Veckans ord: höstack

Denna kalla och regniga årstid utbrister man lätt i ett och annat höstack.


Hope and hops

It struck me that my relation to religion is much the same as to beer drinking: While I see that it clearly is important and enjoyed by many, not least as an excuse for meeting friends (but may get you into fights about which brand is best), possibly may have health benefits under certain circumstances, has been historically very influential, and arguably may even have enabled civilisation, I still don’t quite get why anybody would see it as enjoyable, and suspect it is probably not good for you in the long run, especially as your arguments become increasingly more unintelligible the more you have partaken of it.



Prompted by a student project, I started looking into R today. Well, this is what the usual Hailstone program looks like in R:
hailstone <- function(n)
  while (print(n) > 1) 
    n <- if (n %% 2 == 0) n / 2 else 3 * n + 1; 
I started writing it in a very C-like way, but the functional nature of the language made itself increasingly more apparent as I played around with the code.


Still going strong

During my first course in calculus, Ambjörn the TA was going through whatever it was and I innocently asked “Isn’t this, like, fractal?” He spun around: “Yes, exactly!”, spun back towards the blackboard and proceeded, chalk blazing, to explain how the current course segment was tied to fractals, their implications for geometry and how that in turn related to other branches of mathematics, ever faster and further into ever more exotic subjects while we students could just hold on to our desks for dear life in the storm blast of imparted knowledge. Forty-five minutes later he suddenly made a double-take, checked the time, and with an embarrassed cough noted: “I think we ran over the time a bit there, let’s take the break now.”

During the break Å accused me of setting Ambjörn into self-oscillation and suggested I shut up in the future, lest we never manage to cover what was actually coming on the exam.

Well, I did pass the calculus exams, eventually even the dreaded Theory exam, though that took me five attempts (in no way an exceptional number). Still, perhaps that was more due to diligently doing all exercises and repeatedly reading the books, rather than thanks to Ambjörn’s TA efforts, which, while always entertaining and mind-opening, tended to veer off from the official subject into Deep Maths.

Eventually I became a colleague of Ambjörn’s, whose wide-ranging interests could no longer be contained within either the Department of Mathematics or that of Physics and thus had moved into Computer Science (which at the limit contains all other sciences). Passing his room would often imply getting drawn into impromptu lectures on maths and their relation to everything else in (and occasionally outside) the universe. He even stored some of his parabolic rock-melting mirrors in our lab, though we irreverently ended up using them as towel racks.

Today, Ambjörn was officially retired, though, as is the custom in academia, that simply means the end of salary, but not necessarily the end of research. So, I returned to the Alma Mater for Ambjörn’s Last Lecture, which, true to form, ranged from how to explain what weekday it will be in a million days, over homotopies of snakes on a torus, to how human culture is an integral over time.

I regretted Honeybuns wasn’t there to get some kind of idea of where I come from, intellectually, but the OBCM was there and afterwards we had a nice chat about teaching and geometric modelling over a cuppa.


If this is the last time I hold you

A song that pops up in my head every now and then, but that I hadn’t been able to place. For some reason I thought it might come from a Fame episode, but googling around I eventually found it was actually from the final episode of Secret Army, which in addition to this has the most haunting opening titles of any TV programme I’ve seen (the images played in reverse for the end titles).


Växeln hallå

I would assume it would be easier to confuse the connections between Ipswich and Norwich, rather than Northwich, but I guess Naarich just doesn’t sound nice to sing. When I saw the title, I first assumed it was about someone travelling on train, but the song is instead about the modern social media of its day. Note also the very careful enunciation of the singer, which makes every word of the lyrics come across clearly in spite of distortion high enough to make grown men cry.


Clean lyrics

As noted earlier , well-known songs often have a far older original, so here is a famous Monty Python piece in its 1930s guise:


List of songs about Stockholm

Liza Minelli, in one of her shows, told of how she’d investigated what city had had the most songs written about it and, of course, found it was New York, giving her cause to sing “New York, New York”. Number two was apparently London, so she did a London-themed song as well. I was a bit patriotically incensed that she didn’t even mention the number of songs written about Stockholm. Fortunately others have addressed that issue.


Forgotten lyrics

All too often, and especially with lyrics in foreign languages, I don’t catch the exact lyrics and so I’ve long been humming on this rhythmic piece that goes something something breakfast in London. But, of course Wikipedia has a List of songs about London and halfway through that I found it: “Last train to London”.



Another song that’s stuck in my head: “Song of the Musketeers” from the 1935 version of The Three Musketeers.


The Only-Begotten Children

I’m not the only one to have Only-Begotten Children, but so does Prince Philip, as witnessed by the Reverend Hubert Rumtumtibumbum (starts at 5:00):


Version originale

The Flash animation “Shii’s song” with an up-pitched version of Jennifer Stigile’s recording of “Wind’s Nocturne” was an Internet phenomenon long before the term “viral video” was invented, but here is the original Japanese version.


More 1970s ballads

I’m sure the YouTube comments claim that they just don’t make music like this anymore. Well, why would they? It’s already been made.



Now is the time for the JavaScript version of the Hailstone program:

  function hailstone(seed) {
    var output = "";
    for ( ; 
   output += seed, seed > 1 ; 
   seed = seed % 2 ? seed * 3 + 1 : seed / 2) { output += ", "; }

  function submit(seed) {
    document.getElementById("output").textContent =

  Seed: <input type="text" 
<p id="output"></p>

Put that into an HTML page and it generates the following box: (Try it, it actually works!)