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I agree, Andrew. And it seems we agreed about this before. I did once write something along the lines you are asking for at HowTo. I am not sure that I can provide what you seem to be askig for beyond that.
I keep getting away with the feeling that you have a very particular idea about what a text on aim and objectives of the nLab should be, but are waiting for somebody (me?, Toby?) to write it so that you can compare if it matches your view.
Maybe it would be better if you simply write up what you think needs to be written up. Then we can discuss it here and likely produce a widely accepted quasi-official statement after a bit of discussion.
Sorry, I meant I wrote something like this at About.
I did once write something along the lines you are asking for at HowTo.
My apologies. I interpreted that as being simply to update the technical info.
I keep getting away with the feeling that you have a very particular idea about what a text on aim and objectives of the nLab should be
I have a very particular idea about what "aims and objectives" are in general. What the specific ones should be for the n-lab is not something that I feel too qualified to answer. But aims and objectives should be testable and verifiable. In a little (but not much) more detail:
Aim: The purpose(s) of the project.
Objective: A method to achieve that purpose.
Target: Something that can be objectively tested to see if it has been reached.
So, we might have:
Aim: To increase collaboration between mathematicians.
Objective: Provide a place on the internet where mathematicians can explore and discuss ideas (the n-lab).
Target: Five peer-reviewed collaborative publications from projects started on the n-lab.
The problem is that while I could have a stab at writing that for the n-lab, I don't really know enough about the core mathematical aims to do so. What I could try doing is a template setting out the broad aims with a blank (or something daft) where the mathematical content should go.
To make it a little more concrete for you, as I put in my 'declaration of interest', I'm keen for this to work as an experiment in using technology to make it easier to do mathematics. So on that basis, I have lots of ideas for little tweaks and hacks to make it run more smoothly. However, if I'm continually changing things around then that makes it harder for the users to get to know the system. Also, it's difficult for me to figure out which to concentrate on. That's what was really so annoying about the latest changes debacle: not that I'd spent loads of time on it (I hadn't really), but that I could have been doing so, and so I'd like to know before I begin which ideas are best to work on. (I should point out that I'm not asking for an ideal system, obviously some ideas aren't implementable but that only becomes clear once one has tried.) Knowing what the fundamental aim of the n-lab is would help me to design my own set of objectives and targets as the sysadmin/tech support.
Objective: Provide a place on the internet where mathematicians can explore and discuss ideas (the n-lab).
Objective: Provide a place on the internet where mathematicians can explore, discuss and record ideas, especially insofar as these subjects touch on higher algebraic structures.
We think of this place as the library, or alchemist’s laboratory, in the back room of the n-Category Café. You come here to work and go there to chat (where chat is short for work by discussion).
I wonder whether setting a specific target, i.e., the 5 papers, is advisable.
One can debate that, and it would be interesting to hear how people would define targets for the n-lab (and for those who don't like targets, these can be purely internal and just as a measure of what it is sensible to spend time on - if something isn't helping us achieve a target then our efforts would be put to better use on a different aspect), but my original list wasn't intended as a template, just as a simple illustration of the difference between 'aim', 'objective', 'target', and 'wishy-washy-mission statement'. It was to make the point that these things are not just buzz-words but do have real meaning and, when used correctly, are extremely useful.
Finally, I would tend to be strict as to exclusion. If no case can be made for connections to higher algebra, then I don't see the point of inclusion.
At the risk of being seen as too facetious, or at being taken seriously, my response would be: Okay then, I'll stop adding content!
To be honest, I don't see any connection between what I do and "higher algebra". A couple of things that I've done have pages at the n-lab: Froelicher space and it's attendant pages, and Tall-Wraith monoid has also recently turned up. Presumably there's some link there, but if there is then I don't see it. Not being steeped in "higher algebra" means that I don't know even know how to figure out what is and what isn't. So if my additions run the risk of being deleted just because they don't link to "higher algebra" then I'd consider not adding them and saving the time and effort.
