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'We're all mad here. I'm mad, you're mad." [said the Cat.]
"How do you know I'm mad?" said Alice.
"You must be," said the Cat, "Or you wouldn't have come here."
- Lewis Carroll, Alice's Adventures In Wonderland
I'm amazed there's even a competition... Still we'd be wiping blood off the architecture if someone was accused of being the *least* disturbing member*.
*Which is me, of course. As the token normal person of the fforum... Didn't that read convincingly!
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'We're all mad here. I'm mad, you're mad." [said the Cat.]
"How do you know I'm mad?" said Alice.
"You must be," said the Cat, "Or you wouldn't have come here."
- Lewis Carroll, Alice's Adventures In Wonderland
Yes, but think of all the strange looks you can get when you have a sudden flash of insight and you stand up and shout (right in the middle of a public area) "A non-trivial quandle can't be a group because the operation can't satisfy identity, reflexivity, and bijectivity at the same time!"
(I didn't actually shout this, but I did say it in the middle of a conversation between friends, recently. And it's true.)
I wonder if Archemedes said something along those lines relating to his theory but he had a really really clever publicist or a really really lazy biographer who cut it down to Eureka!?
Well, I will admit "Eureka" has a much better ring to it, so I wouldn't be surprised. Besides, he got enough strange looks from running down the street with no clothes on… a streak of genius, perhaps?
Of course, he was a philosopher and they get automatic srange looks. I mean, philosophy is a group of people who sit around and decide that the world does not exist, then go get lunch.
And can you translate the mathimatese into English (or as close as you can get)?
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'We're all mad here. I'm mad, you're mad." [said the Cat.]
"How do you know I'm mad?" said Alice.
"You must be," said the Cat, "Or you wouldn't have come here."
- Lewis Carroll, Alice's Adventures In Wonderland
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'We're all mad here. I'm mad, you're mad." [said the Cat.]
"How do you know I'm mad?" said Alice.
"You must be," said the Cat, "Or you wouldn't have come here."
- Lewis Carroll, Alice's Adventures In Wonderland
Do you really want the mathematese translated? I'll try to do it in no more than a paragraph…here goes…
A group is an algebraic structure that was first studied way back several centuries ago. Basically, it's a set of elements of some kind, paired with a binary operation--an operation that takes each pair of elements and gives back a new element from the set. An example would be the set of integers with the operation of addition. In order for it to be a group, there are three axioms that have to be satisfied by the set and its operation. A quandle is a much newer algebraic structure, also a set paired with a binary operation, but it has a different set of three axioms that have to be true. I was thinking about quandles and trying to understand them better, so it occurred to me to ask if a quandle could ever be a group (meaning that both sets of axioms are satisfied). It turns out that if the set has only one element, then it is both, but if the set has more than one element, it can never be a quandle and a group at the same time.
Anyway, the thing I like about philosophers is that they may spend all their time proving the world does not exist, but at least they're practical enough to do all their work in buildings with well-grounded copper roofs!
Martin, you do computery stuff. Have you ever encountered the Dining Philosophers problem?
Hopefully just about everyone who has ever dealt with either academic or real-world computing has experience of this and sleeping barbers? Have they stopped using it as a logic problem?
The trouble that I had was that I always found the contention and queue issues easier to visualise as network or peripherals without the philospher/barber analogies! Perhaps it was just that I could not imagine five philosophers without at least two being drunk.........
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My computer beat me at chess, but I won at kickboxing
But the nice thing about analogies/metaphors is you get to act them out--like my professor had us do last week! He brought cookies and chopsticks into class and we got to pretend to be dining philosophers.
We went through different sorting algorithms on the lawn recently.
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'We're all mad here. I'm mad, you're mad." [said the Cat.]
"How do you know I'm mad?" said Alice.
"You must be," said the Cat, "Or you wouldn't have come here."
- Lewis Carroll, Alice's Adventures In Wonderland