[extropy-chat] Maths ability (was: Fight for Evolution?)

[Adrian Tymes]

--- ben <benboc at lineone.net> wrote:
> I regard this as my own personal disability, as i can see how easy it
> seems to many others, like yourself and Spike. You'll probably laugh
> (or
> cry) at this, but i still don't know the answer to (-1) - (-1). I can
> get several answers to this. I've been told the rules before, but
> i don't understand the why of it (if you subtract, is that going to
> the
> left, i.e. more negative, or is it going towards zero?).

Depends on what you're subtracting.  In this case, you're "subtracting"
a negative number, which means you're actually going to the right (more
positive).

(The next example uses x as a variable.  This is so that you won't
pay attention to x, because it doesn't matter what x is for this
example.  x is some number - any number.)

Look at the equation.  You've got two lines in x - (-1): the
subtraction itself, and the dash in front of the -1.  Put them
together, and you can form a plus.  In other words, x - (-1) = x + 1.
(Likewise, x + (-1) = x - 1, because you've three lines, an odd
number.)

So, in short, the "why" of it is that negative numbers (on the right
side) reverse the meaning of addition and subtraction, in a sense.
Which is one of the reasons why they so often get treated specially.
(They also do funky things to many other operations, like square roots.
But best to understand their impact on adding and subtracting before
trying to understand what they do to other things.)

> That's the kind of confusion that has held me back in maths. I assume
> it's a similar thing with others like Pete. Perhaps it's a result of
> bad
> early education (nobody actually told me what squared and cubed
> really
> mean, i just suddenly realised it one day. A real "DOH!" moment!),
> perhaps i'm just stupid, maybe it's a genetic thing, but i wish i
> could
> overcome it.

>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 that also (way too often, IMO) goes unstated:
when you recognize that you have a knowledge deficiency of this form,
you can look up other peoples' definitions of it.  In a library, or
these days online (hail Google ;) ), you can spend hours or days
looking up various definitions and explanations until you find one that
you can truly understand.  You do this primarily on your own time, on
your own initiative...and by making a habit of this whenever you
recognize that you are in this situation (and by getting good at
recognizing when you are in this situation with regards to some
subject), many of your educational "disabilities" can soon evaporate.

This is something that those who have been practicing it for years -
decades, even - sometimes take for granted.  We can be tempted to
forget that other people don't know this at all.  (Many other people?
Even...most other people?)

A personal anecdote: for most of my K-12 years, I never understood why
high grades were at all important.  No one told me outright, among
other causes.  My parents despaired at my mediocre GPA, right up until
about half way through 11th grade...when I suddenly found out that high
grades = better chance at good colleges (and better chance at
scholarships - you can imagine what ~$10,000 range figures seemed like
to a high school kid).  With that understanding in mind, I finally
bothered to try to get good grades...and you can guess the result.

> I can multiply any number by 11 in my head (any number at all, as
> long
> as its not too big to keep it in my head), but it's just a trick. I
> don't really understand the method. That's not maths, is it? Anyone
> can
> learn the tricks. It's the understanding that's important.

Hate to break it to you, but sometimes it *is* the tricks.  A whole lot
of tricks.  Of course, that depends on where exactly you draw the line
between "tricks" and true understanding.  Perhaps it might be more
accurate to say, sometimes it seems like nothing more than a collection
of tricks.