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introducing : the n-geometry cafe

It all started with this comment on the noncommutative geometry blog by “gabriel” :

Even though my understanding of noncommutative geometry is limited, there are some aspects that I am able to follow.
I was wondering, since there are so few blogs here, why don’t you guys forge an alliance with neverending books, you blog about noncommutative geometry anyways. That way you have another(n-category cafe) blogspot and gives well informed views(well depending on how well defined a conversational-style blog can be).

The technology to set up a ‘conversational-style blog’, where anyone can either leave twitter-like messages or more substantial posts, is available thanks to the incredible people from Automattic.

For starters, they have the sensational p2 wordpress theme : “blogging at the speed of thought”

A group blog theme for short update messages, inspired by Twitter. Featuring: Hassle-free posting from the front page. Perfect for group blogging, or as a liveblog theme. Dynamic page updates. Threaded comment display on the front page. In-line editing for posts and comments. Live tag suggestion based on previously used tags. A show/hide feature for comments, to keep things tidy. Real-time notifications when a new comment or update is posted. Super-handy keyboard shortcuts.

Next, any lively online community is open for intense debate : “supercharge your community”

Fire up the debate with commenter profiles, reputation scores, and OpenID. With IntenseDebate you’ll tap into a whole new network of sites with avid bloggers and commenters. And that’s just the tip of the iceberg!

And finally, as we want to talk math, both in posts and comments, they provide us with the WP-LaTeX plugin.

All these ingredients make up the n-geometry cafe ((with apologies to the original cafe but I simply couldn’t resist…)) to be found at (explaining the ‘n’).

Anyone can walk into a Cafe and have his/her say, that’s why you’ll get automatic author-privileges if you register.

Fill in your nick and email (please take your IntenseDebate setting and consider signing up with to get a nice image next to your contributions), invent your own password, show that you’re human by answering the reCapcha question and you’ll get a verification email within minutes ((if you don’t get an email within the hour, please notify me)). This will take you to your admin-page, allowing you to start blogging. For more info, check out the FAQ-pages.

I’m well aware of the obvious dangers of non-moderated sites, but also a strong believer in any Cafe’s self-regulating powers…

If you are interested in noncommutative geometry, and feel like sharing, please try it out.


bloomsday, again

Bloomsday has a tradition of bringing drastic changes to this blog.

Two years ago, it signaled a bloomsday-ending to the original neverendingbooks, giving birth (at least for a couple of months) to MoonshineMath.

Last year, the bloomsday 2 post was the first of several ‘conceptual’ blog proposals, voicing my conviction that a math-blog can only survive as a group-blog.

A few months later, I launched yet another proposal and promised that neverendingbooks would end on new-years eve, exactly five years after it started.

And, here we are again, half a year later, still struggling on … barely.

Well, don’t expect drastic statements from me today. I’ll continue to post when I do feel I’ve something to say (and won’t if I don’t) ((that is, apart from this silly post)). Also, there won’t be another pathetic cry-for-cooperation. I must have given up on that hope.

In fact, there isn’t much I can add to the post just mentioned (in particular my comment to it) to explain my present state of mind when it comes to blogging (and maths).

Let’s hope google wave will be released soon and that some of you will use it to make relevant waves. I promise to add blips when possible.


Ceci n’est pas un blog…

“Lieven le Bruyn’s NEVERENDINGBOOKS isn’t really a blog at all…”

Vlorbik’s unintentional [smack in the face]( $ left me bewildered ever since.

There aren’t that many [mathematical blogs]( around, and, sure enough, we all have a different temperament, and hence a distinct style. I have no definition of what a mathematical blog should (or should not) be.

All I can say is that I try to reconcile an introvert character with a very public medium, partly because I think it is important for mathematics to be www-visible, but mostly because I’ve enjoyed exploring web-possibilities ever since someone told me of the existence of a language called html.

I’m a [Bauhaus]( and hence like minimal wordpress-themes such as [Equilibrium]( $. Perhaps this confuses some.

