Some comments on information theory

[ark]

@ark So what should it be if not square? :)

You, when asking these questions and trying to understand! Squares, and also computers, do not understand anything. Understanding is an important concept when duscussing consciousness. What do we mean by "understanding". Well cats do understand something, sometimes a lot. So they are also consciouss, especially when they are trying to annoy you "on purpose". So, having a "purpose" is also a part of being conscious.

 

[PabloAngello]

I used square example on computer for modelling the idea. Classical computers also can model the quantum computers behavior by fancy libriaries with pseudo random numbers. For modelling its enough for quantum computers so it could be for consciousness I suppose. I repeat "for modelling".

So, having a "purpose" is also a part of being conscious.

Yes, exactly this, I have the same thoughts. We are at last getting into something, very small step but still ;p
Conscious beings have aims - what is the simplest aim? Looks like "to be or not to be".

 

[mkrnhr]

It looks like we can't escape defining consciousness as an extrapolation of what we experience as consciousness as humans (same as natural sciences started from the observation of natural phenomena via human physical senses). We have awareness of ourselves, and awareness of what lays beyound our selves. There are times when we don't have awareness of ourselves, are in a dream-like state or in a coma, and experience other "degrees" or "qualities" or awareness. By extrapolation, we can assign those qualities of lesser degrees of awareness to animals, plants, objects, etc. Or higher degrees of awareness to higher states, and ultimately to the cosmos (densities?).

If consciousess is beyond time (and space) at some level rather than being in time and in space, then time and space may be part of the information that some consciousness deals with. The stuff (matter, energy, qualities, meaning) that in our everyday experience manifest as things in time and in space could also be information of different degrees that consciousnesses of different degrees deal with. This looks like an arbitrary dualism (consciousness vs. information) until one unifies consciousness and information, either by considering cosnciousness as being a higher organisation of information that has the "capacity" of being aware of itself at different degrees, a view that can fall in the trap of emerging properties (that's somehow evolutionary and "in time"). Or that information, and consciousnesses of various qualities are part of "The consciousness" (ie. the cosmos, existence) and their information exchange is part of The consciousness self-awareness while the parts (including processs involving time and space) are more or less limited in scope. OSIT.

 

[dennis]

Understanding is an important concept when duscussing consciousness. What do we mean by "understanding".

Consciousness, I think resides beyond space and time. I think it is somehow related to what we may call "cosmic intelligence", "intelligent design", "creativity" etc.

Reflecting on the above quotes, does that relegate humans to the role of receivers/transducers of the DCM emission?
When we think we are conscious we are actually becoming focused or aligned with something that is originating external to us. It seems purpose would involve doing something with the information like embedding it in space/time.

 

[Deleted member 4320]

Very little. You can look at my "Comments on super-restistance of consciousness" - a piece from my debate with David Chalmers . People are trying to use quantum theory, but quantum theory needs to be understood first.

Here are my thoughts on the subject, taken from the final paragraph from these "Comments":

"... But the question remains: where is consciousness? Let me present briefly my own thoughts on this subject. Consciousness, I think, has something to do with awareness of oneself, one’s own state, and of the external world. Awareness which is open to knowledge. The more aware we are and the more knowledge we have and use, the more conscious we may become. There is another aspect of consciousness, which is our awareness of the passage of time. This problem goes beyond quantum theory. Time, its ‘flow’, together with its mysterious arrow, is, I think, a mystery to be solved if we want to solve the problem of consciousness. But that would lead us far beyond the scope of your talk.

True, this is not much, but it does look like a step in the right direction however. I would like to use some mathematics in this document that I am able to do something with. Only a few fragments, because as far as the rest of the content is concerned, I would have to research a lot to understand it more deeply.

I will refer to mathematics, more or less at the center of my post.

It's really hard to answer that question. First of all, there are many hypotheses and theories that are more philosophical or even mystical than strictly scientific.

When it comes to a strictly scientific approach, it is supposed that certain aspects of consciousness could be described using the methods of quantum mechanics and neurobiology or science, or rather protoscience, which tries to connect them - quantum neurobiology.

