2019 March 1: Infinity
Toccata in Dm ("Dorian") J.S. Bach (1685-1750)
Fugue (goes with the Toccata) J.S.Bach
Lent is a complex mix of themes, and a major one for me personally is ‘limitations’ — how limited and finite we really are.
I’d like to begin by considering its opposite: ‘infinite’. We say that Space is infinite in extent. But is it? You can progress around a circle as long as you like without ever reaching an end, but the circumference of the circle is finite. In math-speak it is “finite but unbounded.” One of the corollaries of Einstein’s General Relativity is that the universe itself may be finite but unbounded — it’s circular in a 4-dimensional sort of way. Thus some future Columbus could sail ’west’ in a spaceship from Earth and ultimately return to Earth from the ‘east’.
Well, if Space isn’t infinite, isn’t Time? Not necessarily. The current best model of the Cosmos is that there was a Big Bang ("let there be light") about 14 billion years ago – was there Time before that? This question is far from settled in the physics community. Is there passage of time if absolutely nothing changes? When I sit and do nothing, time still passes for me because I breathe, my heart beats, and neurons keep firing (fewer every day!). And what ontological status does Time have anyway? The 18th century landmark philosopher Kant argued that the mind takes in relentless blobs of sensory dough, and like a waffle iron imposes order on it, with Space and Time at the top of his griddle-iron. So maybe Time is purely an artifact of our minds. (At least Time keeps everything from happening all at once, which I for one find helpful.)
Doesn’t Time extend infinitely into the Future? Not necessarily. One school of Cosmology holds that we will ultimately experience the opposite of the Big Bang – namely the ‘Big Crunch’ — when gravity finally pulls all the matter of the Cosmos back into a single point. Another school thinks that the Cosmos will ultimately run down into a motionless mass of entropic goo where absolutely nothing moves anymore – not even any possible clock to measure the passage of nothingness.
Can’t we can still find ‘infinity’ in mathematics? Not necessarily. That concept has remained stubbornly undefinable. One of the more noteworthy examinations of ‘infinity’ arguably shows the concept to be paradoxical at best (Cantor). And within the mathematical community is a school of thought that infinity can and should be banished altogether, and mathematics would be the better for it.
So, arguably there is nowhere we can look in our experience and say "that’s infinite".
Well, isn’t GOD infinite? Hmm: the word ‘infinite’ means ‘not-finite’. And I’d suggest that defining something by saying what it is NOT is problematic. (You:) “What have you got behind your back, William?” (Me:) “It’s not an aardvark.” How helpful is THAT?
Which brings me to my point. When we say that God is ‘not finite’, perhaps we’re really trying to say She is fundamentally unlike us, She is Mystery. Except to the extent that She has chosen to invade our puny human experience personally. The Christ tells us little about God’s Grand Ontological Status, but He told us little baby stories (parables) and showed us simple practical examples of how to treat our fellow humanity. And as baby simple as He made His Message, I still struggle to grasp it and put it into practice.
So as I try to wrap my mind around the grandeur of God, I don’t see how I’m different from a flea — with a flea’s tiny brain — on Einstein’s coat trying to grasp General Relativity. There is certainly nothing wrong with the attempt! But in the end I am doomed to fail. And that’s OK.