The Life of Pi, and Other Infinities
By NATALIE ANGIER
Published: December 31, 2012
On this day that fetishizes finitude, that reminds us how rapidly our own earthly time share is shrinking, allow me to offer the modest comfort of infinities.
Yes, infinities, plural. The popular notion of infinity may be of a monolithic totality, the ultimate, unbounded big tent that goes on forever and subsumes everything in its path — time, the cosmos, your complete collection of old Playbills. Yet in the ever-evolving view of scientists, philosophers and other scholars, there really is no single, implacable entity called infinity.
Instead, there are infinities, multiplicities of the limit-free that come in a vast variety of shapes, sizes, purposes and charms. Some are tailored for mathematics, some for cosmology, others for theology; some are of such recent vintage their fontanels still feel soft. There are flat infinities, hunchback infinities, bubbling infinities, hyperboloid infinities. There are infinitely large sets of one kind of number, and even bigger, infinitely large sets of another kind of number.
There are the infinities of the everyday, as exemplified by the figure of pi, with its endless post-decimal tail of nonrepeating digits, and how about if we just round it off to 3.14159 and then serve pie on March 14 at 1:59 p.m.? Another stalwart of infinity shows up in the mathematics that gave us modernity: calculus.
“All the key concepts of calculus build on infinite processes of one form or another that take limits out to infinity,” said Steven Strogatz, author of the recent book “The Joy of x: A Guided Tour of Math, From One to Infinity” and a professor of applied mathematics at Cornell. In calculus, he added, “infinity is your friend.”
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http://www.nytimes.com/2013/01/01/science/the-life-of-pi-and-other-infinities.html?pagewanted=all&_r=0