The Notion Of The Complex-Number System Governing The Laws Governing The Behaviour Of The World — Viewed Through Systemic Functional Linguistics

Penrose (2004: 73):

Over the four centuries that complex numbers have been known, a great many magical qualities have been gradually revealed. Yet this is a magic that had been perceived to lie within mathematics, and it indeed provided a utility and a depth of mathematical insight that could not be achieved by use of the reals alone. There had not been any reason to expect that the physical world should be concerned with it. And for some 350 years from the time that these numbers were introduced through the works of Cardano and Bombelli, it was purely through their mathematical role that the magic of the complex-number system was perceived. It would, no doubt, have come as a great surprise to all those who had voiced their suspicion of complex numbers to find that, according to the physics of the latter three-quarters of the 20th century, the laws governing the behaviour of the world, at its tiniest scales, is fundamentally governed by the complex-number system.

Blogger Comments:

To be clear, the complex-number system does not govern laws that govern the behaviour of the world, just as the quantitative data that is used to generate a map does not govern the map, and the map does not govern the territory it maps.

From the perspective of Systemic Functional Linguistic Theory, the behaviour of the world is first-order (phenomenal) meaning, and physical laws are reconstruals of the behaviour of the world as second-order (metaphenomenal) meaning that includes the complex-number system. Importantly, the laws of physics reconstrue the behaviour of the world in terms of probability (modalisation), not obligation (modulation).