Pancho wrote:
On 12/09/2019 10:14, Brian Reay wrote:
Robin wrote:
On 12/09/2019 09:00, Tim Streater wrote:
In article , NY wrote:

"Tim Streater" wrote in message
.. .
In article ,
David Paste wrote:

Hello,

When writing, for example, "metres per second per second" for
acceleration, it is noted as ms^-2 (where the caret symbolises
the -2 is in superscript).

I understand that, and why, "per second per second" is "seconds
squared", but in the notation, why is it superscript minus 2? Why
not just superscript 2?

Because its "per", and so you are dividing. which gives you a negative
coefficient.

E.g.:

Miles/hour is speed, and if I say I go at a certain miles/hour for a
certain time, the answer must be miles. So, 30 miles/hour for two hours
is 60 miles. That is:

30 m/h x 2 h = 60 m

So the /h and the h cancel, meaning that as the h is really h^1, the /h
must be h^-1 in order for the coefficients to add up to zero (meaning
there's no h left in the final expression). When you multiply things
you add their coefficients, as in 10^2 x 10^3 - 10^5.

The notation m s^-2 and kg m^-3 always strike me as perverse: what was
wrong with m/s^2 and kg/m^3? I remember being taught m/s^2, and then
when I changed school to one that did a Nuffield physics syllabus, the
notation changed to kg m^-2 which it claimed to be "better" in some
unspecified way.

I'm inclined to agree.


I disagree. Mainly as the superscripts reduce the risk of mistakes
where there are multiple terms. Eg

kg.m^ˆ’1.s^ˆ’2
kg/m.s^2



Certainly if you are analysing a problem and checking the dimensions ( a
useful technique, not always taught these days although I made a point of
teaching it), indice notation is probably far easier to use.

Yes.

I never liked subtraction (or division) because it was non-commutative
as opposed to addition (or multiplication) which are commutative.
Commutative operations are far easier to handle algebraically.

When my son was little I taught him addition of negative numbers rather
than subtraction, he liked the idea. You were a teacher, weren't you? I
always wondered why this approach wasn't more common in schools?



There are several techniques.

Opinions on which are easy to grasp vary.

The same is true for other areas of Mathematics. This is why, for example,
long division wasnt taught for many years in primary schools which has had
a €˜knock on impact even now. Some primary teachers cant handle long
division with confidence so avoid it (they never learned it themselves).

You may think, so what but it is key to algebraic division which you need
later. Yes, I was a teacher, in a Specialist Mathematics School. I
qualified late in life as a second career, Ive degrees in Engineering and
another in Mathematics. I always tried to bring real world examples into my
lessons.

Indicies emphasise multiplication by an inverse instead of division and
hence are commutative. Personally, I don't seem to care about the
notation, I use both.


Once you are confident, coping with different notation etc isnt generally
an issue. Ditto terminology. However, when people are learning something or
less confident, consistency is important.