Some comments on information theory

Cleopatre VII

Jedi Master
Is Free Will possible because of Infinity?
In a way, you can probably say that. The determinism according to which it is impossible to have free will is always a system which is in some way closed. According to this view, everything is somewhat determined, so you can create a finite set of possibilities here. Of course, there are various versions of determinism, so I'm writing very generally now.

On the other hand, in an indeterministic system, where there is a concept that free will is possible, we usually deal with an infinite number of possibilities.
 

ark

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Is Free Will possible because of Infinity?

Yes. But infinities are also dangerous. On the net you can find this:

Georg Cantor was the first to fully address such an abstract concept, and he did it by developing set theory, which led him to the surprising conclusion that there are infinities of different sizes. Faced with the rejection of his counterintuitive ideas, Cantor doubted himself and suffered successive nervous breakdowns, until dying interned in a sanatorium.
 

Human

The Living Force
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Yes. But infinities are also dangerous. On the net you can find this:

Georg Cantor was the first to fully address such an abstract concept, and he did it by developing set theory, which led him to the surprising conclusion that there are infinities of different sizes. Faced with the rejection of his counterintuitive ideas, Cantor doubted himself and suffered successive nervous breakdowns, until dying interned in a sanatorium.

But it seems obvious that i.e. the 'density' of R is of different nature than 'expansion' of N and/or Z, although both are infinite. Doesn't it?
 

Cleopatre VII

Jedi Master
But it seems obvious that i.e. the 'density' of R is of different nature than 'expansion' of N and/or Z, although both are infinite. Doesn't it?
Yes, the set of real numbers is uncountable, while the set of natural numbers and the set of integers are countable, even though all these sets have an infinite number of elements. In purely intuitive terms, a countable set is a set whose elements can be set in a sequence. For example, in a set of natural numbers, you can list them in a sequence: 1,2,3,4,5,...,n,... In a set of real numbers, this is not possible.
 

kenlee

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Yes, the set of real numbers is uncountable, while the set of natural numbers and the set of integers are countable, even though all these sets have an infinite number of elements. In purely intuitive terms, a countable set is a set whose elements can be set in a sequence. For example, in a set of natural numbers, you can list them in a sequence: 1,2,3,4,5,...,n,... In a set of real numbers, this is not possible.
I was thinking that an example of the sequential countability of natural numbers and intergers would be like lining people up and counting them in sequence into infinity one person at a time.

Now lets say we go from counting them sequentially as individual bodies we zero in on each particular body of the countable set and see them each as a person with all the infinite (or quasi-infinite?) possibilities (both actual and potential)of what is possible for that person as a individual human being. We couldn't count this density of possibilities sequentially but this density of actual and potential states is still real nonetheless. So I was thinking that this might be an example of one 'lesser' infinity compared to a 'higher infinity' that Cantor talked about, but both still being infinities nonetheless. FWIW!
 

Ellipse

The Living Force
FOTCM Member
Yes. But infinities are also dangerous. On the net you can find this:

Georg Cantor was the first to fully address such an abstract concept, and he did it by developing set theory, which led him to the surprising conclusion that there are infinities of different sizes. Faced with the rejection of his counterintuitive ideas, Cantor doubted himself and suffered successive nervous breakdowns, until dying interned in a sanatorium.
One day, I really thought about the infinite concept and I tried to imagine it. I felt my brain "twisting" and, on the moment, I believed I will not be able to stop it. I thought "never again". It was really disturbing. Just to think of it again I'm afraid.

Recently, while I approached incidentally the subject with one of my right-brained colleague, he immediately stop me by saying: "I'm not at all at ease with this subject, let's skip it". I got the sensation he had the same kind of weird experience as me.
 

ark

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I got the sensation he had the same kind of weird experience as me.
Believe me, students of mathematics (in the mathematics department of a really good university) at the university level have no problems whatsoever with infinities of any kind. For them dealing with infinities is like fishing. You sit, you drink beer, and you collect your fish and sort them into your baskets.
 

