Thursday, February 14, 2013

the siege: once a battle .. now a war of attrition!

the functional analysis "battle" from a few days ago seems to have deteriorated into a siege.

as a general rule, sieges are troublesome. they have the potential to be long and drawn out affairs, and hence wasteful for limited resources. (every night i'm exhausted from trying to work out ideas, build variants of spaces, or look up relevant theorems and tools.)

on the bright side, i'm the one doing the invading;
i think the enemy is weakening, too. (-:

// updated, 15 feb 2013 @ 10:08
things are fitting together more and more nicely.
this feels like the building of siege engines, the alchemic stirring of potions, pitch, and greek fire, the readying of catapults and trebuchets to launch.

i look at these mathematical machinations and i smile:

piecewise linear cells, hyperplanes, subspaces,
Lipschitz functions, both old and new kinds,
weaκ-star topolοgies and linear inclusions and well-defined dualities!

i can't help but imagine myself now: a cruel smile, bent on destruction.
ha! soon, i feel like crying havoc! and letting loose the dogs of war [1] .. but not yet. my plans remain unready. the time to strike is soon .. i'll have my chance soon enough ..

.. and it will be bitter, yet sweet.

// updated, 18 feb 2013 @ 10:47

the siege is in full swing, there's already trouble on the front lines;
i'm invading the fortress of a claim and cannot breach the walls.

so i'm going to need heavier artillery in the form of vector-valued functions and Bοchner integrals .. but these aren't just any vector space targets;

these are flat chain-valued functions!

[1] yes, i know: the real quote is 'let slip the dogs of war' .. but 'slip' just doesn't sound right, to modern ears ..

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