What is the newest installment of 'Random Thoughts' on Physics Forums?

[WWGD]

...and only if it's got the right transformation laws.

I found the answer through meditation : Hom, Hom,...

 

[fresh_42]

...and only if it's got the right transformation laws.

Only for physicists. For me it's only important how many asterisks are involved! That's sufficient for me to know what to do. And don't bring up co- and contravariances. My book about homological algebra uses them differently anyway.

 

[Ibix]

Only for physicists. For me it's only important how many asterisks are involved! That's sufficient for me to know what to do. And don't bring up co- and contravariances. My book about homological algebra uses them differently anyway.

OK, but still you have a condition over and above being a square matrix. The Christoffel connection coefficients are representible by an NxNxN matrix, but aren't a tensor.

 

[fresh_42]

Every "rectangle" collection of numbers in any dimension can be interpreted as a tensor, a cube is just $\sum x \otimes y \otimes z$.

 

[Ibix]

Can be interpreted as, sure. But can be interpreted otherwise too (e.g. the connection). So I object to the "is" part of "a matrix is a tensor".

 

[WWGD]

OK, but still you have a condition over and above being a square matrix. The Christoffel connection coefficients are representible by an NxNxN matrix, but aren't a tensor.

But isn't a matrix just a 2D array? Or maybe it is the confusion of notational/definitional differencees?

 

[fresh_42]

It's the old discussion what a transformation and what its matrix is. A tensor to me is simply an element of a tensor algebra, resp. space, if only tensors of equal rank are involved. As soon as I have a basis of the constituent vector spaces, I have a cube or whatever a matrix (not necessarily square) in higher dimensions shall be called. Their use by physicists makes me dizzy. It always sounds curved somehow, but it's flat as a board.

 

[WWGD]

Every "rectangle" collection of numbers in any dimension can be interpreted as a tensor, a cube is just #\sum x \otimes y \otimes z##.

What type of or theory of Homology are you using?

 

[fresh_42]

What type of or theory of Homology are you using?

Covariance and contravariance determines, whether a functor keeps the direction of mapping arrows or converts them. I have never seen a second category by the way physicists use these terms - there are always only vector spaces present. If at all, it's the transition $V \rightarrow V^*$, but they attach it to either $V$ or $V^*$, so again no second category.

 

[WWGD]

It's the old discussion what a transformation and what its matrix is. A tensor to me is simply an element of a tensor algebra, resp. space, if only tensors of equal rank are involved. As soon as I have a basis of the constituent vector spaces, I have a cube or whatever a matrix (not necessarily square) in higher dimensions shall be called. Their use by physicists makes me dizzy. It always sounds curved somehow, but it's flat as a board.

This looks more like geometric algebra. Or Simplicial.

 

[fresh_42]

This looks more like geometric algebra. Or Simplicial.

No, it looks like homological algebra, the category thingies, at least the books are titled so, both, the English and the German ones.

 

[WWGD]

Can be interpreted as, sure. But can be interpreted otherwise too (e.g. the connection). So I object to the "is" part of "a matrix is a tensor".

So it depends on what "is" is?

 

[WWGD]

Yo mama so fat , when she walks around the house... she _really_ walks around the house.

 

[Psinter]

Whenever you get a new job and meet your new co-workers:

Edit:

Scene from the movie: https://en.wikipedia.org/wiki/Penguins_of_Madagascar

 

[fresh_42]

Can someone please find a word for "Erkenntnis". The only possibility I see is "knowledge", but there is a fundamental difference between knowing something and understood something! Too bad we don't have philosophy here. I would be very interested which consequences it has to a society, that only knows things and doesn't care about "Erkenntnis".

And, no, re-cognition doesn't count. It's only to realize what's already known. I'm looking for the knowledge behind "Eureka!".

 

[Jonathan Scott]

Can someone please find a word for "Erkenntnis". The only possibility I see is "knowledge", but there is a fundamental difference between knowing something and understood something! Too bad we don't have philosophy here. I would be very interested which consequences it has to a society, that only knows things and doesn't care about "Erkenntnis".

