Quote:
Originally Posted by Craig Sawyers
Watts RMS is alas similar to measuring area in metres, or the height of a building in square yards.
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Are we sure about this ? If we square a quantity, then operate on it in such a way as not to change its dimension (as in taking a mean of a distribution), then take the square root again, we'll end up with something which has the same dimension that we started with. So the dimension of 'watts RMS' will still be watts, which is correct for measuring power. It might not have any helpful meaning (see posts above) but it won't actually be dimensionally incorrect.
Quote:
Originally Posted by Radio Wrangler
It's a bit like seeing someone discussing 'square acres'
square yards, square miles, square metres are fine, but acres already include the squared measure bit ...
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Yes, trying to read any meaning into the squared bit would be difficult. But once we've 'rooted' it back to acres then, well, that's clearly just an area again and we can open our eyes and breathe out
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Quote:
Originally Posted by merlinmaxwell
Surely a square acre would be a volume, 9 million cubic feet ish.
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A volume has three space-like dimensions, but a square acre would need four. In our everyday world we don't think of there being more than three space-like dimensions, but it has been theorised that there might be e.g. here
https://phys.org/news/2014-12-universe-dimensions.html.
I once went to a very good talk by Steven Weinberg (Nobel prize winner) who tried to illustrate how the dimensions beyond three might be 'compactified' so small that we can't ordinarily perceive them. He held up a drinking straw and said that the people at the back of the lecture theatre would perceive this as a one-dimensional object. If you asked them where a dot on the straw was they'd just tell you how far along the straw it was. But if you asked an ant, who was walking on the straw, then it would tell you both how far
along and how far
around the straw the dot was, because on a small enough scale (an ant scale) it was clear that the straw was a surface, with two dimensions, not just a line with one.
Cheers,
GJ