Good night from Spain!

I have “bad news” (at least, from my experience). Free wordpress doesn’t like “copying”…If you use the FREE version of wordpress (without registered domain and server/web hosting), there are no solutions to that problem to my knowledge. Indeed, the MAIN reason to go further with my blog (including the “hard part” of having a domain, to register it, to search for a good web-hosting server, etc) was that problem since I wanted to write mathematics and LaTeX equations (of course, there were many others, but having to edit LaTeX code from the beginning is “a waste of time”, like you are now discovering! Now, I am very happy, despite I have reduced my blog-time (job and life are difficult) because with some plugins, and since I own in the “paid” version, I can use pure LaTeX code, use packages as if I were writing an article, and some other cool stuff (but I have limited time to these things)…I can also copy-paste what LaTeX I want to… Or even better, create my own shortcodes…

I don’t know if you or your institutions can provide you aid for web-hosting services or help you to obtain a more advanced version of wordpress. I did it all alone…And, if you want to produce and leave here more of your great works, I highly recommend you this (upgrade your free wordpress account to a public domain PLUS find a web-hosting PLUS add good plugins). I could recommend you plugins if you decide to do “that quantum leap”. If not, maybe you could consider to ask some other bloggers how do they do with their equations. I presume than some bloggers including math on their blogs either make a capture/screenshot, or use something like mathJax (like Lubos Motl), or directly avoid using math (the most used option, something that I did not like too much; and I decided to include mathematics because there are FEW bloggers doing that, so my blog is special because people use math and not include LaTeX or avoid it…).

If you want any other clarification, let me know. I will be pleased to answer if I know how…

Best regards,

JF.

]]>What is the large and small scale structure of space-time – it’s very geometry?

Neither, large or small scale structure, have been adequately answered by the various models.

For over a thousand years debate on Euclid’s 5th postulate, the parallel postulate, that holds in Euclidian Geometry was the world that most thought they lived in.

We don’t live in ‘flatland’ – and few see beyond.

The few that did, including Lobachevsky, Poincaré, Riemann imagined affine, projective, hyperbolic and spherical geometry, where Euclid’s 5th postulate does not hold.

In a watershed, Eugenio Beltrami in 1868 proved the 5th postulate is independent from others.

Gregorio ‘Ricci’-Curbastro and his protégé, Tullio Levi-Civita, invented and fostered Tensor Analysis, that has enabled the depiction of large scale structure of space-time.

General relativity (GR), our present model for the large scale structure, is dependent on ‘parallel transport’, metric, and the covariant derivative – as defined in Tensor (Ricci) Analysis and Riemannian Geometry.

Tensor (Ricci) Analysis while eminently useful for GR, as the equivalent of the ‘hammer’, it fails as a complete tool to define many of the contemporary models of small scale structure.

So many tools have been taken out of the ‘algebraic toolshed’, that Physics is ‘troubled’.

Quantum Physics had rediscovered heavy artillery in the algebra of Élie Cartan, Hilbert and Marius Sophus Lie.

Geometric Algebra (GA) intiated by Hermann Grassmann and William Kingdon Clifford was left on the byways, as Tensor (Ricci) Analysis replaced GA around the turn of the century.

For those in Physics today, GA resurgence is due to David Hestenes, who has demonstrated William Kingdon Clifford’s original geometric interpretation.

Fig. 1

David Hestenes – ‘Oersted Medal Lecture 2002: Reforming the Mathematical Language of Physics’: http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf

Let’s get back to geometry – perhaps Geometric Algebra, as a tool, and Intuitionism, as a Philosophy.

]]>Cheers and all the best! ]]>