If men define situations as real, they are real in their consequences. – Thomas theorem

Fractality

Posted in Today by bendyourcircuit on 23/06/2009

Fractal is a word Mandelbrot coined to describe the geometry of the rough and broken—from the Latin fractus, the origin of fractured. Frac­tality is the repetition of geometric patterns at different scales, revealing smaller and smaller versions of themselves. Small parts resemble, to some degree, the whole. […]
[…] The veins in leaves look like branches; branches look like trees; rocks look like small mountains. There is no qualitative change when an object changes size. […] Mandelbrot designed the mathematical object now known as the Mandelbrot set, the most famous object in the history of mathematics. It became popular with followers of chaos theory because it generates pic­tures of ever increasing complexity by using a deceptively minuscule recur­sive rule; recursive means that something can be reapplied to itself infinitely. You can look at the set at smaller and smaller resolutions with­out ever reaching the limit; you will continue to see recognizable shapes. The shapes are never the same, yet they bear an affinity to one another, a strong family resemblance.
These objects play a role in aesthetics. Consider the following applica­tions:
Visual arts: Most computer-generated objects are now based on some version of the Mandelbrotian fractal. We can also see fractals in architec­ture, paintings, and many works of visual art—of course, not consciously incorporated by the work’s creator.
Music: Slowly hum the four-note opening of Beethoven’s Fifth Sym­phony: ta-ta-ta-ta. Then replace each individual note with the same fournote opening, so that you end up with a measure of sixteen notes. You will see (or, rather, hear) that each smaller wave resembles the original larger one. Bach and Mahler, for instance, wrote submovements that resemble the larger movements of which they are a part.
Poetry: Emily Dickinson’s poetry, for instance, is fractal: the large re­sembles the small. It has, according to a commentator, „a consciously made assemblage of dictions, metres, rhetorics, gestures, and tones.“

Nassim Taleb, The Black Swan: The Impact of the Highly Improbable

Снимка: Уикипедия

a black swan #2

Posted in Today by bendyourcircuit on 01/06/2009

There is another, even deeper reason for our inclination to narrate, and it is not psychological. It has to do with the effect of order on information storage and retrieval in any system, and it’s worth explaining here because of what I consider the central problems of probability and information theory.

The first problem is that information is costly to obtain.
The second problem is that information is also costly to store—like real estate in New York. The more orderly, less random, patterned, and narratized a series of words or symbols, the easier it is to store that series in one’s mind or jot it down in a book so your grandchildren can read it someday.
Finally, information is costly to manipulate and retrieve. […]

[…] We, members of the human variety of primates, have a hunger for rules because we need to reduce the dimension of matters so they can get into our heads. Or, rather, sadly, so we can squeeze them into our heads. The more random information is, the greater the dimensionality, and thus the more difficult to summarize. The more you summarize, the more order you put in, the less randomness. Hence the same condition that makes us simplify pushes us to think that the world is less random than it actually is.

And the Black Swan is what we leave out of simplification.

nassim taleb, the black swan: the impact of the highly improbable

a black swan

Posted in Today by bendyourcircuit on 30/05/2009

I push one step beyond this philosophical-logical question into an em­pirical reality, and one that has obsessed me since childhood. What we call here a Black Swan (and capitalize it) is an event with the following three attributes. First, it is an outlier, as it lies outside the realm of regular expectations, because nothing in the past can convincingly point to its possibility. Sec­ond, it carries an extreme impact. Third, in spite of its outlier status, human  nature makes  us concoct explanations  for  its occurrence after the fact,  making  it explainable and  predictable.

The human mind suffers from three ailments as it comes into contact with history, what I call the triplet of opacity. They are:
a. the illusion of understanding, or how everyone thinks he knows what is going on in a world that is more complicated (or random) than they realize;
b. the retrospective distortion, or how we can assess matters only after the fact, as if they were in a rearview mirror (history seems clearer and more organized in history books than in empirical real­ity); and
c. the overvaluation of factual information and the handicap of authoritative and learned people, particularly when they create categories—when they „Platonify.“

nassim taleb, the black swan: the impact of the highly improbable

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