Today was my wife's fiftieth birthday and the day that my wee brother got married. So this morning I found myself lying in a bath of bubbles reading a book about partial differentiation. New problems.
I've never really grokked continuity and limits; and for functions with more than one dependent variable!? In the text I recognized an ε/δ argument [big deal neil] but one for two discrete limits. I didn't understand. No, that's not right, I had a vague idea, but it was the vagueness of an might-as-well-be ignorant.
I've been berating myself lately for my inability to work the symbols slickly, I should have been flaying myself for a lack of comprehension of the concepts. You can always train yourself to work the symbols, understanding this stuff is rather more challenging.
My life often seems one long saga of my annoyance re my stupidity. And I'm glad that it is so; I spent today with my family, my friends and my new family, eating, talking and laughing. I bored many, entertained a few, pissed-off a few. We all enjoyed ourselves hugely.
I'm part of a team of nutters who can play chess, drink irresponsibly, argue about the right way to clean wine stains off walls, hold a conversation with a Spaniard with a nine year old translating, talk vacuously about block ciphers and internet security, spit filth about pensions, discuss whether the only way is Essex really means anything, tell wonderful stories of our excess...
A person, then, who needs to go back to the books to understand continuity; otherwise how will my, new, and bigger, family understand this?
Comments
New comment
N
I love it when you write properly
Rosie
New comment
The whole classical continuous apparatus of mathematics resides on the assumption that being able to judge the progress of the system at infinitesimally small we can predict it's behaviour at an arbitrary distant moment.
Not surprisingly it breaks down on chaotically behaving phenomena which respond inadequately to small disturbances of initial values and fractals which make the term "sufficiently small" meaningless.
The history of the theory of light propagation gives a clear example how the succession of continuous and discrete approach pushed the science a few leaps forward. I bet the same path still has some surprises lying in wait.
New comment
@Rosie cheers!
@Valentin that's what I don't seem to be getting. I know that I will get it. Eventually.
The funny thing is that I didn't have any problems with calculus when I first met it, it's only lately that I've developed scruples.
n