Marcus, I just found http://yolanda3.dynalias.org/wb/whoiswb.html [Broken]; check him out.
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Marcus,marcus said:Instead of saying 4D simplex I will say "chunk"
A chunk has 5 points and 5 tetrahedron for its sides.
the easiest way to picture a chunk is to put down a tetrahedron as a base
(like the base of a pyramid, sort of) and then put a new apex point "up in the air" and imagine drawing lines from each point of the tetrahedron base up to the the new point.
here is something you can visualize because it is in ordinary 3D:
take a tetrahedron and put a point in the middle of it and connect the 4 orig points to the centerpoint. Presto you have divided the orig tet
into FOUR tets.
each of the four orig. faces becomes like the base of one of the four new tets and the centerpoint becomes like the common apex
Now to business:
now we are in 4D and we have a spatial tetrahedron in the present and two apexes one up in the future and one down in the past. So we have a CLUSTER OF TWO CHUNKS meeting at a shared tet.
put a centerpoint into that shared tet, dividing it into FOUR tets, and connect each of them to the two (future and past) vertices.
pretty clearly we now have a CLUSTER OF EIGHT CHUNKS.
so that is what is called the move (2,8)
and there is an obvious reverse move (8,2)
there is a 3D thing that is easy to visulize where you start with TWO tets butting together at a shared triangle, like two pyramids base-to-base with one's apex out East and the other's apex out West. And you erase that triangle and draw a line between the east and west apex points and suddenly you see that you have THREE tetrahedrons.
well now in 4D suppose you have two tets in the present, butted together like that, and each connected to an apex up in the future and to an apex down in the past-----so you have a cluster of FOUR chunks
if you do that 3D redivision of the spatial pair of tetrahedrons so you now have 3 tetrahedrons in the present----and then connect each of them up and down to the future and past apexes as before, then you have a
cluster of SIX chunks. that is the (4,6) move and the reverse move is obvious.
The (3,3) and the (2,4) moves involve cluster of fewer chunks. I guess I will take a break here and describe them later.
These are spelled out and depicted around page 23 of hep-th/0105267
no I am counting on the new point being actually inside the tetrahedronnightcleaner said:Are you accounting here for the condition that the new point has to be non-co-spatial with the original 4 of the tetrahedron?
Here is a brief response to this question. I would be glad if anyone wants to explain it in more detail.nightcleaner said:Marcus, in regard to LQG and DT, you said:
"they are kindred approaches, even though they do not agree about the
discrete spectrum of area and volume (which I think makes it likely that only one can be successful in the long run)"
Marcus could you take a moment to expand on this? I would like to understand more about what is meant by discrete spectrum of area and volume. ..., in what respects do not agree?
I read an article about that too. I think you mean WMAP.godzilla7 said:... read an article about the IMAP data being flawed because of polorizations in our solar system, if this is true does it have implications ...
marcus said:this is page 3 of http://arxiv.org/hep-th/0411152 [Broken]
Semiclassical Universe from First Principles
by Ambjorn, Jurkiewicz and Loll
it begins a section called "Observing the bounce"
Richardnightcleaner said:Would it be possible for you to translate into words the terms in equation one from your reference, the partition function for Quantum gravity? I mean a literal translation of the formula into English. If it would not be too much trouble for you to do so, I am sure it would help me understand, and perhaps help others also.
When you speak of dynamics in the spacetime structure, as if spacetime itself changes over time in a manner of a history, or of a path integral, how many dimensions are you counting?
What are the numbers?nightcleaner said:nc
No it was an undergrad topology class.Kea said:Are you sure it wasn't a
course in Differential Geometry?
You're lucky. I never had a proper topology course as anShoshana said:No it was an undergrad topology class.
Correct. It is difficult to find a topology course at many Universities, but Columbia University offers undergrad topology. My first topology professor at Columbia University was Michael Thaddeus. Amazing speaker!Kea said:You're lucky. I never had a proper topology course as an
So - do you know Nightcleaner?