*Clubber Lang* by Cornelius Boots

from the album SC100

(also has Jens’ *your beat kicks back like death* … did you know that song’s a cover?)

my maths blog is on http://isomorphismes.tumblr.com

*Clubber Lang* by Cornelius Boots

from the album SC100

(also has Jens’ *your beat kicks back like death* … did you know that song’s a cover?)

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Re-analysis of the gross economic production and personal income for cities in the United States, however, shows that the data cannot distinguish between power laws and other functional forms … and that size predicts relatively little of the variation between cities. The striking appearance of scaling in previous work is largely artifact of using extensive quantities (city-wide totals) rather than intensive ones (per-capita rates).(Sorry if that’s hard to read. Horizontal axis

Linear combinations of eigenfaces — images like the above — are the cheapest way to store and search photos of faces. Like if you want to computer analyse the faces of everyone at the Superbowl and see if there’s a terrorist.

All of the terrorists’ faces are saved in a database as like **{**11% Eigenface_1, 6% Eigenface_2, 1% Eigenface_3, …**}**. So the real face breaks down to just a list of percentages **{**11%, 6%, 1%, …**}**.

Articles on Eigenfaces: 1, 2, 3, 4, 5, 6 (sorry to reinforce the google hierarchy)

If you break the faces in the live Superbowl crowd CCTV’s into such a list of percentages, then you can have a computer do a search against known terrorists. (Imagine having the computer search pixel by pixel. It would be like, Hey, the top left of your head looks like the top left of a terrorist’s head! Whoops, that was just the soda machine.)

Final point. There is more than one way to mathematicise a face. Surface normal vectors are one way; the manifold limit of polygons is another; projection is another; and eigenfaces are another. Each way has you conceive of a face differently.

Imagine you have a small collection of things **{…}**. You take linear combinations (in the spirit of “When Doves Cry inside a Convex Hull”) of them, making varied and interesting combinations that explore — even span — a “space”.

Maybe it’s

- the space of all possible faces
- the space of all possible songs
- the space of all possible configurations of a heat engine
- the space of all possible orientations of a sculpture
- the space of all possible paintings
- the space of all possible artistic schools
- the space of all possible states of your desk
- the space of all possible functions ℝ⁴→ℝ
- the space of all possible functions ℝ[0,1]→ℝ[0,1]
- the space of all possible directions in 3-D
- a subset of the space of all possible graphs
- the space of all possible quantum configurations of a molecule
- the space of all possible notes
- the space of all possible ways a week can go

(It’s possible to mathematicise these things in part because of the modern, abstract notion of a “vector”.)

*Think about this large space instead of the original *small-collection-of-things **{…}** *that generated it.* Could a different small-collection-of-things have spanned the exact same space? Surely so.

*What about different small-collections {..A..}, {..B..} that could have generated the space*? Is there a really simple collection? One whose parts don’t self-interfere. One that’s representative and easy to work with.

If there is such a “canonical basis”, the elements of the basis are called eigenfaces, eigenmodes, eigengraphs, eigenstates, or some other kind of eigenbasis.

Eigenboogers are fundamental to how abstract mathematics made “linear” algebra hugely relevant — to ODE’s, image compression, spectral analysis, crystallography, economics, statistical analysis, geophysics, and teaching artificial intelligence how to spot terrorists at the Superbowl.

Finally, eigenstates and eigenmodes are pretty good for meditating on how the universe is a song, singing itself.

Plum Creek Timber Company is organized as a profit-making business, not as a charity. If Montana citizens want Plum Creek to do things that would diminish its profits, it’s their responsibility to get their politicians to pass and enforce laws demanding those things, or to buy out the lands and manage them differently.

Jared Diamond, in the book *Collapse*

Regarding the banking industry, the financial crisis, and questions about the future of capitalism, I would extend Diamond’s recommendation like this:

**It’s the government’s job to make sure that businesses get ahead by serving others and only by serving others.**

The corollary, also from Diamond, is that voters must signal to the politicians that the above is what’s important — not handbags, abortion policy, gay marriage, or other cheap wins.

The wealth required by nature is limited and is easy to procure; but the wealth required by vain ideals extends to infinity.

Epicurus, Principal Doctrines, 300 B.C.