The idea of quantum neurobiology is based on the fact that certain structures in biological cells are so small that quantum effects take place there. This applies, for example, to microtubules or individual sections of ion channels. Hence, for example, the study of the flow of ions through ion channels is one of the examples of research in the field of quantum neurobiology. But at the moment there are many questions, but there are almost no answers...

So let us not be afraid to tell it to ourselves, the answer is: NOTHING. We know nothing about Consciousness as such, nothing directly about it. Interestingly, this "nothingness" hides a hint of what Consciousness is, I think...

I have one theory about this, how this can be with this Consciousness and why it is so elusive and indescribable mathematically. Unfortunately, so far these are philosophical considerations, but I would like to share, because maybe someone will find it interesting. Generally, I should have to describe it in details to make it all clear and I'm going to do it sooner or later. However, at the moment when I was considering the structure of the Universe, I generally distinguish three basic forms of It.

This is Being/Order - All there is. Everything that exists.
This is Non-Being/Chaos - Everything that is not there. Everything that doesn't exist.
This is Nothingness

...and what I mean because I distinguish Non-Being from Nothingness. Non-Being can be described eg. as "all that is not." In describing it, we are already giving it some definition, which is not the same as Nothingness. Because Nothingness is something that is completely beyond what we would be able to think, and it is impossible to relate to it directly. And it only takes shape when it enters into a relationship with Non-Being or Being and only then can it be grasped by us and possibly described mathematically, etc. I have hypothesized that Nothingness is the same as... Consciousness.

Nothingness/Consciousness is something we could define as "something that is indefinable, something that escapes any definition, something that can potentially be anything and everything, and something that goes beyond 'being all and being nothing'. Nothingness is something like Being and Non-Being at the same time and everything else what is unprecized and goes beyond that at the same time.

The difference is that I can find what is Non-Being by looking for the opposite to what is Being, while there are things in the Universe that cannot be precisely specified, and they do exist or may exist. They cannot be defined more precisely because they do not have such a definition and interestingly there are two such elements of the Universe, Nothingness and Consciousness. This experimentally prompted me to equate Consciousness and Nothingness.

Let's move on to the situation of Consciousness/Nothingness in its original form, beyond the Creation we are in. Go back to a much earlier phase of Consciousness/Nothingness. In the situation where there is nothing around it and there is no reference to anything. It can only interact with itself through an act of self-awareness. I hypothesize that this leads to this leads to the collapse of itself.

This act of collapsing in itself (act of self-awareness) is mirrored by the interaction of Consciousness with Non-Being. We can visualize it as a circle with black in the center. The line of the circle are Consciousness and the field in the center is Chaos/Non-Being. This circle tightens on this black field that exists endlessly and, despite constant pressure, does not change its 'size' or anything like that because constantly expand toward down keeping its width.

Visualizing such a relationship between Consciousness and Non-Being is a presentation of the relationship between these two forces resulting from the Consciousness turning towards itself, and thus falling into itself (Consciousness which, as I previously called interchangeably Nothingness, remember it is something not really restricted or defined in any way, from which we can expect anything and everything etc...). The effect of the pressure on this black circle is the production of Information. Which can be visualized as particles that are released in the opposite direction to this circle, originating in, and expressing outer from the line of the circle that symbolizing Consciousness.

So the act of self-awareness performed by the Consciousness allows for the emission of Information. Consciousness starting the process of the release of Information that will later be used to organize it. Information is not yet Being, and is a byproduct of the interaction between Consciousness and Non-Being. So we have Information at the scene. Let focus on the process of obtaining information.

I relate to the formula: "2.1 Example 1 - the qubit" from the Ark's "Comments on super-restistance of consciousness".

The "only one point of the spectrum" would be the simplest, smallest, local meeting point of Consciousness and Non-Being, which can be related to the matrix included in the "Comments...: 2.1 Example 1", where:
variable "a" - would mean the Consiousness itself.
zero ("0") would be equivalent of the Non-Being/Chaos.

