Information Paradox: How a Drawing Can Represent Two Things

[chaoseverlasting]

As far as I know, net information content in the universe is constant. How about this:

A child draws a simple skeleton of a house connected to another house with a pipe and draws a similar pair of houses right next to them with a fallen tree between the two houses. The second pair of houses has an antenna on the external face of the right house.

This drawing is supposed to represent a neighbourhood or a street, but when a chemist looks at the drawing, he sees an organic reaction with two closed 5 membered rings (bond line representation), where the tree represents the arrow.

Nothing has been added to the drawing, but it represents a neighbourhood and an organic reaction at the same time. The information has increased without anything being added to the original drawing. Isnt this an information paradox?

 

[russ_watters]

What about all the molecules that were broken apart to provide the energy for the child to make the drawing?

 

[tehno]

As far as I know, net information content in the universe is constant.

Disagreed.

 

[cesiumfrog]

Consider the universe once the drawing is completed. In principle (classically) you can measure the microstate: where every atom is, and its velocity. This is the final information content. You could also have done the same before the drawing. The two microstates must contain exactly the same amount of information because (in principle, by the deterministic nature of the laws of mechanics) knowing the initial microstate is completely sufficient to deduce the final microstate, and vice versa. Besides, in the situation you describe, the chemist obtains no new information anyway because in his context the child's message is just random noise.

 

[chaoseverlasting]

Disagreed.

So, the information content in the universe is not constant? How so?

 

[chaoseverlasting]

Besides, in the situation you describe, the chemist obtains no new information anyway because in his context the child's message is just random noise.

The chemise, however, can see both the drawing as a neighbourhood, and as a chemical reaction. Where is the random noise? They are two different interpretations of the same drawing. The information derived from it however, changes from observer to observer. Where is the inconsistency?

Wishing everyone a very happy and prosperous new year to all.

 

[chaoseverlasting]

What about all the molecules that were broken apart to provide the energy for the child to make the drawing?

What about them?

 

[Crosson]

Interesting thought. First of all, don't assume that information in the sense of information theory as corresponding exactly to intuitive ideas about information.

Information theory quantifies the information in a signal (analog or digital).

If you like, the resolution of your paradox is that the chemist's brain contains more information then the child brain. The childs perceives two signals: the visual information and the information his memory provides. The chemist receives 3 information signal, in this sense.

Also, it is not true that the "total energy of the universe" is constant, because this quantity is not defined. Information is much less understood, and so your assumption that the total is constant is not even a question we can ask (yet).

 

[russ_watters]

What about them?

They represent a net decrease in the information content of the universe.

Btw, that's what the 2nd law of thermodynamics says. The information content of the universe isn't constant, it is decreasing.

 

[cesiumfrog]

The chemise, however, can see both the drawing as a neighbourhood, and as a chemical reaction. Where is the random noise?

Imagine I pull scrabble letters from a bag and write down whatever they spell. Perhaps I will obtain the sentence "everest is the highest mountain", and think that I have pulled information from the bag, but I would be mistaken to think so. I could just as easily have obtained "everest isthe smallest mountain" or "as djhfkajshdf kjbasdfkjhzskdfh". Realising this, I know that the sentence contains no information, no matter how it happens to appear.

 

[billiards]

I agree with cesiumfrog, the information that you are considering is cultural it has no definitive meaning, it means what your culture attaches to it. Its like you take a pure thing like a perfectly natural number 666 and immediately attach conotations based on your culture.

The other information contained would be deducible to a highly intelligent alien with no cultural bias, things like how hard the human pressed, what materials humans use for writing, traces of human DNA on the paper etc..etc..

 

[disregardthat]

Yeah, I don't think the information sent depends on what is written. It depends on the person observing it and how he interpret it.

 

[Q_Goest]

The only information needed to represent the drawing is 'information' about the position of every particle in the simple drawing. That information is not a house or a chemical reaction. It is the information regarding the particles' position/momentum/etc... in the simple drawing. There is nothing intrinsic about the positions of those particles such that they represent a house or a chemical reaction. They don't represent anything, a person's mind is needed to interpret those positions as symbols which can represent something else.

When observed by a child, the child's mind interprets the symbols she sees on the page, such that the position of some set of particles in the child's brain results in the child thinking "house".

