Page123Sentence6to8HstarWeblog.Page123Sentence6to8 HistoryShow minor edits - Show changes to output October 02, 2006, at 07:28 PM
by - Doh.
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Ordinarily I snub my nose at blog memes, but [[http://confluence.za.net/blog/index.php?entry=entry060928-215628|someone I can't refuse]] has tagged me with the "sentences 6-8 from page 123 of your nearest book" one, so here goes: to:
Ordinarily I October 02, 2006, at 07:28 PM
by - Tagged by "page 123, sentences 6 to 8" meme.
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!!Page 123, Sentences 6 to 8 [- 2 October 2006 -] Ordinarily I snub my nose at blog memes, but [[http://confluence.za.net/blog/index.php?entry=entry060928-215628|someone I can't refuse]] has tagged me with the "sentences 6-8 from page 123 of your nearest book" one, so here goes: I'm also going to cheat by reaching for the books on my bedside table rather than those under my monitor since I'm not sure telephone directories have sentences per-se and I'm certainly not going to quote anything from Sommerville's "Software Engineering" -- there's a reason it's ''under'' my monitor. >>font-style=italic margin=1.5em<< From the complex perspective we see that 1/z is indeed a single function. The one place where the function 'goes wrong' in the complex plane is the origin, z = 0. If we remove this one point from the complex plane, we still get a connected region. >><< It's from ''The Road to Reality'' by Roger Penrose. I'm not a big fan of Penrose's ''Mind'' series ([[wikipedia:The_Emperor%27s_New_Mind|#]], [[wikipedia:Shadows_of_the_Mind|#]], [[wikipedia:The_Large%2C_the_Small_and_the_Human_Mind|#]]) but his new book appeared much more closely focused on what he's famous for (mathematical physics) and so I bought myself a copy with some of the book vouchers I received on my birthday. In the quoted sentences he's examining how 1/x (where x is a real number) which appears to be disconnected at x = 0 (the graph seems to be two separate curves) becomes a connected graph when we extend it into the complex plane as the function 1/z (where z is a complex number). I'm about a sixth of the way through and so far I've been getting exactly what I wanted out of it - insights into which pieces of mathematics Penrose considers important for physics and why. We'll see how the rest goes. :) |