[extropy-chat] Maths ability

[Samantha Atkins]

On Mar 5, 2006, at 9:09 AM, ben wrote:

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

Think negation.  Negating a negative yields a positive.

>
>> 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?

This is the seizing up thing perhaps for you.  Why "see" it?  It is  
just logic.  You don't need to see it to be comfortable and competent  
with it.

> 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.:
>

They mean going toward the negative side (left in your model) or  
toward the positive side (right) in your model respectively.  It has  
nothing to do with going toward or away from zero since that is  
merely one point out of many on the line. The problem you experience  
in part may be clinging to this sort of clunky limiting picture and  
getting lost in it.   Teachers do kids a disservice when instilling  
some of these pictures.

> + 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.
>

Or let go of visualizing it, at least in a way that isn't working for  
you.

>
>> 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?!?)
>

Sure.  Depending on what you mean.  Sometimes we try to read too much  
into things like "unity" and miss by "trying too hard" in  
unproductive ways.  It is sort of like Zen.

> 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.

It is certainly not just a collection of tricks.  I think what was  
referred to is a set of "tricks" or  ways brains process information  
and concepts which is required for really "getting" math.  I think  
those "tricks" are learnable but they can be very difficult to tease  
out and teach or to let go of blocking habits of thought and  
expectation long enough to learn.

>
> 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?
>

Not answers per se but ways of relating things in the mind.  How some  
people get them and others don't is an interesting puzzle.

- samantha