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Maths Café

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The Kate Bush Conjecture

petegriffin 15 May 2009 19:48 - Last edited by petegriffin on 15 May 2009 19:49
Assistant Director (Secondary)
Did anyone hear the item on Radio 4's "More or Less" (Friday May 15th)?
Apparently Kate Bush wrote a song called "Pi" in  which she sings five digits of pi from the 51st digit onwards - she sings "58231".
This is apparently is not correct and she should have sung "58209".

It was then asserted by Tim Harford, the presenter, that because pi is an infinite non-recurring decimal, even though 58231 isn't correct for that part of the decimal, it would appearsomewhere in the decimal expansion of pi!!

Enter Dr Toby O'Neill from the O.U. introducing us to an early 18th century mathematician Emile Burrell and his notion of a "normal" number and after a fascinating 5 minutes or so we end up with what Tim Harford refers to as the "Kate Bush Conjecture" which is that:
"The sequence of numbers that Kate Bush sings in the song "pi" actualy does appear in pi".
Fascinating stuff.

You can hear it on BBC iPlayer and if you don't want to listen to the whole programme (although the other bits are very interesting too), the "pi" item is from 11 mins in to 15 mins in.
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sallyb 17 May 2009 00:07 - Last edited by sallyb on 17 May 2009 00:12
have you never searched for dates of birth etc in pi?  I have classes fascinated to find out whose birth date comes first - we used the 6 digits ddmmyy. My numbers are at position 323,483.
Kate Bush's number is at position 17,378.

Despite it really not meaning anythng, whoever comes "first" seems to be  really pleased...
There are a variety of websites which will search for you - one is http://www.angio.net/pi/piquery which also answers/explains some questions.

Happy number hunting
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vjosullivan 15 January 2010 13:15
Kate Bush's birthday is 30 July 1958.  There is no combination of these numbers that falls close to position 17,378.  17,378 is the position where the incorrect sequence "58231" actually occurs.  This, too, is entirely arbitrary since the first two digits of this "incorrect" sequence are, in fact, correct.
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brookes 17 January 2010 15:24
I've always thought it true that each and every number combination is "in Pi". Furthermore, if you give each letter a number (1 for a, 2 for b and so on). you could find every word. In fact, every sentence ever spoken, every book ever written, every conversation ever said and any that will ever be said. So... surely the song that Bush sings would be in Pi?
(I feel as though I must have gone wrong somewhere, someone will explain how and I'm about to feel foolish).
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MarkDawes 19 January 2010 07:18
Nice idea, brookes!  Not sure if this has been proved, but it feels like it ought to be true. 
Carl Sagan, in his novel "Contact" has scientists discovering that Pi (in base 11) suddenly consists of only zeroes and ones for a vast number of digits.  When placed in a rectangular array the ones trace out the image of a circle within the zeroes.  This is taken by some characters to be evidence for the existence of a higher power [as in God, not quartics ...]

Presumably we would find it easier to "read" the sentences in pi if it were written in base 36 ?
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sallyb 20 January 2010 19:00
as pi is transcendental we know that its decimal expansion has no sequence repeating, so because it uses all 9 digits then short sequences are almost certain to occur, but  do we know that all sequences are in pi?  Clearly it is easy to construct non-repeating sequences that don't contain every sequence.

for a discussion.

My personal feeling, having studied infinities, is that the existence of some string of numbers of length k, which is not in pi is likely - however there is no way of proving that my number isn't in pi as the task of checking for my number would continue forever... 

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