Monday, October 24, 2011

Of Hair Dryers and Geometry, Part 2

To sum up the last entry, an atheist blogger said that Hair Dryer = God.  I reigned in my instinctive reaction to vigorously pontificate, thinking better of ranting in light of a deeper problem at hand.  That of Axiomatic Systems.

I could just say World View, but I think axiomatic systems better illustrate a concept that we all think we know.  Everyone has world views, but not everyone knows what their own one is, let alone what other people’s are.  World views are very much like axiomatic systems (AS).   AS’s are mathematical concepts.  Here’s a great, though technical, article describing AS’s.  The definition given on that article is, “An axiomatic system consists of some undefined terms (primitive terms) and a list of statements, called axioms or postulates, concerning undefined terms.”  If you ever took geometry, you have been exposed to AS’s.  The geometry you studied was Euclidean geometry, based on the axioms posed by an ancient Greek, Euclid.  Axioms cannot be proven.  They must be granted, taken as givens.  Euclidean geometry is based on five axioms, and everything you learned in geometry can be proven from those five axioms alone.  I think that’s pretty neat.

But do you want to know a secret?  That geometry you had to learn doesn’t completely line up with the world in which we find ourselves.  Everything works if the world is flat.  But we in on a roundish planet.  Euclid’s fifth postulate, the parallel postulate, has some difficulties with it (see here for a technical explanation).  Here’s a simple example of the practical applications of those difficulties with this axiom.   Take out an atlas, and tell me the shortest way to fly from Portland, OR, to Frankfurt, Germany.  You’ll use a ruler and draw a straight line.  Now take out a globe and tell me the shortest distance—it’s by going over the pole, not straight across the Atlantic. 

The vast majority of the geometry you learned is still useful.  Some of it doesn’t apply to the world we live in, our reality.  But all of it is true in its own system, in that it is all proven from the initial five axioms.  The axiomatic system of Euclidean geometry is a cohesive system, where everything can be proven based on the five stated axioms.  It’s just that one of those axioms doesn’t match up with reality. 

Now, back to our hair dryer/authority problem.  The problem is our individual axiomatic systems—the things we accept as givens, and can’t prove.  These are what we base our world views on, and from that, what we base our lives on.

The problem with the Atheist vs Religious person argument is that the two axiomatic systems are not the same.  Both accept or do not accept different things as unprovable givens.  One of the typical axioms of the atheist’s world view is that the material world is all that there is—there is nothing above the material/natural world, no supernatural.  One of the typical axioms of the religious person’s world view is that there is a super-natural being(s) that interacts with matter and nature.  Both are unprovable givens—axioms—around which their entire world views are based. 

That last sentence was a purposefully inflammatory sentence.  I hear you say, “You’re telling me I base my life on things I can’t prove? Yeah right.”  You’re probably thinking about some links you want to post in the comment section below, which reference the best argument you’ve ever read for pure materialism or for the existence of God.  However, before you start to prove something, anything, you must start with some givens.  Before you build a house, you must first lay your foundation.  You must have a starting point.  Your axioms, your givens, are that starting point. As in geometry, if the underlying axioms of a system are not accepted, the proofs based on the axioms are not accepted.  If you reject Euclid’s first postulate, which essentially defines a line, you’re not going to get very far in geometry.  It’s a fundamental assumption, and it must be accepted before you can move forward and reason anything out.  

Also, when you are discussing with someone and trying to prove something, you both must agree that each step in the reasoning is true.  If one of you thinks that one of the steps is false, you end up not agreeing to the conclusion.  Here’s a kind of a nonsense example.  You ask me what two plus two equals, and I say six.  You tell me that it’s actually four.  We both look at each other like we think the other is silly, since we know our answers are correct.  What you don’t know is that I had parents with a weird sense of humor who taught me to count, “One, three, two, four, five, six.”  The axioms in this example are the values of the names of numbers.  For me, I associate “Two” with 3, not 2 like you do.  So when you ask me what two plus two is, I say 6.  The example breaks down, because unless I’m amazingly stubborn, you can teach me that “Two” actually is the name for 2 not 3.  But the point is that we disagree on what the word “Two” means, so we can’t agree on any problem that involves “Two”.  Our axioms are different.

So an atheist and a deist walk into a bar and start talking.  How do they overcome their differences, instead of yelling, getting into a fist fight, and getting kicked out of the bar?  Tune in next week for the final gripping installment, of Hair Dryers and Geometry!  ♪♫ Dun dun dun. ♪♫

No comments:

Post a Comment