Some comments on information theory

Natus Videre

Jedi Master
Inspired by the recent discussions about crop circles, I decided to model reality using only circles... and a few arrows!
Let's see how deep the rabbit hole goes!
🕳️

Introduction
Since "consciousness is matter and matter is consciousness," every circle corresponds to a consciousness (unit).
Arrows represent directional movement, rotations, or state transitions.


Free Will
Each circle can freely spin (clockwise or counter-clockwise) around itself or move along the edge of the biggest circle, i.e. 7th density. Circles can also collide with each other. Guess which ones don't impose their will on others. 😉

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STO/STS Orientation
Each consciousness unit is free to chose whether it wants to feed on positive (light, objective) or negative (dark, subjective) energy. Consciousness units are initially "objective until they choose to be subjective." The size of each circle corresponds to the number of lessons learned. Bigger circles have greater awareness and knowledge.


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Soul Groups
A circle can be a member of a soul group which is "an affiliation that can be due to origin or graduation."

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Disintegration
Once a circle grows past the threshold of negativity (4D STS), it starts to decay. It is absorbed by a black hole. The cycle is complete when primal matter, as a result of the disintegration, is given a new chance to learn, and to be in "union with the One."


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Union with the One
Circles on the STO path are not subject to disintegration. Once they "learn all their lessons," they effectively become "One," i.e. the system, the structure that they once sought to master.

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Time Travel

Circles align with "themselves in the future" or "themselves in the past" to access knowledge that is not known to them.

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Conclusion
As you can see, circles are very versatile shapes! There are only so many "degrees of freedom" to explain the unexplained from a two-dimensional perspective. However, surprisingly, I think there is some logical foundation to this visual exercise, possibly due to the inherent properties of circles. Shapes seem to have "universal truths" embedded in them. Plus, the act of organizing shapes gives them additional meaning. Is there such a concept as "geometric logic?"

Q: Wait, I asked what is the second loop. The second loop is included but not inclusive?
A: Remember, you do have cycles but that does not necessarily mean cyclical. 3 Dimensional depiction of loop, seek hexagon for more. Geometric theory provides answers for key. Look to stellar windows. Octagon, hexagon, pentagon.
Q: Are those the different levels of density?
A: No, but it relates. Geometry gets you there, algebra sets you "free."
 

ark

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Is there such a concept as "geometric logic?"
Graph theory, Markov chains.
Interesting. I read in Wikipedia:

"In mathematical logic, geometric logic is an infinitary generalisation of coherent logic, a restriction of first-order logic due to Skolem that is proof-theoretically tractable. Geometric logic is capable of expressing many mathematical theories and has close connections to topos theory. "

I will have to look at it, even if it is not my domain. I think Cleopatre VII is closer to such an abstract view of the world. I am more "down to earth" and happy with what can be calculated.
 

PabloAngello

Jedi Master
@ark I have also read that. But imho graph theory and markov chains (especially this) are also kind of geometric logic concepts - where you draw relations between events/objects in geometric way, by nodes, lines, circles, whatever. It all depends how you define "geometric" in logic. Geometric algebra also fits here in some way.
 

ark

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@ark I have also read that. But imho graph theory and markov chains (especially this) are also kind of geometric logic concepts - where you draw relations between events/objects in geometric way, by nodes, lines, circles, whatever. It all depends how you define "geometric" in logic. Geometric algebra also fits here in some way.
Category theory is of this kind as well: http://ism.uqam.ca/~ism/academics/category-theory-and-applications/
1658641276296.png
As for Markov chains - I don't know. I think it is just a branching tree with probabilistic weight. Only one-way connections, no loops. Too simple.
 

PabloAngello

Jedi Master
There are loops in Markov Chains. And 2 or more way of connections can be just drawn with more connection line to same object.

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PabloAngello

Jedi Master
I also assume we can expand Makov Chain connections by new, feedback line like:
1658654039084.png

In connection A, STO 75% of time will share information to STS (just an example, Others can be here as well) and STS will send respond to this info back to STO with 10% probability. Additionally STO will use all gathered information to his own needs 25% of times.

In connection B STS will share information to STO 15% of time and will get processed by STO information back with 60% of probability. In addition STS with use all gathered information to his own needs 85% of times.

We have loopbacks here.
 