If we write down determinant of this matrix, we have: a*a - 0*0
"a*a" - act of self-awareness of the Consciousness, and it is the multiply of the Consciousness by itself (being also a part of the bigger process that is described by the entire formula).
"0*0" - it will be Non-Being powered by Non-Being, Non-Being that expands infinitely into chaos.

So, we have "a*a - 0*0". Putting it together, we have the process that is composite with activity that happens as itself ("a*a"), which always, at the same moment, entails the influence of Non-Being. Only then can the process take place that produces the smallest particle, which we can call "the qubit". This is also the smallest possible form of Information. When we have it, we can go to the next step.

So, now we have: Consciousness, Non-Being and Information. Then go to the "2.2 Example 2 - the qubit and the switch" of the "Comments..."

Then by counting the matrix we have "a*d-0*0".
a - it's Consciousness
d - particle/(s) of Information (that is counted like in the previous example)
0*0 - Still we have expanded Non-Being (Non-Being * Non-Being)

Now Consciousness is multiplied by the Information (a*d), which are "negatively" affected by Non-Being. Multiply of the Consciousness with Information allow anastomosis (close connection) of the Consciousness to the Information and also expansion of the Consciousness because Information is something what come from Consciousness itself, and this we saw in previous example.

Further, to describe the whole process we need to mention the minus effect of Non-Being (this part of the equation "- 0*0"). In order to make a thing to be something what has meaning, we must already have a point of reference that make this meaning, and that point of reference is Non-Being, expanding infinitely (0 * 0).

a*d gives us a "thing", it means that Consciousness which how I assumed previously has it's specific structure that is Being/Non-Being/Nothingness (it is something undefined, but it is) at the same time. This can create an infinite amount of Information, giving it infinitely many shapes, and the next stage is to become it meaningful if you set their "distance" from the Non-Being. To find this "distance" you need to make operation of subtraction "- 0*0".

So if we have the whole formula then we have "a*d - 0*0" Consciousness gives meaning to particular pieces of Information by distinguishing their "location" in relation to Non-Being and further Consciousness can also set it in relation to the other piecies of Information that also subordinate to the center of Non-Being.

In such a case, if we already have Information, then we are left with the last stage, and this is the stage when Consciousness has all the Information at its disposal, and start the process of organizing this Information and develop Being. To do this, Consciousness needs the Creation. And so Creation is what we are in, and we ourselves are divisions of this Consciousness in work.

Finally, a few points:
- As Consciousness itself is not anything precise and fluctuates between Being/Non-Being/Nothingness, it also does not convey any purpose of existence, because it cannot deliver one to Creation, because does not posses by itself. There is no goal as such, but there are Lessons. The Universe is one big school that is about organizing all this Information and learning lessons by it, and as a result our being and at the same time Being of Consciousness grow, what is happening as a natural, and unforced or intended effect.

- Consciousness can create everything into the infinity, this It's hard to say what it is because Consciousness has no limits and second because the Non-Being that frees the whole process itself is infinite. As one can theoretically understand what an ever-expanding Non-Being is, it is so hard to understand what an ever-expanding Information resource can be. Only the continuous organization of this Information resulting in the growth of Being is able to prepare for further Information resources to read them.

- Consciousness in its purest form is permanent, eternal, and is at the root of everything. Individual consciousness can only loss or gain Information, which also results in the loss or grow of being, still being connected to the (main) Consciousness.

- Even though Consciousness is all there is, we can still see clearly that "consciousness is unequal to consciousness." When we perceive other beings, we can distinguish between levels of consciousness, states of consciousness, forms of consciousness, and more and more, they differ from each other and undergo various transformations, development and degradation. This process can be desribed in relation to the time frame, defined as past, present, future and more, by the consious observer. All this suggests that the key here is the existence of time, the flow of which is correlated with the kept forms and states of consciousness, and which we can take as an "objective measure of time".

Okay, Ark, please be lenient with me, I'm not a physicist, but I wanted to relate to "Comments ..." somehow. I know I'm not talking about exactly what's out there, and certainly not in the same way, but it inspired me to think about the thought experiments that I share.

