"RichD" wrote in message

I've been trying to learn tensors, without success. The notation
sucks, for one thing. But II don't see the purpose. Einstein
needed
it for his theory, apparently. But it's also used for solids; stress
and
strain. Why can't you use vector algebra?

I'm not looking for an explanation of what/how, but the why and
whatfor.
Is there any intuition, or is it just formal, abstract manipulation?

--
RIch
=====================================================Your question is akin to asking "why use multiplication when repeated
addition works just fine?"
a) 3+3+3+3+3+3 = 18.
b) 6*3 = 18.

a) is easy to compute but clumsy -- ideal for a computer
b) requires you learned your multiplication tables by rote when you were 6
years old.

There is a description and history here:
http://en.wikipedia.org/wiki/Tensor

Try this problem:
A theatre has booked a famous entertainer for Saturday night.
All patrons want to see the show and some will pay more for a
front row seat, others have little money but will pay for a seat
"up in the gods", the upper gallery. There are 10,000 seats, 50
wide by 100 deep in the stalls and 100 wide, 50 deep in the
horseshoe gallery.
Front gallery seats in the arms of the horseshoe are closer to
the entertainment and more desirable. The nearer the seat is
to the stage the more you can charge per seat.
As manager your job is to price the seats for the maximum profit.
The richest will pay $1,000 for one seat. The poorest will pay $1,
so you are guaranteed a take of $10,000.
If you charge $1000 per seat you have the potential take of
$10 million, but only one patron will come to the show and your take
will be $1000, your profit will be negative as you still have to pay
overheads and the entertainer, who wants $100,000 for his
performance.
If you charge $1 per seat everybody will come, your take will be
$10,000 and your profit still negative, but that's 10 times better
than charging $1000 per seat with 9,999 empty seats.

What is your seat pricing strategy?
At first you may compute distance (seat to centre stage) as
d = sqrt( x^2 + y^2 +z^2) and say price = 1/d * k
You may be surprised to learn that you maximise profit when you
have some empty seats.
As the price comes down the number of seats taken goes up,
but there comes a point where lowering the price any further
reduces the profit.
The real question is, should I hire you to manage my theatre
while I'm off sailing in my yacht in the Mediterranean?
Do you have "knows tensors and how to apply them" on your
resume?
And that is the why and whatfor, I don't give a hoot for
Einstein's theory, it doesn't buy me anything.

-- Lord Androcles, Zeroth Earl of Medway