When observed by a chemist, the chemist's mind interprets the symbols he sees on the page, such that the position of some set of particles in the chemist's brain results in the chemist thinking "chemical reaction".

The position of the particles on the paper hasn't changed, thus there is no more information needed to describe the simple drawing. However, in order to create two different interpretations, two different sets of particles that are not part of the drawing must be created to interpret the symbols seen by the mind.

A single person could also interpret the drawing in multiple ways, but in that case, the configuration of that person's mind must also have different configurations for each interpretation.

 

[chaoseverlasting]

The only information needed to represent the drawing is 'information' about the position of every particle in the simple drawing. That information is not a house or a chemical reaction. It is the information regarding the particles' position/momentum/etc... in the simple drawing. There is nothing intrinsic about the positions of those particles such that they represent a house or a chemical reaction. They don't represent anything, a person's mind is needed to interpret those positions as symbols which can represent something else.

If you like, the resolution of your paradox is that the chemist's brain contains more information then the child brain. The childs perceives two signals: the visual information and the information his memory provides. The chemist receives 3 information signal, in this sense.

So does information here mean the position of all the molecules present on the drawing or what we can deduce from processing the drawing?

And since we can see the drawing because of the light reflected off of the drawing, is light here be the signal and the brain just the processor of the signal?

 

[chaoseverlasting]

And when the child draws the drawing, isn't the child coding information on the paper in the form of different colors? The chemist can decode the encoded information to a greater extent even if that wasnt the initial intent.

 

[chaoseverlasting]

Yeah, I don't think the information sent depends on what is written. It depends on the person observing it and how he interpret it.

If that is true, then the information received is greater than the information sent. The child only drew the house, but the chemist saw the house and the reaction.

 

[russ_watters]

Could you guys please read my post #9. All of what you are discussing is irrelevant.

 

[cesiumfrog]

All of what you are discussing is irrelevant.

That may be so, but with regards to your post: (since it seems "well known" that the total information in the universe is supposed to be conserved) do you think you should give a reference to support your contradictory assertion?

 

[disregardthat]

Not everyone understands your post, and you did not explain yourself further, making your post 'just' another one in this thread. To me it gave no meaning. And probably not to everyone else here, since they also are discussing

 

[Q_Goest]

So does information here mean the position of all the molecules present on the drawing or what we can deduce from processing the drawing?

Let's clarify what "information" means. From Wikipedia:

In physics, physical information refers generally to the information that is contained in a physical system. ...

Quantum information specifies the complete quantum state vector (or equivalently, wavefunction) of a system, whereas classical information, roughly speaking, only picks out a definite (pure) quantum state if we are already given a prespecified set of distinguishable (orthogonal) quantum states to choose from; such a set forms a basis for the vector space of all the possible pure quantum states (see pure state).

http://en.wikipedia.org/wiki/Physical_information
In the case of the OP, I think we should limit ourselves to classical information. Because although quantum information may be applicable, it isn't necessary to understand why the question isn't a paradox. For the sake of clarity, and because I'm no expert in QM, let's just consider the particles in the 'drawing' to be Lego blocks. Some of the Lego blocks are white, others are black, and together they form a picture. The analogy should be clear enough.

The information needed to describe the picture now consists of what color Lego blocks are at each point. There is no other physical information which is contained within the drawing. The drawing doesn't contain information about a house or a chemical reaction. The information is only the location of the Lego blocks.

Where I feel the mistake is being made is in assuming that the drawing is a representation of something, such that the representation is yet another bit of information. It's not. The representation of a house is 'seen' by the child, such that the subjective experience of the house is had only by the child who must have additional 'Lego blocks' that correspond to that subjective experience. Similarly, the chemist has a subjective experience of a chemical reaction, such that the subjective experience of the chemical reaction is had only by the chemist who must have additional Lego blocks in his head to correspond to that subjective experience.

Russ said: They represent a net decrease in the information content of the universe.

I'm not sure what exactly you had in mind here, Russ. I think you meant that the interpretation of the drawing of the house or chemical reaction represented a decrease in the information content because the drawing could be 'reduced' to a single concept. If that's not what you meant, please clarify.

 

[billiards]

I think Russ was talking about the increase in entropy according to the second law of thermodynamics...?

 

[russ_watters]

That may be so, but with regards to your post: (since it seems "well known" that the total information in the universe is supposed to be conserved) do you think you should give a reference to support your contradictory assertion?

