Some comments on information theory

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I think of infinity as the limitless space of the total multiplicity of fields (And then some) in which finite limited or defined events can occur which includes our existence.

Going from there, the C’s talk of a realm border. We often talk about the man behind the curtain with the curtain being a boundary that differentiates or hides the awareness of the differentiation. So the nature of the actual boundary or limited field of differentiation between two sub fields of infinity is a question of a special case phenomenon that supersedes the normal laws and understandings applying to either side of the randomly moving wave boundary which applies some kind of change of state. The wave is rolling through infinity a bit like an automated vacuum cleaner and perhaps we are the fascinated cats pensively watching and wondering in super slo-mo at what point it will actually sweep over our micro sector of the cosmic kitchen floor and apply that state change up close and personal.

Infinity is a limitlessness space that contains finite eternities. (Otherwise we’d never get anywhere.) So, ultimately our Physical existence is finite, no matter how many incarnations there may be. And That limited number is what makes each life special no matter how crappy the circumstances may subjectively be experienced.

“Dammit Jim, I’m a writer, not a theoretical physicist!”

This all Sounds kind of like the intro to a joke.

A theoretical physicistS, a mathematician, a philosopher and a priest walk into a bar....

The mathematician says “why are there 4 of us? Don’t these jokes usually involve threes?” The priest quite agrees as he is fond of the trinity. The theoretical physicistS says “What makes you think there are 4 of us here?” The priest says “Look, to do the right thing we need to decide on a designated driver.” The philosopher says “What does it matter what we decide now? We will judge who is least drunk later and give them the keys”. By this time the bartender is getting impatient. “Are guys going to order a drink or not?”

They look at each other, laugh, and walk out as one.
 
Isn't there a distinction between the terms density and dimension?
Dimension is a physical matrix or substrate, density is a non physical information field(s).
Is this a correct understanding?
Thank You!
 
dennis said:
Isn't there a distinction between the terms density and dimension?
Dimension is a physical matrix or substrate, density is a non physical information field(s).
Is this a correct understanding?
Thank You!
Click to expand...
Density refers to the level of complexity of consciousness. The consciousnesses with a lower level of consciousness occupy lower densities. The consciousnesses with a higher level of consciousness occupy higher densities.

There are 7 Densities: 3 material that are in the direct contact, 1 density connecting matter and spirit, 3 spiritual densities:
1st Density - minerals, plants, and other organisms with little complexity...
2nd Density - the most of the species of animals...
3rd Density - for instance humans, and other possible existed beings with similiar level of complexity, possible having a home in other parts of the universe...
4th Density - beings more complex than us, more intelligent and more conscious, occupying a higher level than we do not have direct access to, living in the world with changing physicality (partly spiritual, partly material) like Lizards for instance...
5th Density - the first entirely spiritual density, home to all beings who lived in the 1st to 4th density worlds; in the event of the extinction of the body, they have the option of transitioning to the 5th density...
6th Density - this is also spiritual density, having no any direct relation to the material worlds; the density of knowledge and light, the Cassiopaeans tell us that they occupy this density
7th Density - "god", the absolute, "all that exists and non-exists"

That's it in short when it comes to densities. For more, I'd suggest focusing on The Wave series for example. Available here: The Wave Volume 1 – Cassiopaea

When it comes to dimensions, we can speak of two meanings. The first meaning is that dimensions can exist in large numbers parallel to each other at the same level of density.

For example, we are on Earth in one of the dimensions. We have the situation we have. But there are other possibilities as well. In other dimensions, where people have made different choices, there may be a different reality; such as perhaps somewhere in one dimension of many possible dimensions America's president is Trump, and no one has heard of something like the "global Covid pandemic".

Perhaps in another dimension, the Earth "rock'n'rolled" so hard that it was bombarded by comets before other things happened. There are many possibilities, we can also have many different dimensions, and our and other choices determine which path we choose, choosing a different path, we also choose a different dimension and reality. We do not create dimensions, we choose dimensions through our choices and decisions.

The second meaning is the structure of reality and our ability to interact with it. The reality of density can be structured differently. Our reality of the 3 density is 3 dimensional in which we exist as the 3 density and 3 dimensional beings. It is our natural environment. We have right, left, we know directions, we perceive the depth. We live in 3 dimensions.

But these aren't the only ways to exist. For example, a dog that is a 2 density creature and lives in 2 dimensions has a brain having trouble interpreting 3 dimensional reality. For example, my dog has a problem with determining the speed of an oncoming car and whether it can enter the streets at the moment. If I hadn't kept him on the leash, he could have run into the street and he would have reacted only when the car tried to run into him. We notice various awkwardness of our animals, which have a problem with moving in the reality when for us many things are obvious and comes natural. But this is because they are just naturally designed to exist and function in 2nd density and 2nd dimensions.

