Tuesday, November 29, 2005

unified theory and math anxiety

One thing that’s been interesting to me here is the idea that complexity theory is the kind of thing Einstein (and plenty of physicist since) called a “Grand Unified Theory.” (Just like that, with capital letters and all and sometimes abbreviated GUT.) It’s what Einstein was hoping to figure out after the whole general relativity thing but never did. Last I checked some people in physics think string theory is a successful GUT. Have people heard of this? Basically, for physicists, a GUT would explain in what specific way all forms of energy (electromagnetic waves, gravity, and the forces that hold atoms together) are variations of the same thing. Reading about GUTs in high school was what prompted me to major in physics. But what always bothered me was that even though people referred to this as a “theory of everything,” it didn’t seem to explain anything in my life. I basically kept trying to figure out how this theory would explain how and why my thinking worked…. But I guess really it would never do this: it’s really only a “theory of every elementary particle,” and there are lots of “things” that are clearly not elementary particles.* That’s why complex systems theory is so much cooler: it connects very personal phenomena (how I remember things) with very big (economic development) or otherwise impersonal (particle physics) phenomena….

(*= Or not. This is basically what Arthur told the physicists: “Our particles in economics are smart, whereas yours in physics are dumb…” (141). But doesn’t the distributed cognition/computation approach tell us just the opposite? Isn’t the point there to model tools, technologies, and even individual people as simply as possible?)

Also: The point that I saw Hutchins making comes up again here: the point that it’s not so clear that math is the essence of all things; that math doesn’t actually explain what’s “really” going on behind the things that we observe, but it is just a tool to help us think about what we observe (21). (For Hutchins it was sort of a representational medium, maybe).

But this is not the only statement made about math in the book (maybe different people take different positions). At times, using math is associated with a lack of interest in the real world and irresponsibility; it's "abstraction" and “unreal” and therefore bad. Abstraction is inhuman, as far as most of these guys* are concerned. The physicists, for example, are appalled by how much math the economists rely on. Notice that this is different from saying math is just a tool.

(*Alright, I haven’t gotten through the whole thing yet, but do any feminist literary critics in the room have anything to say about the women in the book?)

I get uncomfortable when people try to make abstraction and weird speculations the enemy. It seems especially strange for anyone in this book to take such a position when it’s clear that complex systems theory wouldn’t work without abstraction and looking at something other than what we “directly” observe in “reality”. Complex systems theory does not study “things” that are obviously things in the world. They go even further than quasi-things like the syphilis virus and look at very un-thing-like things like the possibility/existence of life. It’s all about a big group of problems have the same structure (87). The similar structure that underlies all these “things,” I would argue, is pretty much an abstraction….

In English studies, you might hear similar complaints about abstraction, but in reference to “theory” instead of “math.” What’s really funny is that the theory that “doesn’t help us do anything in the real world” in English studies is sometimes labeled “French theory.” In this book, on 162, you’ll find that any “inhuman purity and abstraction” is also the fault of the French.

4 Comments:

Blogger jmj said...

Anthony:

Interesting post. I had the same thought about the unified theory when I was reading the book.

Here's a possible answer to the fear of abstraction: I think the characters in the book were all responding to disciplines where abstraction had become so important that real world data and results didn't matter. I think their aversion to abstraction is an aversion to using abstraction as the only tool with which to tackle the problems in question.

I think.

7:33 PM  
Blogger Annie said...

Regarding particles, math and abstraction...I want to bring in the topic of assumptions. The way I read it, Arthur was challenging the physicists' assumptions about particles / units of study. It's true that a particle of space dust does not devise strategies about how it will navigate its environment (i.e. it's dumb), but it is also true that it interacts with other particles of space dust, satellites, etc. in a way that may influence their behavior. (don't ask me where that example came from--too much coffee probably).

The point is that complexity science challenges all assumptions. If everything is connected, constantly emerging and unpredictable, then we need to be careful about drawing conclusions based on our assumptions. I found the same argument embedded in the math discussions. I didn't see anyone categorizing math as good or bad; rather, people challenged one another's assumptions about what math was capable of in relation to drawing conclusions about their areas of study.

9:59 AM  
Blogger Annie said...

Last year, PBS showed a great introductory program about string theory. I imagine it would be available on the local PBS channel's web site, but I haven't checked.

It's nice to know we have a physics major in our midst! I'd love to learn more about string theory from you.

10:04 AM  
Blogger Jim said...

Anthony-

I knew you were a structuralist all along - you and your GUTs.

Seriously, though - it seems that GUTs are what Levi-Strauss and Barthes were trying to get at. It also seems that some of "our" favorites (yes, the Frenchies) attempted to blow this out of the water. However, the attempts to blow these theories out of the water - ideas like "differance" - maybe they just replaced the old kind of abstraction with a new kind of abstraction.

I think a healthy fear of abstraction is good, but clearly we need some form of it to function in the world. I think this is what the issue that you're grappling with here, and it's an interesting one.

1:43 PM  

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