Natus Videre

Jedi Master
Graph theory, Markov chains.
I will have to look at it, even if it is not my domain. I think Cleopatre VII is closer to such an abstract view of the world. I am more "down to earth" and happy with what can be calculated.
I was also looking into ways of geometrically visualizing equations. Maybe the following can offer a more concrete foundation, as it is part of algebraic geometry.

In mathematics, a dessin d'enfant is a type of graph embedding used to study Riemann surfaces and to provide combinatorial invariants for the action of the absolute Galois group of the rational numbers. The name of these embeddings is French for a "child's drawing".
A dessin d'enfant is a graph, with its vertices colored alternately black and white, embedded in an oriented surface that, in many cases, is simply a plane. For the coloring to exist, the graph must be bipartite. The faces of the embedding are required be topological disks. The surface and the embedding may be described combinatorially using a rotation system, a cyclic order of the edges surrounding each vertex of the graph that describes the order in which the edges would be crossed by a path that travels clockwise on the surface in a small loop around the vertex.
Any dessin can provide the surface it is embedded in with a structure as a Riemann surface. It is natural to ask which Riemann surfaces arise in this way. The answer is provided by Belyi's theorem, which states that the Riemann surfaces that can be described by dessins are precisely those that can be defined as algebraic curves over the field of algebraic numbers. The absolute Galois group transforms these particular curves into each other, and thereby also transforms the underlying dessins.
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What Is... a Dessin d'Enfant? (Leonardo Zapponi, Aug 2003)

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John G

The Living Force
There are loops in Markov Chains. And 2 or more way of connections can be just drawn with more connection line to same object.
A Markov chain is I think usually thought of as not having time-like loops but you maybe in a not so elegant way could get it to do any kind of time-like loop. The Cs I think have said they don't like string theory but do like branes and branes seem like some kind of state diagram. The use of state diagrams seems useful but what exactly the states and transitions look like is the question. Branes almost seem like states that can have substates (entangled vertices if you make the spacetime discrete) and superstates (superposition of universe brane states) and I'm not sure I'm saying this correctly.
 

John G

The Living Force
I was also looking into ways of geometrically visualizing equations. Maybe the following can offer a more concrete foundation, as it is part of algebraic geometry.


...

What Is... a Dessin d'Enfant? (Leonardo Zapponi, Aug 2003)
Conformal geometric algebra supposedly lends itself easily to projective geometry which uses algebraic geometry techniques. I like a model that has both a conformal connection (preserving angles) and projective connection (preserving volume and orientation) used in a bimetric gravity kind of way (it only has a conformal metric but also has a volume form) so I could see geometric algebra and algebraic geometry as useful. I also like geometric algebra aka Clifford algebra as what Ark referred to as a "mother algebra".
 

ark

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Markov chain moves always forward in time. So there are no true loops. Yes the event can influence itself through another event, but only in the future, never in the past. That is not what we are looking for.
 

dennis

Jedi Master
Something to think about on a hot summer day. In an infinite connected universe are the concepts of bounded states, isolated systems, etc. flawed? What are the effects of computer development and widespread use?





Landauer's principle can be understood to be a simple logical consequence of the second law of thermodynamics—which states that the entropy of an isolated system cannot decrease—together with the definition of thermodynamic temperature. For, if the number of possible logical states of a computation were to decrease as the computation proceeded forward (logical irreversibility), this would constitute a forbidden decrease of entropy, unless the number of possible physical states corresponding to each logical state were to simultaneously increase by at least a compensating amount, so that the total number of possible physical states was no smaller than it was originally (i.e. total entropy has not decreased).

Yet, an increase in the number of physical states corresponding to each logical state means that, for an observer who is keeping track of the physical states of the system but not the logical states, the number of possible physical states has increased; in other words, entropy has increased from the point of view of this observer.

The maximum entropy of a bounded physical system is finite. (If the holographic principle is correct, then physical systems with finite surface area have a finite maximum entropy; but regardless of the truth of the holographic principle, quantum field theory dictates that the entropy of systems with finite radius and energy is finite due to the Bekenstein bound.) To avoid reaching this maximum over the course of an extended computation, entropy must eventually be expelled to an outside environment.

