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Groups > sci.physics.relativity > #672592
| Message-ID | <s8GgXtzZGD2HQR0bAzRY_kmesXY@jntp> (permalink) |
|---|---|
| Subject | Re: Does Pythagorean theorem hold in The Shit of Einstein |
| References | (5 earlier) <18d0a1ba4bf54a6d$2503387$2300$c2265aab@news.newsdemon.com> <cgH_gS07DXKZwyUGL98dmTnuquw@jntp> <18d0a58fb29b8d7b$317838$260416$c2065a8b@news.newsdemon.com> <uQUbp85qTFse_IGur08LsF03xXU@jntp> <18d0d0ff7c0d1cd3$2503503$2300$c2265aab@news.newsdemon.com> |
| Newsgroups | sci.physics.relativity |
| Date | 2026-08-31 13:31 +0000 |
| Organization | Nemoweb |
| From | Python <python@cccp.invalid> |
Maciej,
> Whenever you say "exists a right triangle
> without P property" you say "(every right
> triangle has P property) is false".
Certainly.
And that is precisely why your argument depends entirely on using
the same words for objects in different mathematical structures.
So let's remove that ambiguity once and for all.
I define:
Euclidean triangle:
three Euclidean straight segments joining three points
in a Euclidean plane.
Euclidean right triangle:
such a triangle having one Euclidean right angle.
And I call the analogous object made from three spherical geodesic
segments a "triangloid".
Now Pythagoras says:
Every Euclidean right triangle satisfies
a^2 + b^2 = c^2.
And I say:
Some right triangloids do not satisfy
a^2 + b^2 = c^2.
Where is the contradiction?
There isn't one.
In logical notation, you are confusing
for every x in E, P(x)
with
for every x in every conceivable geometry, P(x).
The first does NOT imply the second.
Your argument works only if you insist beforehand that "triangle"
must quantify over Euclidean triangles AND spherical geodesic
triangles AND hyperbolic geodesic triangles.
But that is exactly the terminological convention we have been
discussing.
And wonderfully, you have now stated your position explicitly:
> Non-euclideanity is when you take a
> half-circle and insist it's a straight
> line.
There we are.
After all these pages about Einstein refuting "FUCKEN BASIC MATH",
your fundamental objection has finally become:
mathematicians shouldn't call those things "straight lines".
Fine.
Don't.
Call them geodesics.
And don't call three of them a triangle.
Call the object a triangloid.
Then:
Every Euclidean right triangle obeys Pythagoras.
Some spherical right triangloids don't.
Pythagoras survives completely untouched.
But unfortunately for your argument, all the mathematics of spherical
geometry survives completely untouched too.
For the spherical surface:
ds^2 = R^2(dtheta^2 + sin^2(theta)dphi^2)
K = 1/R^2
C(r) = 2 pi R sin(r/R).
For the Euclidean plane:
ds^2 = dx^2 + dy^2
K = 0
C(r) = 2 pi r.
Renaming "triangle" and "straight line" changes none of these
equations.
And Gauss's Theorema Egregium still tells us that K is intrinsic:
the inhabitant of the surface can determine it without knowing that
the surface is embedded in Euclidean R^3.
This also answers:
> Not being an Euclidean plane doesn't make an Euclidean sphere
> non-euclidean, however.
Again you are exploiting an ambiguity in "Euclidean sphere".
The sphere is perfectly describable as a surface embedded in
Euclidean R^3.
Nobody disputes that.
But the INDUCED TWO-DIMENSIONAL METRIC on that surface has
K = 1/R^2,
whereas the Euclidean plane has
K = 0.
The cylinder makes the distinction impossible to hide:
plane: K = 0
cylinder: K = 0
sphere: K = 1/R^2.
Both cylinder and sphere can be embedded in Euclidean R^3.
Yet the cylinder can be unrolled isometrically onto a plane and the
sphere cannot.
So "embedded in Euclidean R^3" and "has Euclidean intrinsic metric"
cannot mean the same thing.
Gauss settled that long before Einstein entered the story.
> changing axioms is triffling
> with word meanings and nothing more.
No.
Renaming objects changes words.
Changing axioms changes which propositions follow.
If you prefer, we can conduct the entire discussion with completely
different vocabulary:
Euclidean geometry -> E-geometry
hyperbolic geometry -> H-geometry
straight line -> E-line
hyperbolic geodesic -> H-line
triangle -> E-triangle
hyperbolic triangle -> H-triangloid.
