The Densities

[christx11]

With the "Protection is increased now!", and all of the recent craziness for September 2025, I thought I would give this a try.

I would like to ask a question about the Densities.

I presented a document to the forum in the thread 'Some comments on information theory' back in April of 2022.

Post in thread 'Some comments on information theory'

Apr 3, 2022

The problem is with your presentation of the results. In mathematics we have definitions and theorems and proofs. Can you condense your results in a theorem, clearly stated, and a proof, clearly written? Then perhaps it will be readable.

Thank you. I will try

Here is my attempt to be more clear. I do not have access to a lot of published sources, so I have tried to use a math paper template for organization and logic, but the post/paper is mainly observational. One of the main intentions of this paper is to basically demonstrate how prime numbers are related to many...

• christx11

• 

This was a very strange experience, basically because of the over the top response from 'Cleopatre VII', then the complete ignoring of me as if nothing ever happened, and then the eventual apparent illness and disappearance of 'Cleopatre VII'. A very strange sequence of events.

I tried to revive a discussion in the same thread, but failed to be able to communicate mathematically with Ark. I do not have the 50 to 60 years of academic training to communicate properly and I do not know how to engage Ark to rollback those reinforced mathematical brain pathways to his 16 year old mathematical mind.

My construction of the densities only requires simple math, addition, multiplication, sets, series, geometric series. In fact all it requires is Euclid's unique factorization theorem and the Sieve of Eratosthenes. It makes the densities foundational/fundamental, possibly even first principles. It means the densities and duality, physicality and consciousness, are foundational and fundamental even in mathematics.

I do not want to rehash every aspect of the last six years of my trying to communicate this idea of the densities. You, the C's, are aware of it all. But for anyone that wants to ask a question, I will gladly attempt to explain. I have never even called my construction of the densities, "the densities", until my last post in April of this year (Apr 29, 2025 Some comments on information theory). In the 2022 post and upload of my construction document I listed about 30 session excepts that comport with my construction of the densities, but I called them levels, as I hoped someone else would see the parallels between my ideas and all of the session excerpts describing gravity as a "binder", "the missing link is earlier in the process", "you are going to have to put the puzzle together from many pieces", "the undulating matrix mosaic", "all of creation, of existence, is contained in 1, 2, 3!!!', "the key to quantum jumps is always in discovering "new" mathematics", [Geometry gets you there, algebra sets you "free."], [are you certain these "definitions" you speak of are not limited?], the densities 1 thru 4 as 1/2 material and 1/2 non-material, density 4 as variable, densities 5 and 6 as completely ethereal, Di/bi/double, bilateral dual emergence, and on and on. Since 2022, I have found probably an additional dozen or so session excerpts that also comport.

This post summarizes most aspects of my idea for the densities.

Post in thread 'Some comments on information theory'

Apr 30, 2025

@christx11, I have been reading your posts with a great interest, because I sometimes do some algebra in order to keep the mind stable. I wanted to ask you a couple of questions about algebra work / maths.

I think that the C's hinted at the study of basic algebra/math as positive. I would like to ask you about the "bridge" that math allows. I am having hard times than to translate how algebra/math could be useful. Well, more technically, I am not able to bridge any form of "cosmical knowledge" after having been doing algebra.

I am having hard time, thus, to be able to bind...

• christx11

• 

And here are the Sieve of Eratosthenes linked posts:

The Sieve of Eratosthenes - Backing Up

The Sieve of Eratosthenes - Backing Up

Math, Extraordinary claims, Extraordinary evidence

timefree.blogspot.com

The 'The Sieve of Eratosthenes - Part 2

The 'The Sieve of Eratosthenes - Part 2

Math, Extraordinary claims, Extraordinary evidence

timefree.blogspot.com

In my summary post: Some comments on information theory,
I state "I think the densities are simple, I think they are fundamental, and I think they are sets." So my question is, "Are the densities simple, and fundamental, and are they sets, as I have put forth in the related posts?"
If I am right, then it changes math, it changes science, it changes religion, it changes history, it changes everything.

I will be shocked if the answer is not affirmative.
I think everyone else will be shocked if the answer is affirmative.
I would like to find out who is shocked.

 

[John G]

With the "Protection is increased now!", and all of the recent craziness for September 2025, I thought I would give this a try.

I would like to ask a question about the Densities.

I presented a document to the forum in the thread 'Some comments on information theory' back in April of 2022.

Post in thread 'Some comments on information theory'

Apr 3, 2022

The problem is with your presentation of the results. In mathematics we have definitions and theorems and proofs. Can you condense your results in a theorem, clearly stated, and a proof, clearly written? Then perhaps it will be readable.

