Principia Primordia: Meditations on the Structure of reality – Introduction pt.2

I’d like to offer a second part of the introduction, and revise some of what I have written previously, as well as contextualise and build upon the conceptual geometries stated. This will be useful for the next sections.

First of all, I’d like to replace polarity with symmetry- as I think that polarity is a subset of symmetry, and not the other way around. So, what are the characteristics of symmetry?

We have chirality, a difference in sameness- when one looks in the mirror, if I am to raise my right hand, it is the left hand of my reflection that is raised. This is known as chirality. A non-chiral or achiral reflection/symmetry would be if I raised my right hand, and my reflection raised it’s right hand too – strange to imagine, but it does occur in some symmetries of nature. I think the essence of symmetry is this difference in sameness- I’ll be using it to build up other base concepts, and I hope the process in which I apply it is intuitive. I’ll give an example and explain further; we are all familiar with the idea of yin and yang, and to my thinking of symmetry, if yin were to look in the mirror, it would see yang. This is not entirely geometrical, but conceptual. The two things are counterparts of the same essence- the same subject and conceptual area. The counterexample of an idea of absolute opposites might be best explained with how LLMs work (though I’ll keep it short); LLMs comprise of many many dimensions in which words and their meanings are mapped in proximity to one-another, with similar concepts being generally closer in one or more dimensions. We asked ourselves the question of what exactly these dimensions represent: in maths, usually a dimension is x, y, z, linear. On other spectrums the dimension might be brightness, with bright being one end, and dim the other. It represents a difference in a certain quality. However, in LLMs, as they are trained on words senses and not concepts, the most efficient way of arranging dimensions is to have totally opposite concepts at either end of the spectrum, which is an interesting phenomenon. For instance, when we analysed it on just one dimension (omitting the rest), we found that the two most contrasting words at the far reaches of the spectrum were bernie sanders and airport. This would be the opposite of symmetry. (This is of course assuming that there is some sort of dimensional order to the distribution of word senses in the model – maybe it’s rhizomatic).

All things can be built from opposites. The symmetry can be reflected along any of the characteristics of the fundemental three, and then from its results, gives a fractal expansion of a conceptual map.

For instance, if we are to apply a chiral symmetry to the concept of itself, we might result in achiral symmetry, or the concept of  anti-symmetry- depending on where we draw the line of symmetry (across the whole concept, or just certain characteristics). This is interesting to muse upon, as difference in itself must be a precursor to sameness; the opposite of opposite is same, but the sameness of same is same- which makes it moot as a starting concept. This is why symmetry, or ‘opposite’ or polarity is such an important foundational concept. Difference predicates sameness. My compadre Deleuze was onto something in the richness of difference.

I would also like to change circular motion to circular self-reference. Fractal might be better labelled multiplicity (opposite being singularity).

The nature of paradox in this framework is a singularity with symmetry and self reference. Consider the sentence: “This statement is false”. If we assume on first pass that it is true, it negates itself by virtue of its trueness, which makes it false, which makes it true, which makes it false… A logical mobius strip. It has a symmetry in true/false, a singular self-contained nature, and a self referential nature in its recursive negation. In mathematics we might apply fuzzy logic, but nature calls it superposition.

Building on a physical spatial paradox – the mobius ‘strange loop’ (as coined by Hofstadter), we can add more spatial dimensions and build Klein bottles.

I might also remark that we should define imaginary Vs real. Imaginary corresponding to a factor of the square root of minus 1 (which also doesn’t work in conventional ‘intuitive’ logic and maths). The imaginary number is often found in equations describing quantum systems, but rather than seeing it as a mathematical tool (that always resolves into real numbers at the result of useful predcitions), I’d like to look at it as a fundamental behaviour of the physical system it describes. Imaginary numbers also correlate to spirals and circular geometries, whereas the real often corresponds to a linearity (3 real linear dimensions of space, x,y,z).

Finally, I’d like to suggest that light holds all qualities, and all can be derived from it: It is linear in it’s singularity start-destination path ‘particle form’, it possesses both chiral and achiral symmetry in its charge-polar EM waves- always orthogonal – and their sine-like nature (a propagating circle), as well as a fractal nature in its searching wave form.

Anyway, this is a loose sort of framework that can definitely be better defined- there may be missing factors, but these are the general conceptual geometries I’ll be using as precepts in my explanation of physical phenomena and the universe. Please bear with me.