Tenser, Said The Tensor

[natecull]

"I wrote it for that flop show about the crazy mathematician... " Duffy began to sing:
Eight sir, seven sir, six sir, five sir
Four sir, three sir, two sir, one!
Tenser, said the tensor
Tenser, said the tensor
Tension, apprehension
And dissension have begun.
-- Alfred Bester, "The Demolished Man"

http://tenser.typepad.com/tenser_said_t ... expla.html

This is a thread to talk about rar, scary tensors! Mythical beasts which live in (m times n) dimensions and eat unwary mathematicians. Used in General Relativity and also by Gabriel Kron. They're probably not as scary as they sound however.

Here's an introduction from NASA which does assume a bit of knowledge of vectors and matrices, but is one of the simpler introductions I've read so far. (Wikipedia is not really a lot of help).
http://www.grc.nasa.gov/WWW/K-12/Number ... 211716.pdf

A useful page to have up for those of us who are unfamiliar with Greek letters is this one:
http://en.wikipedia.org/wiki/Greek_lett ... ngineering

I'm still working through this trying to get a handle on what a tensor is, so I can't yet explain it properly, but I'm hoping to be able to when I'm done.

So far I think the main point is that while ordinary numbers (or vectors) measure absolute quantities, tensors measure *differences* between two systems. The main worry of Einstein in General Relativity being that the "laws of nature" should not change from place to place - and the way he chose to get there was to say that the *difference* between quantities always stays the same. Even under acceleration or curvature, which is quite a big ask. How well he succeeded, and whether his maths describes what Townsend Brown's devices do, is the question.

[KarenAnn23]

MATH !!!! LOL

[PeeTee]

Karen, I was looking at the Nasa stuff above and I think the way they explain it is well suited for serious students of physics and math, however I can assure you that the cartoon il;lustrations and moving images in the video by the Annenberg Foundation is much easier to go through. Somehow the visuals combined with the voice-over explanation make it much easier to understand.

So.... If you to grasp anything about Tensors, and Vectors..... Try watching this one half hour video and I'll bet you will get a lot more from it than that paper by NASA.

Here is where you will find it:
http://www.learner.org/resources/series42.htm
Click on the 5th presentation (VECTORS)
Good Luck

Peetee Le Trickfox

[PeeTee]

http://www.learner.org/resources/series42.html

Darn it .............here it is again

[KarenAnn23]

got it...well almost

[natecull]

Once again, I wish I could watch those videos, but they're not viewable in New Zealand. Are you sure however that they talk about tensors and not just vectors? The two are not the same - even a rank-1 tensor is not precisely a vector.

[PeeTee]

Natecull would you like me to burn a few CD copies and send them to you as we proceed through the series?

Tensors are discussed in a lot more detail further in the series.

I promis that you will enjoy this type of media. Ask Karen...This is not dry, it's very practical, rewarding and filled with historical re-enactments of the experiments by the scientists who discovered them.

The way they show the math formulas changing before your very eyes. It helps to understand algebraic and Newtonian math concepts.

It's a very long path that we are on here and here is what's ahead

Once we get the the Electric Field........This is where the secrets of Coulomb live along with Maxwell and others.... Once we get to Coulomb, We are going to make a "departure'.

Peetee Le trickfox

[PeeTee]

Nate
I see your point after going over this thread from the start.....
This thread started off with TENSORS, and I took it back down into the pre-requisite knowledge of Vetors and Matrices.
I agree that Tensors of themselves should take up it's own thread, so I'll see which video is on Tensors and perhaps I can even download it to you as an AVI file that will take 45 minutes or so to get to you on a DSL link. I could also FTP is you have a server.

Ray

[natecull]

Thanks. I don't have a server but I do have a 4mb broadband connection... as long as I'm not violating some copyright treaty by downloading. (I'm never quite sure what's legal these days; it changes from country to country). I think the RIAA/MPAA has more clout than Majestic-12 these days...

[PeeTee]

Here is the way it works best for everyone involved. I just send you a short version of the Tensors portion of the CD video, and after seeing it you love it so much, you end up buying the whole series from the foundation for a more than reasonable price mostly because you really like it so much you decide you want the rest.
I bought the whole series twice, once in the early 80s (in VHS), then a few years ago I bought the CD version
Peetee le Trickfox