This is a new theory of information. Well new is hardly the right word. Decades ago I invested my academic career on this, which was sadly dashed to bits. Every few years I'll submit this to various leading, or not so leading, journals, and watch it get dismissed. Last time (a philosophy journal) they sat on it for about eight months before rejecting it. Why so long? Maybe it has some hints of truth.
If you understand this theory, you will both love it, and hate it. I think you will find it difficult to understand in terms of all its implications. I do.
Why do we need a new physics of information?
If you search the literature, you will find out that this problem has already been answered! We already know how physics and information are combined. Edwin Jaynes wrote the definitive paper combining information theory and statistical mechanics. This was published in Phys. Rev. and has been cited nearly 4,000 times. [Moderator:
Edwin Thompson Jaynes, "Information Theory and Statistical Mechanics," Phys. Rev., 106, 620 (1957)
Edwin Thompson Jayne, "Information Theory and Statistical Mechanics II," Phys. Rev., 108, 171 (1957);
] However, poor Jaynes makes one fatal flaw with his analysis, which is difficult to wrap your head around:
He introduces a special frame of reference, a subjective frame of reference. I invite you to google the paper now, and look at it. Just search for the word subjective in the paper, he has a huge explanation of its justification. [Moderator: I think you failed to understand the papers. Your inability to actually point at the flawed sentence is highly suggestive of this.]
There is a strong desire to introduce subjective knowledge into any consideration of information- it is our intuitive, self centered understanding of information. If you don't know who won the Steeler's game last night- it is a subjective bit of uncertainty to yourself. It is new information to yourself when someone tells you who won the game. [Moderator: If you read the paper and understood it, you would see that Jaynes deliberately seeks to avoid introducing guesses into probability distributions through the maximum entropy method. This is not a subjective choice, but a unique extremum which satisfies certain constraints placed on the system by measurement.]
As such, there has been a long history of various thinkers drawing in subjective knowledge into information. However, for this theory, we are interested in removing the special frame of reference. This concept appears to be so radical that it is actually impossible for most people to understand- at least peer reviewers! [Moderator: While pooh-poohing 52 years of readers, you might at least come up with a better argument than googling for a word which appears in the paper in quotes because it is being used as a label for a school of thought.]
Don't worry there are other scientific thinkers out there who have carefully understood the physics of information- they all eventually get tripped up in subjective knowledge, and fall on their face.
So what is physical information?
Information is related to probability- self information, the information of an object unto itself is equal to the negative log (in an arbitrary base) of the probability. For a physical system, we can only understand the probability of its state with reference to an earlier state.
The self information of any physical object is proportional to the inverse of the probability. A more improbable system has more information, a more probable system has less.
What about the universe?
This question was answered by Hawking a very long time ago, but somehow its implications were missed. This idea was proposed in 1983 in the paper "Wave Function of the Universe" in Physical Review D. Essentially the probability for a state of the universe at the present time, is given by adding up the amplitudes for all the histories that end with that state.
What about thermodynamics?
The entropy of the universe tends to trend upwards. This can be observed by sticking a thermometer in a glass of cold water. The water slowly approaches the temperature of the surrounding medium. So doesn't this mean that the universe is constantly moving towards a more probable configuration?
Yes it does- if you are a thermometer. But once again, we are introducing a special frame of reference and the stated goal of this concept was to remove it.
It is easier to understand this if you look carefully at the thermodynamic changes associated with flipping a biased coin. If there is a 1/10 chance of getting heads, and a 9/10 chance of getting tails, you can see there is a big probability difference. What is the thermodynamic difference of these two states? The thermodynamic difference is none once the coin has finished flipping. Thermodynamics does not pertain to this notion of probability- it pertains to the probability of distributions among ensembles of identical microstates. Identical with regards to a special frame of reference.
What about information itself?
Now that we have sketched out the major ideas, there are a couple of immediate questions- so what? What does that mean, if anything? Even if there is an information content to physical systems, if it is an arbitrary value which has no reference to the outer world, why do we care about it?
Because- information permeates anything which has a bit of true objective probability to it. The leading place of information appears to be in the genome of living organisms, which is subjected to quantum fluctuations which lead to "stored improbability".
sure just give me some moments to respond
in the meantime, sway in the breeze, reach out for some sunlight, listen to the song of the bird. Improbable as it may seem
in the meantime, sway in the breeze, reach out for some sunlight, listen to the song of the bird. Improbable as it may seem
Interesting....
I get it, but am not sure if other viewers do. So, as a friend, I ask of you to put this in laymans' terms.
I get it, but am not sure if other viewers do. So, as a friend, I ask of you to put this in laymans' terms.
All that exists follow absolute laws. There is no such thing as subjective reality or random probability. The only information of physics are the laws that apply.
It should be clear that the results, even using a probability method to gain some understanding of the functions of physics shows and produces order and design. Ordered results can not be produced from chaos. Ordered results can only result from order.
Probability should only be a tool in the search for deeper understanding and is not an indicator of a universe absent of law, order and design.
It should be clear that the results, even using a probability method to gain some understanding of the functions of physics shows and produces order and design. Ordered results can not be produced from chaos. Ordered results can only result from order.
Probability should only be a tool in the search for deeper understanding and is not an indicator of a universe absent of law, order and design.
In my opinion the papers build on Shannon information theory and are not antique. They are downright easy to read for someone with my physics background.
