Some comments on information theory

Hello H2O

The Living Force
FOTCM Member
Mine as well :) But from programmer/algorihtmic perspective.

What does it mean?
I had no idea either, so put it into DuckDuckGo, and got:

Q.E.D.​

From Wikipedia, the free encyclopedia

This article is about the Latin phrase. For the physical theory, see quantum electrodynamics. For other uses, see QED (disambiguation).

Q.E.D. or QED is an initialism of the Latin phrase quod erat demonstrandum, meaning "which was to be demonstrated".[1] Literally it states "what was to be shown".[2] Traditionally, the abbreviation is placed at the end of mathematical proofs and philosophical arguments in print publications, to indicate that the proof or the argument is complete.
 
I had no idea either, so put it into DuckDuckGo, and got:

Q.E.D.​

From Wikipedia, the free encyclopedia

This article is about the Latin phrase. For the physical theory, see quantum electrodynamics. For other uses, see QED (disambiguation).

Q.E.D. or QED is an initialism of the Latin phrase quod erat demonstrandum, meaning "which was to be demonstrated".[1] Literally it states "what was to be shown".[2] Traditionally, the abbreviation is placed at the end of mathematical proofs and philosophical arguments in print publications, to indicate that the proof or the argument is complete.
Exactly. Unfortunately, my posts are waiting for the moderator's approval and hence are displayed with a delay.
 
@Hello H2O I know this shortcut is related to quantum theory, but I can't see a link between that post and this :D
Maybe @Cleopatre VII will enlight us.
So I come and bring the light that is expected. Yes, that's right, QED also stands for quantum electrodynamics. It is the relativistic quantum field theory of electrodynamics.

However, I did not use it in that sense. Q.E.D. (with or without dots) is also written after the proof is completed. My proof was simple, but I just like to write like that, so I write. It's my high school habit.
 
Weird thing, @Cleopatre VII explanatory post appeared before ours ;O WTF? Do you travel in time @Cleopatre VII ?

I remember very well we posted firstly.
I don't travel in time in general... Or I haven't traveled in it yet (although I'm not sure, but it's a discussion on a different thread). No, my dear. The point is, my posts are delayed. They are displayed after the moderator's approval. I have far fewer posts here than you do, and that is likely the cause. I don't know the forum rules that well. I only suppose so.
 

ScioAgapeOmnis

The Living Force
FOTCM Member
Fascinating discussion! I tend to think that free will is at the root of everything. In other words, the universe is inherently biased if and when needed, so randomness seems unlikely to exist in an ultimate “true randomness” sense. I’m not even sure how one could prove true randomness - isn’t it simply the absence of our ability to detect or understand a pattern, but isn’t that a personal problem?

A lot of stuff in math seems to be based on the assumption of “in a hypothetical world where the dice are perfect and the environment isn’t manipulated by consciousness via free will.. and one we can completely control..”. The real world isn’t just more messy and unpredictable due to us having imperfect information about it, but free will would suggest that it is impossible to have perfect information as it is subject to change. So there are biases we may never be able to account for and predict.

However, in order to understand consciousness and free will (never mind explain it mathematically), we must first understand probability as it would work without such a thing. Kinda like learning about Neuton’s gravity before moving on to Einstein, otherwise how can you truly appreciate the latter if you don’t first define and understand the former and where it runs into trouble?

Speaking of probability, here’s a fascinating challenge that drives people, myself included, a little bit bonkers. It’s called the Monty Hall problem. See if you can divine the answer without looking it up tho!

Suppose you’re on a game show, and you’re given the choice of 3 doors: behind one door is a car; behind the others, goats. You’re asked to pick a door, and you pick one, say #1. The host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He then says to you, “Do you want to pick door #2 or stick to your original decision?” Is it to your advantage to switch your choice? Why or why not? Are the odds of the car being behind door #1, which you originally chose, the same as door #2, now that you know that door #3 is a goat?
 

