Taking things to their illogical conclusions

Just listened to last Friday's Front Row, and have found out that the institute of figuring have produced a model of the Great Barrier Reef and it's on display at the Hayward! Apparently the Great Barrier Reef is a hyperbolic surface.

Someone on Front Row (I think someone from the institute of figuring) said that a female lecturer (who wiki tells me is Daina Taimina) invented hyperbolic crocheting when her husband said to her that one couldn't produce physical models of hyperbolic surfaces, and hyperbolic crocheting gave the first physical models of hyperbolic surfaces. Which makes me wonder what M. C. Escher's picture of Angel's and Demons is other than a model of the hyperbolic plane, tessellated by roughly triangular shaped angels and demons. But, even if they were slightly off factually, hyperbolic crocheting is damn cool, and it was cool to hear them talk about it on Front Row. Here is a gallery of crocheted hyperbolic spaces at the institute of figuring.

ed_fortune directed me to the flickr group Song Chart, where pop songs of varying degrees of popularity are represented in graph form.

There are some really witty, pithy, graphs even if they are sometimes quite obscure.

Unfortunately like indexed the ideas are often spoilt by the execution.

It's depressing how many don't understand graphs.

Running with an idea of bob's I posted this.

Each of the seven pieces in tetris are composed of four squares. So is it possible to fit one of each into a seven by four rectangle?

Two weddings in two days. Much too much to much to say, so I'll just leave you with an equation from the second r = 1-sinθ and a poem from the first:


I appreciate the sentiment, but I feel the poet really didn't need to go three stanzas without putting in a full stop, I do need to breathe at some point.

Most of what I do day-to-day involves algebraic manipulation, which is a glorified way of saying shuffling symbols round till they say what you want them to. Everyone who's remotely numerate knows that you can rearrange sums with finitely many terms any way you want:

   1+2+3 = 2+1+3 = 1+3+2 = 2+3+1 = 3+1+2 = 3+1+2.

I knew that problems could occur if you tried to do the same with sums with infinitely many terms, but until last week I didn't realise how badly wrong things could go. Riemann's Series Theorem states that (under certain conditions) you can rearrange the terms in an infinite sum so that, not only does the value of the sum change, but if you rearrange the terms carefully enough you can make it have any value you like. It's one of those counter-intuitive results that that show you how different the infinite is to the familiar realm of the finite, and how careful you need to be with your manipulations if you don't want to risk changing or destroying meaning.

    "When I was little, I didn't realise that you could change a few sounds in a name or a phrase and have it mean something entirely different... Meaning, if it existed at all, was unstable and could not survive the slightest reshuffling of letters. One gust of wind and Santa became Satan. A slip of the pen and pears became pearls. A little interior decorating and the world became her twold an ungrammatical and unkind assessment of an aging aunt in a singles bar... When you wanted someone to say "I love you" approximate assemblages - igloo, eyelid glue, isle of ewe - however lovely, didn't quite make it."
    Lorrie Moore, Anagrams pp129-130.

In this interview Daniel Handler mentions how much he's borrowed from Lorrie Moore. I finished Anagrams late last night, and I saw a lot Handler had stolen. I think I like Lorrie Moore for the same kinds of reasons as I love Handler. They've both got a similar sense of humour, mostly based around playing with words, though the humour in Anagrams is bitterer than most of Handler's and less likely to make me laugh out loud, but I think her writing in general is less likely to be described as "language playing so ardently with itself that it goes blind".
Anagrams is an odd novel (I think it's a novel) and I'm not quite sure what I think of it, but thought I should mention it to any Handler fans reading this. Oh, and I imagine that he's been sighted in a Lorrie Moore's Paper Losses would be of interest.

Feeling I should write more about maths sometime. But am feeling tired so I'm going to cheat and put up something I wrote too long ago for me to bother working out how long ago it was. On the plus side I did have a weekend worth the tiredness I'm feeling now.

Connectedness

There is no path I can trace between us
but no matter how close to myself I look
I find points which are close to you.