Slightly related musing: I can quickly approximate 1/3 of any number. I suspect this is because that's an operation I've had to use often.

If I had needed cube roots equally often, would I have been just as good at mentally intuition roughly what number it has to be?

Or are humans somehow wired to deal with linearities more intuitively than powers? Or is it our mathematical notation (Arabic numbers are linear, as opposed to some log scale) that creates that impression?