In my previous entry, I neglected to mention an important thing about Gavin Pretor-Pinney and his "Cloudspotter's Guide." This book actually arose from a Website which the author started as a lighthearted venture for cloud fans. It turned out to be astonishingly popular, with thousands of visitors. The Cloud Appreciation Society is everything a cloud lover could want: a photo gallery, scientific information, legends and lore, and even a discussion forum about meteorology. Pretor-Pinney is also one of the founders of a hilarious British magazine called The Idler which extols the virtues of idleness. This ties in nicely with cloud-watching. If by some chance you haven't gotten enough cloud happies from the Cloud Appreciation site, there is also the splendid visual site, Enchanted Ceiling, which features wonderful panoramic sky photographs sent in by viewers from all over the world, though the site seems to be dominated by only a few individuals, one from Tennessee, one from Israel, and one from the Canary Islands. The small group doesn't matter; there are plenty of beautiful clouds in those places.

Calculus Proof Question

Beware, here comes some mathematics. My calculus book has shamefully been open to the same page or two since the beginning of the year. This is not good. Progress is always good. Stagnation is bad. So I have finally devised a strategy to alert my Friendly Scientists to what has halted my track. There is a proof for one of the derivative rules in my math book which seems to contradict basic rules of algebra. There is something I am not getting about this proof. It seems to imply that at a limit of h- - > zero, the subtraction of f(x + h) - f(x) is not zero.

I copied the proof out from my math book, in a clear enough scrawl, and I present it here. My question, "how does this happen," is shown at the relevant stage of the proof. I welcome any clarifying input from readers and Friendly Scientists, through the e-mail address on this Website. I would like to move on, learn more about derivatives, and do more calculus.

Posted at 2:42 am | link