The OP is not. Nowhere does he state what the offending thought in the paper is, since his only objection is to the presence of a word without regard to its context. This reminds me of the Conservapedia's project to edit the Bible and remove words from Jesus' mouth that they don't like. (Jesus seemed to hang out with a bunch of hippies if you hadn't noticed. The word "comrade" appears and "laborers" several times, so the whole thing smacks of Marxism. And Jesus could not have said "Father forgive them, for they know not what they do" because forgiveness isn't part of Christianity. -- or so the would-be editors assert.)
The OP is not. Nowhere does he state what the offending thought in the paper is, since his only objection is to the presence of a word without regard to its context. This reminds me of the Conservapedia's project to edit the Bible and remove words from Jesus' mouth that they don't like. (Jesus seemed to hang out with a bunch of hippies if you hadn't noticed. The word "comrade" appears and "laborers" several times, so the whole thing smacks of Marxism. And Jesus could not have said "Father forgive them, for they know not what they do" because forgiveness isn't part of Christianity. -- or so the would-be editors assert.)
QUOTE (Alaxir Zoa+Oct 10 2009, 11:21 PM)
Interesting....
I get it, but am not sure if other viewers do. So, as a friend, I ask of you to put this in laymans' terms.
Some suggested reading for the general reader:
First a book recommended some time back upon this forum by RPenner:
Decoding the Universe: How the New Science of Information Is Explaining Everything in the Cosmos, from Our Brains to Black Holes
by Charles Seife
(2006)
http://www.amazon.com/Decoding-Universe-In...g/dp/067003441X
Second, an excellent (i.e. engaging and accessible) overview (IMO) of how the subjective came to be introduced into Physics:
The Dancing Wu Li Masters: An Overview of the New Physics
by Gary Zukav
(1979)
"The Role of I"
(pp 101-127 - 2001 edition)
http://www.amazon.com/Dancing-Wu-Li-Master...w/dp/055326382X
Best,
Raphie
I get it, but am not sure if other viewers do. So, as a friend, I ask of you to put this in laymans' terms.
Some suggested reading for the general reader:
First a book recommended some time back upon this forum by RPenner:
Decoding the Universe: How the New Science of Information Is Explaining Everything in the Cosmos, from Our Brains to Black Holes
by Charles Seife
(2006)
http://www.amazon.com/Decoding-Universe-In...g/dp/067003441X
Second, an excellent (i.e. engaging and accessible) overview (IMO) of how the subjective came to be introduced into Physics:
The Dancing Wu Li Masters: An Overview of the New Physics
by Gary Zukav
(1979)
"The Role of I"
(pp 101-127 - 2001 edition)
http://www.amazon.com/Dancing-Wu-Li-Master...w/dp/055326382X
Best,
Raphie
QUOTE (rpenner+Oct 11 2009, 04:25 PM)
The papers are not antique. They simply assume a special frame of reference, which we are attempting to remove from the consideration of information.
The OP is not. Nowhere does he state what the offending thought in the paper is, since his only objection is to the presence of a word without regard to its context. This reminds me of the Conservapedia's project to edit the Bible and remove words from Jesus' mouth that they don't like. (Jesus seemed to hang out with a bunch of hippies if you hadn't noticed. The word "comrade" appears and "laborers" several times, so the whole thing smacks of Marxism. And Jesus could not have said "Father forgive them, for they know not what they do" because forgiveness isn't part of Christianity. -- or so the would-be editors assert.)
QUOTE
In my opinion the papers build on Shannon information theory and are not antique. They are downright easy to read for someone with my physics background.
The papers are not antique. They are simply introducing a specific frame of reference which includes subjective knowledge as a tool of understanding.
Let us suppose there is an established claim that an island is three thousand meters in size. You measure it over and over, measuring the circumference and see that this is true.
Now I come along and claim that in fact, there is an alternative way to measure the island, which involves a different dimension - the height.
This does not mean you are suddenly wrong or antique- it means we have different frame of reference.
QUOTE (->
| QUOTE |
| In my opinion the papers build on Shannon information theory and are not antique. They are downright easy to read for someone with my physics background. |
The papers are not antique. They are simply introducing a specific frame of reference which includes subjective knowledge as a tool of understanding.
Let us suppose there is an established claim that an island is three thousand meters in size. You measure it over and over, measuring the circumference and see that this is true.
Now I come along and claim that in fact, there is an alternative way to measure the island, which involves a different dimension - the height.
This does not mean you are suddenly wrong or antique- it means we have different frame of reference.
Nowhere does he state what the offending thought in the paper is, since his only objection is to the presence of a word without regard to its context.
Indeed, I believe this is sufficient- because we are trying to remove the subjective frame. It is like my pointing out in the island example we wish to measure the height, and are no longer considering the circumference. Your claim that my pointing out the word "circumference" is not complete is not accurate. If I am talking about height, and you are talking about circumference, we can go nowhere until we agree we are talking about something different.
However, it certainly is helpful to look at the original paper, and lets not look at a single line, but a lot of lines. The introduction of subjective knowledge is not the only problem here. For the beginning of this discussion, lets just look at these lines:
QUOTE
The development of information theory has been felt by many people to be of great significance for statistical mechanics, although the exact way in which it should be applied has remained obscure. In this connection it is essential to note the following. The mere fact that the same mathematical expression -sum p(i) log (p(i)) occurs both in statistical mechanics and in information theory does not in itself establish any connection between these fields This can be done only by finding new viewpoints from which thermodynamic entropy and information theory entropy appear as the same concept.
