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A comment on Solving the cube root of 19,683 mentally.

Re:Solving the cube root of 19,683 mentally by kqr on Saturday February 04, 2023 @02:16AM (#34652396)
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?

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Re:Solving the cube root of 19,683 mentally by 8192kjshad09- on Saturday February 04, 2023 @04:50AM (#34653190)
There's some research indicating the opposite, that people intuitively think in logarithms. We perceive sound, light, and possibly even the passage of time logarithmicly[1]

I don't think there has been an explanation proposed for why it's easier to do linear math in our heads, I have to imagine this is just the effect of school.

[1]: https://www.nature.com/articles/s41598-020-75191-6

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Re:Solving the cube root of 19,683 mentally by anon___ on Saturday February 04, 2023 @05:18AM (#34653317)
Everything you listed, and the linked article is about perception, not thinking. Paradoxically, our thinking is linear, and it seems to be useful to change that: https://hbr.org/2017/05/linear-thinking-in-a-nonlinear-world.
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Re:Solving the cube root of 19,683 mentally by hgsgm on Saturday February 04, 2023 @08:51AM (#34654477)
Approximate how precisely?

What is 17463/3 ?

To 2 sig figs, it's trivial because you only have to divide a digit by 3 and then interpolate the fractional part.

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Re:Solving the cube root of 19,683 mentally by kqr on Saturday February 04, 2023 @09:40AM (#34654821)
Exactly. So how come it's not trivial with the cube root? On your description it sounds like the numerals we use are the problem.
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