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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!

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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 Numeo.fr. Rumours have it that our place is connected wirelessly to the web…

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F_un hype resulting in new blog

At the Max-Planck Institute in Bonn Yuri Manin gave a talk about the field of one element, $\mathbb{F}_1 $ earlier this week entitled “Algebraic and analytic geometry over the field F_1”.

Moreover, Javier Lopez-Pena and Bram Mesland will organize a weekly “F_un Study Seminar” starting next tuesday.

Over at Noncommutative Geometry there is an Update on the field with one element pointing us to a YouTube-clip featuring Alain Connes explaining his paper with Katia Consani and Matilde Marcolli entitled “Fun with F_un”. Here’s the clip



Finally, as I’ll be running a seminar here too on F_un, we’ve set up a group blog with the people from MPI (clearly, if you are interested to join us, just tell!). At the moment there are just a few of my old F_un posts and a library of F_un papers, but hopefully a lot will be added soon. So, have a look at F_un mathematics



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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 Last.fm 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…

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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).

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the future of this blog

Some weeks ago Peter Woit of Not Even Wrong and Bee of Backreaction had a video-chat on all sorts of things (see the links above to see the whole clip) including the nine minute passage below on ‘the future of (science) blogs’.

click here to see the video

The crucial point being that blogging takes time and that one often feels that the time invested might have been better spend doing other things. Bee claims it doesn’t take her that long to write a post, but given their quality, I would be surprised if it took her less than one to two hours on average.

Speaking for myself, I’ve uploaded two (admittedly short) notes to the arXiv recently. The shorter one took me less time than an average blogpost, the longer one took me about the time I need for one of the better posts. So, is it really justified to invest that amount of time in something as virtual as a blog?

Probably it all depends on the type of blog you’re running and what goal (if any) you want to achieve with it.

I can see the point in setting up a blog connected to a book you once wrote or intend to write (such as Not Even Wrong or Terry Tao).

I can also understand that people start a blog to promote their research-topic or to have a social function for people interested in the same topic (such as Noncommutative Geometry or the n-category cafe).

I can even imagine the energy boost resulting from setting up a group-blog with fellow researchers working at the same place (such as Secret Blogging Seminar or the Everything Seminar and some others).

So, there are plenty of good reasons to start and keep investing in a serious mathematical blog (as opposed to mere link-blogs (I won’t mention examples) or standard-textbook-excerpts-blogs (again, I’ll refrain from giving examples)).

What is needed is either a topical focus or a clear medium term objective. Unfortunately, this blog has neither…

At present, I feel like the journalist, spending too much time getting into a subject merely to write a short piece on it for today’s paper, which will be largely forgotten by tomorrow, but still hoping that his better writings will result into something having a longer half-life…

That is, I need to reconsider the future of this blog and will do so over a short vacation. As always, suggestions you might have are welcome. Perhaps I should take the bait offered by John McKay in his comment yesterday and do a series on the illusory 24-dimensional monster-manifold.

At the very least it would take this blog back to the only time when it was somewhat focussed on a single topic and was briefly called MoonshineMath. But then, even this is not without risks…



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GAMAP 2008

Next week, our annual summer school Geometric and Algebraic Methods with Applications in Physics will start, once again (ive lost count which edition it is).

Because Isar is awol to la douce France, I’ll be responsible (once again) for the web-related stuff of the meeting. So, here a couple of requests to participants/lecturers :

  • if you are giving a mini-course and would like to have your material online, please contact me and i’ll make you an author of the Arts blog.
  • if you are a student attending the summerschool and would love to do some Liveblogging about the meeting, please do the same.

I’ll try to do some cross-posting here when it comes to my own lectures (and, perhaps, a few others). For now, I settled on ‘What is noncommutative geometry?’ as a preliminary title, but then, I’m in the position to change the program with a few keystrokes, so I’ll probably change it by then (or remove myself from it altogether…).

At times, I feel it would be more fun to do a few talks on Math-blogging. An entertaining hour could be spend on the forensic investigation of the recent Riemann-Hypothesis-hype in (a good part of) the math-blogosphere

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bloomsday 2 : BistroMath

Exactly one year ago this blog was briefly renamed MoonshineMath. The concept being that it would focus on the mathematics surrounding the monster group & moonshine. Well, I got as far as the Mathieu groups…

After a couple of months, I changed the name back to neverendingbooks because I needed the freedom to post on any topic I wanted. I know some people preferred the name MoonshineMath, but so be it, anyone’s free to borrow that name for his/her own blog.

