#information geometry

Things I find interesting: I never really heard "information geometry" really exists and that I just made that concept up... After looking more closely at it, it is really the same as in my conception.

The same case was with the concept of feedback loops in chaos theory. Somewhat I didn't really care enough about chaos theory to look it up more deeply. I called them "re-cycling loops", which is actually the exact same concept as the already known 'feedback loops'...

The key why this happens is my decade-long training to calibrate and fine-tune my intuition to accurately simulate the object of focus, similar to principles of deep learning and neural networks.

Intuition is the 'coordinator' in association-based cognitive processing. Associations are 'pop-ups' from the merely subconscious side of cognition. Analogies are a special from of associations in which one reduces the object of focus to the primary main principle, and comparing it with similar principles in 'the database of knowledge' (memory). Association-based cognitive processing has a primarily unstable state, the stability is created and maintained primarily by large quantities of information that are heavily connected with each other. Furthemore association-based cognitive processing is marked by a dispersion of trains of thought into 'parallel channels', which are merely subconscious in linear (non-association-based) cognitive processing. This dispersion often weakens the strenghth of the working memory.

This also relates to the Bayesian coding hypothesis, which states that the working memory can be portrayed as a Gaussian standard distribution.

The non-linearity in the flow of thoughts then leads to self-interference between the parallel trains of thought, and turns the cognitive processes into a chaotic system. This leads to a huge similarity to the way how quantum-based systems operate.

Furthermore I am baffled that a lot of concepts/explanation models I started to create more than 10 years ago seem to be more and more correct the more I understand the underlying principles and the implications of that.

An example is a pappus' conical helix surrounded by a sperical helix (like a spiral system projected onto a horn torus);

This was the model I came up with to somewhat explain the attributes of elementary particles. Unlike in string theory, the underlying 'geometries' are not seen as literal, physical geometries, but rather a partially metaphorical version of that: Information geometry, hence, a form of statistical data.

This data is, to be concrete, a huge collection of previous interaction patterns. In ourse of time and with every new interaction the information geometry gets 'shaped', and the behavior and interaction pattern "solidifies", leading to the attributes of the various elementary particles. This 'shaping' is a result of emergence.

Furthermore, it is said, elementary particles are quanta of information, and yes, this is true in a literal manner, according to my hypothesis. Yet, this concept requires a medium, called "mathematical reality", in which the physical reality is embedded. Mathematical reality can be regarded as an "unknotted network" of information. If mathematical reality loops and knots itself, then, that is tme point where physical reality arizes.

This train of thought led me to what I named "cosmic weaving", which is about weaving sequences of imaginary numbers, creating the "fours states of reality", which relate to the four combinations of real/imaginary structures/processes. (Structure-process-complexes are, in a sense, self-interfering, self-replicating loops.)

Real processes are active interactions, imaginary processes are passive interactions, real structures are physical structures, imaginary structures are mathematical structures. Combinations of these four relate to the four 'states' of information weaving:

Time (imaginary structure, imaginary process), space (real structure, imaginary process), motion (imaginary structure, real process) and matter (real structure, real process)

In this interpretation, matter can be declared as a kind of 'folded spacetime' - just what John Wheeler defined as "quantum foam"...

So..

Understanding fourier transform through the back door haha

I don't know, but putting the pieces together is so fun. Recently I found what diffraction actually is, how it relates to interference, and simultaneously Gaussian standard distribution was stuck in my mind. Interestingly I have been playing with Fibonacci numbers and the result just looks like probability distributions of the double slit experiment/ diffraction-interference pattern. Haha

Maybe I'm just being silly, but it is so neat to find similar patterns all over again and again.

It also fits with the animations I have in my imagination, which might make sense of - yes - quantum mechanical behavior in general. Regarding elementary particles as a dynamical information geometry makes more and more sense the more I dig deeper into the underlying issues.

It might make sense in my concept of 'information weaving' and butterfly progression (self-interference pattern) and might also allow a concept of a certain space-time loop (similiar like ones imagined in loop quantum gravity). It may sound like a fusion of LQG and string theory in some sense. But the only principle I took from string theory was the uttermost basic definition relating to the fractal-like pattern of nestedness/recursion (The attributes of elementary particles have to stem from an inner principle). Unlike in string theory, the "strings" (which are also responsible for the attributes of elementary particles in my interpretation) are no physical elements in my hypothesis, merely a weaving of mathematical information. Physical reality can be regarded as a certain weaving sequence of mathematical information, hence quantum mechanical superposition and entanglement can be regarded as a moment when mathematical reality weaves itself, (self-interference). One might consider information weaving as weaving of imaginary numbers. To follow the beauty and elegant simplicity of the imaginary number system it makes sense that an imaginary mathematical reality can turn into a real physical reality, as every second power of i is a real number.

A model depicting the concept of information clustering in homogeneous butterfly progression;

Information clustering can be regarded as the "gravity" in progressive/dynamical information rendering in information geometry and defines the distribution patterns of information.

This model has 3 major symmetries.

Each overlapping area increases the "density" or intensity of distribution.

I might illustrate a 2d/ 3d distribution pattern later. It will most certainly be similar to the mexican hat with additional orbitals I have posted earlier (see below), which is an interference-diffraction pattern as well as a fractal pattern itself, as it is self-similar in regards of it's a Gaussian standard distribution consisting of nested sub-Gaussian standard distributions.