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(Not for distribution) We all know what randomness is. We sometimes choose between options "at random", and if we toss a coin we know it will land heads or tails at random. But are events like these truly random? Randomness turns out to be one of those concepts, like "solid matter" in physics, that works just fine on an everyday level but mysteriously disappears once we move in to examine its fine structure. In this fascinating book, mathematician Ed Beltrami takes a close enough look at randomness to make it mysteriously disappear. The results of coin tosses, it turns out, are determined from the start, and only our incomplete knowledge makes them look random. "Random" sequences of numbers are more elusive--they may be truly random, but Godel's undecidability theorem informs us that we'll never know. Their apparent randomness may be only a shortcoming of our minds. Mathematicians have even discovered a string of numbers that appears random--but when you reverse the string, it's completely deterministic! People familiar with quantum indeterminacy tell us that order is an illusion, and that the world is fundamentally random. Yet randomness is also an illusion. Then which is real? Perhaps order and randomness, like waves and particles, are only two sides of the same coin.

Inhaltsverzeichnis

Frontmatter

[1]. The Taming of Chance

Abstract
In the dim recesses of ancient history the idea of chance was intertwined with that of fate. What was destined to be, would be. Chance was personified, in the Roman Empire at least, by the Goddess Fortuna, who reigned as the sovereign of cynicism and fickleness. As Howard Patch puts it in his study of this Roman deity, “to men who felt that life shows no signs of fairness, and that what lies beyond is at best dubious, that the most you can do is take what comes your way, Fortuna represented a useful, if at times flippant, summary of the way things go.”
Edward Beltrami

[2]. Uncertainty and Information

Abstract
A half-century ago Claude Shannon, mathematician and innovative engineer at what was then called the Bell Telephone Laboratories, formulated the idea of information content residing in a message, and in a seminal paper of 1948, he established the discipline that became known as information theory. Though its influence is chiefly in communication engineering, information theory has come to play an important role in more recent years in elucidating the meaning of chance.
Edward Beltrami

[3]. Janus-Faced Randomness

Abstract
The statistician M. Bartlett has introduced a simple step-by-step procedure for generating a random sequence that is so curious it compels us to examine it carefully, since it will bring us to the very core of what makes randomness appear elusive.
Edward Beltrami

[4]. Algorithms, Information, and Chance

Abstract
During the decade of the 1960s several individuals independently arrived at a notion that a binary string is random if its shortest description is the string itself. Among the main protagonists in this story is the celebrated Russian mathematician Andrei Kolmogorov, whom we met earlier, and Gregory Chaitin, information theorist and computer scientist.
Edward Beltrami

[5]. The Edge of Randomness

Abstract
Up to now I have been trying to capture the elusive notion of chance by looking at binary strings, the most ingenuous image of a succession of sensory events. Since most binary strings cannot be compressed, one would conclude that randomness is pervasive. However, the data streams of our consciousness do, in fact, exhibit some level of coherence. The brain processes sensory images and unravels the masses of data it receives, somehow anchoring our impressions by allowing patterns to emerge from the noise. If what we observe is not entirely random, it doesn’t mean, however, that it is deterministic. It is only that the correlations that appear in space and time lead to recognizable patterns that allow, as the poet Robert Frost puts it, “a temporary stay against confusion.” In the world that we observe there is evidently a tension between order and disorder, between surprise and inevitability.
Edward Beltrami

Backmatter

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