Thursday, April 8, 2010

How to make simple things complicated

Today a friend sent me an article from The Mathematics Magazine, April issue with a note saying that there are still people who never heard about crocheted hyperbolic planes.
Here is an abstract:
Drawing a Triangle on the Thurston Model of Hyperbolic Space 
by Curtis D. Bennett, Blake Mellor, and Patrick D. Shanahan
pp. 83–99
In looking at a common physical model of the hyperbolic plane, the authors encountered surprising difficulties in drawing a large triangle. Understanding these difficulties leads to an intriguing exploration of the geometry of the Thurston model of the hyperbolic plane. In this exploration we encounter topics ranging from combinatorics and Pick’s Theorem to differential geometry and the Gauss-Bonnet Theorem.

Well, I was surprised about their difficulties since they have a photo with an actual paper model. This model is made gluing together 7 equilateral triangles at each vertex. It is one of the possible approximations of the hyperbolic plane, not the most convenient one to make and with some roughness, but it give an idea how hyperbolic plane looks. The authors now say that they had difficulties drawing straight line. What is difficult about that? Why don't you just fold your model and you have a geodesic or straight line in the hyperbolic plane?

It is true that this not the way most mathematicians like to describe things, then some artificial,complicated theories are being invented. I have to confess that I did not read the whole article very carefully and I apologize for my ignorance.

 It was not because I think the method I use to explain the straight lines in hyperbolic planes is the best or only one, but because I have lost interest in most of papers in mathematics ( I guess I never had...) published in specialized magazines which are read  (if at all) by some highly specialized others. The Mathematics Magazine is a publication of MAA and is aimed to be more expository type, and this particular paper is aimed to the students. May be students will enjoy it or they will think that simple solutions (like folding a paper to construct a straight line) are not mathematical enough, explanations should be lengthy and with the greatest number of possible theories involved...
Or may be true mathematicians are so appalled that some notions can be explained using crochet that they have decided finally "to put the theory on a strong basis"?

I am happy that I do not have to write any mathematical papers anymore. Once I was sitting with two mathematicians in the famous Tea Room in the Institute for Advanced Studies in Princeton having afternoon tea. Both men are really good mathematicians and I think about them really highly. They both had collaborated on some mathematics, and this collaboration had produced some new result. They both energetically started to discuss in how many different ways they can present it in order to publish in as much publications as possible because each of these publications would have a limited number of readers anyway. I innocently asked - why do you care about the number of publications? why don't you put all of your results together (and they do have a lot) and publish a book where it all will be in perspective and will show all connections. They looked at me like I had sinned in sacred walls of the Institute, and then one of them said: 'A book will count only as one publication, while this way the number will grow significantly. Imagine how big this number will be in my obituary!"
I don't think that at that point I will care what the number is...

Today I was working on a lecture I have to present in June, and found among some notes these quotes from Jacques Derrida:

         I have always had school sickness, as others have seasickness. I cried when it was time to go back to school long after      I was old enough to be ashamed of such behavior.

         Still today, I cannot cross the threshold of a teaching institution without physical symptoms, in my chest and my stomach, of discomfort or anxiety. And yet I have never left school.

Isn't this a normal reaction on too much formalism? Did these experiences made Derrida think of destructivism?


  1. I loved this post and I laughed out loud at the publications story. Maybe it's just that even if simplicity is more insightful and satisfying, complexity is fun for the person who's showing it off?

    By the way, allowing the name/URL option for comments would make things easier--I had lots of goes trying to leave a comment the other day with my Wordpress ID, but couldn't get it to work.

  2. thanks for a comment, Tim!
    sorry for trouble with posting - I'll try to fix it.

  3. Dear Daina - I'm delighted to find your blog - and delighted to see the Coral Reef Exhibition here in Dublin and to find your book in the local book shop. The man told me it was now out of print.

  4. The book is moving toward second printing - I agree - some men would like it to be out of print! :-) But it is not - thanks to such enthusiasts as you!