30 Sep
2012
30 Sep
'12
3:52 p.m.
In fact I try to avoid doign maths if I can find a
neat solution to
the problem. Recently I've been looking at a resisotr network
circuit [1].
...dangling pointer here...
I can (and did) write down the equations givign the
output voltage as
a function of the input voltage (using the superprosition principle
to solve for one input at a time) and solve them.
I'd say that counts as doing math(s)!
This shows me it does indeed behave as I'd
esxpect, but I still don't
feel satisfied. I don't feel I really understnad it. I am still
looking for an intuitive way to figure it out.
Depending on the resistor network, there may not be one.
I wanted to do something of the sort myself, once (prompted by the
resistor network in xkcd #730). I treated it as a case of generalizing
an uninteresting problem enough to make it interesting and then solving
it; I built a program that takes a resistor network, including
resistances and the ability to specify voltages at some nodes, and sets
up the equations and solves them, giving current through each
resistance and voltage at each node. (Of course, anyone who wants a
copy is welcome to it; if you have git set up, you can ge tit by
cloning git://git.rodents-montreal.org/Mouse/resistor-networks; if you
don't, I can mail out copies. You'll also need lcs-cvt, as in
ftp.rodents-montreal.org:/mouse/local/src/lcs-cvt/, or a little hand
tweaking.)
On the other hand, I am a lot more mathmeatically
inclined than 90%
(or more) of the populatiion. It worries me -- a lot -- that none of
the neighbours here had any idea what 'e' was (base of natural
logarithms, not the elctronic chaerge), for example.
I once was at work when someone walked in wearing a T-shirt which said
"SPEED LIMIT" with a formula, 4 pi h-bar / 137 mu_0 e^2 is perhaps
clear enough as a text form of it. I said "h-bar is Planck's constant,
137 is the fine structure constant, mu-zero is the permittivity of free
space, but what's e?" - because I was pretty sure e didn't represent
antilog(1) there.
He said, "You're the first person to have gotten as far as `h-bar is
Planck's constant'.". (e turned out to be a constant which depends on
the material in the vicinity - the expression gives the local speed of
light, as opposed to the vacuum speed.)
Admittedly, knowing what Planck's constant is is of a slightly
different order than knowing what e is in the sense you were using it,
but I'd've hoped that at least a few people would....
/~\ The ASCII Mouse
\ / Ribbon Campaign
X Against HTML mouse at rodents-montreal.org
/ \ Email! 7D C8 61 52 5D E7 2D 39 4E F1 31 3E E8 B3 27 4B