This, here, is me trying it out. With any luck, the appearance of a new toy will get me back to actually blogging some more – it’s been winding down a bit much here lately.

Next stop is the topology in computer science workgroup at Stanford, where I have accepted an offer for a postdoc research position up to 3 years (conditional on my good behaviour .

He has, recently, written a post inspired by the xkcd comic on purity in the sciences. The comic is funny, and rings true, but Ben brings up a severe criticism of the premises of the comic that rings back to my own years as a hotheaded undergraduate.

You should read all of Ben’s post, but if you don’t, you should at least read the following:

And I think one of the key points here is this: mathematics is not science. Mathematics is often lumped in with science, and is often used by scientists. Mathematicians often know more science than normal people, and certainly scientists know more mathematics. But mathematics and science are fundamentally different activities, as different as making a gun and fighting in a battle. I mean, no one would claim there are no links between those occupations, or that gun-makers don’t pay a lot of attention to how guns are used, but not even a child would mistake one for the other. Putting mathematics on a continuum of purity with sciences is like putting it on a continuum with disciplines of art ordered by “highbrow-ness” (actually, I would argue that the latter captures the nature of mathematics better).

The critique here is pretty close to my own age-old hobby horse: the epistemology of mathematics is fundamentally different from the epistemology of the sciences. I used to use this as an argument for transferring the Department of Mathematics at Stockholm University from the Faculty of Sciences to the Faculty of Humanities. Nobody really took me serious back then. However, the basic ideas underlying it all reoccurs: both in Ben’s post, and in Pozorvlak’s excellent shot at classifying academic disciplines by their epistemology. Pozorvlak expands on his treatment of it all, but if we restrict it to the case Ben discusses, his point is basically this:
Mathematics deals with statements that can be proven.
Science deals with statements that cannot be proven, but can be falsified.

These two types of statements lead pretty immediately to different ideas of what truth is – and what knowledge is and all sorts of deep philosophical (as in cannot be proven, cannot be falsified, cannot even find circumstantial evidence for) questions dealing with the meta-level of academic research.

Nowadays, my University has the Mathematics department placed in the Faculty for Mathematics and Computer Science – and I have much less objections to this state of affairs.

Now, in a post just a day or two ago, Ben Webster of the Secret Blogging Seminar called for RSS feeds for the Mathjobs listings.

Imagine my surprise – and probably that of most the readers of the Secret Blogging seminar – to see, the day after posting, the following reply from Diane Boumenot at the AMS:

Hello all. First of all let me say, thank you for the kind words. Also, if you want to send suggestions to Mathjobs.Org, that can be easily done through the web site. However, thanks to Google Alerts and a willing programmer, your request has been received and acted on. As of this morning you can get an RSS feed through the View Jobs page of the Mathjobs website.

Thanks for the suggestion. Thoughts/ideas are always welcome. I will pass the one about Current Publications along to the publications division.
–Diane Boumenot
Manager, Membership & Programs, AMS

Dear Diane. Dear AMS. You’re doing a good job already. This amount of community awareness and swift responses is heartwarming, impressive and thouroughly amazing. Much love!

I’ll be there, and so will bit-player. Join in you too!

January: I decided on a whim to look in at the Dilbertblog, where the top post at the moment has Scott Adams calling all atheists that discuss on the net irrational, using a rather neat strawman carbon copy of most discussions of faith between believers (i.e. mostly Christians) and atheists he has seen on the web.

February: The second carnival of mathematics is up over at Good Math, Bad Math.

March: I just met up with the workgroup in the Deutsche Mathematikervereinigung (German Association of Mathematicians) with interest spanning “Information and Communication” – which turns out to mean that they care about libraries, about communicative tools for mathematicians, and spend their time thinking about these things, and meeting at conferences.

April: The website/forumsite Mathetreff, run by the Bezirksregierung (region government) Düsseldorf, just performed a mail interview with me.

