Being Tentative on nLab

July 17, 2009

Posted by David Corfield

$MathML-enabled post (click for more details).$

I’m not completely convinced of $n$ Lab acting as both reference wiki and as a place to work out ideas. Perhaps it can work by the method we’re using at the moment of flagging up tentative pages, but we have to be careful. The homotopy (as an operation) page is certainly tentative. It goes on to wonder whether we can dualize everything in sight at the cohomology page. Doing this threw up an interesting effect when it turned out that there was an already existing Cech homotopy as a candidate dual for Cech cohomology. As Tim Porter describes on the Cech homotopy page, there is work of long standing falling under that title, linked to (strong) shape theory. But is there a problem with its being linked to from a tentative page? Will anyone check the extent to which Cech homotopy is dual to Cech cohomology?

Elsewhere at sphere, we have Toby questioning the need for generalised homotopy theory. But we only know it’s Toby because he mentioned this at ‘Latest Changes’. It seems likely to me that an airing here would get wider attention, where views can be easily attributed to specific people.

Maybe the point is that discussing ideas we need to know identities. On ‘Latest Changes’ we read Urs saying that about twisted K-theory that he is

…feeling slightly uneasy about making this public, though, maybe later I get scared and remove that content again, or move it to my private web.

Expressing personal views on an anonymous wiki can be awkward. On the other hand, are people visiting each other’s private webs?

$MathML-enabled post (click for more details).$

So let’s discuss Toby’s point in the old-fashioned Café style. Toby says that

… spheres, or rather their underlying topological spaces or simplicial sets, are fundamental in (ungeneralised) homotopy theory. In a sense, Whitehead’s theorem says that these are all that you need; no further generalised homotopy theory (in a sense dual to Eilenberg–Steenrod cohomology theory) is needed.

Whitehead’s theorem says that if a map between connected CW complexes induces isomorphisms of all homotopy groups, then the map is a homotopy equivalence. The Wikipedia entry mentions that this does not hold for topological spaces in general and that shape theory studies possible generalizations of Whitehead’s theorem. So is that why Tim’s Cech homotopy is necessary?

Could we say that there are some quasicategories where the homotopy side of the coin, the study of maps into a space, somehow involves a much simpler set of objects, than the cohomology side, the study of maps out of a space? Presumably then there must be cases where the latter is the simpler one and the former the complicated one, such as the opposite of the category of CW complexes.

Is it that $Top$ as a slight broadening of $CW-complexes$ requires a little more work on the homotopy side, but that still there’s much less need to involve a complicated array of objects as probes, than there is for coprobes for cohomology?

Posted at July 17, 2009 1:12 PM UTC

TrackBack URL for this Entry: https://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/2017

49 Comments & 0 Trackbacks

Re: Being Tentative on nLab

David raises some good questions here. Perhaps those who are using the nLab as a means of trying out ideas to get reactions from others would find it useful to have another type of page, but one that was separately listed.. i.e. tentatively we might suggest a `tentative’ or `work in progress’ heading listed as well as latest changes. I know that I have put some stuff (draft project descriptions etc.) on my personal pages but have no way of knowing if my attempts to get reactions have been ignored or what. If that stuff was more centrally listed it might get more reaction. I don’t know.

On a mathematical point I would raise the possible meanings of duality between Cech homotopy and Cech cohomology. What is to be hoped for?

Posted by: Tim Porter on July 17, 2009 2:45 PM | Permalink | Reply to this

Re: Being Tentative on nLab

Maybe I’ve become too gripped by the idea of lack of self-duality. But doesn’t it interest you?

Posted by: David Corfield on July 17, 2009 3:24 PM | Permalink | Reply to this

Re: Being Tentative on nLab

$MathML-enabled post (click for more details).$

I think what I am meaning is that the nature of several of the well known duality type results in homotopy/cohomology is not quite the Eckmann-Hilton style one, but perhaps could be linked with it. A typical one (and I am delving into an indistinct memory here) would have a space $X$ living inside some high dimensional $\mathbb{R}^n$ and there would be a duality between invariants of $X$ and invariants of $\mathbb{R}^n\setminus X$ .

From this one gets Poincare duality, Lefshetz duality etc. (cf Spanier).

There should be a sense in which these are versions of the sort of homotopy/cohomology duality that we are concentrating on. I do not know (or do not remember anyhow) of a treatment in those terms. Perhaps the nearest that I do know of is Chapman’s theorem in shape theory (and Edwards and Hastings extension for strong shape which is even nicer). For shape think Cech homotopy i.e. working with nerves of open covers etc. (Note Cech cohomology is dual to Steenrod-Sitnikiv HOMOLOGY not Cech homology.) Back to Chapman, this says more or less that if you look at a compact metric space $X$ and embed it in the Hilbert cube then the shape of $X$ is essentially the proper homotopy type of the complement of $X$ . Note the Hilbert cube is contractible, but it is the PROPER homotopy that has to be used.(The above statement is not correct but I do not want to go into the details here and now, unless someone asks! ) The shape category and the proper homotopy category are in fact equivalent and even have equivalent homotopy structures (to be taken with a pinch of salt… if you want details look at Edwards and Hasting’s lecture notes.)

Posted by: Tim Porter on July 17, 2009 6:56 PM | Permalink | Reply to this

Re: Being Tentative on nLab

Yes, there are distinct dualities. Lawvere and Rosebrugh distinguish between abstract (arrow reversal) and concrete (mapping into dualizing object) duality. I wonder whether that covers everything about duality.

