[perching_aix]

After putting significantly more effort than perhaps socially acceptable into this, I completely agree so far, but I'm still horribly confused about GP's point about "mega" being a "squared unit in megapixels".

That to me implies that "mega" in "megapixels" is a planar ("[pre?-]squared") scaling factor, but it's... not really? Are those even a thing?

I think this is what the debate is about at least. Mega does line up with kilo squared, but that's not because mega becomes a planar scaling factor, but because it just so happens that 1000 times 1000 is 1 million. It's kind of a coincidence? Like it's literally 1 million pixels, that's what's being meant. Just like with cm squared, the ohhhhhhhhhhhhhhhhhhhhhhhhh

[davrosthedalek]

I believe the point is that in "centimeters squared" you also square the cm. So it's 1/100 of a meter, then squared. While the mega in megapixels applies to the area. So presumably there are two length multiplied to be a pixel, and then you have a million of those.

I don't think it's a very deep point, and I would say the mega is not squared, but the centi is squared.

[perching_aix]

What finally clicked it into place for me was trying to perform a unit conversion. It's kind of annoying cause we don't really use mega with anything squared usually (I don't recall anything at the moment at least), which added to the confusion.

When one converts from square kilometers (km2) to square meters (m2), one needs to undo the kilo (x1000) not once, but twice, accounting for both dimensions. So as you say, it's actually here where the scaling factor is secretly squared, it's k2, just not written out. Hence despite kilo being a 1000x bump, you need to divide by 1 million, because it's actually squared in kilometers squared.

So if mega in megapixels was behaving "normally", that would imply similar semantics, so to convert into kilopixels, you'd divide by 1000 not just once, but twice. But no, 1 megapixels is 1000 kilopixels. I guess the idea is that instead of being "secretly" squared it's "explicitly" already "square" as a result? So instead of resolving to mega2 pixels2, it's just mega pixels, since pixels is 2D, and so squaring it is unnecessary.

I think I get it now at least, but yeah, I agree with your sentiment. It actually reminds me, when I first learned converting between units of area in primary school, I had quite the troubles with wrapping my head around it exactly because of this.

[davrosthedalek]

Yes, and I think it just depends where how you read the square. For cm^2, we mean that we square a centimeter, not that we have a centi of a meter^2. But a hectare is really a hect of ares, so 100 ares. Here the square "is baked in" into what comes after the modifier.