Re: My week with Linux: I'm dumping Windows for Ubuntu to see how it goes

On Mon, 19 May 2025 19:17:07 +0000, Farley Flud wrote :

Tools are an extension of our physical being that enable us to transcend
our physical limitations.
 
And our mental/intellectual limitations are extended through mathematics.

I like the way you accurately summarized mathematics as a tool extending
our reach much like a stick stuck into a termite's nest to lick them off.

To further quantum theory we need to probe deeper
into the heart of matter and that will require more advanced technology.
Our society currently does not have the technical means, nor the collective
will, to reach that end and may never will.

What I'd love to discover is WHY/HOW mass-energy causes spacetime to rush
inward, which for earth is at 11km/sec (the actual velocity depending on
the mass-energy of the celestial body in question).

Where's the math that describes WHY and HOW (not just how fast) the river
of spacetime flows inward toward mass-energy?

Einstein was able to discover his final solution only through mathematics,
in particular the mathematics of differential geometry (DG).  If DG
had not been developed by Einstein's time then no progress could have
been made.  Again, this illustrates the idea that mathematics is a tool
to transcend our intellectual limitations.

Einstein would agree with you I think, as do I, given Einstein himself was
reputed to have claimed something to the effect that general relativity was
a triumph of the methods of absolute differential calculus founded by
Gauss, Riemann, Christoffel, Ricci, and Levi-Civita (AFAIK).

Hence, I agree with you that Einstein was temporally lucky that Tensor
Calculus (e.g., metric tensors, tensor equations, etc.) had recently been
developed, as well as Riemannian Geometry (e.g., curved spacetime
geodesics), including connectikon coefficients (e.g., Christoffel symbols &
the geodesic equation in non-Euclidian geometry).

Likewise the Ricci Tensor and Parallel Transport and differentiation within
a curved manifold were all recent (to Einstein) necessary mathematical
tools.

He was lucky after the fact that his old professor (who had described
Einstein as a "lazy dog") unified Einstein's theories into Minkowski
spacetime using the Minkowski Metric, to which Einstein is said to have
remarked something to the effect of "since the mathematicians have invaded
my theory of relativity, I do not understand it myself any more".

Tools allow us feeble "monkey-brained" individuals to express great strength,
speed, etc., and the tools of mathematics allow us to express great insight
into higher-dimensional and "curved" spaces.

What I'd love to be able to understand is WHY/HOW spacetime rushes inward
toward mass-energy. What is the mechanism? I'd love to discover that!

Mathematical tools will likely (I predict) be able to answer that in the
future - but I don't possess anywhere near the skills to be the one who
solves that fundamental problem.

Mathematics will continue to develop and possibly extend our mental
vistas even higher.

We're flatlanders. And we don't even realize it. All our tools are missing
fundamental dimensions - much like Euclid was missing the spacetime metric.

But if mathematics will ever be enough to disclose ultimate reality
is a question for generations of the distant future -- if we can persist
that long as a species.

I agree and I just want to make the point which you seem to already be
aware of, which is that we "think" we know a lot and yet almost everything
we think we know is almost certainly wrong.