For this reason I’ve reinstalled the old-theme as default, and leave the reader to decide in the sidebar. This may not make this a blog yet, but it sure looks more like one…

As a one-time attempt to fit into the vast scenery of link-post-blogs, let’s try to increase the google visibility of some family-related sites (sorry, no math-links beyond) :

– The economic crisis is hitting hard at small companies such as my [sister’s-in-law]( offering gardening-services.
– My god-child Tine is away for six months on a scholarship to Austria and blogging at [Tine’s adventures in Graz]( $.
– My daughter Gitte (aka here as PD1) is an [artist](
– My father, who will turn 79 next week, runs one of the most [popular blogs on]( $.

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best of 2008 (2) : big theorems

Charles Siegel of Rigorous Trivialities ran a great series on big theorems.

The series started january 10th 2008 with a post on Bezout’s theorem, followed by posts on Chow’s lemma, Serre duality, Riemann-Roch, Bertini, Nakayama’s lemma, Groebner bases, Hurwitz to end just before christmas with a post on Kontsevich’s formula.

Also at other blogs, 2008 was the year of series of long posts containing substantial pure mathematics.

Out of many, just two examples : Chris Schommer-Pries ran a three part series on TQFTs via planar algebras starting here, at the secret blogging seminar.
And, Peter Woit of Not Even Wrong has an ungoing series of posts called Notes on BRST, starting here. At the moment he is at episode nine.

It suffices to have a quick look at the length of any of these posts, to see that a great deal of work was put into these series (and numerous similar ones, elsewhere). Is this amount of time well spend? Or, should we focus on shorter, easier digestible math-posts?

What got me thinking was this merciless comment Charles got after a great series of posts leading up to Kontsevich’s formula :

“Perhaps you should make a New Years commitment to not be so obscurantist, like John Armstrong, and instead promote the public understanding of math!”

Well, if this doesn’t put you off blogging for a while, what will?

So, are we really writing the wrong sort of posts? Do math-blog readers only want short, flashy, easy reading posts these days? Or, is anyone out there taking notice of the hard work it takes to write such a technical post, let alone a series of them?

At first I was rather pessimistic about the probable answer to all these questions, but, fortunately we have Google Analytics to quantify things a bit.

Clearly I can only rely on the statistics for my own site, so I’ll treat the case of a recent post here : Mumford’s treasure map which tried to explain the notion of a generic point and how one might depict an affine scheme.

Here’s some of the Google Analytics data :

The yellow function gives the number of pageviews for that post, the value ranges between 0 and 600 (the number to the right of the picture). In total this post was viewed 2470 times, up till now.

The blue function tells the average time a visitor spend reading that post, the numbers range between 0 and 8 minutes (the times to the left of the picture). On average the time-on-page was 2.24 minutes, so in all people spend well over 92 hours reading this one post! This seems like a good return for the time it took me to write it…

Some other things can be learned from this data. Whereas the number of page-views has two peaks early on (one the day it was posted, the second one when Peter Woit linked to it) and is now steadily decreasing, the time-on-page for the later visitors is substantially longer than the early readers.

Some of this may be explained (see comment below) by returning visits. Here is a more detailed picture (orange = new visits, green=returning visits, blue=’total’ whatever this means).

All in all good news : there is indeed a market for longer technical math-posts and people (eventually) take time to read the post in detail.


5 years blogging

Here’s a 5 move game from $\mathbb{C} $, the complex numbers game, annotated by Hendrik Lenstra in Nim multiplication.

$\begin{matrix} & \text{White} & \text{Black} \\ 1. & 3-2i & { 3_{\mathbb{R}} } \\ 2. & 3_{\mathbb{R}} & (22/7)_{\mathbb{Q}} \\ 3. & (-44_{\mathbb{Z}},-14_{\mathbb{Z}})? & { -44_{\mathbb{Z}} } \\ 4. & -44_{\mathbb{Z}} & ( 0_{\mathbb{N}},44_{\mathbb{N}} )! \\ 5. & \text{Resigns} & \\ \end{matrix} $

He writes : “The following 5 comments will make the rules clear.