Thank you. I will try

Here is my attempt to be more clear. I do not have access to a lot of published sources, so I have tried to use a math paper template for organization and logic, but the post/paper is mainly observational. One of the main intentions of this paper is to basically demonstrate how prime numbers are related to many...

• christx11

• 

This was a very strange experience, basically because of the over the top response from 'Cleopatre VII', then the complete ignoring of me as if nothing ever happened, and then the eventual apparent illness and disappearance of 'Cleopatre VII'. A very strange sequence of events.

I tried to revive a discussion in the same thread, but failed to be able to communicate mathematically with Ark. I do not have the 50 to 60 years of academic training to communicate properly and I do not know how to engage Ark to rollback those reinforced mathematical brain pathways to his 16 year old mathematical mind.

My construction of the densities only requires simple math, addition, multiplication, sets, series, geometric series. In fact all it requires is Euclid's unique factorization theorem and the Sieve of Eratosthenes. It makes the densities foundational/fundamental, possibly even first principles. It means the densities and duality, physicality and consciousness, are foundational and fundamental even in mathematics.

I do not want to rehash every aspect of the last six years of my trying to communicate this idea of the densities. You, the C's, are aware of it all. But for anyone that wants to ask a question, I will gladly attempt to explain. I have never even called my construction of the densities, "the densities", until my last post in April of this year (Apr 29, 2025 Some comments on information theory). In the 2022 post and upload of my construction document I listed about 30 session excepts that comport with my construction of the densities, but I called them levels, as I hoped someone else would see the parallels between my ideas and all of the session excerpts describing gravity as a "binder", "the missing link is earlier in the process", "you are going to have to put the puzzle together from many pieces", "the undulating matrix mosaic", "all of creation, of existence, is contained in 1, 2, 3!!!', "the key to quantum jumps is always in discovering "new" mathematics", [Geometry gets you there, algebra sets you "free."], [are you certain these "definitions" you speak of are not limited?], the densities 1 thru 4 as 1/2 material and 1/2 non-material, density 4 as variable, densities 5 and 6 as completely ethereal, Di/bi/double, bilateral dual emergence, and on and on. Since 2022, I have found probably an additional dozen or so session excerpts that also comport.

This post summarizes most aspects of my idea for the densities.

Post in thread 'Some comments on information theory'

Apr 30, 2025

@christx11, I have been reading your posts with a great interest, because I sometimes do some algebra in order to keep the mind stable. I wanted to ask you a couple of questions about algebra work / maths.

I think that the C's hinted at the study of basic algebra/math as positive. I would like to ask you about the "bridge" that math allows. I am having hard times than to translate how algebra/math could be useful. Well, more technically, I am not able to bridge any form of "cosmical knowledge" after having been doing algebra.

I am having hard time, thus, to be able to bind...

• christx11

• 

And here are the Sieve of Eratosthenes linked posts:

The Sieve of Eratosthenes - Backing Up

The Sieve of Eratosthenes - Backing Up

Math, Extraordinary claims, Extraordinary evidence

timefree.blogspot.com

The 'The Sieve of Eratosthenes - Part 2

The 'The Sieve of Eratosthenes - Part 2

Math, Extraordinary claims, Extraordinary evidence

timefree.blogspot.com

In my summary post: Some comments on information theory,
I state "I think the densities are simple, I think they are fundamental, and I think they are sets." So my question is, "Are the densities simple, and fundamental, and are they sets, as I have put forth in the related posts?"
If I am right, then it changes math, it changes science, it changes religion, it changes history, it changes everything.

I will be shocked if the answer is not affirmative.
I think everyone else will be shocked if the answer is affirmative.
I would like to find out who is shocked.

I think the problem I had was it seemed like countable and uncountable infinities were too mixed together by an equal sign. Also number theory/infinites related to Clifford algebra periodicity and branching universes and Grothendieck universes I can handle for physics but you kind of have too much number theory for me to fit with physics. At some point you have to be able to see particles/spacetime in the numbers.

 

[christx11]

I think the problem I had was it seemed like countable and uncountable infinities were too mixed together by an equal sign. Also number theory/infinites related to Clifford algebra periodicity and branching universes and Grothendieck universes I can handle for physics but you kind of have too much number theory for me to fit with physics. At some point you have to be able to see particles/spacetime in the numbers.

I am not even going there (At some point you have to be able to see particles/spacetime in the numbers). Ark keeps wanting go there also. This is 2000 years before particles/spacetime. It is just simple addition and multiplication of prime numbers and there powers. That's it. The missing link is back there, not out there in Clifford algebras and wanting to build on someting that already exists. This is new, it is simple but it is new mathematics that does not exist in the texts, but it is silly that it doesn't.