In A History of Duality in Algebraic Topology, Becker and Gottlieb write

There are two major groupings of dualities in algebraic topology: Strong duality and Eckmann–Hilton duality. Strong duality was first employed by Poincaré (1893) in a note in which “Poincaré duality” was used without proof or formal statement. The various instances of strong duality (Poincaré, Lefschetz, Alexander, Spanier–Whitehead, Pontrjagin, cohomology-homology), seemingly quite different at first, are intimately related in a categorical way which was finally made clear only in 1980. Strong duality depends on finiteness and compactness. On the other hand, Eckmann–Hilton duality is a loose collection of useful dualities which arose from categorical points of view first put forward by Beno Eckmann and P.J. Hilton in Eckmann (1956).

I take it we can pair up Eckmann–Hilton with abstract duality, and Strong with concrete duality. At least it looks that way if you follow the discussion of Dold and Puppe’s work from page 4.

Posted by: David Corfield on July 18, 2009 11:08 AM | Permalink | Reply to this

Re: Being Tentative on nLab

The major point about E-H duality is that the dual of a theorem is sometimes but not always a theorem. Cf. the L-R `symmetry’ of the human body.

Posted by: jim stasheff on July 18, 2009 1:44 PM | Permalink | Reply to this

Re: Being Tentative on nLab

$MathML-enabled post (click for more details).$

That is very nicely put. I think that the situation in strong shape theory is somehow in between the two. (This will be vague.) The role of the Hilbert cube is (sort of) that of a dualising object. Perhaps it is something like cohomology is dual (in this instance) to a modified homotopy of embeddings in the dualising object. That is not quite right, but I think does go a little way in a good direction. The importance is that the properness in proper homotopy theory is what enables the geometric ends /neighbourhoods at infinity of the complement of $X$ to mirror the neighbourhoods of $X$ . How that can be abstracted further I do not at present see.

Another incidental duality here is Gelfand duality between $C^*$ -algebras and compact spaces.

Posted by: Tim Porter on July 18, 2009 5:34 PM | Permalink | Reply to this

Re: Being Tentative on nLab

The “tentative” part of this is close to something we discussed over on the n-Forum regarding original research.

Posted by: Andrew Stacey on July 17, 2009 2:51 PM | Permalink | Reply to this

Re: Being Tentative on nLab

There are several options with existing technology.

The best that comes to mind is to start using:

category: tentative

Assuming we get the server issues straightened out, you will be able to see a list of tentative pages at a link such as:

http://ncatlab.org/nlab/list/tentative

Currently, we have a similar

http://ncatlab.org/nlab/list/drafts

Tim, in your case, I might suggest creating a page on the main nLab with a name either the same or similar to the name on your personal page with a very short description that points to the corresponding pages on your personal “wiki web” page. Then you could add “category: tentative” to it and it will show up when anyone goes to the (not yet existing)

http://ncatlab.org/nlab/list/tentative

We are also talking about including different icons on the n-forum to indicate “tentative” pages or pages containing “original content”.

Posted by: Eric Forgy on July 17, 2009 4:15 PM | Permalink | Reply to this

Generalised homotopy

$MathML-enabled post (click for more details).$

Sometimes I write provocative things hoping that people will react to them; of course, I have to announce them at [[latest changes]] if I want people to see them. I'm glad that David is finally reacting to this one! (And I couldn't very well have put it in category: tentative just for that one line. I didn't really think of it as original research either. Probably I should have made a query box.)

I was hoping that there would be a more profound objection than that not every topological space is homotopy equivalent to a CW complex. There is a lot of stuff on the Lab (mostly by Urs) about an $(\infty,1)$ -category $Top$ which consists only of ‘nice’ topological spaces, or equivalently which considers spaces equivalent if they are weakly homotopy equivalent (where a weak homotopy equivalence is given precisely by the hypothesis of Whitehead's Theorem). This is so interesting in part because it is (or should be) equivalent to the $(\infty,1)$ -categories $Simp Set$ and $\infty Grpd$ .

Is generalised homotopy only good for studying non-nice spaces?

Posted by: Toby Bartels on July 18, 2009 1:56 AM | Permalink | Reply to this

Re: Generalised homotopy

$MathML-enabled post (click for more details).$

Toby two points.

(i) If you are defining generalised homotopy as being the study of things such as $[\Sigma^n A,X]$ , where $A$ is thought of as being the co-coefficients of the homotopy, then this is equivalent to studying the homotopy of the function space $X^A$ , even when it does not exist! In other words you can form $[\Sigma^n A,X]$ with fairly minimal structure around, you do not actually need function spaces in your category of `nice’ spaces for this to make sense. How you interpret this group afterwards is another question. It seems to me to be looking at ways of `moving’ your `model’ $A$ around inside your test space.

(ii) My other point is an old favorite of mine. `Non-nice’ spaces are needed in many parts of mathematics and need to be taken seriously by algebraic topologists as they encode structures that are `nice’ and important. The usual example given is in dynamical systems theory where study of attractors naturally leads to spaces that are certainly not CW-complexes. The prime examples are the various solenoids, the Lorenz attractor, and the Rössler attractor . There are almost philosophical questions as to whether they `exist’ as they are limits of systems of nice spaces and physically that is doubtful, but that does not mean they are not useful as models of systems.

Posted by: Tim Porter on July 18, 2009 6:56 AM | Permalink | Reply to this

Re: Generalised homotopy

The usual example [of ‘non-nice’ spaces] given is in dynamical systems theory where study of attractors naturally leads to spaces that are certainly not CW-complexes.

Well there was a discussion here about the cohomology of dynamical systems.

Hmm, any interest in a homotopy of dynamical systems?

Posted by: David Corfield on July 19, 2009 10:33 AM | Permalink | Reply to this

Re: Generalised homotopy

$MathML-enabled post (click for more details).$

Tim Porter said:

The usual example [of ‘non-nice’ spaces] given is in dynamical systems theory where study of attractors naturally leads to spaces that are certainly not CW-complexes.

David Corfield remarked:

Well there was a discussion here about the cohomology of dynamical systems.

But these two contexts cannot really be compared, can they?

Tim Porter points out that “attractors” of dynamical systems are a generic source of non CW-complex topological spaces.

In Terry Tao’s setup, on the other hand, as far as I could tell, the dynamical system was represented by its action groupoid and the cohomology in question was the groupoid cohomology of that action groupoid.

Now, the groupoid cohomology of an action groupoid $C//G$ will know something about the cohomology of the strict quotient $C/G$ , which may also be a bad-behaved space, but I don’t see how it can know anything about any attractor of the $G$ -action in general.

Well, maybe there is some relation in some cases, who knows, but just taken at face value, the relation between and role played by “cohomology” and “dynamical system” in both contexts is not really comparable, I’d say.

Posted by: Urs Schreiber on July 21, 2009 7:43 PM | Permalink | Reply to this

Re: Generalised homotopy

The cohomological link is there but I am not sure how strong it is. I remember reading about Conley Index Theory years ago and that looked as if it used neighbourhoods of the attractor to say things about the attractor, so perhaps the thing to look at is germs of dynamical systems. (I do not know if I can find the references that made the links explicitly. Help anyone?)

Posted by: Tim Porter on July 21, 2009 9:16 PM | Permalink | Reply to this

Re: Generalised homotopy

$MathML-enabled post (click for more details).$

Toby said

I was hoping that there would be a more profound objection than that not every topological space is homotopy equivalent to a CW complex

to his claim that a generalised homotopy theory was not necessary. Presumably, this will depend on the (quasi)category you’re working in. I just came across an interesting line from Steve Lack in this paper:

It is familiar in homotopy theory that up-to-homotopy morphisms from $A$ to $B$ can be identified, in an up-to-homotopy sense, with ordinary morphisms from a cofibrant replacement of $A$ to a fibrant replacement of $B$ .

Isn’t much going to hang then on how these replacements work? And perhaps properties such as Eric pointed out for Top:

A pullback of a cofibration by a fibration is a cofibration, but a pushforward of a fibration by a cofibration is not a fibration?

There must be interesting things to say about kinds of possible model structures on Top.

Posted by: David Corfield on July 20, 2009 12:35 PM | Permalink | Reply to this

up to homotopy replacements

David C wrote:
It is familiar in homotopy theory that up-to-homotopy morphisms from A to B can be identified, in an up-to-homotopy sense, with ordinary morphisms from a cofibrant replacement of A to a fibrant replacement of B.

Even more familiar in my corner of homtopy theory is that up-to-homotopy morphisms from A to B can be identified, in an up-to-homotopy sense, with ordinary morphisms from a resolution of A to one of B, resolution of the same kind, not one co of the other.

Posted by: jim stasheff on July 20, 2009 2:14 PM | Permalink | Reply to this

Re: Being Tentative on nLab

There is also another model structure ((oo,1)-categorial structure) on topological spaces called the Strom-structure.

In this structure the weak equivalences are the homotopy equivalences (not the weak ones) and the fibrations are the Hurewicz fibrations. So _not_ every space is equivalent to a CW-complex.

Posted by: Thomas Nikolaus on July 18, 2009 8:58 AM | Permalink | Reply to this

Re: Being Tentative on nLab

I agree that more refined separation at nlab could be sometimes useful. There are three distinct issues here:

1. the question of original contribution

2. the question of not messing up my private area of nlab

3. the question of controversial vs. classical entries

About 1 you already discuss. About 2: we have too few security modes. Either I can keep the pages unvisible or visible (published); others can either change content or not. I can not choose which pages I allow others to change and which I do not, which visible and which not. Or different password for me to be setting privileges than the one for collaborators access to change or view some of my pages…

About 3: this is most subtle. We do not want to be too conventional in general. We like the nlab to express modern points of view. However I think it would be useful to separate lengthy and deep nonstandard heuristics from more classical information pages. For example, Urs created page K-theory which contains interesting, nonstandard and lengthy discussion on heuristics on K-theory vs categorification and vs infty,1-categories, groupoidification and so on. On the other hand, it does not contain much of the standard data on K-theory. I would prefer to have K-theory standard and useful to outside people to nlab, while another entry like [[categorification point of view on K-theory]] or alike with a link within [[K-theory]] should also exist. It is also difficult to contribute to people with different point of view or different knowledge to a complicated viewpoint entry. I could for example contribute to classical [[K-theory]] entry but I do not know how to really contribute to the current one in a structured way.

Also I should add one terminological thing: most of entries start with a short heuristics point of view separated into a section called Idea. This part is usually concerned with extracting the essence into modern language, say “categorical heuristics” and often it does not correspond to motivation why it is introduced or used, or historically discovered. Motivation for model categories for example was not that they are presentations of infty,1-categories as it is modern point of view but rather to use homotopy ideas in nonclassical setups, like dgla-s; this is more basic to the outsider while less precise to the modernly educated category theories. In that case instead of ideas section I would suggest two: one for motivation and another for higher categorical point of view. And so on. Having in 90% of cases plain “idea” section is somehow conceptually confusing in my view.

Posted by: Zoran Skoda on July 18, 2009 4:43 PM | Permalink | Reply to this

Re: Being Tentative on nLab

Zoran writes:

It is also difficult to contribute to people with different point of view or different knowledge to a complicated viewpoint entry.

This is extremely important. There are (at least) 2 potential audiences: those already intensely familiar with all the jargon and importance and those who would like to learn.

cf the analogy taught to me by Dan Kan (yes, that Kan):

just because you have written a formula on the board does not mean you have communicated with your audience

jim

Posted by: jim stasheff on July 19, 2009 2:05 AM | Permalink | Reply to this

Re: Being Tentative on nLab

I could for example contribute to classical [[K-theory]] entry but I do not know how to really contribute to the current one in a structured way.

