Topology to teleos?

Over at Culture11, Will Wilson (a mathematics student at Yale) has an interesting article up, Screaming Shapes & Seven-Dimensional Donuts:

It is clear that reductionist and demiurgic approaches to science have stood unchallenged on the intellectual landscape for too long, and their profound philosophical and cultural implications left to unfold freely. Many will complain that explanation and understanding -- which shift the purpose of inquiry away from mere accuracy and toward knowledge of propriety -- is not the role of science. This may be true in the aftermath of the divorce of science from philosophy won by the positivists, but perhaps it is time that this split be healed in a way that allows us to gain in both humility and wholeness. Thom's theory alone may be unsatisfactory, but it points the way towards what is needed: a rigorous unification of prediction and explanation that is aware of its political and cultural implications; a postmodern natural philosophy for the masses.

That's the conclusion. You have to read the whole thing to understand what Will is getting at. I am myself a "Three cheers for reductionism!" fellow, but I'm curious if any mathematicians might weigh in (I'm not familiar with René Thom's work, which is the launching point for Wilson's essay).

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Surely the original article is a prank?

It's difficult to tell with post-modern bovine excrement. Post-modernism is intellect without intelligence.

Look at the quivering slush of weasel words:
"Many will complain that ..."
"This may be true..."
"perhaps it is time"
"a way that allows us"
"may be unsatisfactory"

And what does this phrase:
"shift the purpose ... toward knowledge of propriety" mean?

Then this burbler talks about "a rigorous unification" - ha! Since when has post-modernism found anything (other than a wine list) rigorous?

This goo is from dreamers who can see that the reductionist approach, intelligently applied, works wonders, but they have an unfulfilled spiritual urge for something more charismatic.

The last sentence of all is disturbing. It suggests that the science should abandon its search for correctness, independent of deeper implications, and instead adjust its conclusions in terms of social values. Clearly, the allocation of scientific and research effort is (and should be) a political issue, but it's a key idea that science delivers as-correct-as-we-can information, then it's over to politicians and people to decide what to do with that insight. Objectivity is good.

This article is nasty, wordy nonsense.

I remember that Rene Thom's Catastrophe Theory was very fashionable in pop science back in the 70s (yes, I remember the 70s), just like Chaos Theory and Complexity Theory later on. None of them have lived up to expectations (in biology, at least). Whenever someone excitedly claims that some fancy branch of mathematics is going to transform biology (usually meaning 'hey, this is better than boring old Darwinism').I want to shout at them 'Stop talking about it, just get on and do it!'

Personally I think the world can do just fine without a "postmodern natural philosophy for the masses." Furthermore the credibility of anyone who uses the word "demiurge" without irony is suspect.

Thom was one of the creators of catastrophe theory, is that what Wilson is referring to? Catastrophe theory was supposed to revolutionize the social science by 1978 or thereabouts

From another mathematician:

Let me get this straight: he thinks the problem with 20th century social science was too much reductionism and quantitative methodology? It seems to me that a completely non-scientific psychology and sociology were the main culprits.

The importing of quasi-Aristotelian categories using the analogy with topology to justify a metaphysical "form" is an awful generalization. The "example" of embryology is risible; I don't need to tell you that a metaphysical Aristotelian property of "form" is not how the embryo attains its shape.

And... we shouldn't use renormalization because all it does is give us accurate predictions? I mean, if there were a competing method that performed the same but guided our intuition in some way, of course we'd use that. But in lieu of such...

Overall impression: It remains possible that Thom himself had some well-formed ideas on the methodology of science (separate from his Fields Medal-quality topological ideas), though none of them come through in this essay. This is nearly Lyndon LaRouche-quality tripe, I'm sorry to say.

By Patrick (ortho… (not verified) on 13 Jan 2009 #permalink

It is clear that reductionist and demiurgic approaches to science have stood unchallenged on the intellectual landscape for too long, and their profound philosophical and cultural implications left to unfold freely. Many will complain that explanation and understanding -- which shift the purpose of inquiry away from mere accuracy and toward knowledge of propriety -- is not the role of science.

False dichotomy.

David B.:

Whenever someone excitedly claims that some fancy branch of mathematics is going to transform biology (usually meaning 'hey, this is better than boring old Darwinism'

Exactly. I had the same hunch and checked out Structural Stability and Morphogenesis on Google Books and sure enough there's some amusing nonsense about biology and evolution. (Although the foreword tries to excuse the confusion as a problem with the French language.)

There are few things I hate more than a good idea smothered by pompous windbaggery. I'm pretty sure there's a nut of a good idea there if you strip out all the horseshit, but I was only able to spot it because I've been talking about something similar with a math major friend. I don't know enough yet to talk intelligently about it, though -- half the conversation was a little over my head.

By Matt McIntosh (not verified) on 13 Jan 2009 #permalink

Let me get this straight: he thinks the problem with 20th century social science was too much reductionism and quantitative methodology? It seems to me that a completely non-scientific psychology and sociology were the main culprits.

This I agree with. Although my friends in the social sciences don't agree with me, to say the least. (I have to watch what I say around them)

I'd be careful throwing the PoMo label around too wildly. Yeah there's a lot of crap but then there was a lot of crap from the positivists as well. The fact is that philosophy of the social sciences or politics or ethics in general often ends up rather dubious. That doesn't keep there from being lots of Kantians about ethics out there, for example.

The demiurge comment actually makes a lot of sense in context. There really are fellows who think that everything comes from some "law" prior to the existence of the universe. And that does function like a Platonic demiurge. I think it a rather apt analogy. Of course I'd expect mathematicians with their platonistic tendencies at times to be more open to such a demiurge.

I do agree that mathematicians don't have a terribly good track record at making predictions of what math will transform particular sciences. (And I doubt many mathematicians would have picked Lie groups to transform physics prior to it happening)

To add, I think the problem the author has is that he thinks one kind of description (Descartes vortices) counts as understanding while an other (equations) doesn't. This seems wrong on a whole slew of levels. And interestingly both seem equally reductionist.

But overall I disagree with the view of the author on a slew of levels. (Although I do read his blog regularly)