At the end of the day these are just systems of measurement that hold no true value other then as an aid for the person that is doing the measuring. The Taygetans have already stated they don't really like the term density as it implies physical divisions in a reality that is more accurately an undivided continuous full spectrum. A density is just a means of dividing the frequency up into predetermined values to help with human understanding. It is already known that many human mathematical models are false; self-supporting structures based on incorrect premises and assumptions. Our human science is plagued with these structures, many intentionally to muddy the waters as such. Mathematics in many regards has been used a weapon to compromise true understanding of reality. Defining some mathematical or empirical definition of things as the only "truth"; Scienceā¢

Many call mathematics the language of the universe; but considering how easy it is to develop mathematical systems that do not correlate with reality; I never rely on it as a full definition of truth. Personally I don't consider mathematics as a universal language. I see it though as just one of the many faucets of reality that through us as consciousness help define and shape our existence and environment around us, and us along with it.

]]>As the swaruus have said, these aren't the same.

However I'm not satisfied with the way they've explained this (that I've seen).

I have tried to undesrtand this for a while; one of the idea I've tried using to make sense of this is to consider dimensions like "index" and the "densities" as values.

I'm also relying on things I know about numbers as well as on not-known intuitions (not from mathematics that I know).

A crucial notion I rely on, is the fundamental theorem of arithmetic, which states that any number can be written as a unique product of primes (this is enormously significant).

This means that, in a mathematical sense, the prime numbers are the atoms, the building blocks of all other numbers.

Numbers are (initially) understood (defined) as 'succession'. first there's one; next, the after it there's two, next there's 3 and so on.

When I say index I mean to say a direct succesion like this. (this is the defining quality of index). The index is always 1, 2, 3, 4, ... (and so on).

This is an unfounded idea I "discerned" or imagined or hallucinated: that the index is the dimension and the densities are the values.

This led me to make this mapping (paired up list) of dimension (index) => density (value)

1 => 1

2 => 2

3 => 3

but then, here's the kicker

4 => 5

5 => 7

6 => 11

7 => 13

... and so on, the values are the list of all primes.

Four is really just two twice (2+2=2*2=2^2=2^^2). (the last opperation is called tetration)

Therefore, as a "density", four is qualitatively different from the rest. It's the first non-prime number in the succession that are numbers.

I'm not sure why this disqualifies 4 as a density.

This imbues four with a significance comparable to that of two (duality), and three (holy trinities or energy, or whatever).

In the mathematical sense of prime numbers as atoms, four is not a fundamental number, unlike two and three.

Also, mindblowing to me when I learned this (but do not understand why yet), is that the number 5, while typically a prime, is actually the product of two complex numbers: (2+i)(2-i). These numbers are conjugates which is a principlie similar to "duality".

For the same inexplicable reason that drives me to remove 4 from the list of densities, I am driven to remove 5 from this list by folding it up.

Amazingly, the first 3 entries will not change (not ever, me thinks, but to see this I would need to understand mathematically, why is it that 5, 13, 17, and in general, all primes congruent to 1 modulo 4, can be written as a product of complex numbers; Gauss figured this one out; I still haven't.

Regardless, it is the fourth index that must avoid listing the value defineable by a product of prior values.

Now the 5 density is not considered a prime atom (because complex number; i.e. because the imaginary constant).

More weirder intutions about twin primes, and the basic fact that 2 and 3 are the only consecutive primes ever, makes me willing to bet that the first 3 entries of the index(density) => value(dimension) list cannot ever change.

but the rest of the entries from 4-dimension and on, the values get folded. like so:

4dimension => 5,7

5 => 11,13

6 => 17,19

7 => 23. Another kicker. 23 is not a twin prime.

I personally refuse (cannot) go any further without answering some of my own questions. I need to understand better what's up with the modulo 4 congurence and complex-prime factorization. I need to undestand why is it that the densities (as values) need to remain "atomic-prime". And I need to know what the heck is this folding down of taking densities in pairs.

Finally, I wanna highlight that 1 also has a special significance of "self" and the "law of one" notion. In strict mathematical sense, the significance of one is to define the concept of succesion; (the successor of `x` is `x + 1`).

Finally finally, 0 is also extra-special in an even stranger way deserving of its own thread (the significance and nuance of the notion of not-existence or void).

I don't expect this to make much sense to most. But I wanna get it off my chest. I am hoping to better understand what is a "density".

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