So my complaint here is that if we are going to understand the information of a system- the self information of a system- we must understand it as a probability of a specific microstate. The equation -sum(p(i) log (p(i)) in terms of information theory refers to the entropy of a constant signal generating a time series of probable symbols produced in information theory. It is not the appropriate way to understand the information content of a physical system at a specific point in time with a specific observable state, it is the appropriate way to understand the information content of a complete physical system given all other possible states of that system.
If you are examining a specific symbol, you do not examine the entropy of the producing mechanism to know its information content, you examine the symbol itself.
In this context, I am claiming that a symbol is tantamount to understanding a specific state of a physical system. For example, rolling a die. If you roll a die, and end up with the state of a particular face, we understand the information of this state to be a function of the probability, not a sum of the other possible rolls which could have occurred.
If you want to understand the information content of the die itself, then yes we need to understand the information content using the -sum p(i) log p(i). However, if you want to understand the information content of the roll after you are observing the die which lies on the ground, we do not use this consideration. We need to know its log 1/p(i) .
So if we wish to understand the information content of any physical system, be it a die, a planet, or a universe, then we use the same consideration of its log 1/p(i). It is incorrect to consider the entropy of the generating mechanism.
Sadly, I haven't yet gotten to subjective knowledge yet, but will in time.
It is interesting how hostile your overall tone is, I am sorry you feel so hostile to posters, I don't think you will gain the most understanding from conversations by having such an approach.
QUOTE
If you read the paper and understood it, you would see that Jaynes deliberately seeks to avoid introducing guesses into probability distributions through the maximum entropy method.
Unfortunately we are going to possibly be chasing this line of thought down corridors which are perhaps not useful for the general reader. For as stated:
To understand the information content of a system we need to understand the probability the system is in that state.
However, Jaynes makes a compelling connection between statistical mechanics and information theory, which has essentially stifled further conversation in this area. Chasing these ideas of Jaynes may really stifle further conversation on the real idea above, but is instructive nonetheless.
Let us note historically that Jaynes was drawn to this comparison because of Shannon's pointing out the relationship between entropy in information theory and entropy in thermodynamics (hence the chosen name of entropy in information theory). Shannon in turn references Richard Tolman, who uses the same ideas that Jaynes does in assuming that "lack of knowledge of a system can validly be represented as an equal a priori distribution of all possible microstates which would lead to a specific measurable macrostate". Richard Tolman in turn refers to William Gibbs, who suggested this in his earlier writings in statistical thermodynamics. Gibbs was the father of statistical thermodynamics, and so must be taken seriously.
However, Gibbs himself rejected this line of thought as a way to understand physical reality, he proposed it as a way to understand the mathematics in a conceptual way. Let us see how Richard Tolman refers to this overall concept of a priori probabilities. This is in "The Principals of Statistical mechanics" by Richard Tolman 1938. (If it is possible to put in a link to this actual reference that would be much appreciated if it is available).
QUOTE (->
| QUOTE |
| If you read the paper and understood it, you would see that Jaynes deliberately seeks to avoid introducing guesses into probability distributions through the maximum entropy method. |
Unfortunately we are going to possibly be chasing this line of thought down corridors which are perhaps not useful for the general reader. For as stated:
To understand the information content of a system we need to understand the probability the system is in that state.
However, Jaynes makes a compelling connection between statistical mechanics and information theory, which has essentially stifled further conversation in this area. Chasing these ideas of Jaynes may really stifle further conversation on the real idea above, but is instructive nonetheless.
Let us note historically that Jaynes was drawn to this comparison because of Shannon's pointing out the relationship between entropy in information theory and entropy in thermodynamics (hence the chosen name of entropy in information theory). Shannon in turn references Richard Tolman, who uses the same ideas that Jaynes does in assuming that "lack of knowledge of a system can validly be represented as an equal a priori distribution of all possible microstates which would lead to a specific measurable macrostate". Richard Tolman in turn refers to William Gibbs, who suggested this in his earlier writings in statistical thermodynamics. Gibbs was the father of statistical thermodynamics, and so must be taken seriously.
However, Gibbs himself rejected this line of thought as a way to understand physical reality, he proposed it as a way to understand the mathematics in a conceptual way. Let us see how Richard Tolman refers to this overall concept of a priori probabilities. This is in "The Principals of Statistical mechanics" by Richard Tolman 1938. (If it is possible to put in a link to this actual reference that would be much appreciated if it is available).
Gibbs was very cautious in making assertions as to the relation of the systems actually encountered in nature to the statistical ensembles which he discussed, and seemed to regard the properties of these ensembles as providing analogies rather than explanations for the principals of thermodynamics.. we can now afford to adopt a more positive attitude. This we do by clearly introducing and distinguishing between the two concepts of system of interest and corresponding representative ensemble, and by then asserting that an appropriately chosen ensemble would really permit valid predictions as to the behavior to be expected on the average for a system of interest started off in successive trials in the same partially specified condition under consideration. This procedure then involves a more explicit consideration of the hypothesis as to a priori probablities and phases, used in constructing appropriate ensembles, that was needed in the work of Gibbs.
So we can see here that Gibbs viewed this notion of a priori probabilities as a mechanism of analogy, and Tolman moves it forwards towards an acceptable way to understand physical systems. This is what Shannon saw- this notion of lack of knowledge of a system, which is why he referenced it with regards to his lack of knowledge in production of symbol states.
Then Jaynes takes this idea, and formalizes it. This is what Jaynes has to say:
QUOTE
This problem of specification of probabilities in cases where little or no information is available, is as old as the theory of probability. Laplace's "Principale of Insufficient Reason" was an attempt to supply a criterion of choice, in which one said that two events are to be assigned equal probabilities if there is no reason to think otherwise. However, except in cases where there is evident element of symmetry that clearly renders the events "equally possible," this assumption may appear just as arbitrary as any other that might be made.