Then nobody has "changed the meaning" of any word.
And we can still prove different theorems in E and H.
The mathematics hasn't noticed our vocabulary change.
Which brings us back to your claim:
> "The Pythagorean theorem is false."
and
> "This physical system is not described by a Euclidean metric."
> They're equivalent, unfortunately.
They still aren't.
The first says:
E |- P.
More precisely, P is a theorem following from the Euclidean
assumptions.
The second asks whether some physical system X satisfies the
mathematical structure E:
X models E.
Those are statements at two different logical levels.
And YOU already supplied the simplest proof that they cannot be
equivalent:
> There is no observables in EG. It's perfectly
> unfalsifiable.
Exactly.
Pythagoras is a mathematical theorem containing no physical system X.
"Physical system X has a Euclidean metric" contains an additional
empirical assertion about X.
They therefore cannot possibly be logically equivalent.
You keep inserting the missing premise:
Physical reality MUST instantiate Euclidean geometry.
Then, when Einstein questions that premise, you announce that he has
questioned Pythagoras.
He hasn't.
You have simply hidden your physical premise inside the word
"triangle".
So after quite a long journey, your indictment of non-Euclidean
geometry seems to have reduced itself to a vocabulary complaint.
And that is easily accommodated.
No more non-Euclidean "straight lines".
They're geodesics.
No more non-Euclidean "triangles".
They're triangloids.
Pythagoras is safe.
Gauss is safe.
Riemann is safe.
And all the allegedly nonsensical non-Euclidean equations remain
exactly where they were.
If changing two nouns makes your fundamental contradiction disappear
while changing no mathematics whatsoever, it wasn't much of a
fundamental contradiction.
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Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-26 21:01 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-27 15:24 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-27 17:35 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-27 15:39 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-27 18:19 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-27 16:29 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-27 18:49 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-27 16:51 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-27 19:01 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-27 17:11 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-27 19:20 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-27 19:23 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-27 22:20 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-28 05:46 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-28 10:19 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-28 16:04 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-28 14:26 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-28 16:34 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-28 14:40 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-28 16:50 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-28 14:57 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-28 17:12 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-28 15:15 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-28 17:26 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-28 15:30 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-28 17:37 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-28 15:42 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-28 17:46 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-28 18:41 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-29 11:57 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-29 14:08 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-29 12:20 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-29 14:18 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-29 12:24 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-29 17:35 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-29 15:42 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-29 18:07 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-29 16:12 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-29 18:32 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-29 16:36 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-29 18:47 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-29 16:51 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-29 19:19 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-29 22:25 +0000
Re: Does Pythagorean theorem hold in Geometry Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-08-29 18:04 -0700
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-30 07:34 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-30 10:43 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-30 14:21 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-30 12:50 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-30 15:36 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-30 13:55 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-30 16:19 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-30 14:32 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-30 18:21 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-30 16:45 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-30 19:31 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-30 22:26 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-31 08:15 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-31 08:47 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-31 13:31 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-31 16:36 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-31 14:46 +0000
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Re: Does Pythagorean theorem hold in The Trappings of Einstein Python <python@cccp.invalid> - 2026-08-31 15:40 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-31 17:16 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-31 15:39 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-31 17:58 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-31 16:05 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-31 18:15 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-31 16:19 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-31 18:35 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-31 16:38 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-31 19:01 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-31 17:07 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-31 19:50 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-31 19:27 +0000
Re: Does Pythagorean theorem hold in The Shit of Proclus Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-08-31 19:34 -0700
Re: Does Pythagorean theorem hold in The Shit of Proclus Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-08-31 20:53 -0700
Re: Does Pythagorean theorem hold in The Shit of Proclus Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-09-02 11:39 -0700
Re: Does Pythagorean theorem hold in The Shit of Einstein Maciej Woźniak <mlwozniak@wp.pl> - 2026-08-29 18:53 +0200
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-29 16:55 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Python <python@cccp.invalid> - 2026-08-29 11:58 +0000
Re: Does Pythagorean theorem hold in The Shit of Einstein Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-08-27 09:01 -0700
Re: Does Pythagorean theorem hold in QM with GR > SR Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-08-27 09:25 -0700
Re: Does Pythagorean theorem hold in QM with GR > SR The Starmaker <starmaker@ix.netcom.com> - 2026-08-27 14:36 -0700
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