Do you know about Metamath? “It is a tiny language that can express theorems in abstract mathematics, accompanied by proofs that can be verified by a computer program. This site has a collection of web pages generated from those proofs and lets you see mathematics developed in complete detail from first principles, with absolute rigor. Hopefully it will amuse you, amaze you, and possibly enlighten you in its own special way.” Fascinating. You can even LISTEN to proofs!



Bulgarian Solitaire

Today’s new random mathematical discovery: Bulgarian solitaire. It isn’t what your Bulgarian aunt might think it is. It is actually a card game introduced by the famous polymath and mathematician Martin Gardner (1914- 2010). If you don’t know who Martin Gardner was, read his obit.  This year would have been his 100th birthday.

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Questions that UK universities would rather not answer

Below I repost an article in Times Higher Education today. (the long quote) Reading this while sitting in the Free University in Berlin, having done about 25 interviews with young academics here in the past 2 months, is a surreal experience. UK discourse is so much more about money, plain and simple. Wage. Fair pay. The magical figure of 9,000 fees (which supposedly pay for the university’s expense for each student). In Germany, education is public and essentially free (bar a small administrative fee of a couple hundred Euros per semester). Interestingly, quite a few of the postdocs and PhD students who teach here didn’t really talk about how much they are paid. They aren’t paid for each class they teach – instead teaching is part of their general research contract, and is seen as an important part of, so to say, a community service, and part of the life of a young researcher. I think – though I must check the figures – German PhD students and postdocs who teach get less money for teaching, than we do in the UK. But in the UK teaching is decoupled from your life as research student, because it is paid separately. A couple of my interviewees in Germany said that they teach because they enjoy doing it and that you can ask to teach, but not everyone does. I haven’t met anyone who hates teaching yet. Whereas in the UK, teaching seems to be more of a chore.

In a nutshell, my impression is that teaching is more integrated into the life of a researcher in Germany, than it is in the UK. And that academia is less marketised/neoliberal/reduced to money, while at the same time the idea of a “public university” is more alive in Germany than in the UK.  And that – provided this is true – the reason for this is partly in the different organisation of teaching, research and university finances.

I really want to know whether this impression I have is true or just because I’ve spoken to a small number of people. Any thoughts?

So here it is:

“Last week, chancellor of the exchequer George Osborne refused to answer when a seven-year-old boy asked him “what’s seven times eight?”

He was widely ridiculed, but are there any tricky questions that you dread potential students asking when they pay you a visit on open day? Well, you should get your answers ready, because prospective university students are being encouraged to ask difficult questions as part of a University and College Union campaign for greater transparency in higher education, launched today.

The union has produced a list of 10 questions it wants would-be undergraduates to ask. UCU general secretary, Sally Hunt, said that students were “bombarded by information these days”, but that so much of it was “just advertising bumf”.

“We are encouraging students to ask the questions that universities would rather they didn’t,” she said. “We need far greater transparency in the higher education sector and prospective students should exercise their critical capacities even before they join a university.”

The 10 questions universities don’t want to be asked

  1. How much of my teaching will be given by staff employed on zero-hours and temporary contracts?

  2. What is the student:staff ratio at the university?

  3. Does the university pay the living wage to all staff it employs, including staff on casual contracts?

  4. If I take a job working at the university while I am a student will I be paid the living wage?

  5. Are the open day guides who show me around paid the living wage?

  6. What is the ratio of the vice-chancellor’s salary to the pay of the lowest paid member of staff?

  7. What will the university do if proposed cuts to Disabled Students’ Allowance are implemented in 2015?

  8. Does the university want to see tuition fees rise above their current maximum of £9,000 a year?

  9. Does the university believe that student loans should be sold to a private company?

  10. What would this university do if the terms of their students’ loans changed for the worse after they had started their course?”

Jigsaw puzzles. (a post not about mathematics)

Warning: this is not a post about mathematics. But it might fit into the jigsaw puzzle in the end, who knows!

You know what happens when you are making one of those jigsaw puzzles?

Of course you do, you spent your childhood doing those. I did as well. I only had a couple of ones with 1000 pieces, so I did them over and over again. I adored the feeling of assembling a story, even the same, one, out of 1000 small, tangible, concrete, cutely shaped individual pieces none of which bore any resemblance to the final picture. I would keep the ready picture for a few days until it started getting dusty or it was getting in the way too much, and then break it up into pieces and put it away in its box until the next weekend. This was often tomorrow.

But I digress. What i wanted to say was this: when you are making such a humongous puzzle, the board seems huge, twice as big as it should be or more, and all the pieces don’t fit. There are moments of desperation and triumph, of visual aesthetics, of ambiguity and choice. Jigsaw puzzles to me are one of the most beautiful sensory and mental experiences in the world. And then at some point towards the end, when the picture begins to take shape, the pieces suddenly fit and areas which appeared remote and disconnected, neatly tesselate and intertwine with each other. Suddenly everything fits on the white plastic board which my mother found somewhere in the street once and cut it up into two pieces for me, one for a small puzzle and the other for a larger one. I am the same scrounger as my mum. I walk in the streets picking up various bits and pieces, I love flee markets and second hand shops and pavements. I am a “Sachensammlerin”, like Pippi Longstocking.

