Wednesday, December 30, 2009

Duck-poo Soup


On a green pond smooth as glass,
mallards float and pass
the time. I stare
and look away. Splashes
make me turn to see water plumes
collapsing. A pause, a floating
feather: I think of water's plumage
and up spring some ducklings, as
busy as bees in the water-lilies.

A lardy male waddles by
on lobstrous feet, evoking
with his draconian head
a Viking long boat.
A duckling ducks
submerges and emerges
like a broadside
at the adult's broad side
and nippily snatches a fly
from the bottom of the sky.
Flustered, the adult flaps
his wings, flinging off
oddly fluttering splodges. Weary of malarkey,
he fans out his butt like a pack of cards
and onto a flagstone flops. Wary of malady,
he gingerly stretches out
his white-collared neck
for soggy croutons floating
on this duck-poo soup. He wants
that sumptuous bread but he fears
being presumptuous. He does not want
to end up dead. But he cannot die.
He is a picture. I have immortalized
and immobilized him.

Unhinging winds fringe maroon-fingered moon,
like a waiter with a supernatural soup-spoon;
a crater of rubble like a burst bubble serving
as a seat of tranquillity for a duck quacking up
a soporific melody of sounds pacific:
Talk about a duck
floating on a lake,
looking like a wooden decoy does;
talk about a drake
ducking wooden ducks,
making all the ducklings he can make.

Friday, December 11, 2009

Two "proofs" that 2 + 2 = 5

The rationalist proof:

Starting with the concept of a bean, adding two beans and another two beans makes five beans because the concept of a bean is a bean (an ideal platonic bean).


The empiricist proof:

Add together two lines of length 2.36 (of our units of length) to make a line of length 4.72, and then round those lengths to the nearest whole number (of units).

Thursday, December 10, 2009

Deep Thought

First things first.
......And yet I find 'zeroth' in my dictionary, to refer to the one before the first one. In Wikipedia I find: The zeroth item is the initial item of a zero-based sequence (that is, a sequence which is numbered beginning from zero rather than one), and surely 'first' would have done just as well as 'initial' there. In such a sequence, the first element is also the second; that is, a certain equivocation has been introduced, a new sense of "first" added to our initial, informal sense.
......The idea of an ordinal number zero comes from the ordering of the integers on a number line, from negative to positive infinity (exclusive). But when we use ordinal numbers to include negatives, as with years, we naturally make the direction more explicit (e.g. with BC and AD) and exclude year zero (whence all the fuss about when the millenium began).
......Modern maths does not like directions. It finds it best to begin with a collection of natural numbers {0, 1, 2, 3, ...} that are most fundamentally ordinal numbers, and are usually reduced to pure sets. Mathematics does not like directions. Following Euclid's reduction of geometry to logic, geometry was naturally reduced to analysis following Descartes, and then arithmetized, with an arithmetic reduced to set theory.
......And yet mathematicians do like directions. Imaginary numbers were only taken seriously as numbers (like the negative numbers) when it was realised that the positive and negative imaginary numbers i and -i could be regarded as unit distances (like 1 and -1), specifically in the direstions perpendicular to the positive and negative directions of the "real" number line in a "complex" plain (which is how complex numbers are introduced to students).
......Given the foundation of the concept of direction in our experience of space, I would guess that if there really are extra dimensions in physics, they are more likely to correspond to the complex numbers of quantum mechanics (e.g. by representing dimensions of actual physical possibility) than the six dimensions of phase space (nor the ten or twelve of string theory, etc.).