To make it more concrete, I mentioned to Urs a little while ago that I'd like to put my notes on "differential topology of loop spaces" on the n-lab. There's a fair amount of content there, but it would take a little time and effort to translate the LaTeX into iTeX. Urs seemed to like the idea, but I have no idea whether or not that's connected to "higher algebra". Seems about as far from it as it can get, certainly there's no algebra involved. So if that's at risk of being deleted, I'll save the effort and get on with other things.
Don't get me wrong, I do agree with boundaries. But I'd prefer to see the content boundaries as being fairly broad. If you think of the research laboratory model, it's the person and not the specific subject that determines whether they put something in the lab book. So someone coming in through the door accepts that this is a place dedicated to researching "higher algebra" (whatever that is), but then if they decide to make a few notes while they're there on spectral sequences then that's fine: the pay-off is worth it.
If you think of it from the other side, you'll see why this is better. I don't feel a member of the "core group" in the n-scene. But clearly I have something to contribute to the n-group's work (or at least, Urs and John seem to think so). So how are you going to persuade me to contribute? If I have to be continually deciding "Do I put this at the n-lab? Do I put this at the Top-lab?" then that's highly irritating and I'll just decide to stick with one and forget the other.
The other reason for being inclusive is that you never know what's going to be useful. Again, taking the lab book model, you browse through a recent journal (does anyone still do that?) and note that, say, the Dirac operator on the loop space can be defined using co-Riemannian structures. Looks intriguing, you say, so you make a brief note of it and then forget it. A year later, you start thinking about Riemannian structures and looking at categorifying them. Then, as categorists tend to do, you wonder what happens if you reverse all the arrows. Then you wonder if someone did that for ordinary Riemannian structures, and lo! and behold! you look up co-Riemannian structure and come across your old notes. Only now, being on the n-lab, someone else has been along and filled in all the details for you.
But I agree that there have to be boundaries. That's what the sign over the door is for. Figuring out what that sign should say is part of the purpose of this discussion.
I suspect that if we can make navigation a lot easier, and get the design sorted out, then some of your concerns will be met. If all the "junk" is in the corner, and it's clearly marked as "junk" then everyone can happily ignore it until someone suddenly finds a use for those two lumps of "uselessium".
Above, Urs challenged me to come up with a template for this sign. I'll do that. But as it's a template, it'll need a few blanks filling in. So here's the challenge for you, David. Fill in those blanks. Give me a mathematical (physical, philosophical) aim for the n-lab.
I certainly wasn't intending to suggest that entries such as Froehlicher spaces or Tall-Wraith monoids be excluded.
I didn't think that you were. My point was that, in the laboratory analogy, I'm a bit like an invited researcher. I'm here to help out with some of your questions on smootheology, and you're prepared to give me a bit of lab space to work on my own stuff while I'm here.
What I'm trying to get at, but stumbling a bit I'll admit as the ideas are being formed (quantum-like) as they are observed, is that my view of the n-lab is more about people than about subjects. I see this running through a lot of what has been said, including you. But it's not wholly either. Even if it was Urs who started it, a page on the Oxford Comma would be a bit out of place. Essentially, one wants a way of saying that the "closer in" you are, the broader the range of subjects you are allowed to introduce.
That sounds awfully hierarchical, which is going to raise huge shouts from certain quarters!
There are, of course, ways of making it less hierarchical which basically go along the lines of: the more you help out with the core purpose of the n-lab, the more tolerant we'll be of your side projects. I recently came across 'stackoverflow' which has an automatic reputation system which works a bit like this (readers of the algtop list may detect a theme here!).
If you think the wording is likely to deter people from contributing material with that proximity to higher algebra, then it should be changed. I think it would be very difficult to come up with any wording which captures things precisely so that it is at once obvious what falls inside and what outside.
