Pi and the Infinite Mind

I remember one time when I was a kid, talking to my dad about God and stuff like that, and he said that he had read a book by Carl Sagan, and at the end of the book Sagan talked about the number pi. My dad's eyes lit up, and he said "And when I got to the last sentence of his book, I said 'He proved God exists!'" I can't remember if the book was Contact or Cosmos.

Sagan was at worst an athiest, and at best a skeptic. He once said "The idea that God is an oversized white male with a flowing beard, who sits in the sky and tallies the fall of every sparrow is ludicrous. But if by 'God,' one means the set of physical laws that govern the universe, then clearly there is such a God. This God is emotionally unsatisfying... it does not make much sense to pray to the law of gravity." (As a side note, I don't just remember all these quotes and pluck them out of the air - Wikipedia is a great thing and makes you look pretty smart).

Of course, the Laws of Nature didn't just spring into being - if we go back to Aristotle's Prime Mover or First Cause concept, they had to be created. Laws of Nature are not God - but they are certainly from God, and are evidence of his immense power, timelessness, and omnipresence.

Whatever Sagan was spiritually, he had to be honest with himself about the number pi. The number pi is a ratio of two numbers: the circumference of a circle to the diameter of the circle. Or, the area of a circle to the radius squared of the circle. Or, 3 times the volume of a sphere to 4 times the radius of the sphere cubed. There's a ratio for the surface area of a sphere too. We all learned these equations in high school. Pi is also central to understanding trigonometry; the relations between a triangle's angles and the lengths of its legs. Pi is required to explain much of reality mathematically.

What is the universe? It's a bunch of spheres rotating around larger spheres in circular or elliptical orbits, isn't it? I imagine if we could slow down the electrons to view their orbits around the nucleus, atoms could be described in much the same manner.

Pi is an irrational number - its decimal is non-terminating and non-repeating - which means that it goes on forever and has no pattern. It is also a transcendental number, apparently (which sounds really cool doesn't it?), which means that there is no equation of finite numbers that are manipulated by algebraic operations that can equal its value - it can only approximate it.

22/7 has been used to approximate pi. Now, in the age of extraordinary computer power and speed, mind-boggling equations have been discovered to approximate pi. Mathematicians in the past worked out by hand the endless stream of decimals, setting records and publishing books of numbers approximating pi. Some poor souls made it their life's work, only for future mathematicians to discover they made an error on page 100 or so, and the continuing decimals that made up the rest of the book were wrong. The current record using supercomputers is approximating pi to 1,241,100,000,000 decimals (or 1.2411 trillion decimals). To put that in perspective, that approximation of pi would fill a book 383 million pages long! The spine of this book would be almost 16 miles wide - I don't know how many libraries you'd need to house the book, but it must be a few!

(As a further side note, to put our bloated federal budget into perspective, if each decimal place was worth a dollar, the decimal record for pi would have to be 2.5 times larger to equal the proposed 2008 US federal budget - and we aren't taxed enough in America? Gimme a friggin break! But that's a completely different issue)

I keep emphasizing the reality that even though we've figured out pi to 1.24 trillion decimal places, it is still just an approximation. If we took all the computers on the face of the earth and plugged them all together, and let them chug away on calculating pi until Christ comes back, it would still only be an approximation of the infinite number pi.

Pi is a number that is everywhere, and is in everything. The greatest human minds could only calculate it to a few hundred pages of decimals; the greatest supercomputers with the most efficient equations could only calculate it to fill the pages of a book whose spine stretched the distance of a good day's bike ride. But the reality is, a book as thick as the distance to our nearest star would still not be thick enough to contain pi! It is infinite, and has no pattern.

Only the Infinite Mind of God could conceive of such a number, and use it to build His Creation. It is there when you look up into the stars shining above, just as it is there when you gaze down into your child's shining eyes looking back up at you.