[jessriedel]

> but it's a difference in what is being measured, not in how it is quantifiable. Measuring them with the same units doesn't imply that they are perfect substitutes

I agree! Please read my comments carefully. I am not arguing against the usefulness or deep conceptual importance of natural units! I am critiquing the terrible explanations being given in this thread.

> Likewise with spacetime: for most purposes human non-physicists think about, they are completely non-substitutable. So practically, it works well to use a "Troy" sort of system for one. But it's a purely human distinction.

No! Space and time are not interchangeable in any universal sense even if they are universally linked by a symmetry. A space-like interval and a time-like interval cannot be interchanged with each other by a Lorentz transformation. The distinction between space-like and time-like intervals is observer independent.