The Universe is a Markov Chain

[TinyTree]

The universe is a Markov chain. A Markov chain is a state diagram (typically finite), wherein there is a transition matrix which governs the probability of moving from one state to another state. The universe may be considered as a continuous time Markov chain, but it appears that time is granular at a Planck time length, so the continous model may be more of an approximation.

A Markov chain can be understood as a graph, with transitions between the nodes on the graph. Each node represents a state of the system. For example, we might consider a Markov chain which is simply whether a person eat cereal in the morning or not. After careful analysis, we discover that a person will typically eat cereal with a 70% probability if they just ate cereal the day before, and that they will eat cereal with a 45% probability if they just ate something else the day before.

In this graph there are only two nodes:

1) eating cereal (70% goes to 1, 30% goes to 2)
2) eating something else (45% goes to 1, 55% goes to 2)

This Markov chain is a "gross approximation", for it accurately represents the state of the system as it is beholden by the person doing measurements, but leaves a lot of information out of the Markov chain.

For example, what if we found out that the person actually ALWAYS ate cereal as long as there was some in the box, but then would not eat any until they got some more. This still could obey the probability distributions above, but a more sophisticated Markov chain would represent more states- that is the states which include a full box of cereal, a state with a box missing one bowl of cereal, and so forth.

Now, if you get more and more refined, until you are considering the individual atomic positions of every atom in the environment, you are considering the Markov chain of the universe itself. Note that the Markov chain contains EVERYTHING in the system and OMITS the knowledge state of the observer. Or more precisely, the Markov chain contains the knowledge state of the observer as part of itself (the specific neurons that construct the memories of the individual) but omits the perceptual ability or individual's model of the world (if the individual does not know that the box of cereal got thrown out by someone else, this would be represented in the universe Markov chain as a missing cereal box, but not in their conceptual model).

Now for some primer studies on the universe as a Markov chain:

1) Is every state accessible from every other state?

It appears from quantum theory that it is possible this is the case, that is, it is possible that a particular electron can jump a large distance probabilistically. Further, an ensemble of atoms could, in theory, "teleport" to a new configuration. Thus, for a given quantum mechanical ensemble, it appears that it CAN move from any state to any other state, but most state transitions have a probability which approaches zero. Therefore, for all practical purposes, every state is NOT accessible from every other state, although theoretically it is. This is compounded by gravitational forces which do not have a probabilistic element- that is- can an atom shift its state probabilistically relative to a strong gravitational well? This is perhaps an unknown question. However, it appears to be impossible that an entire planet could "jump" to a new orbital position.

2) So which future states are actually accessible to a physical system?

If you observe the macroscopic world, by and large it behaves deterministically- that is- most of the world is completely constrained by the immediate previous history of the system as a whole. For a particular state of the Markov chain- there are actually only a few possible future states which are in reality accessible (at least on a macroscopic level). These possible futures are constrained by the physical laws we know, love, and live within.

3) So why is there a plural "states" available to the future of the Markov chain rather than a singular "state"?

There are a number of physical situations which allow for there to exist multiple futures. These are at symmetry breaking events, such as the folding of the space time continuum during early cosmological expansion, and at "amplified" events which can carry into the future, such as synapsis firing within neural structures, the nondeterministic mutation of DNA on a molecular level, the shattering of objects, the edges of tipping points, so called "chaotic" systems, and others.

4) What are the other nodes on the graph of the Universe Markov chain?

The nodes on the graph represent every physically available configuration which the universe can exist within. Thus, they represent every possible configuration of matter, including every possible configuration of matter which represents yourself. The universe does not enter most of these nodes obviously, but moves from node to node obeying the physical laws of the system as they are defined. If you visualize the graph as a huge piece of graph paper, you can imagine the universe moving from lattice point to lattice point, with possible branches at each intersection, but it ends up following a single trajectory.

5) What do you mean "every possible configuration of matter, including yourself"?

You, as an individual, can exist in many different states- you have experienced a huge number of these states during your life. If we consider the nodes to exist at a time differential of Planck time then you have lived 10e43 configurations times the number of seconds you have been alive. For a 25 year old you have experienced roughly 10e51 states, unless you keep doing the same things over and over, then it is fewer. But also, there exists potentially every other life you could have lived, which is a large, but finite, number of potential states. Note that these states represent your perception of the world in that your memories are contained within the state. Thus, your same biochemstry passing through a different series of events would have a different set of states than the life you have experienced to this time, simply because your perception would be different, and your internal representation of reality would also differ.

