OK, sorry. It appears I’ve rolled a critical failure in communication :-)
I wasn’t referring to the small scale structure, just the ability to comprehend scale. Something like the way that when you’re at the foot of the mountain, the brain doesn’t really capture the difference between a 1km-tall and a 8-km tall one. Or how the distinction between a 10-story building and a 100-story one isn’t really manifest in the mind unless they’re side by side. Now take that and multiply both scales by enough orders of magnitude to span molecule-to-human scales.
Let me try a better example. Take this image. Without using symbolic math (i.e. actually figuring orders of magnitude and doing arithmetic with them), what can your brain do that simultaneously includes numbers of the scales “the width of one of the galaxy’s arms”, “the diameter of one of the stars” and “the height of a person on one of the planets”?
I mean, I don’t have to resort to math to know that ten people in a normal car would be crowded, or that a bucket of nails are hard to fit in a typical person’s pockets. I can have an intuitive comprehension (albeit inaccurate) of how much work might be needed to dig a small ditch. But I have no intuitive feel for similar problems posed at astronomical scales other than “intuition overflow, use math”. E.g., I’ve no chance of estimating the number of people needed to crowd just the solar system, let alone the galaxy, within a couple of orders of magnitude, unless I actually do at least a few back-of-the-envelope calculations.
I think our intuitions work differently.
Something like the way that when you’re at the foot of the mountain, the brain doesn’t really capture the difference between a 1km-tall and a 8-km tall one.
I've walked up a 1 km hill. 8 km is Everest. I've only seen mountains that big in pictures.
Or how the distinction between a 10-story building and a 100-story one isn’t really manifest in the mind unless they’re side by side.
10 storeys is the height of some of the more substantial buildings (other than skyscrapers) in central London. 100 is a skyscraper. ...
Another month has passed and here is a new rationality quotes thread. The usual rules are: