Some comments on information theory

[ark]

The infinite continuation of a specific sum series. I am assuming the exclamation point is a typo. I could be wrong?

What does that mean? Is it mathematics? Or is it a poetic expression? If it is mathematics, I do not know such a concept as "infinite continuation". What would it mean that two "infinite continuations are equal? Is 1+1+1 ... = 1+2+3.... true? When two differently looking infinite continuations are supposed to be related by the "=" symbol?

 

[christx11]

What does that mean? Is it mathematics? Or is it a poetic expression? If it is mathematics, I do not know such a concept as "infinite continuation". What would it mean that two "infinite continuations are equal? Is 1+1+1 ... = 1+2+3.... true? When two differently looking infinite continuations are supposed to be related by the "=" symbol?

I understand what you are saying. I just don't understand where you are saying I am doing what you refer to.

Are you saying for example:

x = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + ...

Are you saying the right hand side of the above ( the sum series of all natural numbers),
Are you saying the right hand side cannot be re-written as two infinite sum series as the evens plus the odds?

As in:

x = ( 2 + 4 + 6 + 8 + 10 + 12 +14 + ... ) + ( 1 + 3 + 5 + 7 + 9 +11 +13 + ... )

Are you saying that the sum of the odds plus the sum of the evens is not the sum of all natural numbers?

 

[ark]

I am saying that I do not know the concept of "infinite sum series". Please define the concept for me. Or give a link. I can't find it online.

 

[ark]

I am saying that I do not know the concept of "infinite sum series". Please define the concept for me. Or give a link. I can't find it online.

Or, more exactly, what the equal sign "=" between two such formal expressions means for you.
In your case both sides are divergent. They produce both infinity. What do you mean by the fact that the two infinities are "equal"?

 

[ark]

Or, more exactly, what the equal sign "=" between two such formal expressions means for you.
In your case both sides are divergent. They produce both infinity. What do you mean by the fact that the two infinities are "equal"?

You probably mean (I am guessing), that with an appropriate procedure on the right hand side (infinite product) you can recover the elements of the left hand side one-by-one? Is that what you mean? Not only "elements" but also partial sums. Is this the case?

 

[christx11]

You probably mean (I am guessing), that with an appropriate procedure on the right hand side (infinite product) you can recover the elements of the left hand side one-by-one? Is that what you mean? Not only "elements" but also partial sums. Is this the case?

You are right Ark. I will try to clean up the nonsense statements like 'infinite sum series', it really makes a mess of everything.

I need to go back to something much more simple and basic. None of what I am trying to show involves calculus. Everything I am trying to demonstrate is historically from publicly available mathematics that existed 1900 years before calculus was even discovered. None of it requires convergence, divergence, limits, partial sums, etc.

To continue my thought experiment requires a starting point that the entire set of natural numbers (expressed as an infinite series) and the entire set of rational numbers (expressed as an infinite series), each have an equality as an infinite product, where each term of the infinite product is a prime geometric series.

1) We know that the infinite series of all inverse natural numbers can be expressed as an infinite product, where each term of the infinite product is a prime geometric series. (Euler's Theorem 7)

2) I will provide the data and logic to demonstrate that a similar equality exists for the natural numbers. That the infinite series of all natural numbers can also be expressed as an infinite product, where each term of the infinite product is a prime geometric series.


3) I will provide the data and logic to demonstrate that a similar equality exists for the rational numbers. That the infinite series of all rational numbers can also be expressed as an infinite product, where each term of the infinite product is a prime geometric series.

*** Note in the above image: "the sum of all rationals", should be "the infinite series of all rational numbers"

Numbers 2 and 3 above I do not think can be proven algebraically. None the less, I think both are true, and the data and logic simply goes back to the sieve of Eratosthenes. The sieve of Eratosthenes has much more information in it than it just being a way to find prime numbers.

I will put the relevant information together and post here. It may take me a while (Jan 2025, maybe sooner).

Interestingly the data and logic from the sieve of Eratosthenes, Ark has already mentioned in a blog post here.

The link Ark mentions is: A periodic table of primes: Research team claims that prime numbers can be predicted
The actual paper is at The Periodic Table of Primes

You can see from one of the links above it is mentioned as a breakthrough-prime-theory...

It is a breakthrough except, James McCanney made this same breakthrough discovery here:

James McCanney
New Definition of Prime Numbers with Sppn Tables and Proofs by Induction

Except Liu Fengsui, made the same breakthrough discovery here:

Liu Fengsui's Prime Formula Problem 37. The Liu Fengsui's Prime Formula

Except Gary Croft made the same breakthrough discovery here: 'The Prime Spiral Sieve' Prime Numbers Demystified by 8-Dimensional Algorithms

And the information that all of the above parties are seeing (breakthrough discovery), is simply already found in the fine details of the information already available over 2000 years ago in the sieve of Eratosthenes.

And it is that same information from the sieve of Eratosthenes, that is the logic and data needed to prove:

2) That the infinite series of all natural numbers can also be expressed as an infinite product, where each term of the infinite product is a prime geometric series.

3) That the infinite series of all rational numbers can also be expressed as an infinite product, where each term of the infinite product is a prime geometric series.

Coincidentally, the same information (data and logic from the sieve of Eratosthenes) appears in Euler's theorem 7.