1 : White selected a complex numbers. Black knows that $\mathbb{C} = \mathbb{R} \times \mathbb{R} $ by $a+bi = (a,b) $, and remembers Kuratowski’s definition of an ordered pair: $~(x,y) = { { x }, { x,y } } $. Thus black must choose an element of ${ { 3_{\mathbb{R}} }, { 3_{\mathbb{R}},-2_{\mathbb{R}} } } $. The index $\mathbb{R} $ here, and later $\mathbb{Q},\mathbb{Z} $ and $\mathbb{N} $, serve to distinguish between real numbers, rational numbers, integers and natural numbers usually denoted by the same symbol. Black’s move leaves White a minimum of choice, but it is not the best one.

2 : White has no choice. The Dedekind definition of $\mathbb{R} $ which the players agreed upon identifies a real number with the set of all strictly larger rational numbers; so Black’s move is legal.

3 : A rational number is an equivalence class of pairs of integers $~(a,b) $ with $b \not= 0 $; here $~(a,b) $ represents the rational number $a/b $. The question mark denotes that White’s move is a bad one.

4 : The pair $~(a,b) $ of natural numbers represents the integer $a-b $. Black’s move is the only winning one.

5 : White resigns, since he can choose between ${ 0_{\mathbb{N}} } $ and ${ 0_{\mathbb{N}},44_{\mathbb{N}} } $. In both cases Black will reply by $0_{\mathbb{N}} $, which is the empty set” (and so wins because White has no move left).

These rules make it clear what we mean by the natural numbers $\mathbb{N} $ game, the $\mathbb{Z} $-game and the $\mathbb{Q} $ and $\mathbb{R} $ games. A sum of games is defined as usual (players are allowed to move in exactly one of the component games).

Here’s a 5 term exercise from Lenstra’s paper : Determine the unique winning move in the game $\mathbb{N} + \mathbb{Z} + \mathbb{Q} + \mathbb{R} + \mathbb{C} $

It will take you less than 5 minutes to solve this riddle. Some of the other ‘exercises’ in Lenstra’s paper may take you a lot longer, if not forever…

Exactly 5 years ago I wrote : “As it is probably better to run years behind than to stand eternally still, I’ll try out how much of a blogger I am in 2004.”

5 months ago this became : “from january 1st 2009, I’ll be moving out of here. I will leave the neverendingbooks-site intact for some time to come, so there is no need for you to start archiving it en masse, yet.”

5 minutes before the deadline, this will be my last post….

of 2008

less entropy in 2009!


beyond the blog

For starters, apologies for flooding your RSS-aggregators a couple of days ago. Ive been copying my posts at F_un mathematics and have cross-posted them here. I will continue to do so as I prefer to search just one blog instead of two to find stuff. Besides, it’s unclear how long the F_un site will survive. Javier will be moving from MPI to London later this month, and is uncertain on the implications this will have for his research. Other people who told they’d like to post at F_un haven’t done so far… and I see little point in continuing a singleton-‘group blog’.

Over at the secret blogging seminar there is an interesting series on TQFTs via planar algebras by Chris Schommer-Pries. They also had a few nice words on the design of the F_un-site (though their commenters prefer a ‘traditional’ blog-layout). I think these days most people read blogs via their RSS-feeds, so are ignorant about the actual layout of a blog until they want to follow up a story that interests them. Besides, the main point of using the open book wordpress theme, which is a so called ‘magazine’-theme, was to try to get more structure in the blog (such as : indicating the intented audience for a post, organizing posts wrt. the papers mentioned etc.). Still, such themes are designed for news-sites having new content every hour/day, something we cannot say of the F_un-site…

Also at the n-category cafe they are thinking aloud on how to improve the blog-medium for mathematics-research. See the discussion following David Corfield’s beyond the blog post. Often, the comment-thread of an n-cafe post is a better read than the actual post, but the blog-concept is not very good at picking-out interesting comments. That’s why they are trying to set up a wiki-like thing with pointers to such interesting discussions. It’s still early days but they’ve started the nLab (powered by instiki) and describe it as “this place is like 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”. Surely an interesting experiment to follow.

