Friday, 20 January 2012

The Notched Stick

I couldn't find a legally available picture of a notch on a stick for this article so I settled for this picture of the Washington Monument by David Iliff (License: CC-BY-SA 3.0)
Human beings regard their knowledge as rather extensive and generally think they are very intelligent.  There is a vast volume of literature on every subject one could think of.  The British Library which is the biggest library in the world in terms of items held has over 14 million books.  The USA's Library of Congress which is the biggest library in terms of shelf space has over 30 million books.  Along with all the other documents, manuscripts, patents, newspaper and so on the total number of words held is stupendous.

Pretty well the sum total of human knowledge is held in written form.

Computers have a way of representing words.  The most common way is to represent each letter by a number and to hold that number as a binary digit.  Which reminds me of a t-shirt a friend has which says:
There are 10 types of people in the world:
Those who understand binary and those who don't.

But I digress.  Any sequence of words can be represented by a number which is a sequence of digits.  If the decimal point is placed at the beginning of the sequence then that number is a fraction.  So, for example the sequence of digits 521 can be represented with a decimal point at the beginning making it 0.521.  If you take a stick and make a notch in it at exactly 0.521 of its length you can give it to someone else who could carefully measure that position of the notch and decode the number.  So any sequence of letters could be represented by a notch on a stick.  In theory you could take all the literature ever written and create a number.  Admittedly it would be a very big number but a number all the same.  This could then be turned into a fraction and represented by a notch on a stick.

All human knowledge can be represented by a notch on a stick!


  1. Yes, but not new.
    Kurt Gödel came up with the Gödel number in 1931, and that's basically what you are talking about.

  2. Well I didn't think it was new but your comment led me to read up on Kurt and I have now spent two hours being totally sidetracked by interesting mathematical theories and concepts. Distracted from being a depressed attic man so thank you for that :)

  3. Well done :-)
    Now go read "Gödel,Escher,Bach" by Doug Hofstadter. It'll blow your mind :-)

    1. Thank you for the reference. I really hate to admit this but I have a copy bought many years ago. I started it and life temporarily got in the way. Then I had the life wreck and it is not accessible and rotting in a damp garage with rodents. I need a house and enough money to pay the broadband the gas and the food. Then I can get back to reading "Godel, Escher, Bach: An Eternal Golden Braid" by Douglas R Hofstadter.