Logarithms and a mathematical day ...

Logarithms explained Bob Ross style
Tibees | 16.IX.2019
https://www.youtube.com/watch?v=up21mvokyQ4

I

0:41 One can study logarithms for fun without testing.

Perhaps not so much in France. Slide rules are "règles à calculer" and the word "règles" evokes something somewhat unpleasant to many women.

I had inbibed a love for slide rules and logarithms before arriving ....

I also came across the question, "how do you raise a number to a fractional power?"

You don't. The fractions are algebra for something else.

X raised to a/b = Y
means
X raised to a = Y raised to b.

While a logarithm is never a fraction, it falls between two. E. g. 10 to the seventh is roughly equal to 2 to the tenth. Forgot whether that was upper or lower limit for logarithm, there is another one on the other side of it.

Sorry, make that ten to the third instead!

And it was lower limit, since it gives you 0.3 rather than 0.301 ...

II

8:22 Please, don't call it Euler's number - it's an irrational ratio, not a number, and Euler didn't call such things numbers, though he used quantitas indistinctly for numerus and ratio ... (for Zahl or arithmos, I'd disagree less, you can have such a thing that goes "1 + 1 = 2" and these are therefore not restricted to what's really numbers!)

III

8:40 I did. I just calculated that if sphere of fix stars is one light day up, which as a geocentric I think is the case, and God's heavenly court and Jerusalem above that, then the aberration so called corresponds to a proper movement of 0.13 sth light minutes.

(Took aberrational angle as 20 arc seconds from memory)