Finally, a link to images des mathematiques which is a news-site-style blog on mathematics run by the CNRS (the French NSF). They give their posts ‘colours’, indicating the intented public, surely a simple idea we can all implement that will make math-blogs a lot more useful. They also have repeating topics, such as ‘the object of the month’, portraits of mathematicians etc. Perhaps an idea to follow-up by other math-societies.

If you have ideas to improve the structure and usability of math-blogs, please share them!

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This week at F_un Mathematics (1)

In case you haven’t noticed it yet : I’m not living here anymore.

My blogging is (at least for the moment) transfered to the F_un Mathematics blog which some prefer to call the “ceci n’est pas un corps”-blog, which is very fine with me.

Javier gave a talk at MPI on Soule’s approach to algebraic geometry over the elusive field with one element $\mathbb{F}_1 $ and wrote two posts about it The skeleton of Soule’s F_un geometry and Gadgets a la Soule. The rough idea being that a variety over the field with one element only acquires flesh after a base extension to $\mathbb{Z} $ and to cyclotomic integers.

I did some posts on a related (but conceptually somewhat easier) approach due to Alain Connes and Katia Consani. I’ve tried to explain their construction at the level of (mature) undergraduate students. So far, there are three posts part1, part2 and part3. Probably there is one more session to come in which I will explain why they need functors to graded sets.

In the weeks to come we plan to post about applications of this F_un-geometry to noncommutative geometry (the Bost-Connes system) and Grothendieck’s anabelian geometry (the theory of dessins d’enfant). I’ll try to leave a short account of the main posts here, but clearly you are invited to feed your feedreader this.

Perhaps I’ll return here for a week mid november to do some old-fashioned vacation blogging. I have to admit I did underestimate Rumours have it that our place is connected wirelessly to the web…

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the future of… (3)

It is always great to hear about new and clever ways to use blogs and the internet to promote (and hopefully do) science better. So, I’m a keen consumer of the Flash-presentations of the talks at the Science in the 21st century conference. Bee of Backreaction is one of the organizers and has a post on it as does Woit of Not Even Wrong.

Chad Orzel of Uncertain Principles gave an entertaining talk titled Talking to My Dog about Science: Weblogs and Public Outreach. Not that much about the dog bit except that two of his blog-posts explaining physics to his dog landed him a book contract (book scheduled to appear early 2009).

He compared two ways of communicating scientific discoveries : the Newtonian way (aka publishing in peer reviewed journals) aiming deliberately to make your texts only readable to the experts, versus the Galileian way (aka blogging or science-journalism) trying to find a method to maximize your readership and concluded (based on history) that the Newton-manner is far better for your career…

Jacques Distler of Musings continued his crusade to convince us to use mathML for TeX-rendering in Blogs, Wikis, MathML: Scientific Communication. Of course he is right, but as long as the rendering depends on the client to install extra fonts I’m not going to spend another two weeks sanitizing this blog to make it XHTML-compliant. We’ll just have to wait for html5 and compatible browsers…

A talk I found extremely interesting was The Future is a Foreign Country by Timo Hannay of the Nature Publishing Group on the new challenges facing publishers in times of internet.

Above a text-message filed in as homework (‘describe your holiday’). When Timo decrypted it, I had to think about my old idea of writing a course using only text-messages…

Truly shocked was I when I saw the diagram below in Paul Ginsparg’s talk Next-Generation Implications of Open Access

It depicts the number of submissions to the arXiv by day-time of submission over 24hours. I would have expected a somewhat smooth pattern but was totally blown away by the huge peak around 16hrs. I’ll let you discover the mystery for yourself but it seems to be related to the dead-line for submission, the corresponding order the papers are mentioned in the emails send out, and its effect on the number of references these papers get within the first year…

Somewhat unlucky was Victor Henning in his talk Mendeley: A for Research? when he wanted to demonstrate the mendeley web-interface but lost his internet connection…

Still, it seems like a good initiative so I’ve registered with the mendeley site, downloaded the software and hope to explore it over the coming days. I really hope this will turn out to be the one web2-idea catching on among the mathematics-community…


the future of this blog (2)

is decided : I’ll keep maintaining this URL until new-year’s eve. At that time I’ll be blogging here for 5 years…

The few encounters I’ve had with architects, taught me this basic lesson of life : the main function of several rooms in a house changes every 5 years (due to children and yourself getting older).