Just as we have life in 2 dimensions and 3 dimensions, so we can have 4 dimensions. We cannot imagine what life in those 4 dimensions is like because we are designed to live in 3rd density, which is also embedded in 3 dimensions. However, there are ways to get closer to what the 4th dimension can look like. There are various attempts and ways to project, for example, 4-dimensional objects into 3 dimensions, this obviously does not show what a 4-dimensional object is in essence, but allows us to see it, let's say as "imprint". A way to visualize and approximate what a 4-dimensional object looks like is done for example by the 3-dimensional visualization using sterographic projection. Look at the video below:

Cassiopaeans say that 4th density exists in 4 dimensions. They also say that there are really no limits to such type of the dimensions. Perhaps, for example, such a 7th density once that it lives in infinitely amount of dimensions that occupy the same level density and are parallel to each other, this, in addition to this 7th density exists in an infinite number of dimensions in terms of the structure of reality. Just as 3rd density has 3 dimensions, 4th density has 4 dimensions, 7th density can has infinitely many dimensions, however who knows how to grasp it.
 
Luks said:
Just as we have life in 2 dimensions and 3 dimensions, so we can have 4 dimensions. We cannot imagine what life in those 4 dimensions is like because we are designed to live in 3rd density, which is also embedded in 3 dimensions.
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In one of the previous posts on this thread, I mentioned my dream about the fourth dimension. It seems to me that our image of the higher dimensions is somewhat limited by the logical mind, and that is essentially what you call third density. This does not mean, however, that it is impossible to look deep into the higher densities. This is probably something of a mystical experience. Such an experience is transcendent to the logical mind. Hence it cannot be described in logical terms.
 
Cleopatre VII said:
In one of the previous posts on this thread, I mentioned my dream about the fourth dimension. It seems to me that our image of the higher dimensions is somewhat limited by the logical mind, and that is essentially what you call third density. This does not mean, however, that it is impossible to look deep into the higher densities. This is probably something of a mystical experience. Such an experience is transcendent to the logical mind. Hence it cannot be described in logical terms.
Click to expand...
I think about it alike. Our ability to think logically comes from the proper work of the conscious mind. Which is apparently designed to work in 3 density and 3 dimensions, which is okay, all in all, here we have lessons to go through and that's what we should be focusing on.

Using the conscious mind, logic and willpower in general that comes from our conscious mind is very important, although it's not enough to perceive 4th density, I think. If I had to relate my own experiences to perception of 4th density, it had a more emotional and intuitive dimension.

Several times in my life I had some sensations in the area of higher emotional center (heart chakra). They were characterized by the fact that I had no control whatsoever to trigger or stop it, and the whole sensation could in no way relate to my physical body.

Despite the lack of any physical sources to evoke the feelings that I could relate closest to feeling of "warmth," I still felt that warmth. I think I felt something that was not 3rd density, but still felt. Maybe I could felt 4th density activity then, but it's hard to confirm in any way.
 
I was thinking about these things earlier this morning. I've also endeavored to undertake a remedial math education, getting some understanding of the symbols and operators and what they do beyond what I had in high school, as I took some accounting in college and no other math. Maybe math can be related to the mystical, who knows. I had the notion of perpenculiarity, where the peculiar intersects or informs the normal mundane.

Here is some idea similar in an article referencing Gurdjieff :

As a further element in this mysterious process, the members of the society were able to deviate deliberately from the mechanical flow of psychic events so that, in the intervals of the unexpected, something could be 'inserted' which conveys a truth. This is the practical equivalent to our supposed 'moment of truth' in which we imagined a character who awoke and told us (in the form of the other characters) what was going on in reality. In our speculation, we saw that this would mean the ending of the play. In Gurdjieff's method, the play continues along the mechanical line and consciousness is conveyed indirectly. What it is like is suggested by the unexpected modulation in a symphonic work. Subtly and instantaneously, we are lifted into an unspecified degree of freedom which just as quickly gives way to the new order, the new key (or framework). It is experiencing this kind of thing in ourselves that teaches us, for the teaching here is not of merely external information.
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As promised, I will write about Bayes theorem today. However, we will start with the definition of conditional probability, therefore
P(A│B)=(P(A∩B))/(P(B)),
P(B)>0.

In the above formula P(A│B) denotes probability of occurrence of event A, provided that event B occurs.
To better "feel" the above definition, I will present two simple examples.

Example 1.
A cubic dice is rolled. Calculate the probability of rolling more than three dots if it is known that the result was an even number.

Solution.
Let us introduce the following designations:
Ω- one roll of the dice,
A- more than three dots have been obtained,
B- an even number of dots has been obtained,
P(A∩B)- an even number of dots greater than 3 has been obtained.

We want to calculate the probability of event A, provided that event B happened. We will use the formula:
P(A│B)=(P(A∩B))/(P(B)).

We calculate the cardinalities of the sets (numbers of their elements).
|Ω|=|{1,2,3,4,5,6}|=6,
|A|=|{4,5,6}|=3,
|B|=|{2,4,6}|=3,
|A∩B|=|{4,6}|=2.

