Thanks.

Singularities in fluid dynamics and other areas of physics are certainly not uncommon. I think Stefan was asking whether there was a deeper connection.

Cheers,

-cvj

I’m sure you’re in the good company of very many others!

-cvj

Can you tell me, if the Dynkin diagrams and the points on a Sylvestor surface/ Cayley model have some value when looking at this subject?

Also, if it would be wrong to see “UV coordinates of a Gaussian arc” can be seen in this light as well?

The first and last professor of mine who did this regularly was David Benney, who taught multivariable calculus my freshman year. It was remarkable, perhaps more so in retrospect: just ideas flowing from one head to many others through slate and chalk intermediates!

More recently, I’ve heard Greg Chaitin give a clear and entertaining presentation without slides, notes or a blackboard: he’s the one-man show of computational complexity.

best,

-cvj

I can’t think of anything off the top of my head. I seem to remember that Kentaro Hori wrote a book a few years back called Mirror Symmetry. I do not know what level he pitched it at.

d-brane:

So sorry. Yes, there are some typos, but people have found it very useful, nonetheless, I hear. I maintained an erratum page for a while (google for it) but it is a bit out of date since I incorporated some of it into a later printing.

Best,

-cvj

Well, that’s my conclusion, based on a host of calculable phenomena. You get to pick: You’re free to conclude other things. Alternatives include saying that there are X numbers of geometries describing a given situation, and that they are dual to each other and so forth, and the one you use to describe the physics depends upon your point of view, the probe you’re using, and so forth. That’s possibly a fine way to proceed.

I think it is simpler to declare that the focus on the geometry is the problem (especially when there are also intermediate situations where there’s no reliable geometry at all, but the string theory continues to make physical sense).

-cvj

It will surely be hard to visualize this deeper understanding but it’s not so easy to visualize quantum tunneling either. It does get more natural with experience in solving actual problems and therein lies the hope. You write very well and I look forward to your future posts.

Thanks

How can you conclude “There’s something deeper than geometry at the core, which probably isn’t geometry at all.”? It seems to me that at least T-duality is a consequence of using a 1-dimensional object(string) rather than a point to describe the geometry.

thanks a lot for this post - that’s very interesting! About your nice series of illustrations: the similarity to a drop of water falling from a tap is probably not a coincidence? I’m not sure about this, but I think I remember that the mathematical description of the separation of drops also involves singularities developing in the standard mathematical formalism for the handling of the surface of the drop? I that true, and is there are connection to singularities in GR beyond vague analogy? Was this discussed in the talk?

Best regards, Stefan

Since it’s built from Clifford algebra, it is considerably easier to do stuff with elementary particles. I would think string theorists would be all over it, but it seems like the stuff got ignored.

Hestenes wrote about the methods extensively and his papers may be easier to understand, see his website.

Now the point of all this is that you have a choice. You can define gravity using tensors and symmetry principles. The result is what the mainstream lives with; articles on arXiv that read like bad science fiction. Or you can use the mathematics of particle theory to model general relativity. You will get exactly the same results so long as you stay outside of black holes, but no bad science fiction papers. AND NO SINGULARITIES IN SPACETIME, except the usual singularities at mass points that you already learned to deal with in flat space E&M. And you get to use mathematics that fits the elementary particles.

I mean really, the best people in geometric algebra worked this stuff out. They’ve been steadily grinding out peer reviewed papers using the techniques. And it’s why I wrote the simulation in Painleve coordinates, these are the coordinates that fit a black hole to a Minkowski background.