... at the time mathematicians developed non-Euclidian geometry, the world was experienced as fully Euclidean. Although science and mathematics are frequently taught together, mathematics, unlike science, is a closed, deductive system in which conclusions can be derived from assumptions even if the assumptions do not correspond to any known reality. In short, it is not the absence of reason that distinguishes religion from science, but rather the willingness to accept starting assumptions from outside of shared experiential space — James's unseen order — sometimes including the miraculous.
Saturday, January 10, 2009
Not the same thing ...
... Intelligent Design or Intelligible Design?
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Hmmm.... not so sure about the world being experienced as "fully euclidian". People did know the earth was round before that, and that the shortest way between two points of the earth wasn't a straight line but a geodesic (a "great circle"). Mapmakers have known the corresponding problems for years...
ReplyDeleteQuite right though that maths and science are completely different things.
And for those who think it's just a "closed, deductive system in which conclusions can be derived from assumptions" should watch this:
http://uk.youtube.com/watch?v=CPRnUPH8sME
But then there's Gödel's incompleteness theorems, which would seem to reinforce the science/faith connection. Personally, I think people ought to train themselves to become more comfortable with uncertainty at all levels of existence. The unfortunate aspects of both religion and science derive from attempts to be certain (obey this commandment, follow that practice and you will surely be saved; or use this notion - Darwinism, say - and you can explain everything). I don't think life works that way. The moralists fail to understand that any sane person knows when he does something wrong - and that it often has nothing to do with anybody's rules. And the Darwinian explanations of everything from why I fell in love with my wife to why I like Mahler's eighth symphony strike me increasingly as downright risible. What think you?
ReplyDeleteGödel's theorems shouldn't really be applied to anything outside maths, in my opinion. They are theorems about formal systems and state that there are things that cannot be proved within a formal system but which we know to be true.
ReplyDeleteAnd while plenty of scientists (biologists, mainly - Richard Dawkins please stand up) would like to think that we're "formal systems", I beg to differ.
Gödel's theorems can't even be applied to language, because language isn't a formal system either.
I agree when you say: "the unfortunate aspects of both religion and science derive from attempts to be certain." But they're coming from different directions towards the same point. One favours knowledge, the other faith. One tries to limit ignorance, the other doubt.
They both hover around "certainty".
And yes, I fully agree that people should learn to deal with uncertainty more. Being in this internetular (ahem) age and having had a couple of centuries of easily accessible information means we've grown to assume answers always exist.
They don't. Lots of our current cultures need to grow-up and realise that our parents (and encyclopedias and priests/rabbis/imams) don't always know the questions, let alone the answers.
(Apologies if this seems to be a rant!)
"... don't always know the questions, let alone the answers."
ReplyDeletePrecisely.
I often wonder if we're hardwired for ambiguity, perhaps even among different systems.
ReplyDeleteGood point about Gödel, though in fiction I reserve the right to redefine the bounds of my formal systems! (And a good introduction to his work, which I'm now trying to struggle through, is Peter Smith's An Introduction to Gödel's Theorems).
Fiction, however, could be a formal system. See the Oulipo
ReplyDeletefor that!
Oh, and I had the misfortunate of sitting in the university library to read through Gödel's actual proof once. Brain twisting but fascinating. (I have a dark and shady past as a maths graduate... :os)
ReplyDelete'Fiction, however, could be a formal system.'
ReplyDeleteYes, I know the Oulipo (In fact, I keep a copy of Queneau's Exercises in Style on my desk as a salutary reminder of the limitations of style - since I tend to focus on it!) It makes for an interesting debate whether what they wrote was fiction ...