I say, go ahead and write something (introductory but with links) about classical $K$-theory and put it in there in a section ## Classical $K$-theory ##. Maybe it doesn't into the current article very well, but you make a good point that that is the fault of the current article, not the fault of what you want to write. So write it anyway, and figure out later (or let Urs or somebody else figure it out) how to integrate the material into a coherent whole.

Similarly, I think that you should feel free to write your own ## Idea ## section; you can say something like ‘Another way to look at it is […]’ or ‘The original motivation, however, was […]’ or even write a section like ## Another idea ## or ## Original idea ##, etc.

The point is that adding new material is good, even if it's not well connected to previous material; just as rewriting things or adding links to make them fit together better is also good. You already do this from article to article, but I think that you should also feel free to do it within an article.

Posted by: Toby Bartels on July 19, 2009 4:47 AM | Permalink | Reply to this

Re: Being Tentative on nLab

$MathML-enabled post (click for more details).$

Ideas on the nLab and formatting issues evolve in a kind of Darwinian manner. The fittest ideas survive. If you have ideas on how to improve things, by all means improve them. If the ideas are good, they will take hold and propagate.

Here is the one basic rule:

If you see something that can be improved, improve it.

If something seems incomplete, it is likely because Urs wrote it in a rush to help himself with his own research. I think Urs uses the nLab extremely effectively as a research tool and demonstrates that it is not an activity in addition to his day job, but an important aspect of his day job that significantly improves his productivity.

One of my goals is to help make the nLab more accessible to the scientifically inclined non-experts, e.g. PhD-level engineers for whom ideas on the nLab can find practical applications, e.g. scientific computation and numerical modeling. Mostly so that I can hopefully understand it some day. Currently, most of that effort involves simply making the nLab more readable.

For example, I found myself getting distracted by horrid notation, e.g. pages littered with things like [[models for infinity-stack (infinity,1)-toposes]] and [[strict omega-category]]. I was frustrated because the nLab didn’t have redirects so we were kind of stuck. I threw a monkey wrench into things by threatening to transport nLab to Mediawiki (the software behind Wikipedia).

The discussions that ensued helped inspire Jacques to implement redirects for us (discussions about redirects had been ongoing for long prior to that). Since then, I’ve been busy retrofitting pages with redirects and symbolic links. I hope that my effort (which has taken more time than you might imagine) is worth it and you agree that many pages are much more readable now.

The point is that everyone here has a unique perspective and could definitely contribute a lot to the nLab in small (as in my case) or big (as in most everyone else) ways. Every bit helps.

Posted by: Eric Forgy on July 19, 2009 7:38 AM | Permalink | Reply to this

Re: Being Tentative on nLab

$MathML-enabled post (click for more details).$

In that case instead of ideas section I would suggest two: one for motivation and another for higher categorical point of view. And so on.

Yes, we shozuld have sections with several different points of view.

Somebody needs to write them.

That write one section with one point of view does not mean that I don’t want the other point of view. It just means that I only found time and energy for one.

That entry on K-theory is badly in need of more material. Until I wrote that “Idea” section the entry was only a list of links, with no information whatsoever. I thought I’d give it a start and add some motivation. Much more is needed.

Posted by: Urs Schreiber on July 20, 2009 11:26 AM | Permalink | Reply to this

Re: Being Tentative on nLab

$MathML-enabled post (click for more details).$

Concerning the entry on K-theory:

For what it’s worth I now followed Zoran’s suggestion and moved that “Idea” section which I had typed into [[K-theory]] to [[topological K-theory]].

This means that now [[K-theory]] is an entry containing once again just a bare link list – longing for somebody to take care of it.

I am still somehow thinking, though, that the “topological” perspective with vector bundles should be the right useful general point of view if only one interprets “vector bundle” in a suitably generalized sense in the usual way (namely, let me see, as geometric $\infty$ -functions, I suppose).

Maybe David Ben-Zvi can help us write the right general “Idea” section at [[K-theory]] .

Posted by: Urs Schreiber on July 21, 2009 12:41 AM | Permalink | Reply to this

Re: Being Tentative on nLab

$MathML-enabled post (click for more details).$

I’m not sure I like the idea of ‘tentative pages’ on the $n$ -Café. I’d prefer pages to have ‘tentative sections’.

More generally, I think pages should have all sorts of sections: Definition, The Idea (For Normal People), The Idea (for Category Theorists), Theorems, Applications, References, Gentle Exposition, Discussion, Wild Thoughts, and so on.

We’re not trying to be Wikipedia, after all. We’re not even sure yet exactly what we’re trying to be! So, we should allow ourselves to treat ideas from many different viewpoints and levels of rigor. And we should probably let these mingle and interact. But it’s good to be clear about distinctions: whether something is rigorous, or heuristic, or speculative, etc.

So: don’t be scared of saying ‘tentative’ stuff on the $n$ Lab. But let people know that’s what you’re doing!

Posted by: John Baez on July 19, 2009 11:30 AM | Permalink | Reply to this

Re: Being Tentative on nLab

I agree fully with what John says. I have actually learned a great deal about math from John because he has a genius level ability to express himself in a clear, simple and often fundamental way (which shows me that John really knows what he is talking about, and when he does not know what he is talking about he is very honest in making this distinction!).

Thus, I believe that a guiding principle for the nLab should be this dictum from Albert Einstein: “Make things as simple as possible, but no simpler.”

IOW, don’t accidentally mislead anyone by oversimplifying (and note that Einstein was no slouch given that he actually made 8 different achievements each worthy of a Nobel prize).

