Carnival of Mathematics #44

November 21, 2008

44 is currently a very relevant number, as the historic 44th president will be inaugurted next year. Finally it is a tribonacci number in the sequence 1,1,2,4,7,13,24,44,… where the three previous numbers are summed to give the next.  These are of course linked to the polynomial x^3-x^2-x-1 = 0, but also to the beautiful Rauzy Fractal (shown as an approximation):

rauzy

The Rauzy fractal, the three shapes are similar and together they build the next size up.

 

Now to the posts, and we begin with a news segment.  In Britain the two major mathematics societies, the LMS (London Mathematical Society) and the IMA (Institute for Mathematics and it Applications) are talking about merging.  There has been some debate over this as the two societies have different goals.  The opposition have started a blog on the subject, you can read the case is support here.  More controversy was generated over the strange publications in Chaos, Solitons & Fractals, a refereed Elsevier journal.  Various blogs covered this, but the main story, along with an amusing debate appeared in the n-category cafe.  On a more positive note we had the sesquicentennial of the Möbius strip.  (does anyone outside mathematics use the term sesqui for one and a half?)

Having warmed up we move on to some more serious maths, of different levels.  We start with an example of how knowing maths can help perpetrate reduce fraud, with an explanation of the Luhn checksum algorithm.  We also have the observation from reasonable deviations that a class of 2×2 matrices are isomorphic to the complex numbers.  You can learn how to bound binomial coefficients at the Endeavour, or generate Pythagorean triples at 360.  To stretch your mathematical muscles a little more look for Terry Tao, considering polynomials on finite fields ranging over a finite group.  Technical but interesting.

If you are interested in the culture of maths, you can sample from the ancient to the modern. The mathfactor podcast discusses the Ishango Bone, our earliest record of mathematical thinking from 20,000 years ago, and Curving Normality considers how immigrant children fare in the maths education system.

That’s the hard work out of the way, so its time for some mathfun.   Returning to 360, you can consider a geometric excuse for an addictive game.  Gil Kalai presents a couple of very high quality puzzles, with an elegant solution that is easy to explain, but hard to find.  Another interesting puzzle from Jason Dyer, can be turned into a magic trick, or maybe that should be turned back into a magic trick.  Less thought is required to enjoy Mike Hubin’s Tolkien spoof.

If this list has not given you enough of that math fun, and you want links outside the blogging world Larry Ferlazzo has lists of maths websites and glossaries

To conclude as I began with numbers meaning something other than mathematics, A million good things has a very ambitious project of posting 1,000,000 good things, one every half hour for most of the rest of his life.  He is starting next year and so far only has 30, (15 hours worth) worth lined up.  Lets make sure the list contains lots of good maths!


About my art

November 16, 2008

This piece was originally written for a poster on my art work (shown below).  It had to be shortened, partly as a poster can only have so much text and partly as the font was my own design, so I had to typeset by hand.  This took a long time!

My art work comes directly from my mathematics research, in fact it is hard for me to see a clear line where one starts and the other finishes.  My mathematical work is therefore very visual, playing off the intuition I gain from the aesthetic considerations in pictures.  However, aesthetics should not be seen as something foreign to mathematics.  In fact you will often hear mathematicians refer to work as `beautiful’ or `ugly’.  In a subject where results can see practical use years after they were proved, aesthetics and taste are essential tools.  In fact, even when an area of mathematics does have applications, the reason people choose to study it is often its beauty, rather than its practical use.  

The problem with mathematical beauty is that it can be well hidden.  The language of mathematics requires years of study, almost initiation, to use with any fluency.  Perhaps music gives a good analogy.  Imagine trying to appreciate the genius of J S Bach purely from his written music.  This would require the ability to read music, but also an understanding of the structure of the musical scale, fugues and canons.  In listening, these requirements disappear and one can simply be swept up in the music.  Visual images can play the same role for mathematics, revealing its beauty. 

The importance of revealing the beauty of mathematics (and science in general) is the power of inspiration.  Inspiration, far more than practical applications, has the power to bring people to the subject with the willingness to put effort into learning the more difficult technical details.  In my work I attempt to reveal this beauty, without equations or formulae, and thus inspire people into learning more about mathematics and science.

Poster showing some of my art work
Poster showing some of my art work

Unscheduled Post: Mathematics and Pseudo-mathematics

November 12, 2008

Mathematical language is complicated, in order to make ideas completely precise and rigourous we often make them unclear to each other.  One side effect of this is that it is easy to write technical rubbish and declare that people who say that it is wrong do not understand it.  It can take a lot of work to study something and be able to state with confidence that nothing is going on behind it.  As the volume of mathematics research grows we are increasingly reliant on other people and organisations to say whether something is worth the effort.  One thing that we rely on, despite its faults, is the refereeing process of journals.  To keep things working we need of course to keep discussing with people the important work.  However it is also important to point out failures in the system.

One worrying failure can be editors publishing their own work. Especially when that work appears to be pseudo-science. This might be the case with the journal Chaos, Solitons, and Fractals. Zoran Skoda presented some initially evidence in a comment at the n-category cafe and John Baez followed it up with a full post and more evidence.  There are plenty of comments, my favourite accused the n-catergory cafe of being a character assassin for hire.


Unscheduled Post: Blog Carnivals

November 10, 2008

Blog carnivals are a wonderful idea.  They include an editorialised list of links to blog posts on a given subject.  There is so much out there that it can hard to find new, quality things and this gives a long list that is guaranteed to be at least relevant by a human filter.  

Luckily there is already a well established Carnival of Mathematics, offering many happy hours of procrastination.  The latest is number 43, on the number warrior blog.  The next one will be here, so please submit your articles.  Can you feel the excitement building?


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