The Universe is a Markov Chain

[SteveA]

One of the things that I was obsessed with when I came up with this idea was symmetry breaking. How is it possible for symmetry to break?

In a deterministic flow, how does the symmetry break? It can't, not really.

That's very similar to the problem I saw with trying to combine together time/change with anything deterministic. The two are incompatible. Whenever something is precisely defined without any degrees of freedom, it's just a static object.

Even trying to say that there's a deterministic sequence over time and that A becomes B, becomes C etc. appears to have no manner to indicate which state is "Now".

Consider a program on a computer. It could be seen to describe a deterministic evolution of states ... but in itself, it doesn't supply a mechanism to actually change. There's always a figurative "power cord" leading somewhere else and time can't be fit into a box.

It also appears time has to be tied to an observer as some innate component of experience. For example, imagine watching a crystal rotate. If you saw it rotate some number of times and then stop, there's nothing in it that needs be changed. It's different in the context of you viewing it as having been rotated. Someone else might have been rotating with it and not seen it rotate at all, or another observer could have a different count. There's just one version of events that's witnessed though and that same reference for time has to be shared effectively instantly (it can't propagate at a finite and constant velocity because this would leave separate areas of space unable to maintain synchronization in time).

There are two natural phenomena that are interesting where symmetry breaks- the formation of the initial precipitation points of the star systems, and in so called "bernoulli-cell" formation which occur in non linear dynamics. Typically the system goes through a saddle point in the phase space- it is the trajectory after going through the saddle point which ends up with a symmetry broken.

Ah, non-linear dynamics :) Well that's an opening line to a plethora of subjects! :lol: I'll try to resist, though basically I think the primarily feature of non-linear deterministic structures can be found to lie in a selective removal of information (determinism doesn't add information, and linear structures can be seen similar to lossless transformations. Non-linear structures appear rooted in a lossy compression of information in some aspect. For example, a square root function compresses a linear range of values into a non-uniform distribution and if we assume the density of available representations in each dimension is the same, then the square root conveys less information than the original linear form. I believe there's a natural ordering of operations involved in non-linear forms as to which are least restrictive down to those that are most restrictive and lossy and there's a vague idea I keep coming across that there could be a way to layer or embed these within each other so that all are maximally visible with the least loss of information. As an analogy with filtering an audio or visual spectrum, if you had an array of color filters or audio filters, if you place "black" on the top, then that blocks visibility of any others behind it. Whereas you can layer them instead to block the least information at each stage until you reach black as the last filter. In that manner you can figuratively see the entire rainbow instead. Alternately, imagine that the state of the universe at the present moment is determined by a nesting of spaces beginning with "every possibility" and continually removing some minimal feature from the set of "everything", proceeding toward spaces that are more constrained, but with higher dimensional forms and of greater asymmetry in their context, until you're left with the present moment as having no more degrees of freedom but maximum visibility of the constrains between "here" and everything else ;))

My guess is that symmetry arises from a perceptual compression or selective non-linearities that mask over or ignore the uniqueness of all things. We couldn't count (and communicate via quantities) without an ability to be able to consider two things identical in some respect. In a sense, adding symmetry to a fundamentally asymmetrical system is something larger than solely having asymmetry.

[TinyTree]

Transmission and Storage


What is the difference between transmission of a bit of information, and the storage of it?

Storage is the preservation of a bit of information in a form where it can be retrieved. Transmission is the sending of a bit of information to a distant location. A transmission

is typically a signal. Often in electronics it is a time varying voltage which carries the information.

We can imagine storing a bit of information with a block of wood, which either points up or down. We could send this bit of information to another by placing this block of wood on a conveyance, and then sending the block of wood to them. So this same block of wood can be used for either storage or transmission.

In fact, transmission of a piece of information is really just a specialized form of storage. It is still propagation of the bit of information through time, but it adds the component of transmitting the bit through space.

Is the frame of reference in which we sit somehow special so that storage is relative to our own frame? Do we want to accord physical significance in the universe to our own position?

So therefore we can see that storage and transmission actually are the same thing. For if you were to store a bit of information on our planet, it actually would be moving at quite a high speed as it stayed on the planet, and in fact has become a transmission. A block of wood sitting on the ground looks quite stable, but in reality is moving quickly.

