Friday, July 28, 2006

A mathematical answer to Membership and Inidividuality

While I take a pause for thought in the debugging of my current puzzle at work, I will respond to a discussion from my friend Candlestring.

It is a rather tongue-in-cheek answer, since there is a nice metaphysical question surrounding the idea:
"the category for those who fit in no category"
which gets into all kinds of interesting and sometimes silly set-theory debates, like this paradox:
"In a town where the barber shaves every man who doesn't shave himself, who shaves the barber?"
which is a disease coming from people who do not live in the real world where there actually ARE barbers. Speaking of which, here's an interesting tale of GKC and his barber:
One day GKC came to be shaved after giving a wireless talk on the morals of the day, inferior, he said, to those of his youth. He asked the barber: "What did you think of it?"
"Sorry, I don't agree with you."
"That's very interesting, why not?" And they talked for half an hour.
[Maisie Ward, Return to Chesterton 123]
So in a real town, the mathematician would have nice long talks with the barber.

Anyway, I promised a mathematical answer to the question, and here it is. You see, the question about the categorization of humans can easily be converted into the question whether every individual is interesting or not. (For if we are all interesting, then that category is identical to the set of humans.) And that is even more easily converted into the following:

Theorem: There are no uninteresting numbers.
Proof: Assume the contrary, there exists a non-empty set U of uninteresting numbers. It could not be infinite, for then all its members would be interesting, since they form an infinite partition of the set of all numbers, and all such partitions are interesting. So U must be finite. Now, if U has more than one member, there must be a smallest such number; call it usmall. But then that number would be interesting, for usmall is the smallest member of U. But perhaps U has only one member: in this case, this number is the only uninteresting number, and any number which is so unique must therefore be interesting. Hence, U must be empty, denying our assumption. Quod erat demonstrandum.

But then this very technical solution is equivalent to what Maisie Ward calls "perhaps the most significant phrase" in GKC's notebook:

"I wonder whether there will ever come a time when I shall be tired of any one person."
[Maisie Ward, Gilbert Keith Chesterton 60-61]
GKC, following his Master, would be interested in YOU. And that is a quite a sign of hope. So let us do likewise.


At 28 July, 2006 17:52, Blogger Candlestring said...

Love it. My summer brain had to read this slowly, but I followed you the first time through which most definitely says something for how well you wrote it.

Is it therefore correct to also say that unique = interesting? I don't know how many years it has been since I've done proofs.

At 28 July, 2006 19:15, Blogger Dr. Thursday said...

Well, either the philosophers or the mathematicians (or both - what a terrifying thought!) will be after me for posting this. So, speaking with an eye to the nearest exit, I would say YES, unique = interesting.

But that is the whole point. God makes us one at a time; He does not tell us to love humanity - what is that? He tells us to love our neighbour.

And a person is more interesting than a whole set full of numbers. Hee hee.

At 30 July, 2006 00:57, Blogger Candlestring said...

Here is a quote I read today:

The thing that makes you exceptional, if you are at all, is inevitably that which must also make you lonely. -Lorraine Hansberry, playwright and
painter (1930-1965)

I'm not sure I like the wording and I don't know who Hansberry is, but it does give one pause. Unless you're reading my local paper in which case you'd be given paws. hoHO

At 30 July, 2006 08:21, Blogger Dr. Thursday said...

No, no, no! We may often be lonely, as we are fallen, and live with fallen people. (And to paraphrase St. Augustine, our hearts are restless until they find their connection to the Heart.)

But really: the thing which makes you exceptional is the ONE IMPORTANT THING by which your link into the Mystical Body is most clear.

Isn't there a fairy tale about this somewhere? I'll have to explore. And perhaps I will have to write something about histology - the unique characters of the cells of the body - and how they work together.

OK, I will see what I can do.

At 30 July, 2006 17:49, Blogger Candlestring said...

Good! How about a fairy tale about histology?

I wouldn't mind the quote so much if, instead of lonely, it said alone or unique or special or even supercalifragilisticexpialidocious. And I don't like that "if" in there, either.
She wrote A Raisin in the Sun. (Being smart and black was on her mind with that above quote, I think. Segregation, etc.)
I like this from a character in the play much better:
"Child, when do you think is the time to love somebody the most? When they done good and made things easy for everybody? Well then, you ain't through learning - because that ain't the time at all."
She died at age 34, young enough to have maybe changed her mind about loneliness, had she lived longer. But I have really no idea, so I'll be quiet now.

At 31 July, 2006 07:27, Blogger Dr. Thursday said...

Perhaps you mean plakkopytrixophylisperambulantiobatrix? Hee hee

Anyway, you will be delighted to know that I have started work on a histological fairy tale... I hope to have it done soon, and them you will see it here.


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