From the Brain of Matty

metres squared (12.09.07 10:28 am)

Had more dental work yesterday. Hopefully I'm all done now, for another decade or so. ;)

I felt like blogging on something my parents in law said the other week some time. It just came back to me, and I feel like I've reached an internal consensus.

They complained that someone said "metres squared" instead of "square metres."

They argued that, for example, "three metres squared" actually means 9m2. In that sense, they were interpreting the phrase as "(nine metres) squared." However, on reflection, I realised that in mathematics we use a similar pattern with a different interpretation. For example, if I were to say "A B squared" I mean A × B2. If I wanted to say what my parents-in-law thought above, I'd say "A B all squared", meaning (A × B)2. I don't know about you, but I quite prefer that phrasing, and it's consistent. So "three metres squared" means "three (metres squared)."

That also makes sense when you think in terms of units, in scientific notation. m2 is an accepted SI unit of area, pronounced "metres squared." Since measured values are always pronounced amount-unit, following standard process we'd have to say "three metres-squared."

That's my argument for my way. Now my argument against their way:

What is a square metre?

A metre is a linear unit of measure. It makes no sense to say a "square metre." You could argue that there is a special case for "square" and "cubic," so a "square metre" is a 1 metre unit square. I can live with that. But then if you say something is "three square metres," you're saying it is three unit squares. So it's either a rectangle 1m×3m, or some sort of 4m2 square with bits missing from one half. There are only so many ways you can arrange three squares to make a flat contiguous shape. (Think about it: |, L, T) *

If you then say that "square metre" is a lazy way of saying "squared metre," you're even worse off. Back to mathematical notation: "A squared B" means A2 × B, so "three squared metres" means "nine metres."

I guess what I'm saying is: if you're talking about an arbitrary area, you should say "X metres squared," if it happens to be in a shape that can be reduced to 1m unit squares, I guess you can say "X square metres," and you should never say "three squared metres" because that way lies confusion.

*Note: fractions can also work. For example, "half a square metre" could be a right-triangle 1m×1m×√2m, or a rectangle 1m×0.5m, or any other way you can think of chopping a square in half. I can live with that.

Feel enlightened?