This is pretty geeky and not related
to writing, except that I'm writing about it now. But...
In math class we learned about
identities. X (operation) (identity) = (identity) (operation) X = X.
That means 1 is the identity for multiplication: X x 1 = 1 x X = X.
(Sorry for the capital variable; I can't get the computer to write a
times dot and I didn't want it to get confused with the
multiplication symbol.) 5 x 1 = 1 x 5 = 5. 8 x 1 = 1 x 8 = 8. 0 is
the identity of addition: X + 0 = 0 + X = X. 3 + 0 = 0 + 3 = 3.
But...
Subtraction and division can't have
identities! 0 – X is not the same as X – 0! X divided by 1 is not
the same as 1 divided by X!
To have an inverse, if I've got it
right, you need to have an identity, because X (operation) (inverse
of X) = (identity of operation). The multiplicative (if that's the
right word) inverse of 5 is 1/5... It's like flipping the fraction
upside down: 5/1 1/5 The additive (if that's the right word. I think
additives have something to do with food coloring) inverse of 5 is
-5. Awesome!
And algebra is all about inverses. If
you want to figure out what X is in X + 5 = 40 you add -5... which is
the same as subtracting 5... but we're making all the subtraction
addition and all the division multiplication, because it's so much
simpler to multiply 25 by 1/7 (25/1 x 1/7, 25 x 1 = 25, 1 x 7 = 7,
voila!) which is 25/7 than to divide 25 by 7. When I try to do that
in my head, I make my head gooey.
Another lovely thing... distributive
property! That simply means that a(b + c) (that's a times bplusc) is
the same as (ab) + (ac). (ab is a times b, or a b's.) Simple enough
rule. But...
(X + y)(a + b)(m + n)
That's... xam + xan + xbm + xbn + yam
+ yan + ybm + ybn! PATTERNS! I used to do something like that when I
was younger, and bored, go through my fingers tapping and not
tapping, figuring out the combinations on a hand: taptaptaptaptap,
taptaptaptapdon't, taptaptapdon'ttap, taptaptapdon'tsdon't,
taptapdon'ttaptap, taptapdon'ttapdon't, taptapdon'tdon'ttap,
taptapdon'tdon'tdon't... and on and on to don'tdon'tdon'tdon'tdon't!
I never thought it was anymore useful than thumb twiddling (which,
for some odd reason, gives me thumbaches), but maybe it will be!
Math is rhythm.
Back to school leaves me as excited as
it does exhausted.
Okay, geekfest over.
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