And, no, re-cognition doesn't count. It's only to realize what's already known. I'm looking for the knowledge behind "Eureka!".

Insight?

 

[fresh_42]

Insight?

Oh, I haven't thought about this one. Probably because it means something different in German. Insight here reflects on a revised and corrected position, or the possibility to view formerly closed documents.

 

[Psinter]

Have you even laughed so hard that you could literally feel your ab muscles ripping?

 

[OmCheeto]

Are rainbows chromatic aberrations, or vice versa?

 

[fresh_42]

I've incidentally found a place in town today where people can actually play boules - people who played it inclusively.

 

[Ibix]

Are rainbows chromatic aberrations, or vice versa?

They're more or less a product of chromatic aberration, yes. I'm not sure you can really call it chromatic aberration when it's not part of an optical system designed to form an achromatic image, but it's the same root cause, certainly.

 

[Ibix]

I've incidentally found a place in town today where people can actually play boules - people who played it inclusively.

I play boules
(I need no tools)
Against fools
While eating moules.

 

[fresh_42]

I play boules
(I need no tools)
Against fools
While eating moules.

Correction: Pétanque.

Your turn.

 

[Ibix]

Correction: Pétanque.

Your turn.

I'll be frank
I play petanque
But I don't clank
'less I bring my tank.

 

[fresh_42]

I'll be frank
I play petanque
But I don't clank
'less I bring my tank.

You know this doesn't work with the actual pronunciation?
Our town is considered the most multi-cultural in Germany, but I didn't know that French belong to this mixture.

 

[Ibix]

You know this doesn't work with the actual pronunciation?
Our town is considered the most multi-cultural in Germany, but I didn't know that French belong to this mixture.

It works with the usual anglicised pronunciation. And just Googling it (from an English computer in England, anyway) gives me the same pronunciation. How's it supposed to be pronounced?

 

[fresh_42]

How's it supposed to be pronounced?

[peˈtaŋkɔ]
There is no correspondence to the French nasal syllables in English. Frank was o.k., since the French pronounce it similar, but then I don't think there is a way to make it rhyme in English. That's why I corrected boules.

 

[Ibix]

Hmm. Google is offering pəˈtaŋk - which I think is the same except it's missing the final symbol - and the "listen to the pronunciation" comes out so that it rhymes with frank/clank/tank. But I do vaguely recall how to pronounce frank (or, at least, franc). And there won't be much that rhymes with that in English. As you say, we don't have that sort of sound.

Anyway, my doggerel works in English. And I'm speaking English. Not my fault if foreigners can't pronounce their own language right.

 

[fresh_42]

I just looked it up, out of curiosity, and the statistic counts more than 300 French in town, and only a bit over 200 from UK. I would have expected more. At least the 330 are enough to explain a boules match.

 

[fresh_42]

Not my fault if foreigners can't pronounce their own language right.

Are we talking about the Haggis people?

 

[Ibix]

Are we talking about the Haggis people?

Haggises are people? I thought they were furry creatures with one leg shorter than the other from running round hills. You catch them by scaring them into running the wrong way round a hill, then catching them in a net as they roll down the hill.

 

[fresh_42]

Haggises are people? I thought they were furry creatures with one leg shorter than the other from running round hills. You catch them by scaring them into running the wrong way round a hill, then catching them in a net as they roll down the hill.

I always suspected these things were alive - no wonder Nessie is hiding. ... Are they related to fried Mars bars?

 

[Ibix]

I always suspected these things were alive - no wonder Nessie is hiding. ... Are they related to fried Mars bars?

No - unlike haggis trapping and Nessie, those are real.

 

[OmCheeto]

They're more or less a product of chromatic aberration, yes. I'm not sure you can really call it chromatic aberration when it's not part of an optical system designed to form an achromatic image, but it's the same root cause, certainly.

Thanks! That was my thought.

 

[WWGD]

They're more or less a product of chromatic aberration, yes. I'm not sure you can really call it chromatic aberration when it's not part of an optical system designed to form an achromatic image, but it's the same root cause, certainly.

So is it the real life or is it just fantasy...?