Posted by: Inside-Out Peace | February 22, 2010

God and the Parallel Postulate

If you took geometry in high school, you may remember that the kind you learned is called “Euclidean”.  What makes it Euclidean is the fifth of Euclid’s five postulates – the one that essentially says if you have a line, and a point that’s not on the line, there is one line through that point that is parallel to the line.  Because it concerns parallel lines, it is often referred to as the parallel postulate.  With his five postulates, Euclid proved many theorems that, together, constitute a system of geometry that works very well as a model for flat surfaces.

But, as it turns out, there is not always only one parallel line.  There can be zero, or an infinite number of parallel lines, and in each of these cases, you can use similar methods to prove many theorems which are quite different to those in the Euclidean system.   These systems of geometry are also very useful for modeling other types of surfaces. 

There is nothing that makes any of the three possible parallel postulates any more “true” than any other; none of them can be proved from the other four postulates and none of them lead to contradiction, within their own system.  Despite the fact that they contradict each other, they are all, in a sense, true.  It all depends on where you are and where you are going.  If you are mapping your route across town, Euclidean geometry works great for calculating the distance you’ll go.  If you’re traveling from New York City to Shanghai, you’ll find spherical geometry (the kind with zero parallel lines) much more helpful. 

For me, this holds an analogy to belief and atheism.  The various religions, and belief itself vs atheism, contradict each other, yet none can be proved and none causes an inherent contradiction within its own system (I’m aware there are atheists who disagree on the latter, with respect to belief.  So, too, are there believers who disagree on the same point with respect to atheism.  I’m sticking with “neither”.) 

It’s not possible, or even desirable, to limit ourselves to just one system of geometry, i.e. one parallel postulate, because then we would be unable to model the surfaces corresponding to the other two, each of which actually exist.  Neither is it possible or desirable to limit ourselves to just one God postulate.  Is there no God, one God, infinitely many Gods?  Was God’s word revealed at Sinai, through Buddha, Jesus, Mohammed, to each of us everyday? 

Just as all of us go on about our lives very comfortably despite the simultaneous existence of contradictory systems of geometry, so do we all need to learn to live comfortably with the simultaneous existence of contradictory beliefs about God.  Reality is far more complex than any single God postulate can model.

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If you are interested in hearing more about these different geometries, and some fascinating information about crochet and coral reefs as well, I highly recommend this TED talk:

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