Re: Division by zero (0, 1, infinity)

On 02/01/2025 10:58 PM, Thomas Heger wrote:

Am Sonntag000002, 02.02.2025 um 03:19 schrieb Ross Finlayson:

On 02/01/2025 01:36 AM, Mikko wrote:

On 2025-02-01 08:14:08 +0000, Thomas Heger said:
>

Hi NG
>
I'm actually not really certain, but found an error in Einstein's 'On
the electrodynamics of moving bodies' which is quite serious.
>
>
See page six, roughly in the middle:
>
There we find an equation, which says this:
>
∂τ/∂y= 0

>
Do you mean on page 899 (9th page of the article) in §3?
The operation is not division but a partial derivative.
>

Now, 'tau' is a time belonging to the moving system k.

>
Yes, but it is also a number that is computed from coordinates of K.
>

This system k moves along the x-axis of system K with velocity v,
while x- and xsi-axis coincide and etha- and y axis remain parallel.
>
In other words v_y is permanently zero,

>
Yes,
>

 or: ∂y=0.

>
No. ∂y is not a number but a part of an operator. There are points with
different values of y and ∂/∂y refers to a line where t, x, and z
(but not
y) have the same value at every point.
>
See https://en.wikipedia.org/wiki/Partial_derivative
>

>
Zero meters/second is infinity seconds/meter.
>

yes, but that was my complain!
>
If there is not movement along the y-axis, then time tau would pass, but
y would remain zero.
>
This would mean, that ∂τ/∂y= infinity  (and NOT zero).

It's usually always more
"sensible, fungible, tractable"
when things go to zero instead
of infinity, so that all things
go to some common zero instead of
each whatever infinity.
Yet, it is so that mathematics is replete,
and so "space inversion" and these kinds
of things are mathematical with regards
to a point, and, the space.
One way to look at geometry is that
it is that there's a continuum that
makes a spiral space-filling curve
from an origin, then thusly the Euclid's
geometry can be _derived_ from that,
instead of what needs be _defined_.
https://www.youtube.com/watch?v=9r-HbQZDkU0&list=PLb7rLSBiE7F4_E-POURNmVLwp-dyzjYr-&index=29
"Logos 2000: natural infinities"
"The regular singular points of the hypergeometric
are zero, one, and infinity."
So, indeed, mathematics _owes_ physics
more and better mathematics of infinity,
to explain continuity.  These days there
is something like "quasi-invariant measure
theory" to go along with "the pseudo-differential"
to address problems with "the measure problem"
and about "the real fictitious forces",
about a true sum-of-histories sum-of-potentials
least-action least-gradient theory that's
a continuum mechanics with Poincare completion
in continuous manifolds, replete.
The partial derivatives are merely partial,
and pretty much always involve numerical
methods somewhere thusly always have a
nominally non-zero error term, then that
besides, the theory of potentials is
more than Laplacians (sums of partials).