Fundamental Forms

Fundamental forms are the bread and butter of differential geometry. Everything, from Gaussian curvature, mean and normal curvatures, length, area and angles, geodesics and topological properties mind you are all calculated from the fundamental forms.

Powerful! A whole geometry of surfaces just from something as simple as the inner product.

(I have a exam on the 26th…let me be nerdish and wax lyrical about it for a while).

But what’s this post all about anyway?

‘Fundamentalism’ is a dirty word nowadays. One reason is it gets lumped in together with bigotry, which is not a very nice attitude to have. Another associated idea is ‘foundationalism’ which also has seen it’s sunset.

But I think that these ideas were not the brainchild of desperate theologians or philosophers who were out to enslave the whole world with prudish morals, or some dusty old modernist who just can’t seem to accept change.

Fundamentalism in religion I would think is an honest response from honest people who are dismayed by the mad rush to embrace the latest fashion in theology, philosophy or what nots in a new market place of ideas. Fundamentalism just starts from a very basic question: What are the basics?

Social change is not deterministic as Hegel thought. Change comes about because people make a difference, either good differences or bad ones. In the case of the 21st century, it’s like in the parable of the weeds, weeds growing among the wheat. Social change happens because people make conscious decisions to abandon ideas which they deem is wrong and embrace ideas which they think is right. We are asking for trouble when we try to make our religion up-to-date with the times, because being up-to-date usually means being enslaved by sombody’s wrong idea.

What are the basics?

How about foundationalism? Foundationalism starts when we ask a very commonsensical question: How do you know? Let’s not be caught up with foundationalism talking about some ‘bedrock of truth from which all other propositions are hence justified’. Nobody can say two or more words before his inner man starts asking with a ghostly voice, how do you know this is true?

I believe that we still can believe in a ‘bedrock of truth’ even in this colourful age. Sanity demands it. We must satisfy that ghostly question. Failure to do so drives us closer to a fantasy world of our own.

Well I guess what makes the 21st century such an interesting place to be is because there are so much colourful people out there in thier own fantasy world. But lets not hide the fact that such people are also desperately lonely and hurt, despite appearences to the contrary.

Maybe metaphysical foundationalism is untenable as an epistemology, but we have killed more that we bagained for when we advertise it’s demise in the popular media.


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About me

moogleBorn and bred in KL, Malaysia. Now studying for his Phd in Singapore. Learning to walk one fall at a time.
April 2005
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