 

[Ryan]

Reflecting on the above quotes, does that relegate humans to the role of receivers/transducers of the DCM emission?

I would say that humans, like most self-aware creatures, are to some extent "in union" with the DCM, thus any reception/transduction is only of information or meaning. In this sense, we might say that our consciousness is not "separate", but "given", and that by gaining knowledge we are re-merging with the DCM to a greater degree and "giving back". So, like the DCM, we are all "Created and Creator".

 

[Cleopatre VII]

As I mentioned, my next longer post was to be about the Maxwell’s demon. In Wikipedia, we can read:

Maxwell conceived a thought experiment as a way of furthering the understanding of the second law. His description of the experiment is as follows:

... if we conceive of a being whose faculties are so sharpened that he can follow every molecule in its course, such a being, whose attributes are as essentially finite as our own, would be able to do what is impossible to us. For we have seen that molecules in a vessel full of air at uniform temperature are moving with velocities by no means uniform, though the mean velocity of any great number of them, arbitrarily selected, is almost exactly uniform. Now let us suppose that such a vessel is divided into two portions, A and B, by a division in which there is a small hole, and that a being, who can see the individual molecules, opens and closes this hole, so as to allow only the swifter molecules to pass from A to B, and only the slower molecules to pass from B to A. He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics.

The second law of thermodynamics mentioned in the quoted fragment of the article can be simply written as

∆S≥0,​

where S is entropy. So we say that entropy never decreases. It can only increase. Is there a paradox then? And what exactly is this entropy, how to put it in words?

We say entropy is a measure of the degree of disorder in a system and energy dispersion. According to the second law of thermodynamics, if a thermodynamic system moves from one state of equilibrium to another without external factors (i.e. spontaneously), its entropy always increases.

Thus, this entropy will be the greater, the more potential there are for individual microstates to realize a given state (macrostate) of the system (e.g. arrangement of particles in cells).

But what is order or the lack of it? What is the entropy? The only mathematical definition that I could give is as follows:

S=k ln(W)​

or equivalently

S=-k ∑_ip_i ln(p_i),​

where

W- the number of ways in which the macroscopic thermodynamic state of the system (macrostate) can be realized through microscopic states (microstates),

k- Boltzmann constant,

p_i- probability of the i-th microstate.

However, some vague concepts emerge: disorder, macrostate, microstate...

Let us try to define them. Let’s start from the end. In statistical mechanics, a microstate is a specific microscopic configuration of a thermodynamic system that the system may occupy with a certain probability in the course of its thermal fluctuations. In contrast, the macrostate of a system refers to its macroscopic properties, such as its temperature, pressure, volume and density. We understand the latter quantities classically. They are intuitive to us, but they start to gain meaning only when we talk about the classical understanding of matter, which I mentioned in the previous post. In terms of the calculus of probability, macrostate can be understood as follows:
Each macroscopic state A corresponds to a certain number Ω(A) of microscopic states which are defined (during macroscopic measurement) as the same state A. In statistical mechanics, the entropy S of the state A is given by

S(A)=k ln (Ω(A)).​

What, then, is this disorder? Some concepts are defined by others, a kind of a loop arises. Why?

Well, entropy seems to be a quantity to some extent intuitive, primary, understood in this way by us. For us, the sequence of numbers (1,2,3,4,5) is order and the sequence (3,5,4,1,2) is disorder. The latter seems completely random. And maybe that’s the source of the problem. Maybe this is the reason for the vague concepts in question? So how was the Maxwell's demon paradox dealt with? First, let us look at this issue from a historical perspective.

In 1929 Leó Szilárd and independently Léon Brillouin suggested solving this paradox with the help of measurement theory. According to Szilard, Maxwell’s demon would have to spend energy measuring the velocity of molecules and at the same time be part of a thermodynamic system in which it would disturb the equilibrium by selecting molecules. The source of energy expended by the demon on measurement would therefore also have to be part of this system. Although the demon would reduce the entropy in the air reservoir, it would at the expense of increasing the entropy of its energy source and the entropy balance of the entire system would still remain positive. This allows for the construction of heat engines in which work is produced by gathering information (both quantum and “classical”).