6) Is the universe a recursive object?

Yes, the universe is a recursive object in which a Markov transition probability matrix is applied to each state iteratively, projecting into the future. The Markov transition probability matrix is determined by physical law. Note that the universe did not begin with multiple states- nor did it exist, as far as we can tell, with multiple states in the past. The universe follows a specific trajectory which is recursively defined into the past.

7) Does the universe have an absorption state?

An absorption state in a Markov chain is a specific state which has a 100% probability of moving back to itself. Once a Markov chain enters such a state, it can not escape this state. If the universe collapses back on itself, it might be understood that the final moment is an absorption state, and that then the Universe gets stuck forever in a single point or something. However, it is unknown what the future gravitational trajectory of the universe is. For specific parts of the universe, these specific sections can be considered to some degree to be absorption states. For example, a black hole sucks in all matter and the universe is unable to move to a new state which is not a black hole- HOWEVER, the suspected stream of virtual particles around the black hole which diminish its mass would mean that even a black hole is not truly an absorption state, even for a specific subsection of the universe. If history truly DID repeat itself, then it might be considered that the recurring series of events is in effect a form of absorption state. However, it is difficult to imagine a set of historical events which would deterministically lead back to the same setup over and over, for there are numerous branching points along the time series which would allow the events to be changed. However, it seems conceivable an alternative universe could exist where the participants could get locked in such a loop, although hopefully they would not be cognizant of such a state.

8) If the universe is continuously growing and shrinking from a point, what does this mean for the Markov chain?

If the universe repeatedly "blows up" from nothing it would mean that the Markov chain is repeatedly being run through, over and over. In this case, it might make sense to consider the probability of a specific configuration as a limiting distribution to be technically accurate. However, for the participants in a particular universe it would make sense to consider the universe from the starting point of their particular chain, not going backwards to prior universes which have no impact on the probability of later universes. (presumably)

9) Since Google utilizes a Markov chain, is Google representative of the Universe?

Every physical set of conditional relationships is a subset of the universe itself, so Google does not share any special qualities with a relationship to the universe, besides being a part of it. Any specific abstraction of the universe is a useful tool for understanding that portion of it, but one must always be suspect that critical factors of understanding are being omitted from the model and that it does not truly represent what you think it represents either probabilistically or as a subset.

10) What do you mean by this?

For example, imagine you are watching a stream of digits coming out of a device, and you see 15296.. You may assume these digits are completely stochastic, when in fact you are seeing a series which are from the digits of PI. The relative probabilities of the future digits are completely constrained and deterministic, because your model of the digits (as being stochastic) is inaccurate.

11) Is the Universe a "birth and death" Markov chain?

A "birth and death" Markov chain is a special chain wherein states move through the entire available state space until completion. If there are truly quantum multiworlds, then perhaps it is accurate to consider it as a "birth and death" Markov chain. However, we have no way of knowing if the quantum multiworld hypothesis of Everette is true or not, so we must assume that it is in fact NOT a "birth and death" Markov chain for it is not passing through every available state.

12) Is the universe an ergodic Markov chain?

An ergodic Markov chain is one which "repeats" and can move from any state to any other state through a series of steps. Since our universe is expanding, and dragging objects apart, and allowing for the light to redshift down so that it is no longer blinding, but slowly loses energy- our universe is not ergodic on a timescale within a single universe expansion. Perhaps the universe is Ergodic if it is repeatedly expanding and contracting repeatedly.

[Mike 5]

Note that the Markov chain contains EVERYTHING in the system and OMITS the knowledge state of the observer.

This Markov Chain idea is new for me - very beautiful. Thank you TinyTree.

So does this idea that the Markov chain contains EVERYTHING bring us directly to decide about infinity? In my view, Infinity is a religious intangible. Infinity means the Markov chain has no closed perimeter.

I think the perimeter is closed and the Markov chain forces us to decide one way or the other. There can be no infinity the moment you make a final perimeter to Everything. And until you do, how can you be sure the markov chain is not somewhere disrupted?

Secondly the sheer duality is breathtaking. The knowledge state of the observer is omitted! Reckless, breathtaking, wonderful. Is this not the duality of consciousness and material form? What else is the ultimate duality - here it is simple and you have to declare this ultimate duality. This is for me like a Goedel axiom - you put something outside the system and say, look, that is unprovable, taken for granted or we cannot get started to even think. And here the single element or axiom said to be outside the system - the knowledge state of the observer. Exactly. Of course there are so many observers, who disagree...

