Re: Division by zero

Am Dienstag000004, 04.02.2025 um 10:13 schrieb Mikko:

On 2025-02-04 07:36:34 +0000, Thomas Heger said:
 

Am Montag000003, 03.02.2025 um 16:51 schrieb Mikko:

On 2025-02-03 07:56:53 +0000, Thomas Heger said:
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Am Sonntag000002, 02.02.2025 um 10:30 schrieb Mikko:
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Hi NG
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I'm actually not really certain, but found an error in Einstein's 'On the electrodynamics of moving bodies' which is quite serious.
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See page six, roughly in the middle:
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There we find an equation, which says this:
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∂τ/∂y= 0

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

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You should answer this question. It is not useful to talk without telling
what you are talking about.
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I'm referring to the English translation, which can be found here
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https://www.fourmilab.ch/etexts/einstein/specrel/www/
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The English pdf version has other page numbers than the original article.
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But in a way, these original page numbers are also possible as reference.
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But unfortunately I have here only the English version (the German I have on a different computer).
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So I have to tell you the page from the English version or make the meant part available to you by other means.
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So, § 3 was meant and roughly the middle, which can be found on page 6 of the English pdf version.
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And you are absolutely right, that a partial derivative was meant.
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The problem was: of which function was a partial derivative meant?

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He obviously means the function needed to determine τ. It does not matter
whether he means the function from x, y, z, t or x', y, z, t as ∂/∂y is
the same in both cases.

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There ain't no thing as 'obviously'.

 Of course there is.
 

If an author doesn't write, what he has in mind, the reader is requirred to guess. And the result of such a process is by no means 'obvious'.

 What the author has in mind is not relevant. Relevant is what physicists
at the time understood the text to say.

Well, no....
As I see it, an author tells his story and that story is his.
Therefore the author needs to say, what he wants to say and make it clear, how he wanted to be understood.
The 'background' of current state of science isn't part of the story, but more or less the stage, upon which the author places his piece.
It has something to say, but scientific statements are meant to be absolute and cannot refer to 'common believes' (whatever that might be).
IOW: I cannot grant errors to former scientists, while don't do that with current science.
Wrong is wrong and it doesn't matter, when this occurred.

 

Einstein used τ for three different types of mathematical objects:
a value τ (meaning: time in k)
a function τ (a coordinate transformation between K and k)
as function value τ of that function τ.

 meaning: time in k

No, in this case of
  ∂τ/∂y= 0
the function  τ was meant.
Time of system k was also called τ, but that interpretation would make ∂τ/∂y= 0 wrong.
That 'time in k' was the trap I had fallen into, hence I know how this worked.
It made me a little angry, because I would expect from a scientific paper, that different types of mathematical objects are distinguishable from each other (e.g. by different fonts).
But not so in Einstein's text, where none of the variables are defined properly and where he also switched back and forth between different types.
E.g. vectors and scalars were often used interchangeable, while that is actually an error.
For instance he wrote, that velocity of light is constant, while he actually meant speed.
Also the same symbols were 'reused' or the same quantity was symbolized by different variables.

Therefor it would requirre some brains to find out, which one was actually meant.

 It is reasonable to assume that the intended readers had brains.

Sure, but how much brains would you need to read Einstein's mind?

Correct would have been to make the type explicit, e.g. by different fonts.

 It is sufficient that the target audence can understand the emaning of the
text.

Well, that's why it was said, that only three people in the world could understand Einstein's text.
BUT: if the author tells a story, he had to write for the reader and allow them to estimate, at least after some thinking, what was eventually meant.
This would require, for instance, naming conventions, which common mortals are able to decipher.
Much better would be, if the author writes a little table, where the names and symbols are explained.
But Einstein made understanding even more difficult than it should be by declaring certain conventions for names, but actually used other ones.
In a way the text is more or less a riddle, similar to soduko, where the reader is supposed to fill in the gaps.
...
TH