Natus Videre

Jedi Master
Considering integers, there is the '+' operation which adds two integers and returns their sum, which is also an integer.
Where did the '+' operation originate from? It might look obvious in the case of integers, as 1 + 1 = 2, 1 + 1 + 1 = 3, and so on,
but... didn't we just use the '=' symbol to define the '+' operation? So the concept of equality between two numbers must have been established prior to the concept of addition of two integers. Again, there is this notion of "building blocks" wherever we look. Just like there are infinitely many numbers, there are infinitely many operations. For example, let's pretend '@' is an operation taking two integers and returning their sum plus one. So 1 @ 1 = 3. Another similar invention '(^)' would yield 1 (^) 1 = 4, as it would return the sum of two integers plus two.

How do we know we aren't making stuff up? How do we know the symbol we discovered is significant? Are operations also encoded somewhere, in some space? If some operations are the basis of other operations, is there a fundamental principle behind them? Would essential operations reveal themselves as a consequence of gathering more facts?

Q: (SV) I have a book on the Brotherhood... I get all kinds of things in the mail... one is from a guy who is supposed to be an extraterrestrial... I'll have to bring it... (L) What could we use to represent 7th density as a mathematical symbol?

A: Try this: [draws figure eight on side in ellipse]


Q: (L) When you get to the point of the Big Bang, or mass disbursement, what mathematical symbol would represent that? Plus, minus, multiply or divide?

A: NAB

Q: (L) Do you mean? None of the above?

A: Close.

Q: (L) What mathematical operation would represent this?

A: You have not yet discovered.

When we cannot describe a concept, we invent words for it. If we want to remain as objective as possible, our inventions must be consistent with reality. And on this perpetual self-correcting path, there is no free lunch.
 

Saman

The Living Force
FOTCM Member
Number one is certainly important (unity. Number three too (trinity). Also number 7 (seven densities). There are 3 basic quaternions and 7 basic octonions.
This evening, in looking on the web to find to some sort of visual explanation of what these quaternions and octonions are, I found the following short videos that might be helpful to the layman like myself who are interested in these complex and yet very interesting subjects:

Quaternions and 3d rotation, explained interactively​


Eric Weinstein Explains Octonion Numbers to Joe Rogan​


Eric Weinstein also mentions to Joe Rogan in the video the work of Sydney Brenner in relation to "C Elegans", the most primitive worm known to exist in biology apparently, and here is where I didn't understand how he made the seeming correlation in the video at this point here starting about 6:42 in the video: that the completely mapped architectural plans of this primitive worm, or so it has been claimed to be completely mapped, has some sort of relationship in this explanation of these Octonions...at this point due too many conceptual unknowns for me to understand, I don't understand; however, perhaps someone who is trained in these fields can see the correlation of what he is talking about. Well, maybe he is talking some sort of possible correlation of the micro to the macro, and vice versa; that is something about the "neural network", of this primitive C Elegans worm for example, "and the large-scale structure of galaxies" in relation to quaternions and octonions and the visually inspirational video that Cleoptre VII recently shared above?!? Or so I am only speculating about...and I am likely way off due to making just wild speculations in this case.

FWIW, just some thoughts.
 

Cleopatre VII

Jedi Master
How do we know we aren't making stuff up? How do we know the symbol we discovered is significant? Are operations also encoded somewhere, in some space? If some operations are the basis of other operations, is there a fundamental principle behind them? Would essential operations reveal themselves as a consequence of gathering more facts?
I think you've touched on a famous problem. In the philosophy of mathematics there is an issue related to the question: Do we create mathematics or do we discover it?

Since the debate is still going on, it means that we still do not have a clear answer. The arguments exist on one side and the other.

And how is it with physics and reality? On the one hand, thanks to physics, we can create technology, the operation of which we observe in reality. On the other hand, we know that even Newton's theory is imperfect. It has a specific range of applicability, it works only in the presence of low speeds (much lower than the speed of light) and low intensity of the gravitational field. However, thanks to it, we can construct many useful technological tools, we can say what was the course of a car accident, etc.

However, the models we use in physics are only an approximation of what we are phenomenologically observing. Some of them work to some extent in practice, but the approximate consistency of calculations reality does not answer the question whether mathematics exists objectively.

As for my opinion on this point, I believe that the current shape of mathematics is to some extent a consequence of the operation of our human mind. If our minds were constructed differently, the mathematics would probably be constructed differently. This does not mean, however, that it would not describe the reality we perceive. I think it is possible that it would fulfill this function, would be isomorphic to our current mathematics, but this isomorphism would most likely occur at some meta level.