The duality of every linked position ("state") seems to get us to some progress in thinking about things - step by step, this state connects how to that state, exactly the way to proceed. I'd like to expand the word state to consider this process or flow connects to that process or flow - tricky but reality is not cut and dried.

Recursion - YES! I do not see the specific logic used to declare the universe is recursive, and that would tend to indicate it is just taken as an axiom, a just so story. But the question is spot on - once you think of the Universe as a large birthday cake, you wonder how to slice it and how to keep on slicing it and you focus on recursion. Recursion seems so evident in the structure of all there is - which was first - recursion or reality? So many observed fractal patterns, recursion is the basis of biology and the umbilical cord/DNA life stuff - and recursion answers so many aspects of Everything in a very simple and elegant way. If you were some God, or universe designer, would you not say, recursion is essential?

Recursion, duality, fractals and dialectics, contained finite universe, this Markov chain idea pushes all my buttons.

Where I have trouble with this concept is primarily the concept of frozen time in the word "state" as in "state diagram". There is no reality to frozen time, and our challenge is to map fluid dynamics of processes. It is nice to say, remove all the time and just consider states. Nice but not nice enough. However, apart from using the word "state" the method here does not seem to really concern timeless states, the model here seems to apply smoothly to dynamic flows and processes. A major challenge would be explaining turbulence, and the apparent fickleness of "fate", or chaos, the entropy that we observe, and so on. Look:

So why is there a plural "states" available to the future of the Markov chain rather than a singular "state

"
So I am saying, you have INCLUDED knowledge of the observer in presuming a single time origin state: it is surely a matter of opinion and knowledge to say time is assymetrical with multiple futures and a single origin. Maybe there is only a single future and multiple pasts? Again however shocking to consider this as an observer, it is OUR knowledge as observers that tells us one way or the other, and i prefer to omit observer knowledge, why not simply omit conscious awareness and model that separately?

Finally I have to wonder, is the Markov chain for Everything essentially dendritic, or a neural network? That is indirectly a question about time and origins. Again the word "state" presupposes a viewpoint OUTSIDE of time, where frozen time is actually never observed.

Oh one more - if the knowledge state of the observer is omitted, hold on, there are multiple observers ... every fruit fly has it's own observation of reality ... so i am kind of mapping out a hypermarkov chain, a neural or dendritic network of reality to consciousness as many many dual pairs, observer-reality and reality-observer though interactions. Where the idea of any Gods eye view of a single reality is defunct. Why presume a God just to see a single reality, when clearly we all experience things differently. Hypermarkov would mean a network of interconnected but subtly or grossly different realities defined by the observations of the total finite set of observers. Sure humans share and agree on reality, but the elephants knew the tsunami was coming, in their reality...

Some very stimulating ideas here.

[Guille]

I really find this article one of the best of all, at least in the top 3.

One thing I wonder, TinyTree, do you think that duality impplies neccesarilly dialectics, opposition, contrast and comparison? I don't. And this is one of the basis for my attack on Hegel and Nietzsche.

[mkirkpatrick]

Well researched and written,well done,the forum is richer with your input.



kindest regards michael.

[TinyTree]

Understanding information and thermodynamics

The reason this scientific idea of objective probability has escaped the minds of the scientific world as both a microscopic, and macroscopic, phenomena is because of thermodynamics.

Thermodynamics clearly shows that things move towards a more probable configuration. If everything is moving towards a more probable configuration, why should there be any interest in the probability of the system as a whole?

And the answer is- because there are multiple ways to examine probability. One way involves using a pressure gauge, or a thermometer, and these show both in simulation and experiment that gasses tend to spread out. In fact, both deterministically behaving, and nondeterministically behaving gasses do this.

However, we can perform other experiments ourselves, in simulation and experiment that show there is another probability- an objective probability to the system as a whole. These probability metrics are orthogonal- they are unrelated.

This is similar to measuring the height of something vs the width. Both are valid measures, they are measuring different things, and have different implications.


In this experiment, we use a random die with different probabilities on the different faces and examine the thermodynamic implications of landing on each face.


So which measure of probability is more meaningful?

If you are trying to run machinery, build a dam, or otherwise work with the transfer of energy what matters to you is the thermodynamic principles and equation of probability.

