Pi

I was recently in NYC for a couple of days and got to catch up with some old friends from college, including PG. I've always referred to PG as an "enigma". The guy totally fascinates me. We were catching up over drinks and the conversation eventually turned to PG's hypothesis that pi is a dimension rather than a number. It has always bothered him that π has an infinite number of digits and cannot be calculated precisely. Per the Wikipedia, "the exact value of π has an infinite decimal expansion: its decimal expansion never ends and does not repeat, since π is an irrational number (and indeed, a transcendental number). This infinite sequence of digits has fascinated mathematicians and laymen alike, and much effort over the last few centuries has been put into computing more digits and investigating the number's properties. Despite much analytical work, and supercomputer calculations that have determined over 1 trillion digits of π, no pattern in the digits has ever been found." [Note: In case you're interested, this Web page shows π to 1,000,000 places.] This all got PG wondering whether π is actually its own dimension and we simply experience a projection of it in our three-dimensional environment (or four-dimensional space if you include time).

Admittedly, thinking of π as its own dimension is a little far-fetched. When I mentioned it to JK (another college friend), he asked me "is PG doing ok ... he's not taking drugs, right?" But there might be more to this than we immediately realize. I just finished watching a NOVA documentary called The Elegant Universe. My brother suggested that I check it out (thanks!). The documentary is about the field of string theory. String theory has attempted to unify general relativity with quantum mechanics. Some refer to it as a "theory of everything". One thing which is challenging about this theory is that it requires 10-11 dimensions - six of which form a Calabi-Yau shape. Many string theorists believe that fundamental constants derive their values from properties of these additional dimensions. Therefore, the idea that π is its own dimension is likely not correct but its curious properties might indeed be the result of additional dimensions that are projected onto the 3-4 dimensions that we (as humans) are most comfortable with. Food for thought.