Now we compute the probabilities:
P(A∩B)=(|A∩B|)/(|Ω|)=2/6=1/3,
P(B)=(|B|)/(|Ω|)=3/6=1/2.

So we finally have:
P(A│B)=(P(A∩B))/(P(B))=(1/3)∙(2/1)=2/3.

Example 2.
There are 8 balls in the urn: 4 white and 4 black. We choose randomly without returning 2 balls. Determine the probability that the second ball drawn will be black when the first ball drawn was white.

Solution.
Let us introduce the designations:
A - the second ball drawn is black,
B - the first ball drawn is white,
A∩B - the first ball drawn is white and the second ball drawn is black.

We want to calculate the probability of event A, provided that event B happened. We will use the formula that we already know:
P(A│B)=(P(A∩B))/(P(B)).

We compute the necessary probabilities:
P(B)=4/8=1/2,
P(A∩B)=(4/8)∙(4/7)=16/56=2/7.

So we finally have:
P(A│B)=(P(A∩B))/(P(B))=(2/7)∙(2/1)=4/7.

So we can see that the examples are not difficult to solve and we can use the definitions of probability that we already know from earlier posts. After getting acquainted with the concept of conditional probability, we can move on to Bayes theorem.

Bayes theorem in its basic form says that
P(A│B)=(P(B|A)P(A))/(P(B)),
where A and B are events, P(B)>0 and P(A│B) denotes the probability of event B occurring, provided that event A occurs.
An example will be presented again.

Example 3.
Let B be a "patient has high fever" event and A be a "patient has flu" event. If the percentage of patients with fever P(B) and the percentage of patients with influenza P(A) in the entire population are known, as well as the percentage of patients with fever among those suffering from influenza, i.e. P (B|A), the Bayes theorem allows to determine the percentage of patients suffering from influenza among those suffering from high fever, i.e. P (A|B).

Let us assume that:
P(B)=0.2,
P(A) = 0.1,
P(B│A)=0.7.

Hence:
P(A│B)=(P(B|A)P(A))/(P(B))=(0.7∙0.1)/0.2=0.35.

Bayes theorem can be extended to a case for multiple events. Its subjectivist interpretation is, in a way, connected with certain notions from the field of category theory, and it turns out to be extremely important in the philosophy of science.

However, I will come back to this topic in some post in the future, and now I will give two exercises to solve for readers. If you have any questions or concerns please do not hesitate to ask!

Exercise 1.
A random family with two children was selected. Calculate the probability that a family with two boys is selected if:
a) the younger child is a boy,
b) there is at least one boy.

Exercise 2.
Two urns are given: urn A containing 6 black and 9 white balls and urn B containing 5 black and 15 white balls. A white ball is drawn. What is the probability that the ball drawn comes from the urn A?
 
Are there any takers to solve the exercises?

If I have presented anything not entirely clear, I will be happy to explain it in more detail. I can also add some hints.
 
Cleopatre VII said:
Are there any takers to solve the exercises?

If I have presented anything not entirely clear, I will be happy to explain it in more detail. I can also add some hints.
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It's conditional probability not Bayes theorem for both exercises I think; at least that's what I'm doing to get my answers which I'll mention later if no one else wants to try it.
 
John G said:
It's conditional probability not Bayes theorem for both exercises I think; at least that's what I'm doing to get my answers which I'll mention later if no one else wants to try it.
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In the second exercise, you should use Bayes theorem.
 
Exercise 1.
A random family with two children was selected. Calculate the probability that a family with two boys is selected if:
a) the younger child is a boy,
b) there is at least one boy.
Click to expand...

3 possible outcomes one of which is eliminated by either condition a or b, but the two conditions stated are redundant
(unless the birth order warrants more odds of having a girl next)
otherwise, 50%
 
It's been a while since I've looked at math but I think there are two ways to look at the exercise 1. a) and b) conditions are redundant since you're looking for a family with two children who are both boys. The only thing to consider is that since a) is specifying older vs younger as a condition so you have one extra option on the number of families.

The first way is to calculate the odds of a boy being born twice. So 50% for the older boy and 50% for the younger boy. You can add these two ratios together since 50% is 1/2. So 1/2 + 1/2 = 1/4 so 25% chance.

The other option is to look at all the possibilities. You have 4 options for a family with two children if you consider condition a).

Two boys
Two girls
Older boy, younger girl
Older girl, younger boy

so 1 in 4 odds = 25%
 
Exercise two seems more complicated at first but if you think about the condition "a white ball is drawn" then the solution is simpler I think. For this exercise you can ignore the black balls.

Urn A has 9 white balls and Urn B has 15 white balls. If you're looking for the probability for a white ball being drawn from Urn A then it's 9/24 = 0.375 = 37.5%. You take Urn A's white balls and divide it by the total number of white balls that can be drawn to calculate the odds of a white ball belonging to Urn A. I think since you've drawn a white ball it has a 37.5% chance of belonging to Urn A.

Hopefully my brain is thinking correctly.
 
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