There is really no way to store anything really, it is always moving, and it is always a transmission because there is a frame of reference it is moving relative to. Or one could also argue the opposite- there is no way to transmit something, it is always a form of storage, relative to the frame of reference that is moving with the signal.

They are different words which mean the same thing- propagation of a bit of information through time.

If you were to see a block of wood pointed up on a wagon being dragged- would you think of this bit of information as being storage, or as a transmission? Would you think of it as a signal?

Is it a signal or not?

So now of course, I am going to ask you to look around the room you are sitting in. How are these objects fundamentally different than the block of wood? Perhaps there is no intentional information stored in their relative positions, but there is information stored there all the same. Some of that you placed there in your choices of your environment.

So are these objects sitting around you storage, or are they a transmission? Are the objects sitting around you actually a signal?

They are a signal from the past to the future, currently in the present. You too, are a signal from the past to the future.

Typically we consider the information we write down, the things we draw, the arrangements of matter we make around us as being a form of storage. They are also a transmission, a signal, although the destination is not necessarily to a specific recipient.

Similarly, the ads in magazines, the words in the paper, the signs on the road, the things you read on the internet, the electronic communications, the paper communications, the painted billboards, the text on your car dashboard, all of this is both a form of storage, and a form of transmission. It is a signal from the past.

[labelwench]

Transmission and Storage


What is the difference between transmission of a bit of information, and the storage of it?

Storage is the preservation of a bit of information in a form where it can be retrieved. Transmission is the sending of a bit of information to a distant location. A transmission

is typically a signal. Often in electronics it is a time varying voltage which carries the information.

We can imagine storing a bit of information with a block of wood, which either points up or down. We could send this bit of information to another by placing this block of wood on a conveyance, and then sending the block of wood to them. So this same block of wood can be used for either storage or transmission.

In fact, transmission of a piece of information is really just a specialized form of storage. It is still propagation of the bit of information through time, but it adds the component of transmitting the bit through space.

Is the frame of reference in which we sit somehow special so that storage is relative to our own frame? Do we want to accord physical significance in the universe to our own position?

So therefore we can see that storage and transmission actually are the same thing. For if you were to store a bit of information on our planet, it actually would be moving at quite a high speed as it stayed on the planet, and in fact has become a transmission. A block of wood sitting on the ground looks quite stable, but in reality is moving quickly.

There is really no way to store anything really, it is always moving, and it is always a transmission because there is a frame of reference it is moving relative to. Or one could also argue the opposite- there is no way to transmit something, it is always a form of storage, relative to the frame of reference that is moving with the signal.

They are different words which mean the same thing- propagation of a bit of information through time.

If you were to see a block of wood pointed up on a wagon being dragged- would you think of this bit of information as being storage, or as a transmission? Would you think of it as a signal?

Is it a signal or not?

So now of course, I am going to ask you to look around the room you are sitting in. How are these objects fundamentally different than the block of wood? Perhaps there is no intentional information stored in their relative positions, but there is information stored there all the same. Some of that you placed there in your choices of your environment.

So are these objects sitting around you storage, or are they a transmission? Are the objects sitting around you actually a signal?

They are a signal from the past to the future, currently in the present. You too, are a signal from the past to the future.

Typically we consider the information we write down, the things we draw, the arrangements of matter we make around us as being a form of storage. They are also a transmission, a signal, although the destination is not necessarily to a specific recipient.

Similarly, the ads in magazines, the words in the paper, the signs on the road, the things you read on the internet, the electronic communications, the paper communications, the painted billboards, the text on your car dashboard, all of this is both a form of storage, and a form of transmission. It is a signal from the past.

A very interesting post, TinyTree.

All form does indeed convey information.

The planet which we inhabit is one such system, wherein each form relates to all others and the information stored, retrieved and conveyed interacts to enable continuance. We tend to examine the transmission systems in isolation from one another, and ponder upon the means whereby social insects relay information, birds navigate and migrate, various mammals communicate and interact, yet the non-ambulatory life-forms also have means of transmitting information.

