Tuesday, January 27, 2009

Global Geometry

When Thomas Friedman says that the world is flat, it puts one in mind of an alluvial floodplain, so flat and silty that it poses no obstacle to the relentless spread of water, again and again, redistributing the chemical wealth for those inclined to take risks. And indeed, the major civilisations of the world have lived, died, spawned, suffered and spread by the dangerous wealth of the floodplains.

Globalisation, as Marcelo Suárez-Orozco and others have pointed out, is a phenomenon that has its roots in the human past of about 60 millennia ago. Humans spread. They move and bring culture, community, commerce and conflict. Where a dominant group meets one less dominant, the less dominant group learns more. This ensures that civilisations endure cycles of boom and bust; except that larger ones tend to go bust more slowly. The corollary to that is that when they do go bust, they tend to go bust with a boom.

For Atlantis, our small city-state whose insignium of the Lion of the Sea has spread to places like Venezia and Londinium, globalisation reared its head at least 700 years ago. Yet we treat the phenomenon as if it is ultra-modern, a thing of the late 20th and early 21st centuries in this age of humanity.

There is a kind of secret that the Masons knew and which is also hidden behind the warning on the gateway to Plato's Academy. That warning reads, "Let no man enter here who knows no geometry."

That secret is this. The world is not really flat; neither is it really round. It is not an oblate spheroid as the geographers have it, nor an odd polyhedron as the geometers and cartographers require. It is a lump of rock, physically. But memetically, in terms of the ideas that drive the world of humanity, it is a furious and irregular tempest that is subject to no laws that humans have yet been able to discern.

As Qoheleth says in the book known as Ecclesiastes, "The race is not to the swift, nor the battle to the strong; but time and chance happen to them all." The marketplace of ideas is not dominated by the swift or the strong, or even the durable or diffuse; it is an agora where millions cry out and not all is understood, and even when anything is understood, it is sometimes understood too late.

Blake wrote about a 'fearful symmetry'. This is true to life. The symmetrical, the neatly-ordered ideas of MBA school and the human sciences of politics, economics and sociology — these are dangerous because they are not entirely true, but true enough to lead to disaster.

It is like a stack of bricks, each one placed slightly out of true; each is almost exactly in place, but not quite. That stack will eventually fall as the centre of its gravity is displaced further and further away from the centre of the foundation. Eventually, it will hang over nothing; as it says in the book of Job, "He hangeth the world over nothingness." What an image! What an idea!

I just wonder how true a description it is.

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Monday, December 08, 2008

Hexagons

Personally, I like hexagons. They come together in perfectly tesselating formations, with three of them meeting in perfect unison like the symbol of a Mercedes-Benz. They are perfect for grids, for isometric planning, for wargames and peacegames. They're a bit complicated as maps of human interaction, but once you see them as projections of the octahedral they are fine.

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Squares

In my previous post I was talking about triangles. If tragedies are triangular, comedies are square, or at least quadrilateral in some way. In a comedy, everyone ends up with somebody else, unless they are really minor characters. Look at Twelfth Night or A Midsummer Night's Dream! Shakespeare goes to really extreme pains to make everyone end up nicely, all squared away...

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Sunday, December 07, 2008

Triangles

While teaching literature this year, I was discussing with my students the idea that a tragedy always has leftovers, and hence tends towards triangular relationships. Three sisters, three rivals, three corners of a love affair... all these make relationships impossible to balance and produce disasters.

In fact, even if you have pentagons, they will reduce to triangles and then to tragedies. Someone will be hurt, left out, unbalanced. Oddness is bad. Haha.

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Saturday, December 06, 2008

Stars

There are many ways to link a multiplicity of points. Consider a number of points all at the same distance d from an original point. If you link them all in sequence you will get a polygon approximating a circle if there are enough points spaced out regularly along that circumference. If you link them alternatingly, you get a cycloid if there are many of them and a star if there are few enough.

This is one of those odd thoughts one gets as one sits along the Bay of Bengal and thinks of all the treachery and romance, the arms-trading and the gem-trading that these shores have seen. Tragedy and pain, piracy and profit, war and the elements of a fantasy novel. I think I might come back here after all, one day when I am retired and can finally write the book I have been thinking of all along.

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Note: Thanks, NBL, for that comment... I definitely meant cycloid (as written), of the spirograph type. Sorry, wasn't clear enough. A cardioid (means 'heart-shaped thing') has only one cusp.

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Circles

Things circle around, like vultures. It is said that what goes round comes round, or that the centre cannot hold. But sometimes there are circles within circles. Dante's hell has nine, and it is an eye-opener to see who he puts in which circle.

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Sunday, November 23, 2008

Corners

Corners begin with three sides; if you have two sides or fewer, there are no corners. The word 'corner' means 'projection' and is etymologically related to the word 'horn'. One can only feel cornered if framed by at least three points of reference.

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