Multifractal

When more than one fractal exists in a space (domain, environment...), there find a multifractal. Imagine a Bach fugue played simultaneously with Für Elise. The separate fractalities of the fugue and Beethoven piece would be incoherent.

Two (beautiful) interfering fractals could produce cacophony. In other contexts, separate fractals would not necessarily produce either destructive or constructive interference. Separation and isolation of each fractal could involve a kind of signal filtering.

False Fractals

They're called the "black helicopter crowd"-- those on the Right fringe who see conspiracy in every government or Big Business action. Their roots go back at least as far as the Birchers and "fluoridation is a commie plot". A new crowd of paranoids has arisen with the first election of W. As the election was "fraudulent" and "stolen", any of his subsequent actions, whether failed or fruitful, are part of the grand Rovian plot. Maybe the Bushies were even responsible for 9-11; Left craziness, meet Isalmofascism.

Captain Ed (link) writes, "the peculiar desire in humanity to see patterns and conspiracies where none exists always made us vulnerable to Gnostic-like fables." His post is a commentary on the Church's rebuke of the "Da Vinci Code". I suggest that the conspiracy-susceptibles are seduced by "false fractals". The typical susceptibles see an apparent pattern, one for which they are on the lookout. The template for the anti-W suscepts consists of a set of "axioms": W. is dumb. He takes his marching orders from the smart, but evil people around him: Rove, Cheney, Rumsfeld. If W. clearly succeeds, there's a dark, not silver-lining to the invisible cloud that doesn't obscure the success. A false fractal could consist of a triangle embedded in a pentagon embedded in a square. See the pattern!

Happy Easter!

Equal Probability

Suppose, following Laplace's "principle of indifference", that there is a finite number, n, of exclusive possibilities. Then, if the possibilities cannot be distinguished beyond their identification, each is assigned a probability equal to 1/n. (e.g.: link). It so happens that Shannon's entropy, S, satisfies the principle of indifference:


Equal Probabilities from Shannon Entropy

Note that the probabilities are all equal to 1/n, and the Lagrange multiplier is equal to -log (n).

Jump into the middle...

What's it like to jump into the middle of a sequence of blog posts? The latest don't seem to make much sense.

Simple, start at the bottom, and work your way up.

And a Non-Fractal

So Geraghty translates Chris Oscar Rock:

"We think your mission is corrupt, pointless, based on lies and a waste, and we make that argument loudly and frequently. But considering the views of many of those who buy the tickets to our movies, we also feel it is important that we appear to support you anyway."

Middle East Fractality

If the same signal appears to be present about the same time in several different domains, is this a fractal?

Iraq, Lebanon, Saudi Arabia, Egypt... (link) Add in Jordan.

The question is whether it's the same signal or not -- the rise of democracy in the Arab world. Add in Afganistan, and it's the Muslim world.