[Note from moderator: Someone may revive this subject again next year, but for this round the 48 hour rule is now in effect: nothing further will be posted after December 9, thanks.] On Wed, 7 Dec 2011, Dusko Pavlovic wrote:
I agree that we should not use the term "schizophrenic object" in category theory.
For one thing, it sounds like some sort of a metaphor. We should never use metaphors. For another thing, it does not sound serious. It might suggest that we are sometimes joking.
(A) What's wrong with metaphors? In Chapter 24 of his book "Metamagical Themas", which has some excellent chapters on analogical reasoning, Douglas Hofstadter says: Don't press an analogy too far, because it will always break down. In that case, what good are analogies? Why bother with them? What is the purpose of trying to establish a mapping between two things that do not map onto each other in reality? The answer is surely very complex, but the heart of it must be that it is good for our survival (or our genes' survival), because we do it all the time. Analogy and reminding, whether they are accurate or not, guide all our thought patterns. Being attuned to vague resemblances is the hallmark of intelligence, for better or for worse. (B) What's wrong with joking? Jokes are metaphors, so by (A), they're the hallmark of intelligence. Besides, in my country, joking is the default technique for talking about reality. We'd be lost without it.
I propose that we use the term *bipolar object*.
For one thing, it sounds more mathematical. For another thing, in psychiatry they only talk about subjects, not objects, so there is no confusion.
It's confusing if you grew up as a chemist, which I did. A bipolar object has two ends with opposite properties. For example, detergent molecules are bipolar. One end is hydrophilic and loves the water. The other end is hydrophobic and loves olive oil and bacon grease. If you're lucky, it loves them so strongly that it will wrench them away from your dirty dishes. So to me, a bipolar object has ends, and a difference therebetween; and therefore, it has length. Categorical objects don't.
my 2c, -- dusko
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