A billiard-ball computer, a type of conservative logic circuit, is an idealized model of a reversible mechanical computer based on Newtonian dynamics, proposed in 1982 by Edward Fredkin and Tommaso Toffoli.[1] Instead of using electronic signals like a conventional computer, it relies on the motion of spherical billiard balls in a friction-free environment made of buffers against which the balls bounce perfectly. It was devised to investigate the relation between computation and reversible processes in physics.

And a little humor

 

PabloAngello

Jedi Master
Interesting view, quite close to my internal feelings.
Its called: MULTIMODAL USER INTERFACE (MUI)





There is also similar topic named: Quantum Bayesianism (QBism):



 

Natus Videre

Jedi Master
Compressing Information
It would be quite fascinating if we could construct a special mathematical function which, when evaluated repeatedly, would produce a message of our choice.

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Now, imagine that the message is not 12 characters, but an entire book! The difficulty lies in finding the appropriate mathematical relationship that ties together all the characters of a message. Ideally, the function would be much, much shorter than the message. The function wouldn't be a piecewise function or a correspondence table (as shown in Step 5), because it would be longer than the message itself. Basically, the function would encode a series of instructions that can be linearly "played" to reveal an arbitrary message.

Let's consider the function f(x) = 2x + 1.
Evaluating it from x=0 and incrementing x by 1 each time, we get 1,3,5,7,9,11, and so on. In this example, this function can hold an infinite number of integers, i.e. meanings. It's a case where a finite representation holds infinite meanings. In order for another person to understand the outputs of the function, this person needs to be aware of the mapping between numbers and characters that is encoded in the function. If the mapping (in Step 1) is used in this example, the function returns "BDFHJL..." which is nonsensical. If we decide to stay with the same mapping, then the function needs to change, and if we decide to stay with the same function, a new mapping needs to be communicated to the person. We quickly get to a point where we have to constantly adjust the mapping or the function to "fit" our message. For this reason, the mapping should be fixed in order to minimize information exchange between two people, but this opens a can of "mathematical" worms!

Onion routing is a different, but close analogy to what was described above.
Onion routing is a technique for anonymous communication over a computer network. In an onion network, messages are encapsulated in layers of encryption, analogous to layers of an onion. The encrypted data is transmitted through a series of network nodes called onion routers, each of which "peels" away a single layer, uncovering the data's next destination. When the final layer is decrypted, the message arrives at its destination.

In the following diagram, the process of Onion routing is applied to our initial message "WAIT AND SEE". This time, a (symmetric) key needs to be shared between two people. This key will be used to encrypt and decrypt the message. Here, encryption is analogous to finding the function that ties together a sequence of numbers mapped to characters. Decryption is analogous to evaluating the function linearly in order to uncover the message. The order in which the sub-messages are encoded will determine the order of evaluation once the sub-messages are decoded.

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But then the size of <Encrypted Message 3> is bigger than the size of "WAIT AND SEE", so we are back at square one. We might as well send "WAIT AND SEE" in plain text to the person of our choice, since we are not interested in shielding the message from attackers.

Information and Consciousness
Somehow I feel that the approach we are taking to solving problems (like above) is not fully in tune with the Universe. Instead of setting up the right conditions to receive an answer, we are forcefully hammering through possible solutions in the hopes of achieving a desired outcome.

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Q: (L) Well, we talked about Stonehenge before, that it was an energy transducer, so to speak. So, was Stonehenge put there because of the location, or did Stonehenge create... (T) Why don't you just ask what it is about Stonehenge? (L) Okay, what is it about Stonehenge?
A: Location attracted those spirit types on the proper frequency, who in turn, placed stones in proper location to receive the coded communications in code telepathically, in order not to have to chase around the countryside reading encoded pictographs.
Q: (L) Multiple user necessity implies that a number of people must do the spiral. Is that correct?
A: No. Must hear and feel and understand precisely the same thing. The molecular structure of the rock, when properly sculpted sing to you.
Q: Is consciousness stored in the universal information field similar to how information is stored in water? Is the universe an information field as the medium in which consciousness resides?
(L) Information field... The medium in which consciousness resides...
A: Vice versa.
Q: (Chu) The other way around.
(L) So consciousness is the medium in which information resides.
If our thoughts and actions are engraved in consciousness, then our efforts should be directed at accessing information as opposed to "computing" it. Creating an artificial subset of the Universe to transfer information is to limit our possibilities.
 
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