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I was looking at causal set and noticed that there was no link to domain theory and in particular to Prakash Panangaden2 and Keye Martin's work linking bicontinuous posets and interval domains with hyperbolic spacetimes. (Commun. Math. Phys. (2006) ) nor to Sorkin's work. That seems to link up with several of the topics of interest to the n-POV, but as I am in no way an expert I would prefer not to start a page on that paper. My query is : would an entry on that approach be worth doing? and how much domain theory should be discussed in the process?
Tim, I can't quite imagine a reason not to put any material that you think is interesting on the nLab.
I am not sure if you are really worried about whether we would agree with you adding some material, or if your request is a polite way of asking somebody else to do it. In the former case, you can rest assured that not only don't we mind if you add stuff, but we very much value your contributions and would appreciate whatever addition you may have.
I would love to see even vague connections between that stuff and the nPOV...
@Urs My reasoning was that domain theory lives on the border of Theoretical Computer Science, and 'our' POVs and I am not sure that I am able to do more than write a very minimal stub on the subject ('cos I do not understand it very well!!!!). I was hoping that one of the other contributors to our esteemed Lab who know more than me on this, would start the entry :-) That would help me to understand papers like that by Keye and Prakash which I find hard going in places. (I have tried to learn the basics of domain theory but do not seem to retain them in enough detail to write much. If it so happens that there is no one else who knows the that stuff,..... :-(
I also have a feeling that I might 'jump on my horse and ride off in all directions' if I started it, as there is a lot of fascinating stuff in Theoretical Computer Science that just might be of use, or interest, to the collective 'us'.
@Eric That was what I felt! :-) It was just my hope that perhaps someone had some notes or something that could be quickly edited to give some entries that would bridge the gaps between the causal set stuff and the TCS stuff which in not yet evident on the lab. As you know I wrote that Dagstuhl paper on the links between this and directed homotopy ideas, but am not sure that I represented the ideas `correctly' in that.
I also have a feeling that I might 'jump on my horse and ride off in all directions' if I started it,
Please do!!
:-)
Seriously, Tim. You are a highly esteemed contributor. Go ahead, don't feel restricted, show us what you are thinking about. We love to see it. There is no risk that the nLab will run out of free pages before you are finished.
Note: Doh! I lost my original comment...
Tim, I would LOVE to see you write ANYTHING about this stuff. You know a lot more about it than we do.
Plus, if you write something completely wrong enough, you might embarrass the real experts to come in and clean things up :)
By the way, I think we could use an nLab ambassador to extend invitations to experts, e.g. "Over at the nLab, we are beginning to write some material on blah. Since you are an expert on blah we'd love to hear your thoughts on the subject. Even better, we'd be excited if you joined the effort."
I have stubbed with some references!! The link is domain theory, of course.
Tim, in a day which for me has been filled with irritation, your stub brought me a big chuckle! Thank you!
I added a reference to domain theory.
I like this author. He’s got a ton of very interesting looking papers.
This might be relevant to Urs’ and Domenico’s discussion:
Our more abstract stance also teaches us something new: a globally hyperbolic spacetime itself can be reconstructed in a purely order theoretic manner, beginning from only a countable dense set of events and the causality relation. The ultimate reason for this is that the category of globally hyperbolic posets, which contains the globally hyperbolic spacetimes, is equivalent to a very special category of posets called interval domains. This provides a profound connection between domain theory, first introduced for the purposes of assigning semantics to programming languages, and general relativity, a theory meant to explain gravity. Even from a purely mathematical perspective this equivalence is surprising, since globally hyperbolic spacetimes are usually not order theoretically complete, but interval domains always are.
@Eric Yes Prakash is a very clear writer. He is also a great guy!
Please invite him here :)
Skimming his papers, I REALLY like the way he writes. Poetic even :)
Thanks, Eric,
that’s very useful. I hadn’t been aware of this.
I need to have a look at these articles when I find a free second (not before the weekend…)
I skimmed it a bit after all.
Very nice, so in particular that question that was briefly mentioned in discussion with Tim van Beek is answered in A domain of spacetime intervals in general relativity: global hyperbolicity does have a nice category-theoretic formulation and meaning.
Will try to get back to this later, but that’s very nice.
I thought you would like it, which was doubly disappointing when that bad character got in there :)
Does anyone feel like adding an entry on globally hyperbolic spacetimes with a brief survey of the nPOV statements in A domain of spacetime intervals in general relativity, while I am (overly) busy with something else?
I went ahead and took the plunge, writing a few paragraphs on domain theory which others should feel free to add to or improve upon (please!).
Does anyone know of a quick Rosetta stone to the notation used in A domain of spacetime intervals in general relativity?
For example, what is $\sqsubseteq$?
Edit: Just printed out the paper to read on the train home and asked this quickly. Is $\sqsubseteq$ just $\le$? It seems to be.
It denotes the partial order of a given poset. Traditional notation in domain theory.
Thanks Todd. I printed the paper on the way out the door and saw some weird symbols and panicked. I didn’t want to get on the train and be stuck due to the notation. It turned out to be tame and very readable.
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