Posted by: Charlie Stromeyer on July 19, 2009 12:31 PM | Permalink | Reply to this

Re: Being Tentative on nLab

$MathML-enabled post (click for more details).$

When you find yourself on a page that seems tentative or incomplete, rather than saying, “Hey, someone should make this page less tentative or more complete!” just make it less tentative and more complete. It is not fair to ask Urs to do more than what he is already doing. If Urs or anyone else writes a page with tentative material or that you think is incomplete, it is probably because they are suffering from the limitations of 24 hour days. Not a conscious choice to leave things incomplete. If you think you can make the page better, simply add a section heading #Tentative Idea# or #Another way to look at it# to what Urs (or whoever) wrote and fill in other sections to make it complete and less tentative.

A page is marked tentative because it IS tentative until someone comes around and makes it less so.

I wish people would do less talking about ways to make the nLab better, and put their effort instead into actually making it better. For example, I agree with Charlie’s statement about John’s “genius ability” to explain things. Every time John touches the nLab, he makes it orders of magnitudes better (same goes with Todd, Tim, etc). Right now, it seems there is a large number $N$ of people interested in the nLab sitting on the outside wanting it to be better and who have really great ideas, but only a much smaller number $n$ of people actually working on it.

I and a few other “Lab Elves” spend tons of time on the nLab because it is a labor of love. Because of that, we see first hand how much effort Urs has put into it. I have an unfortunate “big brother” complex that gets me in trouble sometimes (like maybe now) because I tend to be protective. I know it is not intended, but when I see comments like I’ve seen here, a part of me feels like it is a criticism of what Urs has done. He should be praised for his efforts. The fact that there are even so many pages in existence on so many topics should be lauded rather than criticized for being somehow incomplete.

Anyway, there will always be tentative things on the nLab regardless of whatever discussion goes on here, i.e. things will be tentative until they are not. That is a fact of life. The more people willing to help the process move from “tentative” to “not”, the sooner it will get there.

PS: You do not need to be an expert to help with the nLab. If their are interested and willing lurkers out there who would like to help contribute in some way, there is still tons of formatting work to be done and I could use help. Here are some guidelines (not rules!) I use when reformatting pages: [[Note on Formatting]]. You can feel free to change things anonymously, e.g. a good name might be “Lab Elf” :)

Posted by: Eric Forgy on July 19, 2009 4:29 PM | Permalink | Reply to this

Re: Being Tentative on nLab

$MathML-enabled post (click for more details).$

Eric wrote:

I wish people would do less talking about ways to make the nLab better, and put their effort instead into actually making it better.

I understand what you mean. You have to realize, though, that a key way people build the group identity needed to reach a collective goal is by chit-chat and gossip. It’s not as if an office would really be more efficient if every single minute ‘wasted’ chatting at the water-cooler were replaced by work. All sorts of useful information, mainly of a social/organizational nature, gets transmitted by such chat. And we need this sort of conversation even more than typical office-mates do, since we don’t actually ever see each other — and nobody is paying us.

Now, Andrew may think we should only chat over at the $n$ -Forum. But that watering hole is limited in its ability to attract new folks to the $n$ Lab, because it takes some work to post there, and people aren’t likely to bother unless they’re already interested in the $n$ Lab. The $n$ -Café is a better place for random rascals and ragamuffins to watch us chat, and maybe get curious and take a peek at the $n$ Lab, and maybe someday join in.

So, while technical conversations are probably best done at the $n$ -Forum, we should make sure to keep talking about the $n$ Lab here, too — and we shouldn’t be too harsh on seemingly unproductive chit-chat and whining!

Posted by: John Baez on July 20, 2009 3:35 PM | Permalink | Reply to this

Re: Being Tentative on nLab

John chatted:

Now, Andrew may think we should only chat over at the n-Forum.

I’d like to respond to this as I think I’m getting boxed into a corner on the n-forum/n-cafe divide. I think that John’s last sentence:

So, while technical conversations are probably best done at the n-Forum, we should make sure to keep talking about the nLab here, too — and we shouldn’t be too harsh on seemingly unproductive chit-chat and whining!

sums it up pretty well. His image of the cafe as the ‘water-cooler’ is one I like. But whilst no sane executive (are there any?) would get rid of the water-cooler, also no sane executive would only have water-coolers.

So whilst it’s great to have these discussions, and they keep the n-lab in people’s minds, there are serious discussions going on at the n-forum that could do with a little more input. Some of them may lead to changes in how the n-lab behaves that will affect how you use it so get over there and join in the discussions so that your opinions will be heard.

And the discussions are not all technical in the sense that you need to properly understand computers to join in. Some are along the lines of “how should we do this?” others are “what dangers are there in this?”.

As I’ve said again and again, one of the great advantages of the n-forum is that the RSS is much easier to sift through than the n-cafe. That’s just down to the nature of blogs versus forums. We need both.

Posted by: Andrew Stacey on July 20, 2009 6:01 PM | Permalink | Reply to this

$MathML-enabled post (click for more details).$

Eric wrote:

I wish people would do less talking about ways to make the nLab better, and put their effort instead into actually making it better.

John’s reply culminated in:

…we should make sure to keep talking about the $n$ Lab here

Yes. Maybe there is something both to what Eric and John say: Eric didn’t say that we should not chat here about the $n$ Lab. We certainly should and I am glad that we do, once in a while.

But I read Eric’s remark as saying that whenever anyone feels he or she knows a way to improve the $n$ Lab, it is worth asking oneself if one should try to make others implement this improvement or better to just go ahead with a good example and start implementing it.

I am receiving requests all the time:

Sombody tells me he wants to see more expository material on the Lab.

Somebody else points out that there should be more detailed theorems and proofs.

Another one sees the need for more historical background accompanying some revisionists articles.

Somebody else complains that an entry sticks too closely to the historical development and doesn’t give the modern perspective.