DNA is one of the forms of information storage and transmission which we are currently studying, and finding more and more detail contained within. As a gardener, I am ever surprised to observe that some of the most intricate flower forms arise from the tiniest of seeds, that mammals are created from the information stored as microscopic seed.

The universe as a system of information; stored, retrieved and transmitted through form.

An interesting contemplation.

[SteveA]

Thank you for your insights and comments. I agree that in many ways the difference between storage and transmission is subjective. How could something be known to have been transmitted from one position to another without being able to observe both contexts in which (what's believed to be) the same information exists.

In that case, the knowledge of transmission arises from a unification of two or more pieces of stored/observed information in which a property is shared between them, while surrounding contexts have changed.

Notice that context is also subjectively determined. Two physically separate observers can't witness the same photon. We can imagine that a single photon detection is amplified in a manner such that two separate observers can verify a detection, "objective" to both, but I have a feeling that if we dig into the details, quantum mechanics could cause some grief in verifying this.

But beyond differences in positions and environmental contexts between observers there's also a more fundamental issue of the mental context in which events occur.

Motion itself appears to not be precisely verifiable in an objective sense. In order to witness a motion in common, the same timelines of events must be observed. If a ball has rolled from position A to B, but someone else arrives to only sees it at presently stationary at B, then the objective reality of the motion is questionable.

Is the frame of reference in which we sit somehow special so that storage is relative to our own frame? Do we want to accord physical significance in the universe to our own position?

I believe this has come to be an unavoidably significant influence (if we could consider it an influence).

It depends upon how you look at. It does appear that some of the imagined and unverifable components of objective reality have to be removed if first person verifications to a ToE are to be possible.

For example, if someone claims there exists such and such objects inside a room behind a closed door, can it be considered that this is proven to be true from the claim alone? The first person "fact" would appear to be that such a claim was made, but to the extent it determines that such and such actually lies behind the door remains questionable.

There are many areas in science where broad generalizations have occured in this manner and it appears this has come back to bite in some areas where more detailed views show those claims as unverifiable.

I think quantum mechanics has been seeing this rather clearly and is a good example, though there are many other areas in science in which effectively the same issue arises - for example, the Big Bang is just a theory and the width of the (known) universe can't truly be measured in a directly verifiable manner as being billions of light years across. Notice as well that the assumptions of translation invariance in space would appear to have a problem is we consider that observations are being made from a rather precise center of the the known universe and it appears there's not much to work with regarding the unknown.

In one sense, it could be said that the Earth isn't the center, and in some ways the Sun has been used as a more significant gravitational center to the solar system, but the center of the Milky Way galaxy could be considered more significant than that ... etc. These are all manners of projecting beliefs regarding various experienced properties into a spacial context and it appears that a firmer foundation for science would have to lie closer to ones manner of experiencing and constructing those beliefs - recognize that these could be constructed in a manner, similar to your comments of the past as a persistent influence on the present and future, though I've been wondering if cause and effect over time might not be a fundamental truth but instead that cause and effect arise from statistical aggregates or equivalent inertias constructed by interactions made under the assumption of causation (in this case the contextual space of interactions becomes deterministic, even if the events themselves were not such - a belief could construct the equivalent of a space of reaction to an event that's deterministic and it's interesting to consider how such forms of causation could accumulate over time, especially if such an influence could be present since a form of unconscious action at birth. In that manner, the equivalent of physical laws could even be the equivalent of something inherited ... yes, that's difficult to imagine how such could be possible, but if we looked at mathematics as a common language of relationships between structures and how information can be transformed over time etc., then it's not so difficult to imagine a diverse set of perspectives and interactions over space and time that though apparently different on the surface could be entirely compatible. That's a view I've been considering for quite a while now. It appears many string theories have picked up on similar possibilities, though I think most string theories begin with a weak foundation in assuming spacetime is fundamentally 4 dimensional and then working with concepts of resonance that resemble continuous fields - they end up quantizing things anyway and it seems best to simply begin with the necessity of quantization and any deterministic laws appear to automatically construct a linear dimension of time, from there the 2nd dimension is effectively the source of acausality, though it might actually be that every dimension arises from statistical accumulations and macroscopic cause and effect arise statistical forms. I've found quite a few correlations there with an appearance of constant velocity waves as well as gravity quite possibly arising from a diffused growth of space).

