h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

There's the old story about this infinite hotel, with an infinite number of guests. However, one single infinitely large bus brings an infinite number of new guests. How do you fit them in?

!secaps eht ni stseug wen eht tup dna ,langiro eht elbuod rebmun moor a stseug dlo eht etacolla uoY: rewsnA

Just now found this approved entry on natural units.
The attached earth/sun illustration appears to me out of scale.
I would suggest scale is what makes the units relevant.
Please correct, thanks.

There is no way you can get the sun and earth on the same picture in scale. It's only a cartoon, isn't it!
Yeah, scale is pretty important.

Perhaps pictures can show scale, words can touch reality.
From this given time and place they do.
It's not all only a cartoon, I won't think that way.
Pretty is important, I like this shade of blue, don't you?

Yes, this blue is nice. Visit lastminute.com and see there h2g2 pages, they are UGLY!

I'll not go then. Will be checking limits still.

I think there is a little misunderstanding here. Of course, every physical quantity (that is not dimensionless!) can be set to 1 and called a natural unit. But this is garbage. It only makes sense (and is done) if the quantity is a general natural constant. The AU is neither a constant (albeit almost) nor general (Mars has another). So if you want to write quickly some formulas you may omit the distance Earth--Sun and call this 'using a natural unit'. But I think there are no books using a unit scheme where AU=1. At least, none to speak of.

Instead the article doesn't mention the really important natural units. There aren't that many of them: h, c, e/m, maybe k_B.

On the other hand I agree that natural constants are very annoying.

But natural units remove natural constants (sometimes)

Imagine a world of maths where PI was one (and one was 1/PI) ...

Well, this is exactly what I said: You use eg h as a natural unit, thus set it to one and -- magic -- it disappears!
I also mentioned that this doesn't work with dimensionless units, therefore it doesn't work with PI.

It'd be fun if it did.

I doubt whether you would like a world where PI was one.
Anyway, I remember there was an obsolete imperial unit called 'circular inch'. I think with it you could write formulars like perimeter = diameter etc. However in some way this is self-deception.

Indeed. It's like saying Sun-Earth distance = meter rule length. Well, they're both one...