Indeed, it is not only arbitrary- whatever choice you make about how to assign this probability becomes a subjective probability, independent from the objective reality of its probability. So it is not a valid tool for making a real understanding of physical systems.
QUOTE (->
| QUOTE |
| This problem of specification of probabilities in cases where little or no information is available, is as old as the theory of probability. Laplace's "Principale of Insufficient Reason" was an attempt to supply a criterion of choice, in which one said that two events are to be assigned equal probabilities if there is no reason to think otherwise. However, except in cases where there is evident element of symmetry that clearly renders the events "equally possible," this assumption may appear just as arbitrary as any other that might be made. |
Indeed, it is not only arbitrary- whatever choice you make about how to assign this probability becomes a subjective probability, independent from the objective reality of its probability. So it is not a valid tool for making a real understanding of physical systems.
It is now evident how to solve our problem; in making inferences on the basis of partial information we must use that probability distribution which has maximum entropy subject to whatever is known. This is the only unbiased assignment we can make; to use any other would amount to arbitrary assumption of information which by hypothesis we do not have.
For those not following this language, he is saying that - whatever we do not know, we will assume an equal and maximum distribution of possibilities. That is- our lack of knowledge is being incorporated into the physical system as a physical reality. This is the objection which is being raised. This is akin to saying - since I do not know if it will rain or not tomorrow and I am in my basement, I will look at the past history of whether or not it rained in the past on this date to decide if it will rain tomorrow. If we were to look at the doppler radar and see a massive storm cloud coming in- this may certainly affect our notion of this and the reality of whether or not it would rain. But since we do not have access to this doppler radar in our basement, we are going to go based on our knowledge and assume maximum distribution of possible outcomes, which could be found reasonably by looking at past weather on this date. That is to say- we accept the reality of if it will rain based on our own lack of knowledge. This is ludicrous. The physical reality of if it will rain does not depend in any part on what our knowledge of the state of the system.
The introduction of a subjective frame of reference can not be considered as a valid frame of reference for actually understanding physical systems. This is why William Gibbs rejected this line of reasoning (even though he invented it in this consideration as a tool for understanding systems).
Lets make this less abstract, and consider Jaynes proposal another way. There exists a deck of cards, which you know has been shuffled. You are allowed to sample the top fifteen cards and find out how many are red and black before making bets on what the next card will be. You find out 7 are red and 8 are black. This our "macroscopic measurement" of what the state is, which is not granular.
It turns out the shuffle was a perfect interleaved shuffle of the red and black cards, so they alternate. However, your measurement system does not show you this.
Now you are entering a gambling game, where these top cards are going to be flipped over one by one and you can bet on each one (observation of the future of the system). If the card is black, you double your money, if it is red, you halve it. Now you must decide how much to bet each card.
According to your observable knowledge, the strategy would be to bet all your money each turn (or something slightly more complex). You must assume that all possible distributions are equally likely for the cards. It could be all the blacks before all the reds, or vice versa. Your subjective uncertainty leads you to this decision. You know you will end up with double your money at the end of the game.
However, the correct betting algorithm would be to bet everything every other card. This is the objective reality of what the correct action would be. The objective reality strategy does not correspond to the subjective knowledge strategy.
If one is truly interested in using the theory of maximum entropy distribution as your basis for understanding physical systems, please give me a call and we can play some cards.
However, I will note that if you accept Jayne's line of reasoning you will come to his same conclusions. However, if you consider there exists an objective probability outside of subjective probability, you will come to a very different conclusion.
Let us note a couple of interesting things here. First of all, whether or not you care about the information of a system is not relevant. What is interesting to note, and first astounded me when I realized it, is:
There exists a probability for physical systems which is independent of statistical mechanics / thermodynamic considerations.
(See the top of this thread for links to Jayne's papers). [Moderator: This does not accrue to your credit since I placed the links and citations there.]
Then you aren't talking about either statistical mechanics nor thermodynamics. The burden has been on you not to tear down Jaynes, but to build up your own useful, predictive and comprehensive theory of some realm of phenomena and then by virtue of the proven superiority of your theory's usefulness over that of all other theories which cover that realm of phenomena will Jaynes' stature diminish.
Instead you attack his use of technical labels even though he is entirely technically correct and as of yet, you show no comprehension that he is correct in word choice or that the axioms of probability are not influenced by the use of probability.
My hostility is based entirely on objective and communicable reasons. You wrote a cargo-cult pseudo-scientific post, you fail to be useful, and you are unclear and misleading in your claims and goals. My appointed duty is to educate you in your failings and to otherwise improve the quality of the board as a whole, so to begin with I have to parse your claims which rest only on your own self-declared authority. You make this harder than would be necessary, because of the unscientific nature of your lack of specific citations and to the complete lack of definitions and argument.
Confused2, here are some links to what Subjective means in this paper.
http://plato.stanford.edu/entries/probabil...terpret/#SubPro (Section 3.5.1)
As you see the OP has confused subjectivism with unconstrained subjectivism with maximum entropy subjectivism.
http://en.wikipedia.org/wiki/Probability_interpretations
Instead you attack his use of technical labels even though he is entirely technically correct and as of yet, you show no comprehension that he is correct in word choice or that the axioms of probability are not influenced by the use of probability.
