meeting the magician

I think that the last time I went to see a magician was about 1973, when I saw Ali Bongo at the King's Lynn Festival. All that I can remember of his act is that he made sausage dogs out of balloons; impressive, but scarcely sleight of hand, and certainly not magical. I adore the French word for conjourer--prestidigitateur--which reveals those cunning digits that perform the "magic". And I love the scenes in Cranford that involve the conjurer. (I'm not sure whether or not they made it into the BBC adaptation; if they did, they were in the episode that I missed).

Yesterday, however,I encountered magic of a very different, awe-inspiring kind; and in the most unexpected of places: a maths lecture. (Though maybe the truly unexpected thing is that I should be anywhere in the vicinity of a maths lecture. I think the sigh of relief when I completed my final GCE 'O' level maths paper in 1976 could be heard throughout Norfolk).

I want to try to explain what happened yesterday, but it still seems inexplicable, so please bear with me if I offer you a rather garbled account. (And apologies for the absence of photots, I forgot my camera).

Let me begin with why I was (suddenly) taking an interest in maths... Kettle's Yard is currently the venue for an exhibition about the areas where art and science meet and a friend (waves to Ann, blogless) had tipped me off that some of Dr Daina Taimina's hyperbolic crochet would be on show. Then I discovered that Dr Taimina would be giving a talk and spread the word to fellow KToggers. I was rather scared, to say the least, that the lecture would be all maths and no crochet. (Actually, I might not have gone but I had a bagful of yarn tht I needed to deliver to Ann). So you can imagine my relief when the curator introduced my magician by saying to all assembled "I don't suppose that you imagined that the next hour will be about crochet" (or words to that effect). Dr Taimina, however, quickly spotted that at least 5 of the crowd HAD come in search of crochet, and kept referring to us as "the artists".

So where was the magic? It was in straight lines of yellow yarn, worked in running stitch along crocheted hyperbolic shapes (work with regular increases that occur so frequently that the work will buckle, rather than rest flat). In traditional geometry, working on flat surfaces, the interior angles of a triangle will add up to 180 degrees. But the sum of the angles is far, far smaller on the hyperbolic plane. It was amazing to see such tiny angles, yet sides so obviously forming triangles. Indeed, if you could stretch the sides to infinity, the sum of the angles would be zero. (Needless to say, Dr Taimina has not done quite that much crochet!)

But what has left me speechless is the grid. If, on a flat piece of paper, you have lines crossing each other at 90 degree angles, all regularly spaced, you get a square (graph-paper-style) grid). But do the same on a hyperbolic surface and right-angled pentagons appear. I'm still not sure that I believe my eyes, nor even that I've absorbed the information correctly. Now that is magic!