Humans are hilariously bad at understanding the size of things. We have evolved great systems for counting small amounts and estimating large amounts but it is only relatively recently that we have had to grapple with truly massive sums. As a consequence, we know a billion is a lot but we are often laughably wrong when we try to reason about numbers of that magnitude. It would be a short days work to move a billion grains of rice into bags and put them in a truck. It would be a lifetime of work to give each of them a number.

One way to better understand very large or very small numbers is to put them in context. However we often fail at that too by focusing on the wrong details. My favorite new twitter account is “Relatively Risky” which demonstrates how often an article citing something like a “40% increase in risk,” for example, is often generating fearful clicks on what is a negligible increase in absolute risk.

As if those weren’t enough, we are also very bad at estimating trends. We tend to assume everything is linear which leads us to be constantly surprised by trends that are geometric or exponential. Indeed this has been a source of arbitrage for investors for decades. Savvy capitalists look for areas of nonlinear opportunity because they are often priced incorrectly.

The solution to all of these things is to be skeptical of ones own instincts as it relates to numbers, relationships, and trends. We must be especially cautious when those instincts confirm a narrative we already believe.

These observations have lead me to ponder a cliché we hear often in technology: “We sent a man to the moon but you can’t do this?!” It turns out the list of things that are harder than sending a human to the moon is dramatically bigger than people expected. Many of our fixed points of reference are secretly misleading, and rather than using them to contextualize new information we should be using new information to recalibrate our reference points.