Just the idea of the limited definition:


That last constraint, "where a finite number of the n_i are positive integers, and the others are zero", is the limiting condition and I get it. It is necessary because the definition is specifically for natural numbers (positive integers). But, all natural numbers (positive integers) can still be created when removing that constraint. It is just that when you remove that constraint, a second set of numbers is also created, a set where all members/elements have infinite factors.

The objective observation is that there are countably infinite prime numbers. The objective observation is that each term (prime number) can have either 0 or a positive integer choice as an exponent value. Those two observations taken together simultaneously creates two parallel sets. A set where every member/element has finite factors and a set where every member/element has infinite factors. To this day no one has asked what are these other numbers. The thrid statement, "where a finite number of the n_i are positive integers, and the others are zero", is the limiting factor and it makes us and our math purely STS. Why STS? Because the veil is still intact. After 2000 years we still see only what we wish to see, the finitely factored set. This in iteself should make one want to ask my question,

And if all of our mathematics is based on a foundation of seeing only what we wish to see, then so is our physics, and so is our engineering, and so is just about everything else. We are more STS than we even realize.

 

[christx11]

======================
Session 23 April 2022
======================
Q: (L) Alright. I guess we'll start with questions. Honey, you can start.

(Ark) Yes?

(L) Yes.

(Ark) What are densities?

A: States of awareness in interaction with information.

Q: (L) Does that mean the state of awareness interacting with the information somehow affects what is "real" to use a loose term?

A: More or less.

Q: (Ark) Awareness of whom?

A: Consciousness that is capable.

Q: (Ark) I don't understand. Which consciousness? Whose consciousness? I don't understand.

A: Wave reading consciousness units.

Q: (Ark) Where is this wave reading consciousness unit? Where is it?

A: You are one.

Q: (Ark) It means densities are totally subjective, or is it objective?

A: Both.

Q: (Ark) How is it objective? In which sense? How is it objective if it is related to wave reading consciousness unit. Wave reading consciousness unit is subjective, so how can densities be objective? Physics needs objectivity.

A: If the wave reading consciousness unit aligns with the consciousness of the field, then the perception is more objective than subjective.

Q: (Ark) What is consciousness?

A: Life.

Q: (Ark) What is life?

A: Consciousness.

Q: (Pierre) It's getting circular.

(Ark) What is information?

A: All.

Q: (Ark) Can physics describe densities?

A: Yes

Q: (Ark) How?

A: Algebra.

Q: (Ark) What kind of algebra?

A: Simple.

Q: (Ark) What is the relation between densities and dimensions?

(L) They've already answered that question. That's in the transcripts.

(Ark) Yeah but there is no answer for that.

A: Dimensions are a human construct we have used as there are no better available terms.

Q: (Ark) But algebra is also a human concept, yes?

A: Yes

Q: (Ark) Everything we use in physics is a human concept, yes?

A: Which is why you are having so much confusion.

Q: (Ark) But algebra is using dimensions. It's not a human concept. It's an algebraic concept. And we need dimensions if we want to use algebra.

A: Yes

Q: (Ark) How many dimensions?

A: Infinite.

Q: (Ark) Are these dimensions related to space and time?

A: Yes

Q: (Ark) But space is 3-dimensional. Where is the rest of the infinite dimensions?

A: Many iterations.

Q: (Ark) Many iterations... Iterations of what?

A: Space and time.

Q: (Ark) Does it have anything to do with quantum theory or not?

A: Very little, actually.

Q: (Ark) Does it have anything to do with Einstein's theory of gravity?

A: Even less.

Q: (Ark) So, with which part of physics it has to do?

A: Modern concepts do not define as such.

Q: (Ark) Can you please explain it, this sentence?

A: There is no relevant construct that you can name or mention from your modern terminology.

Q: (Ark) What about ancient terminology? Were there such concepts that have been forgotten?

A: Possibly.

Q: (Arky) No clue? What concepts would do? If not ancient, if not modern, then what? No hope? Hmm. Okay, I am done.

(L) Next?

A: If the wave reading consciousness unit aligns with the consciousness of the field, then the perception is more objective than subjective.

It is a very difficult thing to contemplate, that possibly our mathematics is not aligned with the consciosness of the field.

 

[BlueKiwi]

And if all of our mathematics is based on a foundation of seeing only what we wish to see, then so is our physics, and so is our engineering, and so is just about everything else. We are more STS than we even realize.

I'm no mathematician, or physicist but from what I know from music, and what the C's have said about the number of densities I would conclude that the universe is in "Base 8" or octal.