So, from january 1st 2009, I’ll be moving out of here. I will leave the neverendingbooks-site intact for some time to come, so there is no need for you to start archiving it en masse, yet.

Previously I promised to reconsider this blog’s future over a short vacation, but as vacation is looking to be as illusory as the 24-dimensional monster-manifold, I spend my time throwing up ideas into thin and, it seems, extremely virtual air.

Some of you will think this is a gimmick, aiming to attract more comments (there is no post getting more responses than an imminent-end-to-this-blog-post) but then I hope to have settled this already. Neverendingbooks will die on 31st of december 2008. The only remaining issue being : do I keep on blogging or do I look for another time-consumer such as growing tomatoes or, more probably, collecting single malts…

For reasons I’ve stated before, I can see little future in anything but a conceptual-, group- blog. The first part I can deal with, but for the second I’ll be relying on others. So, all I can do is offer formats hoping that some of you are willing to take the jump and try it out together.

Such as in the bloomsday-post where I sketched the BistroMath blog-concept. Perhaps you thought I was just kidding, hoping for people to commit themselves and them calling “Gotcha…”. Believe me, 30 years of doing mathematics have hardwired my brains such that I always genuinely believe in the things I write down at the moment I do (but equally, if someone offers me enough evidence to the contrary, I’ll drop any idea on the spot).

I still think the BistroMath-project has the potential of leading to a bestseller but Ive stated I was not going to pursue the idea if not at least 5 people were willing to join and at least 1 publisher showed an interest. Ironically, I got 2 publishers interested but NO contributors… End of that idea.

Today I offer another conceptual group-blog : the Noether-boys seminar (with tagline ; _the noncommutative experts’ view on 21st century mathematics_). And to make it a bit more concrete Ive even designed a potential home-page :

So, what’s the deal? In the 1930-ties Emmy Noether collected around her in Goettingen an exceptionally strong group of students and collaborators (among them : Deuring, Fitting, Levitski, Schilling, Tsen, Weber, Witt, VanderWaerden, Brauer, Artin, Hasse, MacLane, Bernays, Tausky, Alexandrov… to name a few).

Collectively, they were know as the “Noether-boys” (or “Noether-Knaben” or “Trabanten” in German) and combined seminar with a hike to the nearby hills or late-night-overs at Emmy’s apartment. (Btw. there’s nothing sexist about Noether-boys. When she had to leave Germany for Bryn Mawr College, she replaced her boys to form a group of Noether-girls, and even in Goettingen there were several women in the crowd).

They were the first generation of mathematicians going noncommutative and had to struggle a bit to get their ideas accepted.
I’d like to know what they might think about the current state of mathematics in which noncommutativity seems to be generally accepted, even demanded if you want to act fashionable.

I’m certain half of the time they would curse intensely, and utter something like ‘steht shon alles bei Frau Noether…’ (as Witt is witnessed to have done at least once), and about half the time they might get genuinely interested, and be willing to try and explain the events leading up to this to their fellow “Trabanten”. Either way, it would provide excellent blog-posts.

So I’m looking for people willing to borrow the identity of one of the Noether-boys or -girls. That is, you have to be somewhat related to their research and history to offer a plausible reaction to recent results in either noncommutative algebra, noncommutative geometry or physics. Assuming their identity you will then blog to express your (that is, ‘their’) opinion and interact with your fellow Trabanten as might have been the case in the old days…

I’d like to keep Emmy Noether for the admin-role of the blog but all other characters are free at this moment (except I’m hoping that no-one will choose my favourite role, which is probably the least expected of them anyway).

So please, if you think this concept might lead to interesting blogging, contact me! If I don’t get any positives in this case either, I might think about yet another concept (or instead may give up entirely).