I want something that is clear. I fully agree with your comment, but I think that there's still room for improvement.
Perhaps easier then to adopt case law practice and reason in terms of precedent, hence my interest in the differential logic case.
How British! But, as another Brit, how could I disagree?
If nobody else is prepared to come out and say they want it excluded, then there's little point in our having this discussion.
But this specific discussion was about much more than that particular subject. Before one can have cases, one needs some general principles that need to be worked out. Not everything is case law, rather case law is the practical interpretation of the general law as laid down by parliament (gosh, Google's "suggest a term" feature in the firefox search box is fantastic for finding the right spelling).
So maybe we need to find "twelve good men and true" (though I hope we'd be a little less sexist, and of course there's nothing perfect about 12) and you can prosecute and Jon can defend. Perhaps the defence has started making its case over in the other discussion.
I don't feel remotely qualified to comment on that particular case, though, so I'm more interested in the generalities. I realise that this is a little frustrating for you, and I apologise for that! Perhaps it should be said that if we can't find "twelve good men and true" for a particular topic then the prosecution case is automatically carried (the implication being that not enough of the group have a clue what it's about so it ought not to be there).
However, I'm feeling the presence of thin ice here. I'd like to make it abundantly clear that if the choice is "cacti and Toby" or "neither" then I'll join the cactus train. Even if I haven't the foggiest idea where it's headed.
I don't know if you (any of you) noticed, but the idea that everything is best seen from the perspective "higher algebra/higher geometry" is more alive than ever. This is exciting times. See things like scheme as locally affine structured (infinity,1)-topos.
Part of the nLab goal I see more in unravelling the secret higher structure behind apparently "ordinary" concepts.
But apart from that, it would seem that anything category-theoretic is very at home in the Lab, even if no higher connection is (yet) available.
So I would think material which is much less evidently of higher nature than what Andrew is working on would already qualify for the nLab. Andrew's work on loop spaces is even manifestly a higher thing. Dirac operators on loop space etc. pp. are supposed to be aspects of "2-Dirac operators". That's what all this geometric model for elliptic cohomology-business is about, anyway.
Certainly, I would be more than happy to see Andrew's differential topology of loop spaces on the nLab.
I'm not sure what to write for the whole Lab, so I'll write a very personal version for myself. (If everybody does this, then we just take a colimit, right?)
Aim: To amuse myself. (That sounds flippant, but it's why I'm here. Fortunately I'm not the sort of person who's amused by trolling, and you wouldn't be asking my opinion if I were.)
Objective: To write about mathematical ideas that interest me, which I've already summarised for the Lab (hereby included by reference), to read what the other contibutors write (at least in summary, and closely if it also interests me), and to work out ideas collaboratively through editing and discussion. Secondarily, to work on the organisation of the Lab so that it will be useful for me and others.
Target: I continue to want to contribute, indefinitely.
Re: Andrew Stacey
First, a declaration of interest. I'm keen for the n-lab project to succeed because I see it as a great example of using technology to make it easier to do mathematical research. … But I do think that mathematics is missing out on modern technology and I'd like to see it put to better use.
This is something that I've been thinking and working on for the last 30 years or so. Getting a handle on the work takes expanding the clearing from mathematical knowledge representation to knowledge representation in general and then looking at the cognitive and cultural activities that provide us with provisional knowledge — processes that fall under the collective heading of inquiry.
I haven't really digested all of this yet, but my gut reaction is very much against an output-measure such as 5 papers. I could count the nlab a success even if no traditionally peer-reviewed papers are ever published based on projects worked on there.
I haven't really digested all of this yet, but my gut reaction is very much against an output-measure such as 5 papers.
I'm strongly tempted to go back and edit that post (I shan't, of course). I didn't mean these statements to be taken seriously. They were examples of the sort of thing one might come up with. The point, such as it was, was that targets should be measurable: one should be able to say objectively and definitely whether or not a target has been reached.