**know** **it all** » (say)
**no**
(to) **it all** » no, no, *no** **!*** **» nien, nien,
*nien** **!*** **» 999 **!**

In 1927 the French mathematician
Émile Borel ^{1}^{,2,3}
(1871-1956) gave a method for constructing a real number that he dubbed the “**know it all number**”. This real number encodes the answer to all
possible yes/no questions!

Borel’s “know it all number” is the motivation for Jorge
Luis Borges’ ** ^{4}** famous short story

The details of Borel’s
construction are given in the fascinating and very readable article “How Real are Real Numbers?” ** ^{7}** by
Gregory Chaitin

The spirit of Chaitin’s question “How real are the reals?”
is captured in the following Chaitin quote.

*Geometrically* a real number is the most
straightforward thing in the world, it's just a point
on a line. That's quite natural and intuitive. But *arithmetically*, that's another matter. The situation is quite
different. From an arithmetical point of view reals are extremely
problematical, they are fraught with difficulties! ^{12}

1. http://scienceworld.wolfram.com/biography/Borel.html

2. http://en.wikipedia.org/wiki/%C3%89mile_Borel

3. http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Borel.html

4. http://en.wikipedia.org/wiki/Jorge_Luis_Borges

5. http://en.wikipedia.org/wiki/The_Library_of_Babel

6. http://jubal.westnet.com/hyperdiscordia/library_of_babel.html

7. Chaitin, G., “How Real are Real Numbers?”, *International
Journal of*

* Bifurcation
and Chaos*, Vol. 16, No. 6 (2006)
1841-1848.

8. http://en.wikipedia.org/wiki/Gregory_Chaitin

9. http://www.cs.auckland.ac.nz/CDMTCS/chaitin/

10. http://en.wikipedia.org/wiki/Chaitin's_constant

11. http://www.plus.maths.org.uk/issue37/features/omega/index.html

12. Chaitin,
G.,”Epistemology as
Information Theory: From Leibniz to Ω”,

*Collapse*, Vol. 1, 2006 27-51.