 

[christx11]

Here is the logic for the proposition that all 3 sets of numbers ( inverse naturals, naturals, and rationals ) have equalities where the infinite series of each set can be expressed as an infinite product where each term of the infinite product is a prime geometric series.

There is no calculus. Just simple addition and multiplication.

I have created posts on my blog explaining the additional data in the 'Sieve of Eratosthenes' that leads to my conclusions.


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

 

[PabloAngello]

I have a feeling this interview somewhat fits this thread:

"Christopher Michael Langan (born March 25, 1952) is an American horse rancher and former bar bouncer, known for scoring highly on an IQ test that gained him entry to a high IQ society, and for being formerly listed in the Guinness Book of Records high IQ section."

 

[msasa79]

Regarding the information flow, perhaps it might be useful to consider that most probably nothing in nature ever happens in veritable vacuum. Wherever we looked, we observed some background field, in most general case a rotating cosmic EM fields, even when particle densities were considered infinitesimally small. Using that observation as a sort of analogy also for most probably rotating cosmic information field, as the Universe observes itself, we then might conclude that at a certain depth level in the field, the information transfer would naturally, due to in effect kind of Coriolis and shear stress forces and sort of a drag, flow in opposite direction compared to the direction just below or near the surface.

On smaller scales that's observed with so called wind induced "horizontal" sea currents, and modeled in simple way by so called Ekman spiral (Wikipedia link).

The Ekman spiral is an arrangement of ocean currents: the directions of horizontal current appear to twist as the depth changes. The oceanic wind driven Ekman spiral is the result of a force balance created by a shear stress force, Coriolis force and the water drag. This force balance gives a resulting current of the water different from the winds. In the ocean, there are two places where the Ekman spiral can be observed. At the surface of the ocean, the shear stress force corresponds with the wind stress force. At the bottom of the ocean, the shear stress force is created by friction with the ocean floor. This phenomenon was first observed at the surface by the Norwegian oceanographer Fridtjof Nansen during his Fram expedition. He noticed that icebergs did not drift in the same direction as the wind. His student, the Swedish oceanographer Vagn Walfrid Ekman, was the first person to physically explain this process.

Tentatively, this observed phenomenon and its mathematical model, might even provide analogy for how natural communication between different densities, as levels or sort of layers of different density in the probably rotating cosmic information field occurs. Kind of providing a possible explanation or mechanism, or just part of it, why we usually refer to souls, as a sort of our 5D selves, perceiving what we usually see in everyday lives in a kind of reversed or upside down fashion. Also, it might suggest a mechanism for establishing sort of a natural feedback loop between observer and observed, for example when communication or information transfer happens during an observation.

In a more practical, down to Earth way, if we take into account the scaling difference in density and it's gradient, we also come to a natural simple addition to EM effects presented in ECHCC for possible explanations for spiraling phenomena in the Earth's atmosphere, like tornadoes and hurricanes and cyclones etc. Since in the atmosphere density decreases with height, and it changes on much larger scale, in addition to scaling difference in its value, density of air to density of water roughly as 1:1000, if we look from upside down stance, the Ekman spiral model would suggest sort of an enlarging spiraling transport going from the surface up, towards higher altitudes in the atmosphere, just like the waterspouts for example appear to us standing on the surface.

FWIW.

 

[palestine]

Here is the logic for the proposition that all 3 sets of numbers ( inverse naturals, naturals, and rationals ) have equalities where the infinite series of each set can be expressed as an infinite product where each term of the infinite product is a prime geometric series.

There is no calculus. Just simple addition and multiplication.

I have created posts on my blog explaining the additional data in the 'Sieve of Eratosthenes' that leads to my conclusions.


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

@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 understand of course that it has to do with "information theory"; "intelligent design", and how the information channels are relating to prime/basic geometrical shapes (for example).

Pierre Lescaudron, for example, has been developping a model hinting at biophoton emissions - akin to generic geometric bits of light. That's not exactly what he said but I hope that you get my point. And so, from there, I would understand that algebra/math are hinting at the basic fabric of the Universe, especially in regard of information structure. When we think, when we learn, it's about geometrical prime structures which are undergoing some "motions", so to speak. Pierre hinted at the Information Field, and so it would represent a potential factor to take in consideration, in addition to the basic motion of "geometrical shapes".

I am having hard time, thus, to be able to bind algebra with any form of further study. The above is my naive understanding of it but I wish, one day, than to be able to work more deeply on those matters. Would you have any suggestion? How do you "see things" or would explain/teach others in terms of "algebra/math >>> an objective cosmological model"? It seems to me that this is more or less what mathematicians would be aiming for.

I don't find your pics complicated; except for a few hints that you provided, I am having hard times seeing where you would be headed, after the theory is validated (it remained at some pure math level: how would you use your findings?). You surely have an idea but I could not see what would be "the next step" I am sure that you, yourself, see the next "stage" - and I would be very happy to understand, then, how a mathematician would proceed! Thank you for any lights on this spec!

If you don't have the time (or for another reason), that's okay. Any way this is fascinating! I was thinking if we could set up some basic algebra class rooms! Doing math puts the brain back to 1+1=2 and I found it very useful during chaotic times, with a lot of nonsense. It helps the mind to remain structured, and provides an additional logical and sane structure.