If you are trying to understand evolution, nondeterministic phenomena, and the universe as a whole with regards to information and complexity, the objective probability is what you want to understand and study.


This is a scientific experiment where we roll a truly random die. It has six sides, and is specially built so that there is a 1/100 chance that it lands on a 1 side. The remaining 99/100 are distributed evenly between the remaining 5 faces.

It takes energy to roll this die, and energy is dispersed when we perform the roll. When we roll the die, it randomly lands on one of the potential faces.

Now the question is-

If we land on the 1, which has a 1/100 chance of being rolled, what is the thermodynamic comparison to landing on the 2 side, which has a 19.8/100 chance of being rolled.

They both take the same amount of energy to reach as a final state. Both of these final states disperse the same amount of energy.

Yet one of the states is 19.8 times as probable as the other state. How can we reconcile the difference between these two final states from a thermodynamic point of view?

Does not thermodynamics states that we move towards a more probable state?

The classic response to this dilemma is to suggest that it is fine for the die to move into a more improbable state, as long as energy is used up and dispersed in the process. This dispersal in energy, according to the classic argument "makes up" for the die moving into a more improbable state.

However, now we can see that in fact the die's final state is an aspect of the objective probability of the system. By separating this consideration from the thermodynamic consideration, which may be deterministically ending up in the same final energy distribution, we can see that the question did not make any sense in the first place. The question of "how can we reconcile the difference between these two final states from a thermodynamic point of view?"does not make any sense. There are two different probability considerations.

One is with regards to the distribution of energy.

The other is with regards to the objective probability of the state of the system.

These are different aspects of probability of the system, and should not be confused with each other.

[SteveA]

Thank you for your posts. It's been quite a few years that I've been trying to puzzle out how time/change is possible and it appears a growth of the universe must continually require more information to define it and that information must effectively be non-deterministic relative to everything present.

I posted some ideas regarding how macroscale wave mechanics can appear to arise from stochastic accumulation over time, but the idea of physical cause and effect over time may fundamentally not exist. A rigidly deterministic system appears to be incapable of describing how any dynamics are observed. It could even be that there's a nesting of statistical systems, though this might appear no different than a single source or layer (it could dependend upon to manner in which wavefunctions are non-uniformaly biased).

http://www.toequest.com/forum/your-t...tml#post131899

Thanks again for your posts.

[TinyTree]

it appears a growth of the universe must continually require more information to define it

This is an awesome observation. It certainly does appear the growth of the universe requires more information to define it.

macroscale wave mechanics can appear to arise from stochastic accumulation over time

This is a very interesting idea. I am looking over your linked post and it has some very interesting concepts. Stochastic accumulation appears to be a significant factor in certain phenomena.

a nesting of statistical systems

It is a very interesting question to ask- what is the recursive nature of our universe? What parts of it can not be effectively defined through recursion or nesting? Where does recursion break down as an explanation, and where does it hold up?

[SteveA]

A few related ideas that you might be interested in could be correlated to analogy of a game of Go.



Let's make a couple of assumptions:

1) Time proceeds "forward" and doesn't repeat previous states. There are some logical reasons why we could make this assumption, but I'll skip them for now.

2) The present exists as a context arising from past influences. If we're to have any possible form of physical laws, this would appear necessary simply that some form of continuity across time exist.

So basically, if we analogize this with a discrete/quantized spacetime describing all possible states for the present, the past would exist encompassing some volume by which future states unfold relative to. That would mean that future states could not be seen to jump some infinite or unrelated distance to past states, even from the simply fact that such a transition wouldn't be comparably measureable to any finite quantity of information available.

In that case, there could be the equivalent of a space filling in spacetime with the present moment continually on a leading edge of this volume.

A purely predetermined sequence can describe a rigid string of quantum units. It could be described as 1 dimensional and would appear to possess no dynamics.

If we add evolutionary branches for possibilities, then something outside that cause and effect chain needs to act as an equivalent energy of selection to extend this (at which point any number of subsequent, predetermined events could occur in a period of time that's uncorrelated to units of time in terms of branch selections).