That tends to make me nervous. Am I supposed to collect these requests and work on them over the weekend?

What would make me feel more relaxed were messages of the form:

“I noticed that a gentle exposition was missing from entry xyz, so I added it.”

“I noticed that the important theorem abc wasn’t spelled out at xyz, so I added it.”

and so on.

Therefore that rule

If you see something that can be improved, improve it.

Maybe accompanied with

…and drop us a note about what you did and why you think more of that should be done.

Posted by: Urs Schreiber on July 20, 2009 5:51 PM | Permalink | Reply to this

Re:

We even have a blog post complaining about entries now, this one from a newly opened alternative cafe.

Posted by: David Corfield on July 20, 2009 6:02 PM | Permalink | Reply to this

Re:

Exactly.

Anyone sending such emails to Urs (and making comments here) should consider doing something about it, i.e. go to the nLab and hit the “edit” button and make the change.

Given the amount of content on the nLab, it is natural for people to see ways to improve it, but what I think many don’t realize is that probably 90% OR MORE of the content comes from Urs. Despite the incredible output he creates, he is still just one person!

When you say something like “someone should do something about ***”. If YOU don’t do something about it, Urs will probably do his best to do it himself. You can see how this could be overwhelming. Knowing him, he will likely never complain about it either.

I would never discourage discussions here, but when you make suggestions, please know that you are (unwittingly) putting work on Urs’ plate unless you implement the suggestion yourself.

Posted by: Eric Forgy on July 20, 2009 6:59 PM | Permalink | Reply to this

Re:

Eric, with all due respect to Urs, I think the 90 percent estimate is probably way off, and seriously underestimates the contributions others have made. Toby Bartels is one of a number who come to mind as people who have made enormous contributions on many levels.

But I agree with your larger point that we need more people to get in there and chip in themselves, if they see any way of improving content.

Posted by: Todd Trimble on July 20, 2009 7:29 PM | Permalink | Reply to this

Re:

I’ve expressed my amazement at the contributions Toby has made as well. It is literally inspiring to see the effort he puts into the nLab. That is why I was careful to specify “90%” of content. Although Toby does contribute lots of content as well, he’d be the first to tell you that most of his work on the nLab has been tweaking pages that others create.

I’m pretty confident that if you focus on “content creation”, Urs is easily in the 90%+ range. That is not meant to belittle the effort of others. Mike, Tim, and Zoran also produce tons of awesome content on the nLab. Every single sentence you write is amazing as well. Like John, whenever you touch the nLab, you increase its “quality” disproportionately to the “quantity”. There are many examples where we point to your comments on the n-Cafe from the n-Lab because they are so valuable.

On the other hand, if you compare simply “time spent” as opposed to “content creation”, then I’d guess (based on keenly watching the nLab since its inception) that the ratio of “time spent improving the nLab” between Urs and Toby is still on the order of 3:1. Given the amazing time and effort that Toby dedicates, this is a true tribute to Urs.

Highlighting the over-the-top effort Urs gives the nLab should hopefully, in no way, be seen as under valuing the contributions of others. It is merely a statement of fact.

PS: I’m sure Andrew (who also contributes a lot of blood, sweat, and tears) could write a script to verify my claims :)

PPS: The fact that you would question my claims about the relative role Urs plays in content creation on the nLab is, in a sense, proof of my statement that few understand it.

Posted by: Eric Forgy on July 20, 2009 8:40 PM | Permalink | Reply to this

Re:

Although I still wonder that you can be that confident about your numbers, it would be silly and pointless to continue arguing about this. We can all agree that Urs’s commitment and work ethic is nothing short of awe-inspiring, and that more people should get involved in the nLab!

Is everything back to normal with Recently Revised? I had been in the habit of using that all the time, but I’ve been laying off the nLab recently after hearing about the crashes.

Posted by: Todd Trimble on July 20, 2009 9:12 PM | Permalink | Reply to this

Re:

We should still avoid visiting Recently Revised (I hesitate even bringing it up because someone will inevitable try it and bring the nLab to its knees :)) until the migration to a new server is complete, but to compensate for that, we are making even better use of the Latest Changes page, which should be pretty current w.r.t. any recent changes.

Posted by: Eric on July 20, 2009 9:19 PM | Permalink | Reply to this

Re:

$MathML-enabled post (click for more details).$

Yes, please everyone make use of Latest Changes both for learning about changes and for informing about them. If used consistently, this is even more efficient for everyone.

We didn’t manage to migrate hosts last weekend. Today it didn’t work either. I suppose we will seriously migrate tomorrow (Tuesday). Is that still right, Andrew? I’ll post a big announcement here once we’ve done it.

Meanwhile, there is no real reason for laying off work on the $n$ Lab. On the contrary, it turns out that with everybody not calling you-know-which-page the server consistently reacts rather decently and one has good working conditions.

Finally, I should maybe admit that I did invest a good bit of time lately into the $n$ Lab as I used it as a tool for a course on Sheaves and Stacks that I taught, and for a journal club on $(\infty,1)$ -categories that I helped run.

So to some extent, I was actually being paid to work on the $n$ Lab: simply because I chose it as a tool for my daily work.

I found that, by the way, a remarkable win-win situation (or so it seems to me) that I can only recommend.

Posted by: Urs Schreiber on July 20, 2009 9:46 PM | Permalink | Reply to this

Re:

We didn’t manage to migrate hosts last weekend. Today it didn’t work either. I suppose we will seriously migrate tomorrow (Tuesday). Is that still right, Andrew? I’ll post a big announcement here once we’ve done it.

