Re: (ReacTor) Defining Our Terms: What Do We Mean by "Hard SF"?

On Tue, 20 Aug 2024 10:13:10 -0700, The Horny Goat <lcraver@home.ca>
wrote:

On Mon, 19 Aug 2024 20:54:58 -0400, Joy Beeson
<jbeeson@invalid.net.invalid> wrote:
>

One of the commenters mentioned that he never got the hang of
calculus.
>
I got first-semester calculus fine, and I got second-semester calculus
fine (both faded away during the intervening six decades), but
calculus itself I never got.
>
Many years later, I learned that this was because my teachers not only
didn't explain the fundamental thereom to me, they didn't even tell me
that calculus *had* a fundamental thereom.

>
Oy veh! I got that in 2nd year though back in elementary school we got
a glimmer of that trying to "prove" the area of a circle was pi * r
squared by counting progressively small squares (mostly where the
circle went through including those where the line went through versus
those where the squares were outside the circle vs inside which
demonstrated the area of the circle had to be between those two limits
- and having to do it 2 or 3 times with progressively smaller squares
- we had to do 3 or 4 iterations of this)

Archimedes computed pi by using inscribed/circumscribed polygons. This
is the sort of thing that led to the discovery (or, better perhaps,
conceptualization) of limits.
--
"Here lies the Tuscan poet Aretino,
Who evil spoke of everyone but God,
Giving as his excuse, 'I never knew him.'"