#quantaraum

[art-of-mathematics]

is mathematics dealing with absolute truth?

That question is really thrilling to answer, to be honest.

We have to define 'absolute truth' first.

If we consider this "absolute truth" as logical consistency, then I'd like to introduce Gödel's Incompleteness Theorems:

Gödel's Incompleteness Theorems, for instance, state that mathematics will never be complete, because it will always have parts that cannot be proven. Either it is incomplete, but consistent, or complete but inconsistent (in form of being self-referent).

Mathematics cannot prove itself by its own rules, WITHIN its own system.

As for another track of thoughts/perspctive: (Now it becomes an utter mess... And I am sorry for leaping between multiple different conceptions rn. My thinking process IS like what I describe here - a sort of "extraction process" of "truth", or correct and exact thoughts. )

The only "absolute truth" there is, is actually that there is none - as a kind of "structure" at least, as in a "static", non-chaotic linear axiomatic system (Classical logic). When it comes to non-linear axiomatic systems [networks] (inserting chaos theory in meta-math - neat feedback-loop INSIDE mathematics as recursive system itself btw) I would rather refer to such "truth" as a process of oscillating around the most exact reality description - the symmetry axis is hence the equilibrium state and the actual structure of absolute truth. But- this is exceeding the margin now - The absolute state is an information singularity I call "invertium". Reaching that equilibrium causes an 'inversion', a process of inner polarity. That recursive inner polarity IS that absolute truth.

Furtherly, I somehow sense a strange logical twisted mindfuck fusing Gödel's Incompleteness with my concepts on non-linear axiomatic [networks] (Quantum logic, in a sense). (Transcendence of a paradox, huh???)

Also, in regards of these trains of thought, "absolute truth" is what I would call a "superposed entangled state of all truths and lies" - like an information singularity. A state in which an Invertium happens - the indistinguishabilty of two extreme states - 100% dense information can't be distinguished from a 0% one. A singularity is hence, in a sense, an isolated [conservative] system itself, from a rough viewpoint.

What happens in this state? I suppose a desintegration of said information as "self/own complex", and integration of its information parts into its super-ordinate medium. (That is how I interpret entanglement) (The information strangely "dissolves"/integrates.)

Absolute truth bears every partial truth - and all partial truths, well, I would refer here to Feynman's Path integrals, virtual pairs in Feynman-diagrams and statistical mechanics.

And I am sorry for the confusion. Maybe one day I will be able to turn these highly compressed thoughts into fathomable chunks.

(In my upcoming book a lot of the concepts stated above will be some of the primary issues.)

[art-of-mathematics]

chaos theory was my first tattoo.

the first actual theory which changed my life.

my question for you is what is the value of variance and is there a way to predict the variability or the patterns which may form in chaotic systems?

i love your work, it is true art for me

Ohh that is a lovely tattoo!

And I am glad you like my stuff. 👌

I agree, chaos theory has had also a large impact on my -or our, in a way- life.

It is deeply satisfying to see order in chaos, to find elegant simplicity in complexity.

And somehow, for us it has also ensured a feeling of safety and certainty in times of utter lack thereof.

Finding certainty in uncertainty - this brings us closer to your question on variance:

For introduction concepts to answering I can recommend Hermann Haken's stuff on synergetics: self-organization and emergence, which describes that patterns in a system emerge which its elements don't offer themselves. But which patterns, well, my concept about information weaving could explain how information can re-distribute iitself, which might be a part of the answer to your question. Emergence is like a form of "gravity"; quantum gravity, a re-distribution of information density, equivalent in their interpretation to the concept of probabilty intensity distributions in quantum theory. Given that elementary particles are a collection of certain "information geometries" I regard as "complex information weaving sequences", this quantum gravity interpretation is about the distribution of information density in its weaving patterns, and, this is a major leap of thought: The other side of quantum gravity brings us straight to the issue of Navier-Stokes and turbulences, which are, per my interpretation, complex interference patterns, still obeying given 'symmetries' I regard as "butterfly clones" - pairs of possible anthitetic states. (Could also be related to virtual pairs in Feynman diagrams) In a way these turbulences are feedback-loops. The conversation of energy, as in Netwon's second law, "Every action creates a reaction", becomes non-linear, and hence probabilistic and chaotic. And well, this brings us to non-linear causal networks and quantum logic.

Iterative approaches.

And additionally, currently I develop an algorithm that tries to do that - how to 'tackle chaos to unravel itself' - it's a recursive iterative combinatorial approach and highly adaptable to the input you feed it with.

So, to summarize my answer: Predictions might be possible, but I can't say to which degree of exactness and accuracy. Yet, I "sense" a way, and it is primarily "imitating the chaos you want to unravel" - and letting these, the object of study and your imitation of it, interact - somehow you also use self-reference as tool. It's like you throw that chaos in a view between mirrors and it dissects itself.

Lol.

That is literally what happens in LASERs - they are a result of self-organization.