He kind of has a point about volume not being a great way to think of it, but I’m not convinced by the assumption that length is better because it’s one-dimensional. That “X laid end-to-end” trope was already a subject of mockery at least 90 years ago.
But that does make me wonder, what is the role of dimensionality in visualising different quantities? It’s notoriously harder to estimate a complex object’s volume than its length, which I guess is what he’s thinking of; but then, it’s just as hard to estimate its surface area or circumference, so it’s not simply a line-square-cube type of issue.
If you’re talking about spaghetti, then volumes are easier to compare than lengths. With real estate, a room’s longest span may be more descriptive than its floor area (and no one cares about its volume). So, we intuitively measure different things in different numbers of dimensions. And money is a purely abstract thing (unless you’re talking about cash, which we never are in this sort of discussion), so the ideal number of dimensions isn’t necessarily an integer, or even less than four. It’s interesting to think what that might mean, in terms of political economy for example.
Also! Part of our problem with visualising numbers is that quantities of physical stuff are linear, but our positional numbers are logarithmic. By which I mean, [999999] is twice as long as [999], while $999,999 is a thousand times as much as $999. That definitely distorts our thinking at times.
Indian people are always using the word “lakh” (in English) to mean 105, but neither “lakhaire” nor “lakh-millionaire” would be very useful terms. Although, if “thousandaire” were in common use, it might help illuminate the difference between millionaires and billionaires.
Most people’s use of either term isn’t quantitative anyway; they’re just thinking about a binary difference between whether or not you have enough.
