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Curious if you feel the same about scale on maps, or does your mental model work differently there?

Not sure. I've never heard someone say or write "this is a 1:50 scale map" or something of the sort.

At least the scale gives you an idea even if not as immediately intuitive as you would like. In model railway world you have O, HO, OO, N and plenty of other scales that sometimes are not even a scale - track guages can be different in scale to the trains.

1:60 is the convention for planes which is not the same as the 1:64 scale used for die cast toy cars. But these are the standards we are stuck with. Well it is convention for planes to be in 1:60 scale

It's not 1/60 the size of the original?

Nope. Volume varies with the cube of the length. A 1:60 scale model only takes up 1/216,000 the space of the original.

You're right. I think it's time to hang up my username and go learn some math.