March 24 – Toddlers Need to Know Non-Euclidean Geometry


Last week Becky and I made a quick trip to Boston to see our son and daughter-in-law and their three wonderful children who just happen to be three of our five wonderful grandchildren. The youngest of the three is twenty-months old, and is happy and full of life. Gideon is a good eater, but prefers carbs to vegetables. Just the sight of carrot sticks and cucumber slices on his lunch plate the second day of our visit threw him into the kind of meltdown only a twenty-month old knows how to pull off.

I think Gideon needs a good course in non-Euclidean geometry.

I was a history major in college, but had to take some math and science classes to fulfill the general education requirements. The college offered a series of math courses for non-math majors, and I chose non-Euclidean geometry. The particular form of non-Euclidean geometry we studied was Lobachevskian, for those of you who care about such things.

Non-Euclidean geometry is not much different than Euclidean geometry of the kind you may have taken in high school.  Just one small difference. It rejects (for good reason) the absolute truth of Euclid’s Fifth Postulate about parallel lines. A non-Euclidean universe questions the notion that parallel lines will remain parallel into infinity.  Once you question Euclid’s Fifth Postulate, you have to be willing to imagine triangles with the sum of all angles being less the 180 degrees.  You can’t draw a picture of such a triangle, however. Your ruler and compass won’t allow it. Some of my fellow non-math majors were thrown into the kind of meltdown only smart eighteen-year olds know how to pull off when things don’t go their way.

That non-Euclidean geometry class for non-math majors was the last math class I ever took. And the most important.

The sum of the angles in every triangle I have encountered since I took that class has been 180 degrees.  But it might not always be that way. Not if one little assumption is not true.

We create our worlds around assumptions, postulates, if you will.

Twenty-month old Gideon holds fast to a postulate that claims one does not need to eat cucumber slices and carrot sticks if one does not wish to do so. He goes into meltdown mode when his parents challenge that postulate. His universe falls apart.

All indications are that, like his older brother and sister, Gideon will learn to love cucumber slices and carrot sticks. Especially with some garlic humus.

All these years after my last ever math class, I still struggle with the reality that not all my assumptions about life, postulates, if you will, are necessarily true.

Euclidean geometry is built around five postulates. They have served us well as we use them to build dams and bridges and skyscrapers, cars and airplanes and smartphones. But what if the fifth postulate is not true? Theoretically, we’ve got problems.

I want life to be fair. I want justice to be done. Justice should be done. It’s one of my postulates.  I’ll call it Bill’s Fifth Postulate: Justice should be done. The people who hurt me and those I love should not get away with it (are you listening, Lord?). If I trust the reliability of my Fifth Postulate, however, my universe falls apart. I may go into meltdown mode. The failure of my Fifth Postulate is more than theoretical. It fails all the time. Justice is not always done. I bear the scars of resentment and hurt that remind me that justice is not always done.

Obedience to the Scriptures calls us to a non-Euclidean world. Things are not as they seem. Hard work doesn’t always pay off. Cheaters sometimes prosper. Justice is hard to find. It’s not that Scripture doesn’t value hard work (but, Martha, you can take a break). It doesn’t affirm cheating, and God’s justice will prevail (thank God that his definition of justice is not mine). But not everything I assume to be true is true.

In non-Euclidean geometry, Euclid’s first four postulates are always true. They should be. But number five is called into question and apparently it should be.

Are there any reliable postulates in God’s non-Euclidean world, things you don’t have to call into question? To be sure. Among them:

Trust in the LORD with all your heart,
and do not lean on your own understanding.
In all your ways acknowledge him,
and he will make straight your paths.  Proverbs 3:5-6

Gideon will learn to love cucumber slices and carrot sticks. I need to learn that justice by my definition is not always done. I need to quit seeking that justice and to learn to trust in the Lord with all my heart…

See you Sunday