May: In about 23 hours, I’ll step on to the train in Jena, heading for T’bilisi, Georgia.

June: Too harried to blog.

July: … or another bout of more-or-less shameless self-promotion.

August: Trying to make the time until my flight leaves tomorrow go by, I played around a bit with the proof assistant Coq.

September: No mathematical content today.
Note: The first september post consisted of a CAS interaction dump. Not fun to quote, so I took the second post.

October: In a conversation on IRC, I started prodding at low-order wreath products.

November: In a recent column at The Chronicle of Higher Education, the columnist writes:

December: I just received my first ever referee’s report.

In conclusion – living in Germany affects me adversely. The number of first sentences that span the entire first paragraph of the posts I’ve been looking at is staggering.

A short background blurb for those who haven’t read this blog before – and for those who haven’t heard the story: I’m a mathematics PhD student from Sweden in Germany, living apart from my wife for about 2½ years now. She has a position waiting for her in Michigan, and my advisor told me to get that thesis written and go for a postdoc to stay at least on the same continent.

Hence, I currently try to finish up my thesis (progressing surprisingly well!) and land postdoc positions for fall 2008 (~25 applications out, contacts duly notified, and a LOT of job search angst).

I find myself on the career path I have been going for since I was 4 years old – there’s a story I’ve been told over and over by my family: on the way back from a children’s theater show with my aunt, I chatted in the subway with an Iraqi immigrant, who asked me what I wanted to be when I grew up. I proudly answered “Scientist!”.

All, significantly, that has happened since is that I now know more precisely -what- kind of scientist I want to be, and how to get there. Thus, my striving for a postdoc comes with a standard issue set of rosy-coloured glasses and a large bunch of optimism. We’ll see how much of that remains 6 months from now.

Tying in with the postdoc carnival theme, this places my theme song for that pie-in-the-sky firmly at Knocking on heaven’s door.

The more exotic varieties couple more or other senses to each other.

The whole thing gets Really Interesting, and ties in to quite a bit of philosophy as well, when you start coming near the really odd cases. Qualia are the philosophical term for “how things are perceived by us”. Basically, it boils down to the following: if I see something red, is this intrinsic to the object, or something existing in my perceptive neurons only?

And so far, arguing about it has been more or less all there was. At least known to me.

Then I stumbled across one of the latest post at Making Light. They link to the story of a colourblind synaesthete. Who perceives colour through his synaesthesis that he DOES NOT perceive in the real world.

I don’t really have much of a philosophical point of my own – I seem to get entangled whenever I try to start writing one – more than Go! And Read! The Making Light thread is a good starting point for this, and the comments are – as is normal over there – absolutely brilliant.

The resulting discussion there amuses at least me.

I’m a latecomer to it, in part because I have a very hit-or-miss interest in new technologies. (I still don’t own a cell phone, for example, though I check my e-mail 4,000 times a day.)

Now. There are 24 hours in a day. 1 440 minutes. 86 400 seconds. Thus, checking e-mail 4 000 times in a day would require you to check your inbox every 21.6 seconds. Day and night.

Either the author is innumerate or hyperactive.

What differentiated this offer from all other spam I get was that it was actually written well enough, and tailored enough, that I believe this guy would even go through with it. Only …

I am not interested.

I run this blog because I like running it. I do system admin myself too. The domain name is mine since my family wants it, and my parents chip in. The net connection also is something that the family chips in on, and is handled without significant cost.

All in all, I do not NEED ads to keep this place up and running.

Furthermore, I do not WANT ads here. I want this place to be my venue of expression. Not some advertiser or other. I want complete control of my content, and no bullshit with banners or whatever.

If you want me to recommend something of yours, make sure I get to try it. I write about things I end up liking occasionally, and the best way to get me to write about your things is to produce things I like and make sure I’m exposed to them.

But I will not publish your ads.

I took the initiative, and invited some of the relevant Powers That Be to start an -themed group blog: The Infinite Seminar.

