Update, 2008: The writeup that this was a response to seems to have disappeared. The italicized passage is a quote from that writeup.

The point is that all areas of mathematics (and their more worldly cousins in the realm of physics) begin with a set of unquestioned axioms. As I stated above, it is this situation that leads most critics of science to ignore physics and math because they believe these axioms are so fundamental as to be unquestionable.

Mathematics1 is not ignored because its axioms are seen as inviolate; rather, because the axioms are acknowledged as arbitrary as a component of the mathematics themselves. Euclid freely admitted that he worked from postulates that must be assumed, sans evidence, and millenia later, Riemannian geometry emerged, working from a changed set of postulates. More recently, formulations of algebra have been developed where 1 and 1 don't equal two2; while these are no less quantitative than the math we're used to (and are generally less useful), they can't be proven false except by infinitely long proofs, which don't really count. (See also: Godel's incompleteness theorem)

(Of course, mathematicians sometimes debate whether mathematics represents some sort of Truth or whether it's just contrived, abstracted burrito-counting, but when they do so they're engaging in metamathematics, not mathematics itself.)

At a more fundamental level (and setting aside the dangers of ascribing gender to ways of thinking) it seems like incorporating empathy and intuition into scientific studies in the way some feminists seem to advocate would be a giant leap backward -- Newton, for example, spent much of his life doing alchemy, believing that his state of mind when mixing potions mattered as much as the contents of those potions; having spent six months inventing physics, he accomplished basically nothing during his remaining decades. This is not to disparage empathy and intuition; in life (including the act of creating science -- phycists will often call a theory elegant, for example) they can be harnassed to help yeild valuble truths; but science itself should be based on the objectively measurable3 for very good reasons, which can be boiled down to this: the human mind is way too good at finding patterns where none exist. (Tangentally related: The Psychology of Randomness)

In a famous sociological study (can anybody remember its name? /msg me) participants were, separately, given a device with a switch and a light, and ten minutes to determine how to use the switch to modulate the light's flashing. When the time was up, most of the subjects reported that they'd figured it out, and explained their methods to the researchers. But the switch and the light weren't connected; it had been flashing randomly.

To extend and formalize the metaphor (grotesquely) : the things we see in our lives are lights; our actions are switches. Most of us have informal theories of which lights attach to which switches; science helps to test those theories, to determine which lights are unconnected.

Intuition is valuble as a component of a larger knowledge-gathering framework; it can point in the right direction, it can supply ideas that might have remained unthought (and in social situations, interacting with fellow human beings who think as we do, it becomes essential). But determining fact is best served in checking intuition with quantitative analysis. Record the exact times the bulb flashes and the exact times you flip the switch, and simple mathematics (Excel can handle it fine) will tell you the two have vanishingly little probability of bearing a relationship to one another. (See: prayer. Sorry.)

I haven't taken any courses in feminism, though, and intellectuals in specialized disciplines tend to use certain language differently from laypeople (so much so that academia has been completely detached from mainstream society); there remains, therefore, the possibility that I've completely misinterpreted Cabin Fever's writeup.

  1. I'll leave out a discussion of physics for simplicity's sake, and because I'm not sure I disagree on that point.
  2. ariels seems to know a lot about math and doesn't seem to think this is actually the case. Regardless, there are plenty of analogous mathematical phenomena.
  3. Here defined as measurement that holds relatively stable in separate instances among separate people.

Yeah, I know, writeup doesn't mean respond. And, in fact, this started as a response I was going to message to Cabin Fever, written in notepad only because it was easier, but as it quickly grew I realized sending it like that, as about 83 separate messages, would make me look completely psychotic. I've done my best to make it more standalonish and comprehensive, but yes, maybe this is misplaced. Should I really have called it "A critique of the feminist critique of the sciences", though? (On the gripping hand, if anyone can think of a better name/location, feel free to /msg me.)

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