As we know, the world (and the internet) is especially polarized. We all have our own ways of looking at life/religion/economics/everything, and we’re all convinced that we’re right. Liberals do it. Conservatives do it. We’re all guilty of some kind of knowledge bias.

I’m also highly guilty of it (I mean, you can see it in almost every blog post). I have something mathematical to share that reminds me of this. Here goes.

A Triangular Lesson in Knowledge Bias

A lesson from school:

The interior angles of a triangle always add up to 180°.

interior triangle

Seems pretty reasonable, right? I mean, there are many proofs for this – old historic ones dating back to Euclid. Diagrams and books and such.

As it turns out, not only is this rule rarely true, it is in fact demonstrably false in almost all situations. The rule only applies within the very rigid confines of two dimensional space.

As soon as you make things spherical (or any other kind of curved surface), farewell to Euclid:

Thanks to Andrew Steele's website for this awesome right-angled all the way round triangle.
Thanks to Andrew Steele’s website for this awesome right-angled all the way round triangle.

It reminds me that fundamentalists tend to operate in two-dimensional space – where things are either right, or wrong, and it’s easy to observe which is which.

The world, however, is three-dimensional. It’s complicated, and it’s infinitely greater than any paper-based construction of strict angles.

Rolling Alpha posts opinions on finance, economics, and sometimes things that are only loosely related. Follow me on Twitter @RollingAlpha, and/or please like the Rolling Alpha facebook page at