Category: Music

In two words, Im-possible: The problem with counterintuition

Nearly 40 years ago, we were asked this question at school:

Imagine a string tied around the middle of an orange, in effect forming a circumference. Now imagine another string, this time tied around the middle of the earth, at the equator.Okay? Now increase the length of each of these strings by a foot. Imagine each string now suspended around its sphere as an annulus. Tell me, which string will be further away from the sphere it contains?

And we all answered “the one around the orange, of course”. Or words to that effect. And we wondered why someone would ask such a silly question.

And then we did the math.

  • C=2pi r
  • C+1=2pi R
  • R-r=(C+1)/2pi -C/2pi
  • Or (cancelling out the Cs), R-r=1/2pi

What?!?! How can this be? How can the change in radius be independent of the circumference of the sphere (or for that matter the radius)? You mean that both strings will be the same distance away from “their” sphere? Im-possible.

It didn’t matter how many times we invoked Sam Goldwyn (he was still alive at the time), the answer did not change. No hidden tricks. No small print. No scams involving oranges and geoids. Just the facts. When you increase circumference by X, the radius increases by X/2pi. Regardless of what the original radius was. Regardless of what the original sphere was. One string round a table tennis ball, the other round the sun, same answer.

I tell you, it kept me up nights as a boy, it just didn’t make any sense to me. I had to drill the answer into my head, drag it there kicking and screaming. It took time, but the pain subsided in the end.

And then.

And then I bought two fascinating books by Julian Havil: Nonplussed and Impossible. Books that were tailormade to fit in to that odd space in my library, between Martin Gardner and John Allen Paulos.

And went through all that pain again. From “does not compute” to “im-possible” to “I don’t believe it”. So if you’ve got a similar penchant for mind-masochism, go out and buy the books. Both of them. You won’t regret it.

I need to keep challenging my biases and prejudices, the anchors and frames I cannot see. And books like these help me exercise my mind, they ensure that I don’t reject ideas just because they’re counterintuitive.

Thinking lazily about problem-solving methods

A little while ago I saw this somewhat unusual list of words:

It appeared on the xkcd blag, and Randall shared very little about it: It was in his handwriting, it looked faintly familiar, and he had no idea what it was about. You can see the whole story here.

I whiled away some time just thinking about how I would go about solving it.

That took me back a while, letting me reminisce about problem-solving techniques in general, how I learnt about them, what I found enjoyable about that learning.

For example, I still remember the first time I was presented with the “n” players in a knockout tournament, no ties, how many matches in the tournament question. n was set at 128; some people were doing the traditional 64+32+16+..+ thing, the rest of us had listened to the teacher. He very pointedly said “Think. How many losers?”. And we were ecstatic children, discovering for ourselves the truth that each match produced precisely one loser, and that the tournament needed 127 people to lose….

And so I thought to myself, of all the problems I’d seen where there was a lesson in problem-solving to be learnt, which one had I enjoyed the most?

I decided my personal winner was this one, presented to me in two parts:

(a) There is one, and only one, ten-term arithmetical progression of primes between 1 and 3000. Find it.

(b) Prove that no arithmetical progression of primes, containing eleven or more terms, can possibly exist between 1 and 20000.

I may have got the precise wording wrong, but the salient numbers are correct. See what you think. And if you have similar examples, where you learnt a simple problem-solving technique that stayed with you for the rest of your life, then please do share it.

[Incidentally, I still have no idea what Randall’s list is about. I used a progressive google search approach on the words (where you add one search term at a time and see how the top results behave) and the best I could come up with was “words at the top of successive pages in Animal Farm“. But it feels lame and unworthy. I quite liked one of the suggested answers, that the words were a sequence of captcha words. When I last looked not even Randall had figured it out.]

The rise of the creator class

I was very taken by the launch of SoundIndex from the BBC, which came to my attention today. Why? Take a look at this partial screenshot:

The chart by itself is not particularly remarkable. Not until you take a look at the rubric for the colours under each track, shown as the Power Bar Key.

