Always remember: the buckets are made up.

If there are only a small number of individuals, we can keep all of their richness of all of the individuals in our heads.

But it gets super-linearly harder to do that as there are more individuals to know.

At the top end, say, a principal of a 150 person elementary school, you might be able to keep a rich, multi-dimensional picture of all of the students in your head, with extreme effort.

But it's not just you who has to--you have to coordinate with other people.

Even if you somehow have 150 individuals in your head, the other people you have to coordinate with will only have a subset--maybe each teacher knows all of the kids in their own class, but only the most stand-out ish of other students (the very bad kids, the very smart kids).

So when you coordinate, the number of "individuals" you can think of declines precipitously.

When we have too many individuals to coordinate around, we use summary statistics.

We choose the dimensions, we measure them, and place the individuals continuously along those dimensions.

Our brains don't do well with smooth continuum; they do better with discontinuous buckets..

So we put different regions of that continuum into buckets so we can talk about parts of the continuum in a more concrete way.

But the buckets are a convention we chose to allow us to talk about the swarm of individuals!

They are made up!

They introduce a number of illusions right off the bat.

For example, an individual at the top of bucket 1 might be way more similar to an individual at the bottom of bucket 2, but that will be hidden; all of the individuals in bucket 1 are implicitly assumed to be more similar to everyone else in bucket 1.

Another illusion that can only show up with bucketing is Simpson's paradox, an illusory backwards correlation that shows up entirely due to bucketing.

Another way that bucketing misleads us is that we forget about the dimensions we chose not to plot.

They just fade out of our awareness, even if they are extremely important.

As time goes on, the buckets come to feel more important than the individuals.

The individuals habituate to their bucket, assuming it is their destiny.

The individuals are changed by the bucketing and it imprints itself on reality in ways that might be counterproductive or dangerous, and make it harder to erase later.

So if the bucketing is leading you to an odd or surprising conclusion, remove the buckets and check: is it just an illusion of the bucketing?