Wednesday, January 9, 2013

Finite Infinity

Finite or Infinity?--The Life of Pi, and Other Infinities--In the ever-evolving view of scientists, philosophers and other scholars, there really is no single, implacable entity called infinity--

". . . . In the late 19th century, the great German mathematician Georg Cantor took on infinity not as a means to an end, but as a subject worthy of rigorous study in itself. He demonstrated that there are many kinds of infinite sets, and some infinities are bigger than others. Hard as it may be to swallow, the set of all the possible decimal numbers between 1 and 2, being unlistable, turns out to be a bigger infinity than the set of all whole numbers from 1 to forever, which in principle can be listed. In fact, many of Cantor’s contemporaries didn’t swallow, dismissing him as “a scientific charlatan,” “laughable” and “wrong.” Cantor died depressed and impoverished, but today his set theory is a flourishing branch of mathematics relevant to the study of large, chaotic systems like the weather, the economy and human stupidity. With his majestic theory of relativity, Einstein knitted together time and space, quashing old Aristotelian distinctions between actual and potential infinity and ushering in the contemporary era of infinity seeking. Another advance came in the 1980s, when Alan Guth introduced the idea of cosmic inflation, a kind of vacuum energy that vastly expanded the size of the universe soon after its fiery birth. New theories suggest that such inflation may not have been a one-shot event, but rather part of a runaway process called eternal inflation, an infinite ballooning and bubbling outward of this and possibly other universes. Relativity and inflation theory, said Dr. Aguirre, “allow us to conceptualize things that would have seemed impossible before.” Time can be twisted, he said, “so from one point of view the universe is a finite thing that is growing into something infinite if you wait forever, but from another point of view it’s always infinite.”. . . " (source: New York Times)

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