We live in a world of contradiction.

Stewart Brand is famous for the quote "information wants to be free". But this is only a piece of the quote. The full quote is:

"On the one hand information wants to be expensive, because it's so valuable. The right information in the right place just changes your life. On the other hand, information wants to be free, because the cost of getting it out is getting lower and lower all the time. So you have these two fighting against each other."

As humans, we are programmed to want tidy, clear cut answers. It's why this quote is often truncated to conform to our own views.

It's why famous stock gurus will never say "I honestly have no idea where the market will go". And it's also why there's an inverse relationship between the fame of a forecaster, and the accuracy of their predictions (check out Superforecasting if you get a chance).

This idea has become even more clear during my philosophy of space and time course this semester.

Let's take the idea that space and time are continuous, a concept upon which most of math and science is built upon. Now let's engage in a simple thought experiment. Imagine there is a rod, exactly one meter in length. If we divide the rod into two pieces, we will have two pieces, exactly 0.5 meters in length. The length of the rod is unchanged.

But because space is continuous, we should be able to divide the rod into infinitely many lengths. So if we divide the rod into infinitely many pieces, what is the length of those pieces. There are seemingly two options, no length or some length. If each of the pieces have no length, then the sum of all of the lengths should be 0. If each piece has some length, then infinity multiplied by any length should be infinity. Paradoxically, the length of the rod is changed in either scenario. This is known as Zeno's part-whole paradox.

The point here is that uncertainty is inevitable. We have to build imperfect models to continue making progress. Parts of fundamental mathematics are built off of shaky grounds, but the benefit that these parts of math provide us far outways their uncertainties.

Mental models are by definition oversimplifications and imperfect. There are always contradictions. The trick is to use them in ways that help us see the world more clearly, rather than distorting the truth.