Complex numbers and negatives have served humanity extremely well. I suspect that even the most ardent supporters of complex numbers must realise there is something unsatisfactory when they study the method of squaring a complex number. To square a complex number a new concept is introduced. A complex number is squared by multiplying it by its conjugate. The conjugate of a complex number is found by reversing the sign. i becomes –i and vice versa. This allows i to be eliminated when multiplying. Instead of (2 + i)2 = 4 + 4i + i2 = 4 + 4i – 1, it becomes (2 + i)(2-i) = 4 +1. This just smacks of convenience as a way to overcome the problems with negative numbers. Not particularly scientific.
At this stage you might be getting fed up of my rant against negative numbers and be saying to yourself that there is no better alternative. Well, I believe we should find one. This project requires your help. Imagine the benefits of not having negatives.
Being a gentleman scientist, by which I mean an amateur with broad but limited education in many spheres, let me propose a new system of mathematics called Wave Numbers. This system uses the concept of Opposite Values. Negative numbers as quantities of an opposite quality have been used to keep track of economic transaction since red and black counting rods were used for negative and positive quantities in China 2000 years ago. Bhaskara II, during the 12th century, interpreted negative numbers as geometric lines with an opposite direction. It can be seen that these mathematicians were seeking an understanding of numbers based on opposites as opposed to negative.
The name Wave Numbers is used to distinguish from our current number system which will now be referred to as classical maths. Below is the spatial description for Wave Number Line with the superscripts ^ and v standing for Opposite Values ‘Hat’ and ‘V’.
