On Mar 8, 11:10 pm, JanPB wrote:
On Mar 8, 10:10 pm, Koobee Wublee wrote:



On Mar 8, 8:50 am, JanPB wrote:

On Mar 7, 11:10 pm, Koobee Wublee wrote:
How can you argument with the mathematics? ds^2 is a scalar according
to the mathematics above. shrug

Take a 2D sphere of radius 1 (say). Pick a point p on it. Tell us,
what real number is ds^2 equal to at p?

Given

(ds)^2 = g_ij dq^i dq^j

Where

** i, j = 1, 2

Then,

(ds)^2 = g_11 dq_1 dq_1 + g_12 dq_1 dq_2 + g_21 dq_2 dq_1 + g_22 dq_2
dq_2

So, wise guy, go ahead and assign the numbers to g_11, g_12, g_21,
g_22, dq_1, and dq_2. Then, you will find a number for (ds)^2.
shrug

Where is the number? You said ds^2 was a scalar. Which number is ds^2
equal to on the sphere? Either write down the actual number or say
that you were wrong.
There is no other exit.

Not to interfere, let KW have 1st crack,
but I think that's a good problem.
I think I could give it a shot.
Regards
Ken

Jan Bielawski