My hostility is based entirely on objective and communicable reasons. You wrote a cargo-cult pseudo-scientific post, you fail to be useful, and you are unclear and misleading in your claims and goals. My appointed duty is to educate you in your failings and to otherwise improve the quality of the board as a whole, so to begin with I have to parse your claims which rest only on your own self-declared authority. You make this harder than would be necessary, because of the unscientific nature of your lack of specific citations and to the complete lack of definitions and argument.
Confused2, here are some links to what Subjective means in this paper.
http://plato.stanford.edu/entries/probabil...terpret/#SubPro (Section 3.5.1)
As you see the OP has confused subjectivism with unconstrained subjectivism with maximum entropy subjectivism.
http://en.wikipedia.org/wiki/Probability_interpretations
OFF-TOPIC
==============================
Trout Posted: Yesterday at 6:31 PM
Negative -
==============================
Would you care, Trout, to explain to me and others, specifically RPenner, the purpose and merit of your most recent negative feedack, which I can only (reasonably) assume to be in some manner a response to my above post?
Thank you in advance.
Best,
Raphie
P.S. I would hate to think that someone, anyone, would deem the act of another simply "speaking" due cause for negative feedback, Trout. Although, of course, I will grant you that it is quite 'important' to keep (racially decontextualized...) 'niggers,' such as myself, in their place...
==============================
Trout Posted: Yesterday at 6:31 PM
Negative -
==============================
Would you care, Trout, to explain to me and others, specifically RPenner, the purpose and merit of your most recent negative feedack, which I can only (reasonably) assume to be in some manner a response to my above post?
Thank you in advance.
Best,
Raphie
P.S. I would hate to think that someone, anyone, would deem the act of another simply "speaking" due cause for negative feedback, Trout. Although, of course, I will grant you that it is quite 'important' to keep (racially decontextualized...) 'niggers,' such as myself, in their place...
rpenner,
Both Jaynes and TinyTree are saying the same thing. You have your focus on the wrong issue. You are defending the mechanics of mathematics. That is not the issue here. The mechanics of mathematics are valid and not in question. What is the problem? The mechanics of a physical process can not be understood with the use of the mechanics of math. Math can only describe a relationship of a physical process through its formulas.
Let me give you an example. Life is extremely complex. What is the mathematical probability? This is an unfair question for math or a physical process since everything is an unknown. I will not go into the logic for either because it is very speculative. But two paths are usually chosen, chance and a higher power. Without further accurate reproducible information about the physical process neither can be dismissed. Of course neither can which, warlocks and magic.
Both Jaynes and TinyTree are saying the same thing. You have your focus on the wrong issue. You are defending the mechanics of mathematics. That is not the issue here. The mechanics of mathematics are valid and not in question. What is the problem? The mechanics of a physical process can not be understood with the use of the mechanics of math. Math can only describe a relationship of a physical process through its formulas.
Let me give you an example. Life is extremely complex. What is the mathematical probability? This is an unfair question for math or a physical process since everything is an unknown. I will not go into the logic for either because it is very speculative. But two paths are usually chosen, chance and a higher power. Without further accurate reproducible information about the physical process neither can be dismissed. Of course neither can which, warlocks and magic.
Instead you attack his use of technical labels even though he is entirely technically correct and as of yet, you show no comprehension that he is correct in word choice or that the axioms of probability are not influenced by the use of probability.
You can be mathematically correct for the wrong process. He just limits the labels to the mechanics of math.
He was neither unclear nor misleading. He separated math mechanics and process mechanics very clearly. I suspect your hostility was based on a different understanding of what you read. Preconceived possibly.
He was neither unclear nor misleading. He separated math mechanics and process mechanics very clearly. I suspect your hostility was based on a different understanding of what you read. Preconceived possibly.
My appointed duty is to educate you in your failings and to otherwise improve the quality of the board as a whole, so to begin with I have to parse your claims which rest only on your own self-declared authority.
Its a well known fact that math can not prove a physical process. If you believe math can prove a physical process you are the one with the failings.
What citation do you need to show math can not prove a physical mechanism? He gave examples. I have more if you like.
What citation do you need to show math can not prove a physical mechanism? He gave examples. I have more if you like.
As you see the OP has confused subjectivism with unconstrained subjectivism with maximum entropy subjectivism.
Nowhere was the math considered subjective as far as I can see, just the physical processes.
QUOTE
Then you aren't talking about either statistical mechanics nor thermodynamics. The burden has been on you not to tear down Jaynes, but to build up your own useful, predictive and comprehensive theory of some realm of phenomena and then by virtue of the proven superiority of your theory's usefulness over that of all other theories which cover that realm of phenomena will Jaynes' stature diminish.
Both Jaynes and TinyTree are saying the same thing. You have your focus on the wrong issue. You are defending the mechanics of mathematics. That is not the issue here. The mechanics of mathematics are valid and not in question. What is the problem? The mechanics of a physical process can not be understood with the use of the mechanics of math. Math can only describe a relationship of a physical process through its formulas.
Let me give you an example. Life is extremely complex. What is the mathematical probability? This is an unfair question for math or a physical process since everything is an unknown. I will not go into the logic for either because it is very speculative. But two paths are usually chosen, chance and a higher power. Without further accurate reproducible information about the physical process neither can be dismissed. Of course neither can which, warlocks and magic.
QUOTE (->
| QUOTE |
| Then you aren't talking about either statistical mechanics nor thermodynamics. The burden has been on you not to tear down Jaynes, but to build up your own useful, predictive and comprehensive theory of some realm of phenomena and then by virtue of the proven superiority of your theory's usefulness over that of all other theories which cover that realm of phenomena will Jaynes' stature diminish. |
Both Jaynes and TinyTree are saying the same thing. You have your focus on the wrong issue. You are defending the mechanics of mathematics. That is not the issue here. The mechanics of mathematics are valid and not in question. What is the problem? The mechanics of a physical process can not be understood with the use of the mechanics of math. Math can only describe a relationship of a physical process through its formulas.
