
04 May 2009
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I don't like to think about myself as not scientifically minded, but I've done some research about your last question. It seems that other people have done it, too. :-)
http://www.surlalunefairytales.com/boardarchives/2001/sep2001/significanceof3.htmlThis one costs a bit, but might be useful: http://www.azete.com/preview/20854.
I'm with the thinking that temperature is by preference, not by cooling, so the story isn't in error. That is, mama bear likes her porridge cold, so it was served chilled.
It's not just animals. Want to jump off a cliff simultaneously with someone else? You "go on three". Some languages only have words for specific numbers up to three. It seems like we count up to three subconsciously. Suppose you and someone else walk past a table where some people are eating lunch. An hour later, ask your companion how many people were at that table. I'll bet that you see a dramatic drop off in accuracy when the number of people at the table reaches four. Our minds seem to have some sort of fuzzy cutoff point at three dividing the built-in numbers from the ones we've constructed. Jokes come in threes (an engineer, a scientist, a mathematician) etc.
I suspect that one of the reasons joke things come in threes is that two is the minimum number of things you need to establish a pattern. Hence, three is the minimum number of things you need to establish a pattern and then break it.
What I want to know is, why do axioms often come in threes? The open-set axioms for a topology, the axioms for a sigma-algebra, the axioms for a partial or total order...
My guess regarding jokes: Three appears in jokes so often, because it's the smallest number after two, and two is the least number of points required to determine a straight line.
For many of these jokes involving three people, the joke usually builds up in a certain direction, and the punchline comes when the joke takes a sudden twist in some other direction.
The building up is usually done by relating what the first two people have done/said. Build up is not possible with only one person, because then we won't know what it's building up to.
In short, two points are required to establish a trend, and the third point is required to "break" that trend.
We can have more "points" in the joke, but most people don't do that, either to keep the joke short, or because they've run out of characters/stereotypes. :)
oops. 10 minutes too late. sorry for the double post! :P
Why do axioms come in threes? Because God plays jokes too.
No need to apologize! It's nice to know I'm not the only person who thinks this. :)
Threes? Male, Female, then some of us others, trangendered
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