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Michael Daum lives in Hamburg, Germany with his wife Constanze and his three children Cosima, Toni and Arthur. He's a fulltime Foswiki developer and runs this consultancy firm to help people unleash the power and fun of wikis.

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The discovery of Nullity, a new number

07 Dec 2006 - 09:41 tagged maths, nullity by Michael Daum

Dr. James Anderson, from the University of Reading's computer science department solved the 1200 year old problem of dividing by zero, which results in a new number called ``nullity''.

So now if I divide something by nothing, nothing will happen anymore, as it is all nullity. Here's the full ``explanation'':

Definition:

Usage:

Nullity was first introduced in ``Representing Geometrical Knowledge'' (Anderson 1997). See also ``Exact Numerical Computation of the Rational General Linear Transformations'' (Anderson 2002) available in full text online. Or simply watch the a video of Mr. Anderson (nichname Neo) explaining it in short on a whiteboard.

So the original publication was in 1997, already 9 years ago. Nevertheless, the new number is still a newcomer compared to all the others. And it will possibly take some time till nullity will be integrated into everyday's electronic devices. A good start would be to translate the ``division by zero'' error message into something like ``can't handle nullity'' in all kind of languages.

Update (08 Dec 2006)

From Book of Paragon: Transreal Arithmetic and Analysis: Two papers have been released. The first paper, Perspex Machine VIII: Axioms of Transreal Arithmetic describes how to divide by zero consistently in a non-trivial way. This shows that division by zero is no longer an error. Amongst other things, the paper explains why the standard model of arithmetic is not valid. The second paper, Perspex Machine IX: Transreal Analysis explains how to extend calculus so that it works with transreal numbers. This paper disposes of various counter "proofs" that attempt to show that division by zero is impossible. The paper ends with a very simple equation demonstrating the possibility of division by zero and challenges the reader to accept it.

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