# You Can’t Rank Order Multi-Dimensional Things

One of the most surprising things I learned in math was that complex numbers had no natural ordering. Meaning, less-than and greater-than are not defined for complex numbers. It makes sense when you think of it for a minute. The same applies to other multi-dimensional things like matrices and vectors.

So, why do we think we can rank order people? I’m specifically talking about companies that do this for their employees, but it comes up in other contexts (e.g. class rank).

Even if you were to think of people as a number, it wouldn’t be expressed as a 1-dimensional one. When I wrote about the concept of lowering/raising the bar, I said that that a bar is a 1-dimensional concept. So is rank ordering.

Just like with complex numbers, you can make up an order if you want. But then you lose information. For example, if you choose to order based on magnitude, then direction would no longer matter. Similarly, when you rank team members by, say, seniority, you lose orthogonal characteristics, like the ability to catalyze others.

The reason companies do this anyway is when they are looking to downsize. If they do need to lay someone off, it might well be the lowest ranked person, but it’s a terrible way to do this. I do have a suggestion, but I’ll get to that Monday. [EDIT: Here it is – Comparing People is Not Transitive]