Pyramid Philosophical

Monday, March 12, 2007

Imaginary Numbers

We have to invent imaginary numbers to make the 'maths' work sometimes. Where 'j=(-1)1/2'. The explanation of such 'fiddle factors' to the learning and inquisitive child in order to convince them they are not being lied to is a betrayal of trust.

Being told that there are no solutions to square roots of negative numbers, but then invoking the concept of 'j'. The loss of trust can be incalculable.

Newton allegedly invented calculus to solve some of the problems he had. Some maths has undoubtedly not yet been discovered and after all mathematics is only an attempt to describe the real world. Mathematics is a collection of 'models' that are held to be not in conflict with each other. Mathematics defines the box. Not its size or shape, but effectively just a (very extensive) set of constraints. Perhaps a single mathematics system exists that is entirely different to the accepted 'model'. But then the concept of mathematics precludes such a different concept. The description that defines the concept of the mathematics-box is accepted as being written in stone. This can be extended as new theorems and ideas are discovered and developed, but every fact must still fit. The shape of the box may be constantly changing, but the only contributors are the mathematicians themselves who define the shape and size. Little ever gets challenged except by other mathematicians. An exclusive group (Catch 22).

Numbers are a human concept and perhaps mathematics isn't the answer. Possibly something is yet undiscovered that will produce a different concept where solutions to currently unanswerable questions may become obvious. Some of those answers that are currently just imponderables: how the universe works.

A single theory. There must be one since the universe does work.

At least it appears to work and if honesty prevailed much that is currently regarded as so definite would be rationally relegated to the 'don't know' box. Being so effectively trapped on Earth, and to where any living human traveller must return in order to stay alive, renders everything an actual and complete mystery.


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