In 1960, Rolf Landauer stated, however, that it is theoretically possible to measure without increasing the entropy of the system, provided that the measurement is based on any thermodynamically reversible phenomenon on a time scale proportional to the speed of the selection process for these molecules.

However, in 1982 Charles H. Bennett defended Szilard's concept by applying the information theory to it. Even assuming that a demon can measure particle velocities using some kind of reversible phenomenon, it must be gathering information about those velocities somewhere. It can even be assumed that the demon is able to collect information using a thermodynamically reversible phenomenon, and therefore the collection of information will also reduce the entropy of the entire system. But assuming his memory has a finite capacity, he will have to start erasing it eventually. Erasing information is always a thermodynamically irreversible process, and therefore will eventually lead to an increase in the entropy of the entire system consisting of the vessel with air, the demon and its gigantic memory. So it can be said that a demon can function, but not endlessly, and one day he must finally “surrender”.
So what is it with this entropy? In fact, there are many phenomena in nature that act temporarily like Maxwell’s demon, i.e. they are capable of self-organization, seemingly contradicting the Second Law of Thermodynamics. All living creatures are the best example of this. Such phenomena, however, never occur in thermodynamically insulated systems and they always derive the possibility of self-organization from the increase in the entropy of the environment.

But what is life in fact? Can we speak of life only in relation to biological organisms? What if I could make the substantiated hypothesis that stars are living organisms? However, I will only mention this when I write about information theory, and therefore in the next longer post. The concept of information will be particularly important in it. It will also appear in the context of biology.

Dear readers. I am aware that certain terms or meanings are used in this post that may not be understood by everyone. However, I do not know which of the concepts require clarification, so if anything is not clear, I will be happy to write additional posts answering your questions in detail. I would not like to go on without making sure that everything is clear to everyone. You can ask about anything. If there is a need to clarify the details from previous posts, I am also ready to take on this task.

 

[John G]

So what is it with this entropy? In fact, there are many phenomena in nature that act temporarily like Maxwell’s demon, i.e. they are capable of self-organization, seemingly contradicting the Second Law of Thermodynamics. All living creatures are the best example of this. Such phenomena, however, never occur in thermodynamically insulated systems and they always derive the possibility of self-organization from the increase in the entropy of the environment.

But what is life in fact? Can we speak of life only in relation to biological organisms? What if I could make the substantiated hypothesis that stars are living organisms? However, I will only mention this when I write about information theory, and therefore in the next longer post. The concept of information will be particularly important in it. It will also appear in the context of biology.

There are models where a new universe starts via entropy from the environment of another universe; even a model where this start is a conscious thought:

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The information just prior to the birth-evaporation is coded in the protons within the Planck-mass black hole, one bit per proton, so that the number of bits lost in the evaporation of a black hole in a mother universe MUST be 10^19... In gr-qc/0007006, Paola Zizzi says: the vacuum-dominated early inflationary universe ... is a superposed quantum state of qubits. ... the early universe had a conscious experience at the end of inflation, when the superposed quantum state of ... [ 10^19 = N quantum qubits ] ... underwent Objective Reduction. The striking point is that this value of [ N approximately ] equals the number of superposed tubulins-qubits in our brain ...
Moreover ... The value of the cosmological constant now is

... /\N = 10^(-56) cm^(-2) ...
in agreement with inflationary theories.

If decoherence of N qubits occurred now, at Tnow = 10^60 Tplanck

( that is, n = 10^60, N = 10^120 )
there would be a maximum gravitational entropy

... [ maximum entropy Smax = N ln2 = 10^120 ] ...
In fact, the actual entropy is about

... [ entropy now Snow = 10^101 ] ...
[Therefore] decoherence should have occurred for

... [ Ndecoh = 10^(120-101) = 10^19 = 2^64 ] ...
which corresponds to ... [ n = 9 and to ] ... the decoherence time

... [ Tdecoh = 10^9 Tplanck = 10(-34) sec ] ...".

