Official "This Day In History" thread - Page 2

ewmayer · 2014-12-27, 07:31

Quote:

Originally Posted by rogue

As in "Let a satyr nail ya during Saturnalia"?

ewmayer · 2015-08-10, 00:57

[By way of reviving this dormant thread, which I expected would be somewhat popular, but which resists my every effort to get it to 'take']

On this day 70 years ago, Kokura lived the Damocles sword metaphor and became the luckiest Japanese city in WW2 Japan [please pardon the NYT's '50th anniversary' bad-math.]:

http://www.nytimes.com/1995/08/07/wo...by-a-bomb.html

I see the sword of Damocles
Is right above your head
They're trying a new treatment
To get you out of bed
But radiation kills both bad and good
It can not differentiate
So to cure you they must kill you
The sword of Damocles hangs above your head
-- Lou Reed

jyb · 2015-08-12, 16:33

Quote:

Originally Posted by ewmayer

[[please pardon the NYT's '50th anniversary' bad-math.]

NB: that story was written in 1995, so I think their math is just fine.

ewmayer · 2015-08-12, 22:09

Quote:

Originally Posted by jyb

NB: that story was written in 1995, so I think their math is just fine.

Gah! Done in by the link equivalent of 'old wine in new bottles'...

jasong · 2015-08-17, 08:30

Quote:

Originally Posted by ewmayer

Gah! Done in by the link equivalent of 'old wine in new bottles'...

I believe the old wine in new bottles thing wasn't originally a reference to dating mistakes. If I'm not mistaken, the verse is in Proverbs of the Jewish Old Testament and is...maybe...a comment on morality. Never figured that particular verse out, though I remember it saying that the new bags(not bottles) would burst. Since it was in Proverbs, I assume there was a double meaning going on.

Uncwilly · 2015-08-17, 18:09

Quote:

Originally Posted by jasong

Never figured that particular verse out, though I remember it saying that the new bags(not bottles) would burst. Since it was in Proverbs, I assume there was a double meaning going on.

It is actual a saying of Jesus. New wine generates gas. The new wineskins can expand to handle that. Old wineskins are already stretched and stiff. Filling them up to the neck with new wine will cause them to burst. It is paired with the new cloth in an old garment. The pairing is talking about the old stiff and rotten institution that the Jewish priesthood/nation had become. It was to be swept away.

ewmayer · 2015-08-17, 21:29

In modern usage I've come across 2 variants of the phrase:

Old wine in new bottles: Already-discredited 'old fashioned' notions being gussied up and presented as new;

New wine in old bottles: Something inferior being disguised as a rare and precious thing.

Perhaps there are more interpretations of the same 2 phrases, as well?

ewmayer · 2015-11-25, 02:11

100 years of General Relativity. It's fun to read the paper which accompanied Einstein's lecture on "The Field Equations of Gravitation" - the last of 3 such - to the Prussian Academy of Science in the original. Scans of the first two (of four) pages at bottom - my translation of the first page [p.844]:

Quote:

In two recent communications* I have shown how one can attain field equations of gravitation which satisfy the postulate of general relativity, that is which in their overall form are covariant with respect to arbitrary substitutions of the spacetime variables.

The developmental path therein was as follows. First I found equations containing the Newtonian theory as an approximation and which were covariant with respect to arbitrary substitutions of the determinant 1. Thereupon I found that these equations are generally covariant if the scalar of the energy tensor of "matter" [ewm: modern terminology is the "stress-energy" tensor, and its scalar is the "scalar energy density"] vanishes. The coordinate system was then specialized according to the simple rule that $\sqrt{-g}$ is made equal to 1, whereby the equations of the theory undergo an eminent simplification. Thereby one must, however, as discussed, introduce the hypothesis that the scalar of the energy tensor of matter vanish.

Newly I find that one can avoid the hypothesis on the energy tensor of matter if one introduces the energy tensor of matter into the field equations in a different manner than was done in my two previous communications. The field equations for the vacuum, which I used to explain the perihelion shift of Mercury, are unaffected by this modification. Here I again provide the overview, so that the reader is not required to refer to the previous discussions. From the well-known Riemann covariant of fourth rank [ewm: Riemann-Christoffel curvature tensor] one derives the following covariant of second rank:

$G_{im} = R_{im} + S_{im} \qquad[1]$

$R_{im} = \sum_l \frac{\partial \left{ \begin{array}{c}im \\ l \end{array} \right}}{\partial x_l} + \sum_{l,\rho} \left{ \begin{array}{c}il \\ \rho \end{array} \right} \left{ \begin{array}{c}m\rho \\ l \end{array} \right}\qquad[1a]$

$S_{im} = \sum_l \frac{\partial \left{ \begin{array}{c}il \\ l \end{array} \right}}{\partial x_m} + \sum_{l,\rho} \left{ \begin{array}{c}im \\ \rho \end{array} \right} \left{ \begin{array}{c}\rho l\\ l \end{array} \right}\qquad[1b]$
-----------------
* Session proceedings XLIV, p.778 and XLVI, p.799, 1915.