PabloAngello

Jedi Master
What is not false?
I know it doesnt have established scientific definition, but closest for me is "objective information".

@ScioAgapeOmnis You have used many words, that need explanation first in this discussion:
I tend to think that free will
Define what you mean by free will.
true randomness
Also needs definition. We are working on it.
manipulated by consciousness
Again, needs definition, the consciousness.

Basically in the shortcut, you are saying:
"We need free will (undefined) and true randomness (undefined) and consciousness (undefined) to understand the root of everything (undefined)".
:D This will be hard..

Suppose you’re on a game show, and you’re given the choice of 3 doors: behind one door is a car; behind the others, goats. You’re asked to pick a door, and you pick one, say #1. The host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He then says to you, “Do you want to pick door #2 or stick to your original decision?” Is it to your advantage to switch your choice? Why or why not? Are the odds of the car being behind door #1, which you originally chose, the same as door #2, now that you know that door #3 is a goat?
Basically you are playing 2 different games.
One game has 3 doors and probability of picking the 'right one' is 1/3 = 33,(3)%
In second game you have only 2 doors to pick, so probability of winning is 1/2 50%.
BUT from the first game you know that doors you previously picked had 33.(3)% of winning, so the doors you havent picked but you can now in second game, have 50% winrate. So you should pick new doors if you want to increase you winning chances.
Addition: doors that was revealed in game 1, had also 33% of winning rate, it doesn't matter that there was a goat, instead of goat you can place there 33.3% number.
 

ScioAgapeOmnis

The Living Force
FOTCM Member
I know it doesnt have established scientific definition, but closest for me is "objective information".

@ScioAgapeOmnis You have used many words, that need explanation first in this discussion:

Define what you mean by free will.

Also needs definition. We are working on it.

Again, needs definition, the consciousness.

Basically in the shortcut, you are saying:
"We need free will (undefined) and true randomness (undefined) and consciousness (undefined) to understand the root of everything (undefined)".
:D This will be hard..


Basically you are playing 2 different games.
One game has 3 doors and probability of picking the 'right one' is 1/3 = 33,(3)%
In second game you have only 2 doors to pick, so probability of winning is 1/2 50%.
BUT from the first game you know that doors you previously picked had 33.(3)% of winning, so the doors you havent picked but you can now in second game, have 50% winrate. So you should pick new doors if you want to increase you winning chances.
Addition: doors that was revealed in game 1, had also 33% of winning rate, it doesn't matter that there was a goat, instead of goat you can place there 33.3% number.
I don’t know how to define free will precisely, only as some kind of catalyst for non-deterministic and not random change of state. So the best I can do is say what it isn’t. And as for consciousness, free will is a necessary component of it, but in addition it needs to also have the ability to perceive information, organize it into meaning, and use free will to act on it in some way. We have evidence that humans can influence/bias random number generators, for example.

What always intrigued me is the concept of infinity. It’s somehow greater than the sum of its parts. And I can’t prove it, but my hunch is that free will depends on it to exist. Free will and consciousness is the only thing that seems to explain how a universe with no beginning or end can have a present. How can we exist somewhere “in the middle” of an infinite timeline, having arrived at this point (or any point on this timeline for that matter) without being forced to traverse infinity from either direction to arrive here? You can’t traverse infinity, it takes an infinite amount of time to do so, and we would never get anywhere if we had to start from either infinite direction. So the fact that we are somewhere in this infinity, means we “teleported” here in a sense, we had to entirely disregard time and space to do it.

Like if you have a number line that is infinite in both directions, how can you get to the number 7 for example? Well you just do, you think of 7, and here you are. You didn’t have to count down from infinity or count up from negative infinity until you finally arrived at 7, that’s impossible. And why did you pick 7? Well it’s not random, and it’s not deterministic, it’s because you wanted 7, it was meaningful to you, and you conjured it into being from this infinite numerical ether to serve your aim.

So it seems like when you start to play with infinity, somehow consciousness and free will seem to show up too, at least in my view.
 