Today it’s bloomsday again, and, as I’m a cyclical guy, I have another idea for a conceptual blog : the bistromath chronicles (or something along this line).

Here’s the relevant section from the Hitchhikers guide

Bistromathics itself is simply a revolutionary new way of understanding the behavior of numbers. …
Numbers written on restaurant checks within the confines of restaurants do not follow the same mathematical laws as numbers written on any other pieces of paper in any other parts of the Universe.
This single statement took the scientific world by storm. It completely revolutionized it.So many mathematical conferences got hold in such good restaurants that many of the finest minds of a generation died of obesity and heart failure and the science of math was put back by years.

Right, so what’s the idea? Well, on numerous occasions Ive stated that any math-blog can only survive as a group-blog. I did approach a lot of people directly, but, as you have noticed, without too much success… Most of them couldnt see themselves contributing to a blog for one of these reasons : it costs too much energy and/or it’s way too inefficient. They say : career-wise there are far cleverer ways to spend my energy than to write a blog. And… there’s no way I can argue against this.

Whence plan B : set up a group-blog for a fixed amount of time (say one year), expect contributors to write one or two series of about 4 posts on their chosen topic, re-edit the better series afterwards and turn them into a book.

But, in order to make a coherent book proposal out of blog-post-series, they’d better center around a common theme, whence the BistroMath ploy. Imagine that some of these forgotten “restaurant-check-notes” are discovered, decoded and explained. Apart from the mathematics, one is free to invent new recepies or add descriptions of restaurants with some mathematical history, etc. etc.

One possible scenario (but I’m sure you will have much better ideas) : part of the knotation is found on a restaurant-check of some Italian restaurant. This allow to explain Conway’s theory of rational tangles, give the perfect way to cook spaghetti to experiment with tangles and tell the history of Manin’s Italian restaurant in Bonn where (it is rumoured) the 1998 Fields medals were decided…

But then, there is no limit to your imagination as long as it somewhat fits within the framework. For example, I’d love to read the transcripts of a chat-session in SecondLife between Dedekind and Conway on the construction of real numbers… I hope you get the drift.

I’m not going to rename neverendingbooks again, but am willing to set up the BistroMath blog provided

  • Five to ten people are interested to participate
  • At least one book-editor shows an interest
    update : (16/06) contacted by first publisher

You can leave a comment or, if you prefer, contact me via email (if you’re human you will have no problem getting my address…).

Clearly, people already blogging are invited and are allowed to cross-post (in fact, that’s what I will do if it ever gets so far). Finally, if you are not willing to contribute blog-posts but like the idea and are willing to contribute to it in any other way, we are still auditioning for chanting monks

The small group of monks who had taken up hanging around the major research institutes singing strange chants to the effect that the Universe was only a figment of its own imagination were eventually given a street theater grant and went away.

And, if you do not like this idea, there will be another bloomsday-idea next year…

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NSF annual report – the comic book version

Annual reports of organizations often make extremely dry reading. With available word processing tools, however, several agencies try to make their report at least visually pleasing. A good example is the 2007 annual report of the NSF (USA). It has an attractive cover (left) and has a couple of daring inside pages, such as the one on the right.



I’ve been a researcher with the Flemish National Science Foundation FWO from 1980 till 2000, when I’ve opted for a professorship rather than keeping my permanent research position with them. At the time, it seemed like a sensible move to make, but I’m beginning to have my doubts… The FWO definitely rocks! Single handedly they’ve taken the art of science-organization-reporting to galactic levels with their 2007 year book. Here is the cover



based on the comic book series Jommeke. So what? They have an (arguably) even more attractive cover-picture…

The point is that they maintain this gimmick throughout the entire report! If you don’t believe me, download the entire book from the link above. But as it is over 1Mb, I’ll provide you with two generic illustrations : on the left a typical (as in “every”) page and even pie-charts are way too dry for the FWO-admins so they solved it (right)



Probably the message they want to broadcast is : you guys can easily beat us at science, but we still have the best comic-books!!!

I bet, next year they’ll base their report on the series Spike and Suzy (Suske&Wiske for the rest of us) and the year after they’ll probably go for Tintin (that is, if Flandres can forget by then that Herge was a French speaking Belgian). I’m confident that in 2009 the FWO will spend most of its energy debating this issue…

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