Let me give you an example. Life is extremely complex. What is the mathematical probability? This is an unfair question for math or a physical process since everything is an unknown. I will not go into the logic for either because it is very speculative. But two paths are usually chosen, chance and a higher power. Without further accurate reproducible information about the physical process neither can be dismissed. Of course neither can which, warlocks and magic.
Instead you attack his use of technical labels even though he is entirely technically correct and as of yet, you show no comprehension that he is correct in word choice or that the axioms of probability are not influenced by the use of probability.
You can be mathematically correct for the wrong process. He just limits the labels to the mechanics of math.
QUOTE
My hostility is based entirely on objective and communicable reasons. You wrote a cargo-cult pseudo-scientific post, you fail to be useful, and you are unclear and misleading in your claims and goals.
He was neither unclear nor misleading. He separated math mechanics and process mechanics very clearly. I suspect your hostility was based on a different understanding of what you read. Preconceived possibly.
QUOTE (->
| QUOTE |
| My hostility is based entirely on objective and communicable reasons. You wrote a cargo-cult pseudo-scientific post, you fail to be useful, and you are unclear and misleading in your claims and goals. |
He was neither unclear nor misleading. He separated math mechanics and process mechanics very clearly. I suspect your hostility was based on a different understanding of what you read. Preconceived possibly.
My appointed duty is to educate you in your failings and to otherwise improve the quality of the board as a whole, so to begin with I have to parse your claims which rest only on your own self-declared authority.
Its a well known fact that math can not prove a physical process. If you believe math can prove a physical process you are the one with the failings.
QUOTE
You make this harder than would be necessary, because of the unscientific nature of your lack of specific citations and to the complete lack of definitions and argument.
What citation do you need to show math can not prove a physical mechanism? He gave examples. I have more if you like.
QUOTE (->
| QUOTE |
| You make this harder than would be necessary, because of the unscientific nature of your lack of specific citations and to the complete lack of definitions and argument. |
What citation do you need to show math can not prove a physical mechanism? He gave examples. I have more if you like.
As you see the OP has confused subjectivism with unconstrained subjectivism with maximum entropy subjectivism.
Nowhere was the math considered subjective as far as I can see, just the physical processes.
QUOTE (4Dguy+Oct 12 2009, 10:52 AM)
Its a well known fact that math can not prove a physical process. If you believe math can prove a physical process you are the one with the failings.
ROFLMAO
ROFLMAO
I do believe Maxwell was not particularly comforted with his equations predicting light traveled at constant speed. But Einstein took his equations at face value
QUOTE (4Dguy+Oct 12 2009, 03:52 PM)
Both Jaynes and TinyTree are saying the same thing.
How can that be, when TinyTree starts out by saying that Jaynes is wrong in assumptions and conclusions?
How can that be, when TinyTree starts out by saying that Jaynes is wrong in assumptions and conclusions?
rpenner,
TinyTree
Posted: Oct 10 2009, 11:31 AM
rpenner comments in:
TinyTree
Posted: Oct 10 2009, 11:31 AM
rpenner comments in:
TinyTree
Posted: Oct 10 2009, 11:31 AM
This is not a subjective choice
Jaynes says "its subjective in the physical process." But it is a good predictive tool! The article was very cautious to include the term subjective. I did not see where TinyTree called it wrong. If he did I missed that. But if assumptions in the physical process are subjective it follows that the conclusions of the process are also subjective. This does not mean the math is subjective or wrong. This whole issue is about the fine distinction between the mechanics of math and mechanics of a physical process. How do you combine the two distinct mechanical processes to make predictions if one process is subjective. If you add physical restraints to the system it can increase the value of prediction. Subjective process unknowns can still jump out and bite you.
It may be instructive to compare this concept of objective probability of the wave function of a physical system to other writers on information theory. If someone has a favorite book on this subject, let me know what it is and I'll check it out of the library and compare and contrast this theory to whatever book/theory you are interested in seeing compared. If no one has one, I'll find one.
However, looking at Jaynes a little bit further.
Jaynes vs this theory is like comparing two different ways to measure something. Jaynes incorporates our degree of knowledge of the system. The objective probability metric (Tinytree method) skips our degree of knowledge of the system. These are very different ways to understand something. Let's look at what Jaynes says in his paper:
Entropy as a concept may be regarded as a measure of our degree of ignorance as to the state of the system; on the other hand, for equilibrium conditions it is an experimentally measurable quantity, whose most important properties were found empirically.
As the available information decreases to zero, maximum entropy inference shades continuously into nonsense and eventually becomes useless. Nevertheless at each stage it represents the best that could have been done with the available information.
We can see here that Jayne's understanding of the information of the system is tied to our knowledge of the system. As our ability to perceive the system goes up due to technological or intellectual power, the information of the system changes.
This is in stark contrast to the Tinytree method. In the Tinytree method, our knowledge of the system does not change the information content of the system itself.
So in Jaynes theory, as we develop new technologies to be able to discern the positions and movement of matter, which we are doing, it changes the information content of the system itself.
However in the Tinytree method our ability to know the system does not affect its underlying information content.
So one can ask- what would you prefer to have, a measuring system which depends on both the observer and their technological ability, or a measuring system which yields the same answer independently of who or what is measuring it?