I don’t know how to define free will precisely, only as some kind of catalyst for non-deterministic and not random change of state. So the best I can do is say what it isn’t. And as for consciousness, free will is a necessary component of it, but in addition it needs to also have the ability to perceive information, organize it into meaning, and use free will to act on it in some way. We have evidence that humans can influence/bias random number generators, for example.

What always intrigued me is the concept of infinity. It’s somehow greater than the sum of its parts. And I can’t prove it, but my hunch is that free will depends on it to exist. Free will and consciousness is the only thing that seems to explain how a universe with no beginning or end can have a present. How can we exist somewhere “in the middle” of an infinite timeline, having arrived at this point (or any point on this timeline for that matter) without being forced to traverse infinity from either direction to arrive here? You can’t traverse infinity, it takes an infinite amount of time to do so, and we would never get anywhere if we had to start from either infinite direction. So the fact that we are somewhere in this infinity, means we “teleported” here in a sense, we had to entirely disregard time and space to do it.

Like if you have a number line that is infinite in both directions, how can you get to the number 7 for example? Well you just do, you think of 7, and here you are. You didn’t have to count down from infinity or count up from negative infinity until you finally arrived at 7, that’s impossible. And why did you pick 7? Well it’s not random, and it’s not deterministic, it’s because you wanted 7, it was meaningful to you, and you conjured it into being from this infinite numerical ether to serve your aim.

So it seems like when you start to play with infinity, somehow consciousness and free will seem to show up too, at least in my view.
You raise very interesting points, both in this and in your previous comment. Thank you also for mentioning the Monty Hall problem. I also considered writing about it in one of the next posts.

With this infinite timeline, however, the situation becomes even more complicated, at least in the context of the general theory of relativity. We can actually speak of the timeline in classical (Newtonian) mechanics. In general relativity, however, this concept seems to be meaningless. I already explain why.

Imagine asking the question: What is happening now on Proxima Centauri? The star in question is approximately 4.2 light years from Earth. This means that we see it as it was 4.2 years ago. Getting to know its present requires us to overcome space. We need time to cross the space. Hence, we can say that the present of the considered star is transcendent to us. We will find out about it in 4.2 years, but then its new present will be transcendent to us. I am considering the case of a distant star, but I do not even see the corner of the room in which I am in its present. I can see it as it was some fractions of a second ago. So when we talk about the timeline, we can only mean the passage of time at one point chosen by us, and at the same time we assume that this point rests in relation to all other points. Why?

Because we know from the Lorentz transformation that
∆t=γ∆t0,
where
∆t0- the duration of the even recorded by an observer resting in relation to the event,
∆t- duration of the same event occurring in the frame of reference of the first observer recorded by the observer moving relative to the first observer at speed v,
γ=√(1/(1-β2)),
β=v/c,
v- relative speed of the observers,
c- speed of light.

Moreover, this time flows relatively differently for different observers depending on their velocity and the gravitational field in which they are located! A person approaching a black hole will appear to freeze over time. For that person, those farther from the black hole will appear to be moving very fast. This is a consequence of gravitational dilatation. However, not only the passage of time is relative, but also the sequence of events! The sequence of events may be different for different observers. This is another surprising consequence of general relativity. How then to speak of any order in time? About the timeline? On the other hand, probability is also sometimes related to the passage of time. For example, in the case of radioactive decay.

So what are time and space in essence? Why do we feel the passage of time? Would time pass in the absence of consciousness? How would it then be registered? I recommend Husserl's lectures on time and consciousness here. It is worth reading them very carefully. Husserl's philosophy, and German philosophy in general, is somewhat like contemporary art. One has to go deep into it to see the world it describes.

I also recommend a book that deals with these issues: Carlo Rovelli "The Order of Time". It is neither long nor complicated, it is reading for one day. I recommend it to anyone interested in the passage of time and the general theory of relativity.
 
Top Bottom