14 Jan 2011 @ 00:51, by John Grieve
The Contradictions of the the Imaginary Plane, and the Real as a Solution to the outstanding Problems of Chaos Theory
In the past I have put forward the view that Mysticism and Science need to be unified in the quest for an enlightenment that creates something new in integrating the complementary parts of what already exists.
To this end I am offering the idea that mathematics offers the bridge between these hitherto separate and apparently unbridgeable realms.
There are in my opinion serious contradictions in the concept of imaginary numbers and their representation in real and imaginary planes such as the Argand diagram. I link this to an analysis of the situation that simply squaring such imaginary numbers creates the reality of the non-linear which is an essential characteristic of Chaos theory. When we take into account that the population linear equation and the Mandelbrot set owe their complexity and unique features to the simple act of squaring a relatively basic complex expression, we cannot but realise that it is the very same act of squaring any simple complex number that reveals all the underlying contradictions of the real and complex planes.
In the Argand diagram representation of a complex number, for example A iB, the real number A and the imaginary number iB are complementary which can be converted into each other by the simple act of squaring. Thus 3 4i squared becomes =7 24i which result is completely counterintuitive and if attempted in the reverse order uncalculatable. Added to this is the built in paradox that whereas x,y in a co-ordinate Cartesian system denotes a point in the real positive plane, A iY denotes a complex number which may appear to be a point but in fact 6,7 is a pair of points whereas A iB is a complex number and One point. There are many problems connected with this, and it is well known to be paradoxical.
Furthermore, many people believe the mandelbrot set to be the most complex mathematical entity in the universe. If indeed this is so, then surely it and all these connections have a powerful spiritual import. Again, this Mandelbrot set is created simply by squaring and iterating a relatively simple complex expression.
It is my belief, considering other such entities as elliptic curves and modular forms with obvious relevance to the complex plane, that a spiritual presence is hinted at here. Unifying Science and Mysticism involves certain compromises. It is not conceivable that Mysticism would ever give up its belief in the spiritual but it is possible and even likely that Science will re-embrace the non-material after centuries of agnosticism, atheism and gross materialism. Therefore I have no hesitation in putting forward the idea which is not entirely unique to me, that all these things such as complex plane,complex numbers, Mandelbrot Set, modular forms, and their equivalent elliptic curves are spiritual entities, even things like angels, higher powers, cherubim and seraphim. If this be accepted then some people might believe that goddesses and gods and even demons could be so connected.
In conclusion If Science and Mysticism are to be re-united then this is one way to do it.
|
|
