Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Paul S Person Newsgroups: rec.arts.sf.written Subject: Re: (ReacTor) Defining Our Terms: What Do We Mean by "Hard SF"? Date: Wed, 21 Aug 2024 08:20:55 -0700 Organization: A noiseless patient Spider Lines: 33 Message-ID: <9c1ccjlqk9o28jkfqp56gcimn55tihuqm5@4ax.com> References: MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: quoted-printable Injection-Date: Wed, 21 Aug 2024 17:20:57 +0200 (CEST) Injection-Info: dont-email.me; posting-host="5e189a068eac7326786af774c1127c1a"; logging-data="4116712"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19l7a/vHMnReI49OIR6+YhtIGJU82nFlmo=" User-Agent: ForteAgent/8.00.32.1272 Cancel-Lock: sha1:30Ekookbjh1+v1A0xIkcpBnfP30= Bytes: 2533 On Tue, 20 Aug 2024 10:13:10 -0700, The Horny Goat wrote: >On Mon, 19 Aug 2024 20:54:58 -0400, Joy Beeson > 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. --=20 "Here lies the Tuscan poet Aretino, Who evil spoke of everyone but God, Giving as his excuse, 'I never knew him.'"