Nevertheless, this is a huge field for discussion. However, let us bear in mind that our discussion will take place on a logical level, as we understand logic. It is impossible to understand logic without going beyond it, and it is impossible to comprehend time without going beyond time. I cannot prove a theory to be true from within the theory. But I can prove it using metatheory.
 

Cleopatre VII

Jedi Master
Well, maybe he is talking some sort of possible correlation of the micro to the macro, and vice versa; that is something about the "neural network", of this primitive C Elegans worm for example, "and the large-scale structure of galaxies" in relation to quaternions and octonions and the visually inspirational video that Cleoptre VII recently shared above?!? Or so I am only speculating about...and I am likely way off due to making just wild speculations in this case.
For example, I recommend this article: The Strange Similarity of Neuron and Galaxy Networks - Issue 50: Emergence - Nautilus

In fact, there are many similarities at different levels and on many scales. At the same time, in modern physics, despite the existence of analogies, we use different theories to describe the Universe at different scales. At the subatomic level we use quantum mechanics, at the galactic and extragalactic levels we use general relativity.

Hence, I believe that one of the most important tasks of physics at the moment is to develop a theory that would be a bridge between quantum mechanics and general relativity. Perhaps both theories need some adjustments.

The approaches that have come to my mind recently are gravitoelectromagnetism and teleparallelism. Perhaps having something like UFT, the particular analogies between microscale and macroscale will become easier to explain in terms of the set of applicable laws of nature.
 

dennis

Jedi Master
How about Negate And Balance (or neutralize and balance) where the extreme of running to infinity is balanced by contemplating its polar opposite and emerging a third position being a neutral (or separate/indifferent) observer of both. The infinity symbol and analemma express something like that. A type of closure.

Q: (L) When you get to the point of the Big Bang, or mass disbursement, what mathematical symbol would represent that? Plus, minus, multiply or divide?

A: NAB

Q: (L) Do you mean? None of the above?

A: Close.
1n=-1n
_______
:-D
 

Natus Videre

Jedi Master
How about Negate And Balance (or neutralize and balance) where the extreme of running to infinity is balanced by contemplating its polar opposite and emerging a third position being a neutral (or separate/indifferent) observer of both. The infinity symbol and analemma express something like that. A type of closure.


1n=-1n
_______
:-D
It makes me think of the Riemann Sphere:1640951596522.png
In mathematics, the Riemann sphere, named after Bernhard Riemann,[1] is a model of the extended complex plane, the complex plane plus a point at infinity. This extended plane represents the extended complex numbers, that is, the complex numbers plus a value ∞ for infinity. With the Riemann model, the point "∞" is near to very large numbers, just as the point "0" is near to very small numbers.

The extended complex numbers are useful in complex analysis because they allow for division by zero in some circumstances, in a way that makes expressions such as 1/0 = ∞ well-behaved.
For example, any rational function on the complex plane can be extended to a holomorphic function on the Riemann sphere, with the poles of the rational function mapping to infinity. More generally, any meromorphic function can be thought of as a holomorphic function whose codomain is the Riemann sphere.
But what is the neutral position? The center of the sphere? The sphere itself? Does it relate to the concept of windows that the C's mentioned?

Perhaps it is a matter of correctly identifying the dual character of mathematical objects. Does the neutral/obsever position also have a dual?
Q: (L) What is the link between consciousness and matter?

A: Illusion.

Q: (L) What is the nature of the illusion? (T) That there isn't any connection between consciousness and matter. It is only an illusion that there is. It is part of the third density...

A: No. Illusion is that there is not.

Q: (L) The illusion is that there is no link between consciousness and matter.

A: Yes.

Q: (T) The illusion is that there is not a link. In third density... (L) I got it! (T) Don't disappear on me now! [Laughter] The relationship is that consciousness is matter.

A: Close. What about vice versa?

Q: (L) Just reverse everything. Light is gravity. Optics are atomic particles, matter is anti-matter... just reverse everything to understand the next level... it can't be that easy. (J) Wait a second: gravity equals light, atomic particles equals optics, anti-matter equals matter? It is all about balance. (L) And the answer must always be zero.

A: And zero is infinity.