But I digress again. You know how in the beginning, and also for a whlie longer, all the squares of the puzzle don’t fit, and it’s a big mess, and you have no idea where you are going, but it’s so marvellously disorganised you want to prolong this time forever and not complete the puzzle. I love doing puzzles slowly, bit by bit, savouring every pair of fitting opposite lines. Letting my eyes glaze over the pieces to imagine the picture shaping up in the background. Touching the different shapes, classifying the pieces into similarly shaped and seeking out the odd ones. The odd ones, they are my favourites. I love it so much I often stop in the middle of it, just before I’ve found a mate for a certain piece, just when I am on a wave of finding many fitting pieces. I want to slow it all down, cut the moment in half, stay suspended in mid air beween the first piece and ne of its four long-lost soulmates. Some pieces have fewer than four and others more. But most have four, it is the jigsaw piece nature to have four mates. Just like the flowers of the lilac: they usually have four petals, but if you look long enough, you might find one with only three, and polyamorous ones with five or even six petals. When you find a lila flower with more petals, you must eat it and make a wish. If you find one with less, make sure to forget about it quickly because it is bad luck. Once I found a lilak flower with seven petals. I ate it, of course, although i suspected that pollution from the local oil plant Neftochim might have been the cause.

But I digress again. When you’re doing a large puzzle, the pieces don’t fit on the board just yet. But if I could decide how things go, my puzzle would be so large that I would never quite figure it all out to the last bit, and there would always be mysteries and hidden links between disparate pieces. Berlin is exactly a that sort of a puzzle.

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Gender and maths

One fascinating feature of the contemporary German language is its attention to gender. I don’t mean just that words necessary must “agree” with gender in the grammatical sense, but also that the abstract person tends to be carefully addressed as “She or he” and also the endings of words are carefully tailored to reflect both genders, and more recently, also multiple genders (I’ve been told that you could write Physiker/innen or Physiker_innen, where the / or _ signifies “all others”). Here is the example that prompted this post: the title of a course in mathematics for physicists at the TU-Berlin

Mathematik für Physikerinnen und Physiker IV

It would be interesting to read something about the history of how German became gender aware. For now all I know is based on observations [and my own improving, but still very far from good, knowledge of German].

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“Speak Slowly, We are German”

I’m posting this because I’m in Germany doing interviews, and somehow it feels very relevant. It’s a sweet example of a German-English “Lost in translation” conversation. I’ve often found that when speaking between languages, when one or more of the speakers aren’t native, sometimes more truth shines through the cracks than in the intricately constructed, safe-from-losing-face, faultless expressions of native-speakers.

“Speak slowly, we’re German.”
“What’s your favorite thing about her?”
“…. she’s there.”
“When did you most appreciate her being there?”

He made a slightly puzzled expression, then turned to his wife and started speaking in German. She looked up at the sky for a second, then said: “He is island in my life.”

Found at the Facebook page “Humans of New York”




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Friday 13, 3:14

It’s Friday 13th, it is raining and I have no umbrella, an interview I was hoping to do today fell through, and I couldn’t go to the annual von Mises lecture today because I hadn’t registered in advance. (so confusing, this year it is on 13 June 2014, and last year it was on 14 June 2013)

On the plus side, it’s 3.14 πμ and I’m having coffee (or is that co-ϕ?) in the π-Building of the Free University of Berlin. How cool is that.

Das π-Gebäude der FU-Berlin.

Das π-Gebäude der FU-Berlin.

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A computer passed a Turing test!

Yesterday (which was a public holiday here in Germany) I was so excited when I caught a glimpse of a Guardian article which claimed that a computer had passed a Turing test for the first time. Today (which is no longer a holiday, so I should be reading more serious stuff, but this piece news was too exciting to let pass by unnoticed) I read a better journalistic summary in the Vice magazine of what actually happened. Of course, the Turing test is itself is not stable unobjective because the measure of success is a computer being able to fool a jury of human interrogators.  Turing wrote the following in his 1950 paper (quoted in Vice, you can read Turing’s original paper here):

We now ask the question, “What will happen when a machine takes the part of [the test subject] in this game?” Will the interrogator decide wrongly as often when the game is played like this as he does when the game is played between a man and a woman? These questions replace our original, “Can machines think?”

As Vice author Martin Robbins point out, “the key words here are “reliably” and “often.” Turing didn’t ask whether a machine could ever, on a single occasion, convince a human judge that it too is human; he asked whether a machine could do so reliably. “

So, the jury is still out… still bloody exciting, though!

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