I few months ago I wrote a program to generate the first 300 primes, then convert them into base 8. I then fed that list into Ghat GPT and asked it to find some pattern, since the C's mentioned "AI" is good ar finding patterns in things like this.

Wishfully thinking, I asked it to find the next number in that sequence. It guessed wrong, so I gave it the next 200, and it demanaded to know how I knew the next 200, and how I was calculating them.

 

[Moine]

And if all of our mathematics is based on a foundation of seeing only what we wish to see, then so is our physics, and so is our engineering, and so is just about everything else. We are more STS than we even realize.

More like everything else that has been, is, and will be forevermore, so long as humans keep adhering to systems of thought and dogma, which are quite certain of themselves. If you think that a domain of human knowledge can't be "full of itself", well you haven't seen physics with its Silly String Theories.... This is what they do academically by the way:

While your quantum physicists are busy shooting atomic particles at each other, blowing them up, and watching all the parts disappear into nothingness, their issues with the whole Unity thing were solved ~150 years ago, at least by moderns.

From Session 11 August 2018

Q: (Ark) Yeah, but I didn't finish. [laughter] So, uh...

(L) What's the question?

(Ark) The question is that there are 5 exceptional Lie groups which are being used for a long time to unify physics, explain gravity using String Theory, branes, multiverses, and so on. People are using these exceptional Lie groups and there are only 5 of them. Some people, like Klee Irwin who organized a group and has made million-dollar grants and engaged Tony Smith, and you know... Klee Irwin is on YouTube talking about one of these Lie groups, E8. Okay? E8. They like it. But there are others like E6 which is 78-dimensional [Ark shows printouts of Lie groups] with such a big diagram. There is E7 with such a diagram. And this one has 133 dimensions and is a beloved structure that a friend of Jack Sarfatti, by the name of Paul Sirag, is trying to relate to gravity. There is G2, which is simple 14-dimensions only. E8, etc. Okay everybody in String Theory is doing E8. And there is F4 which is 52-dimensional and kind of nasty-looking [he's not kidding]. Now my question is: Are any of these exceptional mathematical structures of importance in my search for unifying gravity, consciousness, and everything?

A: No. Lie groups lie in wait to entrap the unwary.

Q: (Joe) His name is a lie?!

(Ark) He's Chinese, you know, like Lee. But L-I-E.

(L) They look like spider webs...

A: Indeed.

Q: (Ark) Every symmetry is described by a Lie group. So, symmetry is unimportant? Because this is a mathematical tool for description of rotations, translations, propagation of waves, so... It's all bad. So what is good?? Which mathematics is good?

A: Geometric algebra.

Q: (Ark) Lie groups are at the foundation of geometry and algebra, and they are bad. So, I don't know what to do.

A: You need to be wary.

Q: (L) I guess that means that Lie groups are useful, but you don't need to be entrapped by them.

A: Yes

An excerpt from Maxwell's A Dynamical Theory of the Electromagnetic Field (public domain information at this point -- from the Smithsonian, no less, and Ave to them for it) shows that:

The assumption, therefore, that gravitation arises from the action of the surrounding medium in the way pointed out, leads to the conclusion that every part of this medium possesses, when undisturbed, an enormous intrinsic energy, and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction.

The whole thing's written in quaternion notation, with full equations. So while everyone else was busy trying innovate past Einstein's work, the U.S. Navy just played around with Maxwell's interpolations, plugged them directly into the electrical appliances on the U.S.S Eldritch, and its crew found out the hard way, that 3D STS humans don't do well in 4D.

But foreknowledge of possibilities does not mean forewarning of consequences. Extremely careful consideration and rigorous debate, with all who are present, and can be quickly brought to speed on a subject with simple methods, is required for any technological application. You don't have that.

So if you think that is bad, because all of our knowledge is built upon straw foundations, doomed to fail due to ever-increasingly exponential requirements for "advancement" and logistic (in the Greek, logistikos means arithmetical calculation - compute issues anyone?) constraints upon implementation .... It's really not. Not being constrained due to the "dead ends" of your predecessors, enables you to make free choices, choices that are grounded in something more substantial than your conception of material reality -- truth itself....

So there won't be any Human 4D Federation a la Star Trek, for who knows how many more hundreds of years, if not centuries or millennia. People just don't learn.

 

[John G]

I am not even going there (At some point you have to be able to see particles/spacetime in the numbers). Ark keeps wanting go there also. This is 2000 years before particles/spacetime. It is just simple addition and multiplication of prime numbers and there powers. That's it. The missing link is back there, not out there in Clifford algebras and wanting to build on someting that already exists. This is new, it is simple but it is new mathematics that does not exist in the texts, but it is silly that it doesn't.

