Stroop Theory (lives in category land)

[marcus]

more about
http://math.ucr.edu/home/baez/quantum_spacetime/

Hilb is the core category of Quantum Mechanics
nCob is the core category of Gen Rel

JB is saying that these two categories are LIKE each other in a distinctive way that SUGGESTS they might each be different facets of the same thing

quantum mechanics might be seen to arise from the structure of spacetime, if we only understood the latter better----yeah sure, I know quite a few people have speculated about that but what he is describing is a PARTICULAR TAKE on the idea that QM can be better understood if we see it as part of the spacetime machine.

there are links to Baez HDA:QS webpage in this thread and he gives the definitions of Hilb and nCob, but we can remark in passing that Hilb is the category of hilbertspaces with linear maps from one space to the other as the morphisms.

And nCob is where orientable (n-1)-dimensional manifolds are the objects and the morphisms are n-dimensional manifolds JOINING them.

Usual Gen Rel is about 4Cob, which is where the objects are (orientable) 3D spaces and the morphisms are 4D spacetimes connecting them. So a 4D spacetime is something that morphs you smoothly from one version of 3D space to another.

======================

I look at HDA:QS as having a goal of PERSUADING the listener to be interested in twocategories (and higher groups, higher gauge theory, essetially in doing geometry with higher algebra)
and the message of slides #1-14 is one of comfortableness and RESOLUTION OF PUZZLES

This gets the listener ready to venture into the higher algebra realm of twocategories, because he sees that just a LITTLE ordinary category theory can help a lot to resolve puzzles.

So we need to study slides #1-14 carefully.

They say that Hilb is very analogous to nCob, and if you look at some things that puzzled you about QM they will turn out to have ANALOGS in spacetime, i.e. in nCob, that are TOTALLY OBVIOUS. So what may seem peculiar and paradoxical in Quantum Mechanics becomes VERY INTUITIVE if you go over to the analogous thing in Spacetime.

things like the "clone-taboo" and "teleportation" turn into obvious stuff with wet spaghetti when you look at them in nCob.

This, IMO, makes slides 1-14 worth the price of admission EVEN IF YOU DON'T BUY TWOCATEGORIES.

But remember that the speaker is also hoping that we will get interested in twocategories as well, so I should devote a post to slides #15-23 also.

===================
these sets of slides could also be helpful
http://math.ucr.edu/home/baez/barrett/

they are for three talks given at Knoxville 29 April-1 May at a workshop on Geometric Topology
(the Barrett Lectures)

sometimes they give more pictures, and spell things out in more detail, than was possible in the
single Perimeter talk given 31 May-----what I am abbreviating "HDA:QS" for Higher-Dimensional Algebra: a Langauge for Quantum Spacetime.

 

[Dcase]

Hi Marcus:

I must first ask for some clarifications then I will honor your request and not post further on your thread.
I am trying to be constructive and diplomatic but I will understand if you find some of these comments not to your satisfaction.

Did you actually read the first sentence of this Baez paper abstract?
"General relativity may seem very different from quantum theory, but work on quantum gravity has revealed a deep analogy between the two."

I am agreeing with Baez although my perspective and language is different and imprecise.
I read 'Higher-Dimensional Algebra: A Langauge for Quantum Spacetime'. The last unlabeled figure of two intersecting tubes [worldsheets] has beside it a series of intersecting and non-intersecting loops - but a diagram is missing for the geodesic helical string interaction of the two tubes. Since this may be a geodesic in either Riemannian or Gauassian curvature, such a diagram would likely yield a "noncartesian tensor [perhaps only vector] product, given by the disjoint union of manifolds".
http://math.ucr.edu/home/baez/quantum_spacetime/

For the author to use an analogy for QM and GR and for me not to be able to use analogy for comments on this thread seems - at best hypocritical and disingenuous - at worst dogma and not even wrong.

Hurkyl mentioned in an earlier post [06-03-2006 08:00 PM] difficulty with 1D point particles but would be happy if they were strings. I am attempting to offer a way that they may be helical strings.

My language for this topic is currently inexact. With time my language will improve. I had collegiate experience with German, French and Russian not to mention numerous programming languages - but for now my doctorate language is within another field. I do not mean to imply that I am another Helmholtz, physician and physicist [I hope I am at least half that good], but even though the mathematics is difficult it is not impossible and less difficult than the language of medicine.

I reviewed the 14 slides of ‘Higher Gauge Theory’. I can put this to use in medicine - things, processes and processes between processes - whish is basically the morphism of DNA instructions into amino acid proteins - and more over do so with some of the simpler elements of game theory - which is basically the interaction of these proteins into a relatively cooperative multi-organ system.
In the subsequent slides I visualize a complex rather than real space-time.
I do get a little confused between 2-morphisms and polymorphisms which are more common in my field. The crossed modules are somewhat difficult. I would probably have used virtual rather than 'vanishing fake' curvature. I am probably misunderstanding gerbes by visualizing trajectories. Difficulty certainly increase as the slide progress.
http://math.ucr.edu/home/baez/barrett/

C Keeton, Rutgers and A Petters, Duke hope to search for the braneworld universe contains an extra fourth dimension of space for a total of five dimensions - but an alternative is complex-3D, helical-string-D and time-D which may be consistent with one of the Mathieu subgroups discussed by Baez in week 234.
http://www.space.com/scienceastronomy/060626_mystery_monday.html

In reviewing the guidelines, I do not thank that I am overly speculative, since helicity is discussed by many prominent physicists and this is the part of my discussion that appeared to be most provocative to you.

If your problem is with my inexact terminology, how can I learn without interacting and receiving critical feedback.

I will continue to use the term "stroop" in other settings, since it is so descriptive, but will not credit you unless you specifically ask me to do so.

 

[marcus]

I must first ask for some clarifications then I will honor your request and not post further on your thread.

Good! you may get some useful response if you start a thread.
As I explained, I can not respond to your ideas in this thread (it would be O.T.)
Farewell, and good luck discussing your ideas in some appropriate context!

 

[Kea]

Dcase

It is great to have someone here who (a) knows something about DNA and (b) can see the relevance of category theoretic thinking...but Marcus is right: you need to start a separate thread. Many of the threads here are about similar topics. We are simply asking you to differentiate between helical ideas and basic Stroop theory as discussed in this thread.

Anybody can start a thread here.

Cheers
Kea

 

[Kea]

question for Dcase

P.S. Are you the American biostatistics professor?

 

[Dcase]

response to Kea

Hi Kea:

I do not think that I am the person to whom you refer.

Please feel free to comment on my thread.
I could really use assistance to improve rigor since my ideas may rely too much analogy.
This is probably because I know a little about biophysiology and kinesiology and less about particle physics and mechanics.
I do have military ballistics experience.

 

[Dcase]

Hi Marcus:

I’m posting as a courtesy in respond to Kea.

I have posted a separate thread as you suggested.

I think that the applied mathematicians in electrical engineering have proved that same gauge and period loops and helices are equivalent.
I have not been able to locate such a proof.

I suspect that Penrose spinors are related to Penrose twistors.

Please feel free to comment. I could really use assistance to improve rigor.

The more math I read, the more I realize that medical decision theory is closer to mathematical game theory, especially that of Harsanyi.

I am going to ask Lubos for assistance. I really appreciate that he provided evidence that I was not alone in left field, even though he did not agree with my ideas.