Thus you can see that Jaynes understanding of the physics of information differs wildly from my own. Jaynes incorporates the technological abilities of the measurer. Mine does not.
If we were to take Jaynes method and apply it to a set of symbols which were generated by a markoff generating symbolic device, the information content of the series of symbols would change as we were better able to resolve what the symbols were. In the Tinytree method, the information content of the symbols stays the same no matter how many of them we can resolve. The symbols have an information content unto themselves, independent of the observer.
Note in the Tinytree method we may not be able to actually know the information content until the symbols are resolved. In the Jaynes method we always know the information content (which may be nothing when we can resolve nothing) and we have a changing information content depending on our ability to resolve those symbols.
This is the important difference- that things have objective probabilities unto themselves, irregardless of any particular observer, or their ability to perceive, their state of knowledge, or any other special frame of reference.
I'd like a better term than the Tinytree method please suggest one if you like.
This is 100% correct. The claim is that this is a definition of how to relate information content to physical systems, not that this is about statistical mechanics or thermodynamics.
However, many earlier authors HAVE made this connection. If we are discussing these earlier authors, then we will refer to those concepts.
Also, there is a common lay understanding that statistical mechanics means we are moving to a more probable configuration, and thus all concepts of probability fall into this conceptual framework. For this reason, it will be necessary to bring up this topic to distinguish it from the topic at hand (the objective probability of the physical system).
This is 100% correct. The claim is that this is a definition of how to relate information content to physical systems, not that this is about statistical mechanics or thermodynamics.
However, many earlier authors HAVE made this connection. If we are discussing these earlier authors, then we will refer to those concepts.
Also, there is a common lay understanding that statistical mechanics means we are moving to a more probable configuration, and thus all concepts of probability fall into this conceptual framework. For this reason, it will be necessary to bring up this topic to distinguish it from the topic at hand (the objective probability of the physical system).
The burden has been on you not to tear down Jaynes, but to build up your own useful, predictive and comprehensive theory of some realm of phenomena and then by virtue of the proven superiority of your theory's usefulness over that of all other theories which cover that realm of phenomena will Jaynes' stature diminish.
It is instructive to compare Jaynes theory to my own, and it would be instructive to consider other information theoretic theories as well. I don't think Jaynes stature will diminish any- he is one of the most preeminent statisticians who has ever lived. However, that doesn't mean he has the final word on every topic which he has laid eyes on. There is always room for improvement of our understanding of the world, especially where there are special frames of reference being introduced which break our ability to comprehend the underlying nature of things.
I am not attacking his use of labels, I am attacking his use of concepts. Please read through a couple of the responses here to see what this means. In the last response here, we can see that Jaynes theory as applied to a generated symbol stream is contingent on our ability to resolve what those symbols are. In the objective probability theory, the information content is not dependent on our ability to resolve them.
So let us suppose there is a stream of symbols being handed from one computer to another. My claim is that the information content of these symbols does not change on our ability (as an external agent) to perceive what they are. Jayne's view would be that it does change- because the information content is dependent on our lack of knowledge of them.
I believe he IS correct in word choice- for what he is trying to measure. This is like the circumference versus the height. I do not object to someone measuring the circumference. I object to not acknowledging that the height exists. Jaynes is measuring the circumference. he does this perfectly, articulately, and with the correct word choice and based on the axioms of probability. However, there exists another way to consider things, which is being proposed here.
I am not attacking his use of labels, I am attacking his use of concepts. Please read through a couple of the responses here to see what this means. In the last response here, we can see that Jaynes theory as applied to a generated symbol stream is contingent on our ability to resolve what those symbols are. In the objective probability theory, the information content is not dependent on our ability to resolve them.
So let us suppose there is a stream of symbols being handed from one computer to another. My claim is that the information content of these symbols does not change on our ability (as an external agent) to perceive what they are. Jayne's view would be that it does change- because the information content is dependent on our lack of knowledge of them.
I believe he IS correct in word choice- for what he is trying to measure. This is like the circumference versus the height. I do not object to someone measuring the circumference. I object to not acknowledging that the height exists. Jaynes is measuring the circumference. he does this perfectly, articulately, and with the correct word choice and based on the axioms of probability. However, there exists another way to consider things, which is being proposed here.
My appointed duty is to educate you in your failings and to otherwise improve the quality of the board as a whole, so to begin with I have to parse your claims which rest only on your own self-declared authority.
I look forwards to being educated.
This is similar to your initial comment placed in the initial post- by not referencing specific phrasing in Jaynes paper, you condemn the entire concept. Thus, you place me in the position of having to guess what you need to know, and condemn me for not guessing ahead of time. If I don't guess this, then I clearly have no idea what I am talking about. I think this represents a solipsistic view of reality on your part, but I will do my best to guess what you are thinking to avoid your harshness.
I will attempt to come up with some better citations and increase the definitions and argument. these are certainly legitimate valid points. However, we are not a peer reviewed journal here, so the standards are perhaps a bit lower, but if they are so low that we have no references at all then it is too low. At the time when I pass "newbie" status and can put in links I hope to put in many. I appreciated your linking to the Jaynes paper actually, and referred to it as an act of respect, not of demeanment, I am sorry you took it negatively.
However, you must expect that in the first post attempting to gain attention to itself, it would be difficult to make it both self effacing and also gain the interest of the reader.
This is similar to your initial comment placed in the initial post- by not referencing specific phrasing in Jaynes paper, you condemn the entire concept. Thus, you place me in the position of having to guess what you need to know, and condemn me for not guessing ahead of time. If I don't guess this, then I clearly have no idea what I am talking about. I think this represents a solipsistic view of reality on your part, but I will do my best to guess what you are thinking to avoid your harshness.