Unlike other models, it actually has an explanation for the hyperinflation in the first 10^-34 sec. At the Planck scale, this one vertex single thought could be just one vertex of a much larger thought state.

 

[PabloAngello]

Ow, I have high entropy:

Let's fix it:

 

[PabloAngello]

For us, the sequence of numbers (1,2,3,4,5) is order and the sequence (3,5,4,1,2) is disorder.

It depends who is looking. For average people not interested in this topic, yes 1,2,3,4,5 is sequence in order.

However for someone else, that uses this equasion:

3,5,4,1,2 are in order.

The question is: does universe has its reference point relative to entropy? Or only we as humans have it.

 

[John G]

We need to go beyond space and time, beyond its causal structure. How consciousness (whatever it is) can influence quantum randomness and causal order? How can we "see" the future (and there is some evidence that this sometimes happens"? That goes beyond quantum theory and many worlds. As for free will - I think that non-determinism is an essential feature of the world (material and non-material), and that it gives the concept of free-will an essential support. One day, I think, we will understand that the universe lacking the free will feature would simply collapse out of boredom!

Awareness which is open to knowledge. The more aware we are and the more knowledge we have and use, the more conscious we may become. There is another aspect of consciousness, which is our awareness of the passage of time. This problem goes beyond quantum theory. Time, its ‘flow’, together with its mysterious arrow, is, I think, a mystery to be solved if we want to solve the problem of consciousness. But that would lead us far beyond the scope of your talk.

A single material particle would not have much knowledge thus its "dumb" decisions even if non-deterministic with free will would look random. Somehow you'd have to have a bunch of worldlines to choose from going off well into the future. Something like the placebo effect might consciously in the current state know what it wants in vague terms and somehow the free will choices head for a future state that is like that vague description even though the medical details are never really consciously known.

 

[ark]

Ow, I have high entropy:

Let's fix it:

Very good example showing that entropy can decrease contrary to the law ∆S≥0. But it also shows that for that to happen there must be first an intelligent designer who created the picture and then cut it. And also that the Maxwell Demon who put the picture back together certainly spent quite a bit of energy on doing this for a couple of hours, as argued by Leó Szilárd mentioned in the nice new educative post by Cleopatre.
Though I still do not know what entropy is, and where does the logarithm function comes from! And I want to know!

 

[ark]

Ow, I have high entropy:

Let's fix it:

We have already learned from previous posts that the probability of arranging the pieces exactly as in the first picture is the same as probability of arranging them as in the second picture. If so, why do we consider the second picture as "order" and the first one as "chaos"? This I would like to see explained. Is there more than just probability in the concepts of entropy and information? Or one should be very careful when applying probabilities? And why does Nature care about probabilities? Are they objective? Or are they subjective? And if they are subjective, why they seem to work nevertheless?

 

[PabloAngello]

@ark Question might be extended hooking entropy and probalities together.

From definition: "entropy of isolated systems left to spontaneous evolution cannot decrease with time"

Yep but, what caused isolated system to be created and some particles placed inside it?
For example we have bottle of gas that together are isolated system. Entropy of gas particles inside will decrease in time but the cause of it is that the gas bottle exists and some other process put gas particles inside it. So entropy is highly relative.

Example one (low entropy):


Example two (high entropy of low entropy objects):



Now the question: What is behind creation of isolated object(containter)?

Thoughts: We as people, rest animals as well, are creating their isolated environments all the time. We are creating buildings/houses, things like tools, to help us make other things in desired order. Creating an object or set of objects (isolated systems like) fasten the process of lowering entropy in universe. Living organisms fasten this process as a whole. If lowering entropy is fundamental in nature, then it was natural progress that living organisms were created, because its more efficient then.

Another thought from psychological point of view: its funny that we a tendency to be angry on people that make things out of order :)

 

[PabloAngello]

And why does Nature care about probabilities? Are they objective? Or are they subjective? And if they are subjective, why they seem to work nevertheless?

Why not subjective and objective at once (analogy to superposition), according to interaction or its lacking?