I don't really buy this. That is like 819900000000000000 seconds.
Squaring this number gets you 672236010000000000000000000000000000 seconds.
I feel like my mind doesn't really appreciate either of these numbers or the difference between them. I feel like we just use units that we are comfortable with to make the number readable but there is not easy intuition here.
> Let's make a day be 86400 seconds (already a SI standard), and then you can divide that into tenths, hundreds or whatever.
Why not keep the day as it is, which can be conveniently divided into halves, thirds, fourths, fifths, sixths, eights, ninths, tenths and twelfths, as well as any multiples of those you like?
All unit conversions are actually multiplications by the dimensionless constant 1, i.e., no-ops.
Let's say that you want to convert `2 min` into seconds. You know that `1 min = 60 s` is true. Dividing this equation by `1 min` on both sides is allowed and brings `1 = (60 s) / (1 min)`. This shows that if we multiply any value in minutes by `(60 s) / (1 min)`, we are not actually changing the value, because this is equivalent to multiplying it by 1. Therefore, `2 min = 2 min * 1 = 2 min * (60 s) / (1 min) = 2 * 60 s * (1 min) / (1 min) = 120 s`. We didn't change the value because we multiplied it by 1, and we didn't change its dimensionality ("type") because we multiplied it by a dimensionless number. We just moved around a dimensionless factor of 60, from the unit to the numerical value.
I think that you misremember, or didn't realize that to convert minutes into seconds, you were not multiplying by `60 s` but by `(60 s) / (1 min)` which is nothing else than 1.
You're right, I decided to switch from seconds as base unit to hours as base unit half way through writing the comment, and screwed up the conversion. I was accounting for seconds when I was already in minutes.
update: Ahh, I get it. You'd need to divide it by 10 to get seconds.
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