Something else that seems funky but could be worth considering is that many things that could appear as quite obvious logical requirements for various systems could be, similar to your comments regarding the translations between storage and communication of information, a collection of rather arbitrarily selected "facts". Many times there are implicit assumptions that upon close inspection don't necessarily hold true in all cases.

As an analogy, prime numbers appear very significant whenever we're referring to collections of objects that are identical (for example 5*n describes the total quantity contained by n objects each providing 5 untis), but that's an abstraction that doesn't necessarily hold true on close inspection.

For example, we might try to count protons or water molecules, but in order to do this some difference between the contexts in which each is detected must exist (different positions in time and/or space, for example) and it appears that similar to experiences in time, things exist comprehensibly in terms of compressed representations in which some aspects are considered to be identical and the "raw" information is compressed into something more manageable, but in the case of prime numbers it's interesting to consider that they may not exist as fundamental features of spacetime but instead arise from the manners in which differences between things are overlooked and that compressed form of information then inherits properties arising from the manner of its compression.

A potentially more precise "lower level" representation for events in time would appear to be to remove many aspects of counting and quantities and replace these with a sequencial order of observations of events in time (and similarly in terms of their positions in space). For example, if we tried to describe the dynamics of a system that was just described in terms of the quantities of objects in it, this gives much less information (what's the internal structure or where are those objects in relationship to each other?) than keeping a finer scale record (when it's possible) of their positions - if you told a position on a map as having a bush, tree and rock in the area, this gives some information, but if it was specified that the rock was closest, the bush furthest and the tree between these, this gives an additional 1 of 6 possible directions (there are 6 permutations of these 3 objects) that these were being viewed from and adds additional information (for example, we could predict by various possible configurations of these that it's unlikely that a motion would first see the rock and bush swapped in this relationship).

As a better example of how finer scale observations of sequences of events could reveal more information, imagine that we have an array of sensors detecting photons. If we simply accumulate an average intensity, this could leave use with a "temporally blurred" view of space, but if we instead looked for correlations across these detections in time on finer scales, it could be possible to discover finer scale detail in their dynamics over time (I'm certain this thought isn't unique).

One thing that seems to suggest the possibility of such features is with regard to some observations that lasers generate not solely coherent/periodic waves but have chaotic components embedded within them as well. http://www.eng.yale.edu/stonegroup/science.html

... Well, I'm just rambling on some ideas here that you might be interested in.

[TinyTree]

In "Universe From Bit" in the book Information And The Nature Of Reality Paul Davies asks some provocative questions, and provides some stunning insights along with dragging along some incorrect assumptions and baggage from the old world of information theory.

He touches on two questions which are nearly conflated in the essay- are the physical laws themselves informational constructs, and is information a fundamental characteristic of the universe itself?

For the purposes of our consideration, we are interested in what is objective information in our universe? And the answer is that the information is tied directly to the objective probability of a specific state as defined by the rules that describe the system. Questions about the laws themselves fall outside the domain of this consideration. We consider the objective probability to be a fundamental characteristic of the universe- and the objective probability of a specific state is defined by the laws which govern the universe. The state of the universe has a probability, and this is its information content. It is a real and fundamental aspect of reality. This Davies strongly supports as a philosophical concept.

However, Davies rapidly moves away from a coherent understanding of information. Here is where Davies goes astray from a consistent world view "It has been known for many decades that entropy can be regarded as a measure of ignorance"... "One may think of the entropy of a gas as the information concerning the positions and motions of its molecules over which we have lost cognizance." Thus, we are expected to believe that a particular point of view- a particular set of knowledge about a physical system- has bearing on the information content of the system! This is true for the subjective observer- their ignorance defines the subjective information of the system. But for the physical world as a whole, this is erroneous. The objective information content of a physical system is independent of a particular viewer, or a particular set of knowledge of a set of observers. The objective information content of the system, or the objective probability of the system, exists independent of an observer. Indeed it must be, or there could be no information content of the universe before there was any measurement of the system. Do humans somehow magically create an aspect of physical reality which we are expected to believe is a fundamental characteristic of the universe itself? This is absurd. It is in fact, an inconsistent world view. An observer with changing knowledge only can gain or lose information in a subjective sense, which is not a fundamental property of the universe as a whole.

