stoutfellow (![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png)
stoutfellow) wrote2009-02-28 10:52 am
stoutfellow) wrote2009-02-28 10:52 am
Entry tags:
Orderings
Everybody - well, a fair fraction of "everybody" - likes rankings: the ten best this, the hundred top that, and so on. I do, myself, but as a mathematician I wince a little at them.
Fairly early in mathematical training, we encounter the notions of "partial ordering" and "total ordering". A partial ordering of a set declares certain members of the set to be "greater than" others; the main conditions are that, if A is greater than B, then B is not greater than A, and if A is greater than B and B is greater than C, then A is greater than C. To be a total ordering, one more condition has to be met: given two distinct elements A and B, one of them is greater than the other. So, you might put a partial ordering on a set {A,B,C,D} this way:
C D
|/
B
|
A
That is, B is greater than A, and C and D are both greater than B, but neither of C,D is greater than the other. A total ordering would require one of them to be greater.
The trouble, then, with rankings is that most things that get ranked really need to be partially ordered, not totally ordered. There's nothing wrong with C and D both being "greatest elements" of the set {A,B,C,D}.
All of which is a long-winded way of getting around to my real point, which is this: I'm about halfway through C. J. Cherryh's Regenesis, and I am confirmed in my opinion that Cherryh is a - not "the" - greatest living SF writer. Bujold is more humane, Wolfe more erudite, Bear at his best more mindblowing - but there's no one better at anthropological/sociological SF than Cherryh.
(She's damn good at space opera, too.)
Fairly early in mathematical training, we encounter the notions of "partial ordering" and "total ordering". A partial ordering of a set declares certain members of the set to be "greater than" others; the main conditions are that, if A is greater than B, then B is not greater than A, and if A is greater than B and B is greater than C, then A is greater than C. To be a total ordering, one more condition has to be met: given two distinct elements A and B, one of them is greater than the other. So, you might put a partial ordering on a set {A,B,C,D} this way:
C D
|/
B
|
A
That is, B is greater than A, and C and D are both greater than B, but neither of C,D is greater than the other. A total ordering would require one of them to be greater.
The trouble, then, with rankings is that most things that get ranked really need to be partially ordered, not totally ordered. There's nothing wrong with C and D both being "greatest elements" of the set {A,B,C,D}.
All of which is a long-winded way of getting around to my real point, which is this: I'm about halfway through C. J. Cherryh's Regenesis, and I am confirmed in my opinion that Cherryh is a - not "the" - greatest living SF writer. Bujold is more humane, Wolfe more erudite, Bear at his best more mindblowing - but there's no one better at anthropological/sociological SF than Cherryh.
(She's damn good at space opera, too.)