Question is, if 'i' (sqrt(-1)) spawned a new field of mathematics - ie complex numbers, is there any way that nullity could be used to solve new problems?

More specifically, now with the 'new found' ability to raise 0 to the power 0 (or divide 0 by 0) is there any way classic attractors or fractal equations that escape to infinity (or zero) be tamed in some way to use nullity?

Not being able to divide by zero never sat well with me.

Nor did the concept of infinity!

But I always felt they went together and you could not have one without the other, I just never had enough credentials to get anyone to listen!

Thanks for the link.

I'll check out the article when time permits...

Perhaps the Circle Inversion Transformation could be useful in some way? Solutions to certain classic problems (e.g. the Apollonius 3-circle problem) can be found by inverting the geometry about a circle. This avoids some nasty divide by zeros and preserves various geometrical properties. For example, lines and circles that intersect before the transformation will intersect afterwards and vice versa. Basically you transform the problem into another spatial mapping, solve it there, and then transform it back.

This is relevant to the divide-by-zero problem because NaN/nullity etc is geometrically related to the inversion of the origin point using an inversion circle centred on the origin. To generalise, X/Y can be obtained by plotting Y and then inverting it using an inversion circle centred on the origin with radius X.

Division by zero of a real number r intuitively results in inifinty (becase you can take zero away from any number an infinite number of times). However it also results in negative infinity (since you can take zero away from -r as well). Inverting the origin about a unit circle to compute 1/0 yields a circle of infinite radius centred about the origin. Therefore the geometric meaning of NaN in the complex plane is not a single point but rather "infinity in all directions" (I think).

I wonder if circle inversion in the complex plane could be used to "tame" some fractal equations? I have generated some fractals using circle inversion a while ago but the results are basically simple 2-D distortions of the original fractal.

I agree that he's not bringing in anything new - he's simply teaching the idea of "NAN" at a lower education level than normal.

My own theory is that:

   zero*infinity = 1
  -zero*infinity = -1
   zero*-infinity = -1
  -zero*-infinity = 1

(just kidding)

Charles is kicking the bare ass of the Mandel and Julia sets recently!  I have high hopes Charles is going to hit upon something huge!

And let's face it, we are getting lots more value for money out of Charles than Michael 'pump and dump' Barnsley...

Come on Charles!!   

The discussion of nullity  I am sure will be of suprise to many ordinary people but of course those who have to deal with the impracticality of some of our rules may benefit from following what  Anderson suggests. I too once laboured under the false assumption that mathematics was a natural element of my world instead of part of a constructed model of infinite possibility space as i refer to it. The constructed arithmetic model of the transreals for computational arithmetic has much to recommend it. However the concept of nothingness emptiness etc is not to be confused with the requirements of a pragmatic computational arithmetic for dealing with distinct valuations. The inclusion of nullity and infinity as fixed entities on or off, in or out of the set of reals is a welcome clarification of the constructed nature of these fractal metrics.

With reference to the imaginary valuation i : it was always an operator which we were taught was a valuation at a primary level. For anything to be a valuation it must be a reference to a perceived value or quantity. The reals are so far our culturally neutral quantifiers as are binary representations of the reals. What we do is to try to devise operators and so methods to map our value exeriences onto the reals. Thus millions of colours are now specifiable by a real quantifier which our machine methodology is able to map onto a screen as a colour value. Like i the nullity is an operator and because of machine methodology we can realise both of these to practical advantage.

How does it affect my notion of reality? It further identifies the constructed nature of that concept and the cultural forces that determine or maintain it.