There may be a gap between my understanding of entropy from a theromdynamics point of view and that of how physics sees it. Engineers don't deal with information content. The common "teacup analogy" is that a teacup that falls on the floor and breaks cannot be spontaneously returned to its original state. Doing so requires an input of energy and a net increase in the entropy of the universe.

Googling, it looks like physicists say that information content and entropy parallel each other and in increase in one requires an increase in the other. From the above analogy, though, it seems like entropy should increase faster than information content.

There is also the "heat death" of universe, which theorizes that the universe will eventually "run down" to where it contains no matter whatsoever, only low energy photons.

I'm not sure how to reconcile these, but I don't think it should matter since a child is an open system and takes highly ordered chemicals and converts them to simpler forms while releasing energy, both decreasing the information content and increasing the entropy around him/her.

 

[russ_watters]

Also, the wik link says entropy in physics is "used-up" information capacity. If the energy of a system is fixed and the entropy is increasing, how can the available energy capacity then also be increasing?

 

[cesiumfrog]

a teacup that falls on the floor and breaks cannot be spontaneously returned to its original state. Doing so requires an input of energy and a net increase in the entropy of the universe.

No matter how finely it shatters, if you study the rubble well enough you could in principle reconstruct the teacup (differentiating it from a saucer, and resolving any message printed on the side). In this sense, information cannot be destroyed. Similarly information cannot be created (if the universe is deterministic then by measuring every involved atom at some earlier time in history one could "in principle" calculate exactly how the teacup will be).

On the other hand, it is not easy to make such detailed measurements (if it were we could use them, say, to harness the energy in the ocean's heat). It would effectively reduce the teacup to a state of zero entropy (a perfectly known state); no doubt even greater entropy will only result elsewhere as a thermodynamic consequence of the measurement.

Information is such a curious topic of physics!

 

[gone gator]

Imagine I pull scrabble letters from a bag and write down whatever they spell. Perhaps I will obtain the sentence "everest is the highest mountain", and think that I have pulled information from the bag, but I would be mistaken to think so. I could just as easily have obtained "everest isthe smallest mountain" or "as djhfkajshdf kjbasdfkjhzskdfh". Realising this, I know that the sentence contains no information, no matter how it happens to appear.

so honestly: if you pulled "everest is the highest mountain" tonight (after reading this post) would you argue that no information of any kind had be gained?

Rosaencrantz and Guildenstern ARE dead.

 

[Mk]

Why isn't information constant?

I looked at it like this:
Say particles have two properties... mass and spin.

And let us say the number of particles is constant (conservation).

If we input these two properties of every single particle in the universe into our computer, since there aren't going to be more or less particles, there is going to be the same amount of information in the computer, because there is the same amount of information on each particle. The information changes, but there is the same amount.

Of course in the actual universe particles have more properties, and the number isn't constant. But it is the idea of taking data on "units of the universe."

Now expand it out of just "particles" and into something like (length)(width)(height)(time) with nice small imaginary boxes (with time) constituting the universe that we take information on instead of the particles.

 

[Claude Bile]

Information is the inverse quantity of entropy, thus since entropy must always be increasing (in the universe) information must always be decreasing. (Consider though that Earth is one of the few places in the universe where entropy is actually decreasing - so on Earth information is actually increasing).

Mk - The "information" of the sample particles is not how much data we can record ABOUT the sample particles using OTHER particles, but how much data is being stored by the SAMPLE particles.

Claude.

 

[DaveC426913]

(Consider though that Earth is one of the few places in the universe where entropy is actually decreasing - so on Earth information is actually increasing).

Information is increasing on Venus as well, and in many other open systems where energy in the form of starlight is being added to the system. The winds, rocks, chemical reactions, quakes, terrain, etc. are all forms of information. Why? Because the number of possible states these things could be in is astronomically large, and it would be extremely laborious to encode.

OTOH, a volume equivalent to Venus in interstellar space will have very little information. The various distinct individual states this volume could be in is relatively small and can easily be encoded. You could write a program that could simulate this volume of cold vacuum without very many variables. How many variables would it take to fully simulate Venus?



Now here's how: the TOTAL information in the system - if you include the sun - has gone down. The Sun is slightly cooler, slightly more diffuse and slightly easier to describe (cause it's mroe like cool, grey soup of entropy).