The Life of Pi - Infinities Writ Large

It's nice to see a post in the NY Times regarding infinities, something BRT talked about in an article titled Infinities Within Infinities whereby the notion of an infinite number of infinities residing in the multiverse is equally possible in finite space as subdividing 2, 2 1/2 and 3 space to ever finer dimensions can be accomplished in elegant fashion using the genius of Cantor, Mandelbrot  and Menger, among significant others, to make it happen.

In reality, Pi really is the most accessible way to view infinity as no real math is required save that knowing Pi = the ratio of a circle's circumference C to its diameter D, and is approximately equal to 3.14159 etc., etc., etc. until the end of time. :)

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.

In closing, Wikipedia says it best...More than just irrational, π is a transcendental number – a number that is not the root of any nonzero polynomial having rational coefficients. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straight-edge.

Needless to say, we won't talk about Zero, a most dangerous notion the ancient Geeks avoided at all costs. Just ask Zeno to see why. :)