A good piece of visualisation, I hear you say. Maybe that’s not particularly remarkable either. Not until you take a look at some of the possible implications on distribution models, from a recent Wired article by David Byrne (yes, the Talking Head).

All of which leads to this, also from the same article, well worth a read:

The times, they aren’t a-changing any more. They have changed. It is no longer possible to sustain a situation where overheads and marketing costs take more than half the money from the sale of a CD. The iTunes approach is not necessarily sustainable either, as Byrne points out.


For many years, I have had to put up with the phrase “content is king”, a phrase I personally find irritating, abhorrent, to be classed with words like “audience”. Looking back, I now realise why content was king. Because we’d managed to drive a wedge between creators and their creations.

It’s not going to be that easy any more, separating the creator from her creation.

I think this wedge may have been meaningful in the days of atoms, when copying the creations was not a trivial task, when distribution was valued and had high barriers to entry. Now all that changes, with the internet becoming that great big copier in the cloud, as Kevin Kelly stated so eloquently in Better Than Free.

For a long time now, I’ve been insisting that Jerry Garcia was the father of opensource (as evinced by the Grateful Dead’s enlightened attitude towards taping rows at concerts) allowing . Now maybe that’s coming round full circle. Now maybe it’s time for musicians to take a leaf out of opensource. Maybe we’re going to see more and more of some variant of Creative Commons, where the music is free as long as you don’t make commercial use of it, with all rights belonging to the artist.

When commercial use is made, the artist gets paid. While continuing to retain all rights.

The artist is in control.

Just musing on a Saturday night.

Changing my mind

John Martyn’s May You Never is one of my all-time favourite songs. It has everything: melody, lyrics, the warmth and delivery of a brilliant singer-songwriter, and, in my case, fond memories associated with people who aren’t around any more, in places that aren’t the same.

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Some years ago, a friend told me he’d heard a great version of the song sung as a duet. And I wasn’t having any of it. No way. I wanted my nostalgia my way, felt like sending back the OBE I don’t have, or whatever it is people do in protest nowadays.

And then today. There I was, disturbing nobody, quietly listening to the Mamas and the Papas. And tweeting about it. Bad idea. Along came Halley, tweeting away, disturbing my reverie, letting me know she’d found this gem of a video.

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I was listening to May You Never at the time, so naturally, while dipping my toe into YouTube. I had to look. Only to find this video, containing the duet with Kathy Mattea that I’d heard about and refused to hear.

And this time I heard it. And had to change my mind. What a wonderful treatment. For a wonderful song.

I think I’m going to concentrate on changing my mind a few more times this year. Look to weed out old prejudices with a vengeance. And one of the first things I’m going to do in preparation is to read all the responses to the edge.org question, there are still a few I haven’t finished.

Relaxedly rambling

I’ve been lazing all evening. My older two children are at a concert in Brixton, the youngest is in bed, my wife has her church group over, and I’ve been left to myself. Which is a good thing sometimes, especially when it’s the end of the week and i’ve spent most of it travelling. I like companionable silences. And, occasionally, I even like companionless silences.

So after reading the papers and listening to Gabriela Montero playing Bach (absolutely amazing), I went for a gentle ramble around the web. Started with Christian Cenizal and visualisation, someone I’d bookmarked and written about recently and wanted to investigate a little more. And he led me to this Melbourne tourism video.

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Which in turn led me to wanting to listen more to Joanna Newsom, and on to this video.

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She’s one of these singers you either love or hate. I enjoy her. I first came across her in an ad a few years ago, to do with New York and blackouts and This Side Of The Blue. Her voice is quirky and unusual, it has a Melanie-like quality that combines really well with her harp-playing: I find the effect mesmerising. See what you think. [Incidentally, I’ve just realised that Melanie is over 60 now. Wow.]