Just the idea of the limited definition:
View attachment 112318

That last constraint, "where a finite number of the n_i are positive integers, and the others are zero", is the limiting condition and I get it. It is necessary because the definition is specifically for natural numbers (positive integers). But, all natural numbers (positive integers) can still be created when removing that constraint. It is just that when you remove that constraint, a second set of numbers is also created, a set where all members/elements have infinite factors.

The objective observation is that there are countably infinite prime numbers. The objective observation is that each term (prime number) can have either 0 or a positive integer choice as an exponent value. Those two observations taken together simultaneously creates two parallel sets. A set where every member/element has finite factors and a set where every member/element has infinite factors. To this day no one has asked what are these other numbers. The thrid statement, "where a finite number of the n_i are positive integers, and the others are zero", is the limiting factor and it makes us and our math purely STS. Why STS? Because the veil is still intact. After 2000 years we still see only what we wish to see, the finitely factored set. This in iteself should make one want to ask my question,

And if all of our mathematics is based on a foundation of seeing only what we wish to see, then so is our physics, and so is our engineering, and so is just about everything else. We are more STS than we even realize.

I like the constraint since any single (and thus finite) number has a finite number of prime factors. As mentioned earlier it seems the constraint is necessary to keep countable infinities from being set equal to uncountable infinities. All you need is a power set to go from countable to uncountable. The new math Cs comment was in relation to p-adic numbers and I could see things like p-adic numbers and surreal numbers being useful for branching in physics (quantum jumps) though I tend to play with a single vertex rather than branching between multiple vertices.

 

[John G]

I'm no mathematician, or physicist but from what I know from music, and what the C's have said about the number of densities I would conclude that the universe is in "Base 8" or octal.

I few months ago I wrote a program to generate the first 300 primes, then convert them into base 8. I then fed that list into Ghat GPT and asked it to find some pattern, since the C's mentioned "AI" is good ar finding patterns in things like this.

Wishfully thinking, I asked it to find the next number in that sequence. It guessed wrong, so I gave it the next 200, and it demanaded to know how I knew the next 200, and how I was calculating them.

There is an 8-fold Bott periodicity which for me is useful for physics in the relating of a single vertex to an infinite number of them. AI does seem to need things given to it, it hasn't been great creating patterns I'd like to see it come up with. I had told it where I was getting the pattern from and AI seemed happy but I don't think it checked if I was right but it was a situation where multiple things were technically right but it was trying to find and I was hopefully giving a preferred pattern.

 

[John G]

More like everything else that has been, is, and will be forevermore, so long as humans keep adhering to systems of thought and dogma, which are quite certain of themselves. If you think that a domain of human knowledge can't be "full of itself", well you haven't seen physics with its Silly String Theories.... This is what they do academically by the way...

While your quantum physicists are busy shooting atomic particles at each other, blowing them up, and watching all the parts disappear into nothingness, their issues with the whole Unity thing were solved ~150 years ago, at least by moderns.

From Session 11 August 2018

An excerpt from Maxwell's A Dynamical Theory of the Electromagnetic Field (public domain information at this point -- from the Smithsonian, no less, and Ave to them for it) shows that:

The whole thing's written in quaternion notation, with full equations. So while everyone else was busy trying innovate past Einstein's work, the U.S. Navy just played around with Maxwell's interpolations, plugged them directly into the electrical appliances on the U.S.S Eldritch, and its crew found out the hard way, that 3D STS humans don't do well in 4D...

But foreknowledge of possibilities does not mean forewarning of consequences. Extremely careful consideration and rigorous debate, with all who are present, and can be quickly brought to speed on a subject with simple methods, is required for any technological application. You don't have that.

So if you think that is bad, because all of our knowledge is built upon straw foundations, doomed to fail due to ever-increasingly exponential requirements for "advancement" and logistic (in the Greek, logistikos means arithmetical calculation - compute issues anyone?) constraints upon implementation .... It's really not. Not being constrained due to the "dead ends" of your predecessors, enables you to make free choices, choices that are grounded in something more substantial than your conception of material reality -- truth itself....

So there won't be any Human 4D Federation a la Star Trek, for who knows how many more hundreds of years, if not centuries or millennia. People just don't learn.

That session quote didn't like the spider web traps of large Lie groups but did think Lie groups are useful if careful. It mentioned Geometric algebra as useful too. You can get small Lie groups from geometric algebra and that is probably better than getting small Lie groups from large Lie groups. Large numbers of people do get trapped in things like string theory and smaller numbers of individuals do make progress but it will be slower since there are fewer people.