Q: (L) So, you are saying that it is not that there is a link, the illusion is that there is separation. There is no difference, they are the same?

A: Yes.
 

Cleopatre VII

Jedi Master
How about Negate And Balance (or neutralize and balance) where the extreme of running to infinity is balanced by contemplating its polar opposite and emerging a third position being a neutral (or separate/indifferent) observer of both. The infinity symbol and analemma express something like that. A type of closure.


1n=-1n
_______
:-D
This brought to my mind some elements of Hegel's philosophy. Soon I will have a presentation on Hegel in my theological studies, so perhaps I will present some elements of his philosophy that, in a way, relate to our discussion.

Hegel used the so-called dialectical method, started in antiquity by Plato and developed in an interesting way by German idealistic romanticism. In Hegel's philosophy, the essence of reality and truth is contradiction. It is synonymous with the concept of changing, becoming, an eternal memory of an infinite task. A statement, a negative, a synthesis, this is the real life of reality and truth. This is how the spirit develops, this is how the individual develops, this is how nature develops. Reality and truth are a ceaseless synthesis of eternal contradictions. Each concept essentially contains its own contradiction, which results in a cognitive tendency to produce a higher synthesis, which in turn is again a statement containing its own contradiction. However, it is not only a dialectic of philosophical thinking, but it is also a real development of the world, it is an accord of spirit that expresses itself in the world to liberate itself into full consciousness. The permanent stages of this path are the categories of thinking and reality. The dialectical development of the concept is at the same time the development of logic and metaphysics.

My favourite example of Hegel’s use of the dialectical method is his reflection on my great fascination - time.

For Hegel, time is related to space, which the philosopher calls "abstract mutual externality". According to Hegel, after a dialectical reflection on the essence of space, its being will be revealed in the form of time.

According to the principles of intuitive mechanics of the world, space is a multitude of points that are distinguishable from each other within it.

Paradoxically, a point due to its lack of volume is nothing else than the negation of space, one of the characteristics of which is volume. On the other hand, the point is not outside space, nor does it come out of space as an entity different from it. The successor of the implications of the above statements should therefore be the thesis that space is nothing else than the mutual externality of a point variety, devoid of differences. As a consequence of the quoted considerations, Hegel calls space punctuality and time is called the truth of space.

But why is it time? Well, Hegel looks at it somewhat in line with the assumptions of classical mechanics. We define all events by giving their place (space) and time. Space is made up of points that have no volume, and time is made up of points whose duration is zero.

Hence, volume is to space what duration is to time. However, those points in space that do not have volume are eternal in time, and points in time whose duration is zero eternally exist in a given space. Hence time is the truth of space and space is the truth of time. The deepest truth is born of contradiction.

It is quite twisted thinking, but that is what Hegel’s philosophy is about.

Hegel intended to build a total system of science, comprehending it as a whole, and therefore the only possible form of presenting truth in science. “Truth is whole. The whole is only such a being which, thanks to its development, comes to its final end ”. Hegel’s system of philosophy was to consist of three parts:

1. Logic - the science of an idea in itself and for itself in its complete abstraction, consisting of subjective logic (dealing with the theory of being and knowledge) and objective logic (dealing with the theory of concepts).

2. Philosophy of nature - the science of an idea in its other being (which he divided into mechanics, physics and organics). It involves knowing the spirit in its specificity, the spirit for oneself.

3. Philosophy of the spirit - the synthesis of previous forms in and for oneself, includes full awareness of the completed transition. Within each phase, there are 3 types of spiritual forms. They are: Subjective Spirit, Objective Spirit, and Absolute Spirit.

Hegel’s philosophy of the spirit is very extensive. What is important in the context of our discussion is, above all, that it is also based on contradictions. Deep truth must be the consequence of a contradiction.

For Hegel, the highest goal of philosophy is to know God. However, it is difficult because this God is the opposite of himself. Here it is no longer like with time and space, God is in a way like a photon. The antiparticle of a photon is a photon.

In Genesis, we read:

“And God said, Let there be light: and there was light.”.

So, can light in its nature have anything to do with God? If Hegel had known that the photon was an antiparticle of itself, he would have probably noticed it. Though Ark doubts it (that there are no anti-photons) and so do I, but this is the official paradigm today.
 
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