And of the second [p.845] - I was unable to make out some of the subscripts here due to low scan resolution, so have made my best guess and endeavored to at least make things consistent in terms of the tensor-index summation convention:

Quote:

We obtain the 10 generally covariant equations of the gravitational field in spaces where "matter" is absent by requiring that

$G_{im} = 0. \qquad[2]$

These equations can be simplified if one chooses the coordinatization [ewm: Bezugsystem] such that $\sqrt{-g}$ is unity. Then $S_{im}$ vanishes due to [1b], and instead of [2] one obtains

$R_{im} = \sum_j \frac{\partial \Gamma^j_{im}}{\partial x_j} + \sum_{k,l} \Gamma^l_{ik} \Gamma^k_{ml} = 0 \qquad[3]$

$\sqrt{-g} = 1. \qquad[3a]$

Here we have

$\Gamma^l_{im} = - \left{ \begin{array}{c}im \\ l \end{array} \right} , \qquad[4]$

which quantities we characterize as the "components" of the gravitational field.

If the space of interest contains "matter", its energy tensor appears on the right-hand-side of [2] resp. [3]. We set

$G_{im} = -\kappa \bigl( T_{im} - \frac{1}{2} g_{im} T \bigr) , \qquad[2a]$

where we define

$\sum_{i,j} g^{ij} T_{ij} = \sum_k T^k_k = T . \qquad[5]$

T is the scalar of the energy tensor of "matter", the right-hand-side of [2a] is a tensor. If we again specialize the coordinate system in the usual fashion, then in place of [2a] we obtain the equivalent equation

$R_{im} = \sum_j \frac{\partial \Gamma^j_{im}}{\partial x_j} + \sum_{k,l} \Gamma^l_{ik} \Gamma^k_{ml} = -\kappa \bigl( T_{im} - \frac{1}{2} g_{im} T \bigr) \qquad[6]$

$\sqrt{-g} = 1. \qquad[3a]$

As always we assume that the divergence of the energy tensor of matter vanishes in the sense of the general differential calculus (impulse energy assumption). In specializing the coordinatization according to [3a] this amounts to thw requirement that the $T_{im}$ should satisfy

$\sum_k \frac{\partial T^k_l}{\partial x_k} = -\frac{1}{2} \sum_{u,r} \frac{\partial g^{ur}}{\partial x_r} T_{ul} \qquad[7]$

or

$\sum_k \frac{\partial T^k_l}{\partial x_k} = -\sum_{u,r} \Gamma^u_{lr} T^r_u . \qquad[7a]$

ewmayer · 2015-11-25, 02:11

And pages 3 and 4:

Dubslow · 2015-11-25, 03:48

What about those of us that don't speak Deutsch

ewmayer · 2015-11-25, 06:35

Quote:

Originally Posted by Dubslow

What about those of us that don't speak Deutsch

Es ist nicht zu spät, es zu lernen.

Or you can just settle for the ridiculous Einstein poster so beloved by the college students, of the poofy-white-haired old geezer sticking his tongue out. A much better photo of the Einstein who gave us relativity is this one from 1919, following the Eddington-led solar-eclipse expedition which confirmed one of the key experimental tests of GR, that the bending of light by a massive object would be precisely double that predicted by Newtonian gravitation (the other key test, that of the perihelion precession of Mercury, a fairly precisely-measured but hitherto unexplained quantity, was used by Einstein as a crucial sanity check in his development of GR):

2015-08-10, 00:57	#13
ewmayer ∂²ω=0 Sep 2002 República de California 2⁴×733 Posts	[By way of reviving this dormant thread, which I expected would be somewhat popular, but which resists my every effort to get it to 'take'] On this day 70 years ago, Kokura lived the Damocles sword metaphor and became the luckiest Japanese city in WW2 Japan [please pardon the NYT's '50th anniversary' bad-math.]: http://www.nytimes.com/1995/08/07/wo...by-a-bomb.html I see the sword of Damocles Is right above your head They're trying a new treatment To get you out of bed But radiation kills both bad and good It can not differentiate So to cure you they must kill you The sword of Damocles hangs above your head -- Lou Reed Last fiddled with by ewmayer on 2015-08-10 at 01:04

2015-11-25, 02:11	#20
ewmayer ∂²ω=0 Sep 2002 República de California 2⁴×733 Posts	And pages 3 and 4: Attached Thumbnails

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ewmayer ∂²ω=0 Sep 2002 República de California 2⁴×733 Posts	In modern usage I've come across 2 variants of the phrase: Old wine in new bottles: Already-discredited 'old fashioned' notions being gussied up and presented as new; New wine in old bottles: Something inferior being disguised as a rare and precious thing. Perhaps there are more interpretations of the same 2 phrases, as well?

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