I point that out because that resembles two forms of time that can be uncorrelated. For example, if we had a single photon "collapse" an equivalent "wavefunction" that was just a binary selection, any predetermined relationships constructed from past events could be altered effectively instantly (entanglement and a wavefunction arising from a static and "instantly" correlated past structure, though recognize that this simply needs to be a finite set of dependencies and these could exist "on top of" yet another layer of even faster correlations between properties embedded below them etc. - potentially this could be add infinitum - though I've commented on ideas related to computing a set of irrational numbers on a real number line. These could appear to be unbounded and infinite, but they could also be finite extensions of a predetermined form that are added as required to continually bridge between a present finite state as an approximation of an infinite irrational process).

A clearer analogy of how this might apply would be to say that on that "board" above, the pieces could be constrained to expanding spherically. There are many symmetries that could arise in such an expansion (for example, Pythagorean Triplets), and the placement of specific pieces isn't determined, until some shell is filled, at which point a nested set of operations could proceed to compute the available positions on the next "shell" and similar to how computations for pi on a real number line proceed, though technically pi is an irrational number, all actual uses of it occur as finite representations.

That's just an example of how there could be a fundamentally infinite form, though at any moment only a finite subset needs exist and there can be undetermined symmetries that have no specific "correct" sequence for their evolution.

There appears to actually be a very natural chaotic spectrum that arises (related to prime numbers). For example, if we had to place a "next" state adjacent to an initial state in 2 dimensions, there are 4 possible positions (up, down, left or right) and this requires an equivalent "energy" of selection that provides a uniform 1 of 4 selection.

That same selection could be factored into 2 binary selections 2*2=4. If there were only 3 valid positions, then this is relatively prime to 2 and would require a different "spectral line" of energy prime that. I recently saw some information that appears to confirm this idea that photons can be effectively split and act independently or collectively: http://www.scientificamerican.com/ar...n-entanglement

Time in the universe needs to be synchronized and can't itself be communicated at light speed. Such a method of factoring a larger selection into individual/independent decision of multiple temporally synchronized entities is possible in that manner. For example, if the number of present possible "next" states could be a uniform selection of 1000 possibilities, then this could be factored into 3 independent decisions made as 1 of 10 selections each (10*10*10=1000). That would allow for a manner in which a relative statistical independence could exist, yet still maintain a synchronization in time between entities (otherwise things could move infinitely fast in time and become detached from material properties).

I've made comments on that other thread before regarding the equivalent of a prime spectrum factoring splitting and have generated some images that appear like rather natural 3-D environments using similar ideas for discrete resonance in a system.

Also, there would appear to be no manner to specify a specific moment as "Now" in a purely predetermined sequence (there's nothing to change and represent what the present state would be) and so my assumption is that this selective/creative decision process is part of consciousness.

Another thing you might find interesting to consider is that the information conveyed by a photon doesn't appear inherent in itself - it's in terms of the context/environment in which it's measured - it's ironically every location that it could have been detected, yet wastn't, that provides the specifics regarding where it was detected and a good analogy is with language. The meaning of a word is not really contained by the word itself but instead arises relative to the context of other words that weren't used. If we had a photometer in a dark room, it doesn't detect any photons. Notice that this would not be the same as specifically seeing "black". The photon sees "nothing" instead (it's up to us to measure time and determine that in some period of time it hasn't detected any energy - temperature and intensity of light is relative to rates of time).

Oh, I can ramble on. Anyway, I just wanted to toss out some thoughts I've had along similar lines before. There are quite a few relationships in these ideas with number theory and I've found a lot of correlations with computing the greatest common divisor between different wavelengths or n-way symmetries that appears to recur, and I did some simulations along similar lines and came up with rather interesting images:

http://www.toequest.com/forum/your-t...utation-8.html

If that link doesn't work, try cutting and posting this into your browser, but don't copy the quotation marks (I don't know why links to that thread have such problems).

"http://www.toequest.com/forum/your-toe-theory/5225-theory-consciousness-life-computation-8.html"

Also check out some of the images on page 9.

These could be analogized to the correlations in spectral energies between 2 independent volumes of selection (for example, an x position in the image could be considered to span between 20000 and 20500 possible selections, while a y position could space 30000 to 30500 and then a process similar to a recursive computation of the greatest common divisor is applied to see how closely synchronized/correlated these wavelengths/energies are).

[SteveA]

Another idea you might enjoy checking out. This regards what appears to be a rather natural manner of temporal evolution that simultaneous observations of an infinite number of independent systems could give rise to (from the informational perspective of what properties appear to be novel versus those properties that have been witnessed to have been repeated):

http://www.toequest.com/forum/your-t...tml#post132096

[TinyTree]

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.

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.