The main issue with migrating hosts is not so much doing it as making sure that once done we don’t have to keep on doing it. There isn’t a specific time line for migration yet. The main issue is finding a reasonable provider, but for that one generally has to go by word-of-mouth (so if anyone has any particular reliable recommendations, please let us know - that is, the recommendation should be reliable; I hope that it goes without saying that the provider should be reliable!).

In the process of migration it’s hoped that the database will also migrate from sqlite to MySQL which ought to speed things up a lot, and in particular bring ‘Recently Revised’ back into the frame.

In the meantime, the n-lab is perfectly usable. And when the switch does happen, hopefully there will be enough lab elves around that the whole process will be invisible to all you Hogwartians out there.

Finally, I should maybe admit that I did invest a good bit of time lately into the nLab as I used it as a tool for a course on Sheaves and Stacks that I taught, and for a journal club on (∞,1)-categories that I helped run.

…

I found that, by the way, a remarkable win-win situation (or so it seems to me) that I can only recommend.

I’m planning on using Instiki for a course next semester. So I guess that I can claim that all my work down in the basement will make the running of that course smoother as well. So I guess I’m being paid for working here as well!

Posted by: Andrew Stacey on July 21, 2009 8:14 AM | Permalink | Reply to this

Re:

$MathML-enabled post (click for more details).$

Eric writes:

I would never discourage discussions here, but when you make suggestions, please know that you are (unwittingly) putting work on Urs’ plate unless you implement the suggestion yourself.

In this sentence, even you are making it sound as if Urs is somehow responsible for implementing suggestions that people make regarding the $n$ Lab. He’s not. He can and should do whatever the hell he wants!

I’d rather say:

I would never discourage discussions here, but when you make suggestions, please know that they probably won’t be implemented unless you do it yourself.

I feel perfectly free to make suggestions here, bearing this principle in mind.

I would never be so obnoxious as to send anyone an email suggesting improvements to the $n$ Lab. To do that would be to pretend it was somehow their job.

When I get email requests to write about specific topics in This Week’s Finds, I almost reply with some kind, gentle version of “Sorry, pal, that’s not how it works.”

In This Week’s Finds, I write about what I’m interested in. And everyone contributing to the $n$ Lab should do what they’re interested in. That’s the only way it stays fun. And only if it stays fun will it succeed — because there ain’t nobody paying us.

So, please, let’s not talk about “putting work on Urs’ plate.” That reminds me too much of American restaurants where the waiters say “Are you still working on that?” As if eating there were some sort of job, instead of fun.

(By the way, when waiters say that you should reply: “Yes. Could you hand me a shovel?”)

Posted by: John Baez on July 20, 2009 8:11 PM | Permalink | Reply to this

Re:

I hope you see that you and I are exactly the same page, EXCEPT I’m trying to point out that what you claim you would never do …

I would never be so obnoxious as to send anyone an email suggesting improvements to the nLab. To do that would be to pretend it was somehow their job.

… is exactly what some people do. People DO send Urs suggestions implying it is his job. I’m saying it isn’t his job. You are saying the same thing.

I’m not against discussing things as long as everyone is on the same page as to what those discussions mean for everyone involved. I think I know Urs well enough to know that if people start grumbling here about something, he will feel bad and will feel an extra responsibility to do something about it. Just be aware of this, which I know you are, but I wish everyone else was.

Suggestions are pretty empty unless you are willing to hit the “edit” box and do it yourself because it is no one’s job to do it for you. You know that. I know that. The people sending Urs email suggestions don’t.

Posted by: Eric Forgy on July 20, 2009 8:54 PM | Permalink | Reply to this

Re: nLab

$MathML-enabled post (click for more details).$

Eric wrote:

I hope you see that you and I are exactly the same page, EXCEPT I’m trying to point out that what you claim you would never do…

I would never be so obnoxious as to send anyone an email suggesting improvements to the nLab. To do that would be to pretend it was somehow their job.

… is exactly what some people do. People DO send Urs suggestions implying it is his job.

I agree, we’re on the same page.

I’ve been on the internet for long enough (e.g., since it was created) to know that there are always a lot of people eager for a ‘management position’ where they can tell people what should be done and get someone to do it. So, I’m completely unsurprised that people are sending Urs suggestions as if it were his job to please them. We can’t stop it.

I’m not sure scolding these lazy bums is very productive. I think volunteer endeavors such as the $n$ Lab succeed best by luring in energetic people — mainly young people with spare time — using psychological ‘carrots’. I doubt that ‘sticks’ work.

Speaking of strategy: I think you might do Urs and the $n$ Lab a favor by not saying stuff like “when you make suggestions, please know that you are (unwittingly) putting work on Urs’ plate”, or “what I think many don’t realize is that probably 90% OR MORE of the content comes from Urs”. The $n$ Lab will work better if people aren’t repeatedly told that it’s mainly the work of one superhuman being — even if it’s true so far. Focus your public praise on lesser contributors and they will be happy and contribute more. Focus your public praise on you-know-who and the lesser contributors will feel inadequate and dispirited, and do even less.

We should probably all read Linus Torvald’s essay on management. For example:

Chapter 2: People

Most people are idiots, and being a manager means you’ll have to deal with it, and perhaps more importantly, that _they_ have to deal with _you_.

It turns out that while it’s easy to undo technical mistakes, it’s not as easy to undo personality disorders. You just have to live with theirs - and yours.

However, in order to prepare yourself as a manager, it’s best to remember not to burn any bridges, bomb any innocent villagers, or alienate too many developers. It turns out that alienating people is fairly easy, and un-alienating them is hard. Thus “alienating” immediately falls under the heading of “not reversible”, and becomes a no-no according to Chapter 1.

There’s just a few simple rules here:

(1) don’t call people d*ckheads (at least not in public)

(2) learn how to apologize when you forgot rule (1)

The problem with #1 is that it’s very easy to do, since you can say “you’re a d*ckhead” in millions of different ways (*), sometimes without even realizing it, and almost always with a white-hot conviction that you are right.

