Tessellation and concentration in quantized space by Sydney Ernest Grimm

Have you thought about tessellation using tetrahedra?

Dear Sydney Ernest,

very interesting essay. I will re-read it later on. For now some comments:

If we want to enter into a fruitful discussion we need to be a bit more precise in terminology. I'm not saying that there is an authoritative canon defining what exactly means what, but there are long standing conventions helping us to better communicate with one another.

Phenomenon (Erscheinung) is usually understood as that which appears to us and how it appears to us. As regards space the phenomena are of the type 'in', ''near', 'behind', 'under', 'along', 'through', 'around', etc. pp. Also parallax and distance are phenomena. So, phenomenal space is defined by prepositions, adjectives and adverbs. That's why we can operate in this 'space'.

Euclidean space is a theory not contradicting the phenomena. It is reasonable to assume that it exists, but it can never be proved to exist, for it stands in relations of non-falseness with the phenomena. Of course there are other (affirmative) views that assign existence to Euclidean or some other space.

Now, what are you describing in your essay? From my point of view it is neither a phenomenon nor a theory, but a wild speculation and I mean this in a very positive sense! This is how science begins, but it is only the beginning...!

best,

Heinz

Dear SE.,

maybe the trouble with physics is in its text books?

Heinz

I don't have a new essay to submit to the contest. I'm glad tat you submitted one though.

My previous paper discusses the tessellation of space: https://vixra.org/abs/1812.0423

Imagine that the amount of dark energy per metre cubed is a measure of how much a crystal (space) undergoes dislocations and deformations. I tessellate space using tetrahedra. Regular tetrahedra cannot be used to cover 3D space, and so there must be irregularities, and those irregularities give way to dark energy. It's pretty simple.

If you introduce quantization of space than you have to know how it is related to the given physical object, you need a variable density of space.

E/c2 = m = (Pmax - Pmin) x V

see my article here, I did not manage to attach it

https://www.nature.com/articles/s41598-019-48018-2

Dear SE Grimm

A general concern regarding any theory based upon a smallest particle or space: How can a theory that is limited to one slice of reality, say the Planck scale, determine and define the actions at the atomic scale (it should explain this), at the molecular scale (it can do some of this), at the macro-molecular and protein level, at the cellular level, at the ligament and tissue level, at the organ level, at the human body level, at the meteorological and planetary climate level, at the solar, black hole and solar system level, at the galactic level, at the galaxy cluster level?

How can any theory limited to just one slice of this continuum of scale expect to describe and determine the actions and interactions at all these levels?

If you divide up space at, say, the Plank scale, how does this transpose to our scale or to that of stars or galaxies? The proposal is that all space is either divided up only at this tiny scale, or the universe exists only as tiny particles - even when this is not our experience.

How are we to explain, at only the Planck level, the changes in a beach ball rolling down a dune and scuffing on a rock? The (macro) actions are easiest to describe at the level of the beach ball not the Planck level. Do we eschew the simpler explanation for a very difficult and poor explanation of these events? Why would we not expect to have a theory that works at all these levels - especially across these levels, since we experience actions that cross these levels?

We are measuring the universe in thin slices, like measuring only in the plane of Flatland when the universe is three-dimensional.

We have lost sight of what we are attempting to describe (all reality at all scales) - which is likely due to limitations in our tools (mathematical as well as measurement). Without admitting and addressing these limitations, we are going down a rabbit hole.

We need new tools.

Don

Dear Sydney,

Your response suggests you believe the 'basic structure of the universe' exists at the smallest level. That particle physics (or below) is where and only where these structures must exist. However, this presupposes that actions do not move up or down in scale, but all occur or begin at this one level. It presupposes all structure exists at or extends from this one level - when that is not what we perceive, since we perceive structure at all levels.

What evidence is there for all (explanatory) structure to exist at only one level or that (I guess this is your position) all upward structure is a consequence of structure at the smallest scale?

How does this one-directional structure creation (from smallest to largest) explain the actions of a beach ball rolling down a dune and scuffing against a rock? How does structure only at the smallest level account for this activity of movement at our level impacting objects and actions at a smaller level?

It seems far more plausible that structure exists at all levels, that actions at larger levels can impact activities at smaller levels and that physical laws not only apply across levels, but interconnect levels (upward and downward).

What is missing are the proper tools to measure across these levels, the lack of which could give us the impression one level is all we need.

Sincerely, Don

Dear Sydney,thank you for this essay.I am not fully convinced that your initial claim "mathematics is a language to describe reality in an accurate way", is so straightforward. I tend to agree that mathematics is a constructed, creative human activity, but its relation to reality (if there is an independent reality out there) is not so trivial. Perhaps you might also like to have a look at what I discuss in my essay, about the use of different mathematical entities in physics and how this deeply affects the foundations of physics.

Best,

Flavio

Dear Sydney,

Very important ideas, well illustrated. But there are questions.

Undoubtedly, the key question for physics and mathematics is the nature of space and, accordingly, its ONTOLOGICAL structure. Here it is good to recall the philosophical testament of Paul Florensky: "We repeat: worldunderstanding is spaceunderstanding".

I agree: "However, this has consequences because it is not realistic to assume that the foundations of mathematics shouldn't be identical to the foundations of physics."..."In other words, the existence of observable phenomena everywhere in the universe shows that the underlying structure must be build up on identical basic properties."

But in your justification of the basic structure there is no deepest ontology of the absolute forms of the existence of matter (absolute, unconditioned states), their connection with the structure of space (ideal entity). It seems to me that deeper dialectical and ontological ideas are needed here. Therefore, the holistic paradigm should come to the aid of the atomistic paradigm that dominates science (part paradigm). A methodology is needed, based on the total dialectical-ontological unification of matter across all levels of the Universe's being as an holistic process of generation of meanings and structures (material-ideal), i.e., construction (modeling) of the primordial generating (basic) structure: framework, carcass, foundation for the whole system of knowledge, and not just for physics and mathematics. We all need to "dig" together - from "phenomena" to basic concept-constructs, to "noumenons".

With kind regards, Vladimir