Ordinologist and Synthesist
Feb. 10th, 2006 01:38 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
stoutfellowI do intend to write that post on (or taking off from) "Lodi", but in thinking about it I've been led circuitously to something else.
In Alexei Panshin's Rite of Passage, he describes a pair of - he seems to think of them as occupations, but they strike me more as modes of thought and action. In his own words (through the mouth of Mia, an early-teen, though precocious, girl):
Well, if Panshin can apply the distinction within philosophical ethics, I feel entitled to apply it to mathematics. There is certainly a place for ordinologists within mathematics; I feel myself to be of that bent. (Not just in mathematics; I remember, as a child, being enthralled by articles in The Book of Knowledge on the taxonomy of animals, which I take to be an ordinological concern, and in several of my other interests I see similar foci.) I've mentioned before my deep interest in parametrization, which is precisely a matter of bringing order to a disorganized mass of data. Synthesists also have their place, but that's a big topic, for another post.
The thing is, I'm not sure that the distinction (at this level) is as clear-cut as Panshin suggests. Consider the case of Isaac Newton in developing the differential and integral calculus. Now, most of the pieces of calculus were already in view by Newton's time. As far back as the High Middle Ages, Oresme had discussed infinite series, taking note of the phenomena of convergence and divergence, and Wallis (much later) had taken the subject still further. Viète had developed iterative techniques of approximation. Fermat had studied optimization problems, and come up with a version of the First Derivative Test. Galileo, Cavalieri, and Kepler had worked on problems of area, and Cavalieri in particular had come very close to the notion of integral. Torricelli and de Roberval had devised techniques for constructing tangent lines, and Isaac Barrow had even formulated the Fundamental Theorem of Calculus. Newton's great achievement was bringing all of these scattered fragments together into a reasonably coherent theory, showing that the same small handful of concepts underlay them all and systematizing the procedures others had developed.
So, a question. In doing this, was Newton acting as an ordinologist - bringing order to a jumble - or a synthesist - recognizing the commonalities between different areas of study? How big must Panshin's "rooms" be, for the title of "synthesist" to be earned? Or is it that Newton, being an overwhelming genius, transcended the distinction?
Any thoughts?
In Alexei Panshin's Rite of Passage, he describes a pair of - he seems to think of them as occupations, but they strike me more as modes of thought and action. In his own words (through the mouth of Mia, an early-teen, though precocious, girl):
If you think of the limits of what we know as a great suite of rooms inhabited by vast numbers of incredibly busy, incredibly messy, nearsighted people, all of whom are eccentric recluses, then an ordinologist is somebody who comes in every so often to clean up. He picks up the books around the room and puts them where they belong. He straightens everything up. He throws away the junk that the recluses have kept and cherished, but for which they have no use. And then he leaves the room in condition for outsiders to visit while he's busy cleaning up next door. He bears about the same resemblance to the middle-aged woman who checks out books in the quad library as one of our agriculturists does to a primitive Mudeater farmer, but if you stretched a point, you might call him a librarian.Later, discussing an ethics assignment, Mia describes a critical paper as more characteristic of an ordinologist and a creative one as more the work of a synthesist.
A synthesist, which is what I wanted to be, is a person who comes in and admires the neatened room, and recognizes how nice a copy of a certain piece of furniture would look in the next room over and how useful it would be there, and points the fact out. Without the ordinologists, a synthesist wouldn't be able to begin work. Of course, without the synthesists, there wouldn't be much reason for the ordinologists to set to work in the first place, because nobody would have any use for what they do.
Well, if Panshin can apply the distinction within philosophical ethics, I feel entitled to apply it to mathematics. There is certainly a place for ordinologists within mathematics; I feel myself to be of that bent. (Not just in mathematics; I remember, as a child, being enthralled by articles in The Book of Knowledge on the taxonomy of animals, which I take to be an ordinological concern, and in several of my other interests I see similar foci.) I've mentioned before my deep interest in parametrization, which is precisely a matter of bringing order to a disorganized mass of data. Synthesists also have their place, but that's a big topic, for another post.
The thing is, I'm not sure that the distinction (at this level) is as clear-cut as Panshin suggests. Consider the case of Isaac Newton in developing the differential and integral calculus. Now, most of the pieces of calculus were already in view by Newton's time. As far back as the High Middle Ages, Oresme had discussed infinite series, taking note of the phenomena of convergence and divergence, and Wallis (much later) had taken the subject still further. Viète had developed iterative techniques of approximation. Fermat had studied optimization problems, and come up with a version of the First Derivative Test. Galileo, Cavalieri, and Kepler had worked on problems of area, and Cavalieri in particular had come very close to the notion of integral. Torricelli and de Roberval had devised techniques for constructing tangent lines, and Isaac Barrow had even formulated the Fundamental Theorem of Calculus. Newton's great achievement was bringing all of these scattered fragments together into a reasonably coherent theory, showing that the same small handful of concepts underlay them all and systematizing the procedures others had developed.
So, a question. In doing this, was Newton acting as an ordinologist - bringing order to a jumble - or a synthesist - recognizing the commonalities between different areas of study? How big must Panshin's "rooms" be, for the title of "synthesist" to be earned? Or is it that Newton, being an overwhelming genius, transcended the distinction?
Any thoughts?
no subject
Date: 2006-02-16 03:26 am (UTC)