The consistent world view is to embrace that there exists a state vector for the system as a whole- that it has a probability- and further that this probability is independent of any particular subjective knowledge of the system. In fact, this probability is independent from the thermodynamic considerations of probability as well. Davies actually provides a foundation for this quite well in quoting Laplace, which we will repeat here:

"We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at any given moment knew all of the forces that animate nature and the mutual positions of the beings that compose it, if this intellect were vast enough to submit the data to analysis, could condense into a single formula the movement of the greatest bodies of the universe and that of the lightest atom; for such an intellect nothing could be uncertain and the future just like the past would be present before its eyes" Laplace 1825

One can construct a thought experiment where numerous gas particles begin in the corner of a chamber with various velocities and watch them spread out in a deterministic manner. The objective probability of this system does not change- it is moving in a deterministic way. Therefore, the actual information content of this system does not change in an objective way.

The Laplace intellect which knows the trajectory of every single atom of this system also would suffer from no subjective information change. They are, being the ultimate intellect, effectively an objective viewer. However, we can clearly see the entropy of this system changing. As the gas particles spread through the chamber, the system increases in entropy. The probability of this system is always 100% it will be in a specific state at a specific point in time.

We can imagine another "less intellectual" observer, who is not the superior intellect, who also suffers from a subjective information change of this system as they lose knowledge of the exact positions and velocities of the items in the chamber. However, this subjective information change has no bearing on the objective probability of the situation. This "less intellectual" observer may claim that there is an information change, but they are only claiming their own ignorance, not a fundamental characteristic of the universe.

In this system, the fundamental characteristic of the universe is that it does not change information content, when we consider information to be identical to the objective probability of the system. Thus, the deterministic system does not undergo any changes in information content.

The Laplace intellect serves as an objective observer of this system with regards to probability, and if this same system goes through a bifurcation, or a nondeterministic step such as quantum decoherence, then indeed the system does change information content.


Ironically, Davies comes very close to stating what information is- that is the leading edge of causality, in the following sentences: "Because the speed of light is a fundamental limit, no information can travel faster than light, so the volume of space delimited by the reach of light defines a sort of horizon in space beyond which we cannot see, or be influenced by in terms of causal physical effects."

This statement is very close to stating that information is actually causation- which is in fact what it is from the objective probability point of view. Information is the leading edge of the quantum wavefunction of the universe, and the information content of the system is tied to the probability of the system being in a specific state. The information is propagated through causation. Causation can be understood to be the propagation of the past into the future.

He asks a very interesting question at the end of the essay, which goes like this: "Llloyd advocates that the universe computes itself, but it does so quantum mechanically- the universe is a quantum computer.. We can invisage a corresponding quantum Landauer demon, able to observe all the branches of the wave function- in effect, all possible worlds, rather than a signle actual world... If that ontology is correct, if the ground of being is vested in the quantum wave function rather than the informational bits that emerge via measurement and observation, then the information bound on the universe is exponentially greater... Whether reality does lie in the quantum realm, to which human beings have no access, or whether it lies in the realm of real bits and real observations, could therefore be put to the test with a sufficiently complex quantum system."

Here he is missing the one component which defines the nature of objective reality- it exists, at least at times, in specific states, which are tied to the past through the probabilistic nature of quantum mechanics. The universe defines a gigantic markov chain, and our existence in it has information only because of the probabilistic nature of the quantum realm interacting through quantum decoherence as it creates a present. Therefore the universe is not exactly a quantum computer- for it is not computing anything particularly, nor is it not a quantum computer- for it functions as one in the myriad interactions of its constituent particles. But reality exists at the juxtaposition of these two aspects of physics, not in one or the other.

In conclusion, we need to understand that thermodynamics has nothing whatsoever to do with objective information which is tied to the objective probability of the state. These are orthogonal, and equally important aspects of our universe that need to be understood independently to make progress to a coherent world view.



All of the quoted material above can be found in "Information and the Nature of Reality" by Davies and Gregersen. Cambridge University Press, 2010.


The obligatory web site link: https://sites.google.com/site/markov...iverse/welcome