[extropy-chat] Maths ability

[ben]

Adrian Tymes wrote:

> (Likewise, x + (-1) = x - 1, because you've three lines, an odd 
> number.)

OK, i see what you're doing. But why should the geometry of the symbols
used have any explanatory power for mathematics? I understand that this
is an attempt to make it easy to memorise, but it doesn't help
understanding. x + (-1) doesn't equal x -1 BECAUSE there are three lines
in the symbols, does it. Nor is it because "a plus and a minus make a
minus", although i think that's a lot closer to the actual reason. Well,
maybe it IS the actual reason, but put in a way that isn't very clear to
me.

Excel says (-1) - (-1) = 0. But i still don't really understand why.
"two minuses make a plus" isn't an explanation.


> From my own experiences, I suspect it's partly a matter of no one 
> telling you what it truly means, in a form that you can understand.

> But here's a little trick <snip> (hail Google ;) )

Indeed.

Thanks for that. I never thought of taking that particular approach,
even though i use Google all the time. I'll try it. Maybe i'll find a
way to get a handle on concepts like adding or subtracting a negative to
a negative (this gives me a headache! - What IS it, how do you SEE these
things? I mean there's no such thing as "-6 oranges", is there?).
I always visualised an infinitely long line, with 0 right in front of 
me, negative numbers to the left, positive to the right. So any 
calculation moves up and down the line. My problem is seeing what - and 
+ are in these terms. Do they mean going towards and away from Zero, or 
do they mean going left and right? i.e.:

+ is: <-<-0->-> and - is: ->->0<-<-
or
+ is: ->-> and - is: <-<-

It's neither of those is it? >:(

Maybe i need a different way of visualising it.


> Hate to break it to you, but sometimes it *is* the tricks.

Hmm. I know that maths is not a thing in it's own right, like rocks are,
but an invented tool to help us understand the world. But all the same,
it has an underlying unity (it does, doesn't it?!?)
I want to understand the concepts. A collection of tricks is
unsatisfying, and i feel that approach doesn't do justice to mathematics
as a product of human ingenuity. And anyway, you don't have to worry
about memorising something if you understand it. You can reinvent it if
necessary. You can also use it properly in novel situations.


--- Lee Corbin <lcorbin at tsoft.com> wrote:

>> Damn right.  Me, every since I was a little kid, I had a "math
>> line" that quickly, visually, and easily came to me that told me
>> the answer to many problems.  See "The Math Gene" by Keith Devlin.

What?!
I'm not sure if i understand what you mean. Are you saying that you (and
Adrian) have some kind of intuition about maths, and answers spring out
at you in the way that, say, spelling mistakes in a sentence can?

If so, i find that idea deeply wierd.

Amara is right about teachers. When i was a kid (a long time ago), it 
was a really good science teacher who encouraged in me an interest in 
biology, and that's always been my favourite subject. Thanks for that 
link, Amara, i will check it out.

Anyway, this is getting a little bit off track. My point was not to ask 
for help with maths (!) but to point out that 'try harder' is not really 
much use to someone who has difficulty with it. It's like telling a 
depressed person to just pull themselves together.

Actually, it's quite possible that having people that are inherently 
innumerate could be a good thing. Diversity and all that.

ben