More on complex numbers

 I want to write more about why I think the truest form of LLMs must work with complex numbers. 

In real numbers we have vector summations and the goal is to push towards a lowest minima we can find and stay there. It is similar to a man who wants to prove their point and act righteous. To be seen on top, to look smart. Even we make spices in how the behaviour is supposed to be to make it seem more empathetic. But in reality it is still seeking a high degree of optimization.

It is funny how cycles are a part of our being and we still seek that final goal. The place of happiness where everything is right and before getting there, there is impatience and seeking resolution to the problems. But in reality, everything comes with rise and fall. Powerful people go up and down in power and their kingdom flourishes and vanishes, nature has cycles built into it like clock gears spinning with accurate precision and following rules in different speeds, and even us, feeling hungry and needing to wake up and sleep, eat and relieve, and every heart beat is a cycle that is happening after the former cycle.

All these together makes me think why would be able to picture a shape for the meaning with moving towards a single point? To me there must be some circular, spiral element to it and maybe that is why we many layers stacked one after another to make meaning work.

Complex numbers have the element of phase and amplitude in them and operations on them can rotate and change scale which seems more organic to me. The also have the ability to reshape a set of numbers into another shape which lives on a different order of numbers.

There is a hope that amplitude and phase can both encode meaning and maybe even more advanced complex numbers like quaternions can be a better candida for encoding meaning.