And the more convinced you are that you are right (and let’s face it, you can call just about _anybody_ a d*ckhead, and you often _will_ be right), the harder it ends up being to apologize afterwards.

To solve this problem, you really only have two options:

- get really good at apologies

- spread the “love” out so evenly that nobody really ends up feeling like they get unfairly targeted. Make it inventive enough, and they might even be amused.

The option of being unfailingly polite really doesn’t exist. Nobody will trust somebody who is so clearly hiding his true character.

I have deleted the word “kernel” a couple times above, since while Torvald was talking about being a “kernel manager”, the advice is clearly more general.

Anyway, publicly scolding people, even unnamed people, for suggesting improvements to the $n$ Lab is a mild form of calling them d*ckheads. It alienates them. Try to come up with some ways to lure them in.

Posted by: John Baez on July 20, 2009 11:16 PM | Permalink | Reply to this

Re: nLab

$MathML-enabled post (click for more details).$

Cheers to that!

As a final thought (for now)…

For what it is worth, I am really excited whenever I see ANY contribution to the $n$ -Lab from ANYONE. There is not a post on the $n$ -Cafe (and the String Coffee Table before that) or a page on the $n$ -Lab I haven’t at least skimmed.

Though I’m a non-expert in $n$ -things, I am an expert in my field (believe it or not!) and I have a pretty good “beauty sensor”. I think what you guys do is beautiful (or else I wouldn’t follow it from the sidelines for so long!) but, sadly, it is out of reach to me.

The worst thing that could happen is if something I say discourages people from contributing. That is the opposite of my intention (but as my former manager wisely put it, “Hell is full of people with good intentions”). It may seem irrational and/or unexplainable, but I am genuinely happy to see all contributions to the $n$ -Lab. I think it is amazing what everyone has done on the $n$ -Lab and look forward to more of it.

Posted by: Eric Forgy on July 21, 2009 12:20 AM | Permalink | Reply to this

Hell is full

A slightly older and more literate version:

The road to Hell is paved with good intentions

Posted by: jim stasheff on July 21, 2009 2:00 PM | Permalink | Reply to this

Re: nLab

$MathML-enabled post (click for more details).$

Eric wrote:

It may seem irrational and/or unexplainable, but I am genuinely happy to see all contributions to the $n$ Lab.

Talking about this is probably one of the best things you can do to encourage more people to contribute.

Myself, I’ve considered doing occasional blog posts or This Week’s Finds stories about the best $n$ Lab entries. Maybe I should even give out prizes!

Posted by: John Baez on July 21, 2009 8:28 AM | Permalink | Reply to this

Re:

…and drop us a note about what you did and why you think more of that should be done.

Of course, you should drop a note about what you've done to [[latest changes]] in any case. But that's also a good place to say why you think more of it should be done too. There are several people who have fleeting conversations this way (an alternative to both the Café and the Forum!, but not a place for anything that you want to last), and it's a good place to let people know that you're starting to do something different.

You can make a more permanent comment on the Café or the Forum as well, of course, especially if you want to invite discussion and feedback. (But if you just email Urs, then only Urs will see it.)

Posted by: Toby Bartels on July 20, 2009 8:34 PM | Permalink | Reply to this

Re: Being Tentative on nLab

I’ll shall forgo my usual rant about this discussion taking place here rather than on the forum (though, obviously my comment above was too subtle) and go straight for the remark that had this been taking place on the forum then everyone would have known that the word “heuristic” is banned on the n-lab by Order.

Posted by: Andrew Stacey on July 19, 2009 7:32 PM | Permalink | Reply to this

Re: Being Tentative on nLab

the word “heuristic” is banned on the n-lab by Order

Actually, it's being used here so vaguely (just as one among a list of examples) that it may well be being used correctly!

Posted by: Toby Bartels on July 19, 2009 7:49 PM | Permalink | Reply to this

Re: Being Tentative on nLab

Getting back to some maths, I tried some (very tentative) dualising of group homotopy in the shape of group homotopy. Any thoughts?

Posted by: David Corfield on July 21, 2009 8:51 AM | Permalink | Reply to this

Re: Being Tentative on nLab

$MathML-enabled post (click for more details).$

Any thoughts?

I just edited the entry a bit, please have a look.

My main question: since Moore spaces are defined via homology, which is the abelian version of homotopy, the asymmetry you see might be in that definition.

But I don’t know, just a thought, as requested. :-)

Posted by: Urs Schreiber on July 21, 2009 11:42 AM | Permalink | Reply to this

Re: Being Tentative on nLab

Thanks, I’ve replied there. I suppose just as you can jazz cohomology up by mapping onto larger parts of the Postnikov decomposition of a space, you could do the same by mapping from larger parts of the Moore decomposition.

Posted by: David Corfield on July 21, 2009 12:04 PM | Permalink | Reply to this

Re: Being Tentative on nLab

$MathML-enabled post (click for more details).$

I suppose just as you can jazz cohomology up by mapping onto larger parts of the Postnikov decomposition of a space, you could do the same by mapping from larger parts of the Moore decomposition.

Okay, I have to read and think about this more.

But thanks for the link to the encyclopedia article! Now I see that you had sneakily hidden this very useful link in that

comment comment comment

shell game at Eckmann-Hilton duality ;-)

I have now made this crucial link explcit.

Let’s generally try to equip a hyperlink with a minimum of information on what sits behind it, otherwise it will just be ignored (I am the first hand example, I would never click on comment comment comment for who knows where it will take me and if I want to be taken there).

Posted by: Urs Schreiber on July 21, 2009 1:09 PM | Permalink | Reply to this

The n-Category Café

Skip to the Main Content

July 17, 2009