WEBVTT

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Hi. Imagine two parallel lines. Now, most of

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us learned a simple definition in school. Parallel

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lines are lines that never meet. And that seems

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obvious. And for roughly 2 ,000 years, geometry

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was built around ideas like this from our favorite

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Greek mathematician, Euclid. But Euclid had a

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problem. Most of his geometry rested on a small

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collection of assumptions, or postulates, and

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four of them seemed relatively simple. But that

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fifth one, dealing with parallel lines, was a

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bit more complicated. And for centuries, mathematicians

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tried to prove that fifth postulate from the

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others. And they could not. Eventually, some

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mathematicians changed the game, and instead

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of proving it, they asked, what if we changed

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it? And then something really amazing happened.

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They discovered entirely new geometries. For

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example, on the surface of a sphere, the usual

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idea of parallel lines just doesn't work. Think

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about lines of longitude on the Earth. At the

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equator, they appear to head off in the same

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direction, but eventually they meet at the poles.

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The geometry is not wrong. The starting assumptions

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are different. Literally, one begins on a flat

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surface and the other on a circle. And I find

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that absolutely positively fascinating. Mathematics

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usually feels like the place where things are

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simply true or false. And... they are. And, but,

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mathematics also teaches us to ask a more careful

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question. Under what assumptions is this true?

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Now, I think that's also a valuable question

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that we can ask outside math. Now, last week

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we talked about worldview, and that's the framework

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where we understand reality. We all have starting

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assumptions. What makes a successful life? What

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makes something right or wrong? What gives a

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human being value? Now, sometimes we argue passionately

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about conclusions without realizing that the

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real difference may have occurred earlier. That

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we're starting from different places. Changing

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an assumption in mathematics does not mean anything

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goes. Once we choose our starting point, we still

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have to follow where logic leads. And maybe life

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is something similar. So today, when you encounter

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an idea you disagree with, rather than immediately

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asking, well, how could they possibly believe

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that? Try asking, what might they be starting

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with that I am not? Because sometimes understanding

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another person's conclusion begins by understanding

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their starting point.