I also perceived a lack of blog aggregators, so I started Planet Math Blogseminars to aggregate group blogs in mathematics.

While I was at it, I bought the blogseminar.net domain. I’d be happy to allocate subdomains of this to decent enough blogs that wants in on it.

Do we have the volume for a Carnival of Research Mathematics?

I find Weibel very readable – once the interest is there. It’s a good reference, and not as opaque as, for instance, the MacLane + Hilton-Stammbach couplet can be at points.

The interest, however, is something I blame my alma mater for. Once upon a time, Jan-Erik Roos went to Paris and studied with Grothendieck. When he got back, he got a professorship at Stockholm University without having finished his PhD. He promptly made sure that nowadays (when he’s an Emeritus stalking the halls) there is not a single algebraist at Stockholm University without some sort of intuition for homological algebra.

So, my MSc advisor, Jörgen Backelin, gave me a subject building on from things that he touched in his PhD thesis, since I was obviously interested in combinatorics. And as such, nothing fits me better than looking at Ext and Tor over monomial rings (corresponding to coordinate hyperplane varieties…)

The other Very Interesting teacher, Jan-Erik Björk, at that university held a course in homological algebra that I attended. It was very handwavy, but with enough of deep understanding underneath that some things just clicked into place.

The story goes on. All in all, out of my 5 years at Stockholm University, at least 3 was spent doing homological algebra in addition to whatever else I was doing, and they were spent in a tight clique of undergrads and early grad students that all shared a high interest in the subject matter. In my transcript, I have an imposing distribution of courses:

where one credit corresponds to one week of fulltime study, roughly. The +20 for homological stuff is for my thesis project, which was on homological algebra, but wasn’t a lecture course. I also have some 5 or 10 points of homological stuff I never got exams done for. So all in all, I spent about a year fulltime with only homological algebra (slightly more distributed in time), and a year fulltime with only algebra of sorts that were not explicitly homological in nature.

And as they say, practice does make perfect. I have, from the various lecture courses I took, an intuition for the category of chain complexes, and for the derived category. I have an understanding for the basics of model categories. I have studied Operads and PROPs with Sergei Merkulov, and seen what happens when you take the basic stance that “We want to equate a structure with its free resolution”, and then run for the hills with it.

The other week I was discussing my graduation plans with my advisor, and he asked what my Rigorosum was going to be about. I told him I expected to do it in homological algebra, and he answered that he wasn’t certain that there was anyone available who’d be capable to accurately test my knowledge of the field. He is a group cohomologist, and he outblazes me when it comes to intuition for that – and especially when it comes to the topological notions in the field.

I, however, am comfortable thinking about differential graded modules and dg-algebras, and doing homological algebra with these. And this seems to place me, possibly, as the single person in my state with a good working knowledge of modern homological algebra.

The things I talked about in the post this follows up on are current knowledge. None of it is particularily original, but the presentation is a result of my personal history. You might very well get similar presentations if you ask my course mates from Stockholm University – but then, that school has a very special athmosphere when it comes to homological algebra.

When I got back from T’bilisi, just over a month ago, I had research leads that I expect will end in three different publications.

I was slated with writing one LARP report for a swedish gaming magazine, and a series of various popular mathematics articles for the local student-run mathematics magazine here.

All in all, very many things converged this June/July for me.

It has started paying off though – the gaming article is published, and yesterday I submitted the first of the T’bilisi articles to the Journal of Homotopy and Related Structures as well as to the arXiv.

I now am listed on the arXiv with three papers, out of which one is already published, one is rejected (not unjustly so), and one is just submitted for review.

Note that the name changed for the last paper. I am cheating a very little bit – August 25th, I will marry the most marvelous woman I have ever met, and will – among other reasons for the sake of academic unicity – take her last name in addition to my own.

Aaaaanyway. This is my excuse for having missed .. what is it? three carnival issues?