I will attempt to come up with some better citations and increase the definitions and argument. these are certainly legitimate valid points. However, we are not a peer reviewed journal here, so the standards are perhaps a bit lower, but if they are so low that we have no references at all then it is too low. At the time when I pass "newbie" status and can put in links I hope to put in many. I appreciated your linking to the Jaynes paper actually, and referred to it as an act of respect, not of demeanment, I am sorry you took it negatively.
However, you must expect that in the first post attempting to gain attention to itself, it would be difficult to make it both self effacing and also gain the interest of the reader.
As you see the OP has confused subjectivism with unconstrained subjectivism with maximum entropy subjectivism.
I think you have a good point here. I did not refer to any other authors, but piled them altogether. In piling them altogether, I slurred the concepts which are distinct. Hopefully if I get a chance to compare and contrast other authors, a claim can be made there is a similarity between their views which may be encapsulated by the word "subjectivism" but I haven't made that point clearly at all at this time, and probably would be better served by some other term.
I appreciate your attempt to understand this- don't get me wrong- I think you get this better than any other poster so far.
TinyTree
Posted: Oct 10 2009, 11:31 AM
QUOTE
However, poor Jaynes makes one fatal flaw with his analysis, which is difficult to wrap your head around:
He introduces a special frame of reference, a subjective frame of reference.
He introduces a special frame of reference, a subjective frame of reference.
rpenner comments in:
TinyTree
Posted: Oct 10 2009, 11:31 AM
QUOTE (->
| QUOTE |
| However, poor Jaynes makes one fatal flaw with his analysis, which is difficult to wrap your head around: He introduces a special frame of reference, a subjective frame of reference. |
rpenner comments in:
TinyTree
Posted: Oct 10 2009, 11:31 AM
This is not a subjective choice
Jaynes says "its subjective in the physical process." But it is a good predictive tool! The article was very cautious to include the term subjective. I did not see where TinyTree called it wrong. If he did I missed that. But if assumptions in the physical process are subjective it follows that the conclusions of the process are also subjective. This does not mean the math is subjective or wrong. This whole issue is about the fine distinction between the mechanics of math and mechanics of a physical process. How do you combine the two distinct mechanical processes to make predictions if one process is subjective. If you add physical restraints to the system it can increase the value of prediction. Subjective process unknowns can still jump out and bite you.
It may be instructive to compare this concept of objective probability of the wave function of a physical system to other writers on information theory. If someone has a favorite book on this subject, let me know what it is and I'll check it out of the library and compare and contrast this theory to whatever book/theory you are interested in seeing compared. If no one has one, I'll find one.
However, looking at Jaynes a little bit further.
Jaynes vs this theory is like comparing two different ways to measure something. Jaynes incorporates our degree of knowledge of the system. The objective probability metric (Tinytree method) skips our degree of knowledge of the system. These are very different ways to understand something. Let's look at what Jaynes says in his paper:
QUOTE
Entropy as a concept may be regarded as a measure of our degree of ignorance as to the state of the system; on the other hand, for equilibrium conditions it is an experimentally measurable quantity, whose most important properties were found empirically.
As the available information decreases to zero, maximum entropy inference shades continuously into nonsense and eventually becomes useless. Nevertheless at each stage it represents the best that could have been done with the available information.
We can see here that Jayne's understanding of the information of the system is tied to our knowledge of the system. As our ability to perceive the system goes up due to technological or intellectual power, the information of the system changes.
This is in stark contrast to the Tinytree method. In the Tinytree method, our knowledge of the system does not change the information content of the system itself.
So in Jaynes theory, as we develop new technologies to be able to discern the positions and movement of matter, which we are doing, it changes the information content of the system itself.
However in the Tinytree method our ability to know the system does not affect its underlying information content.
So one can ask- what would you prefer to have, a measuring system which depends on both the observer and their technological ability, or a measuring system which yields the same answer independently of who or what is measuring it?
Thus you can see that Jaynes understanding of the physics of information differs wildly from my own. Jaynes incorporates the technological abilities of the measurer. Mine does not.
If we were to take Jaynes method and apply it to a set of symbols which were generated by a markoff generating symbolic device, the information content of the series of symbols would change as we were better able to resolve what the symbols were. In the Tinytree method, the information content of the symbols stays the same no matter how many of them we can resolve. The symbols have an information content unto themselves, independent of the observer.
Note in the Tinytree method we may not be able to actually know the information content until the symbols are resolved. In the Jaynes method we always know the information content (which may be nothing when we can resolve nothing) and we have a changing information content depending on our ability to resolve those symbols.
This is the important difference- that things have objective probabilities unto themselves, irregardless of any particular observer, or their ability to perceive, their state of knowledge, or any other special frame of reference.
I'd like a better term than the Tinytree method please suggest one if you like.
QUOTE
Then you aren't talking about either statistical mechanics nor thermodynamics.
This is 100% correct. The claim is that this is a definition of how to relate information content to physical systems, not that this is about statistical mechanics or thermodynamics.
However, many earlier authors HAVE made this connection. If we are discussing these earlier authors, then we will refer to those concepts.
Also, there is a common lay understanding that statistical mechanics means we are moving to a more probable configuration, and thus all concepts of probability fall into this conceptual framework. For this reason, it will be necessary to bring up this topic to distinguish it from the topic at hand (the objective probability of the physical system).
QUOTE (->
| QUOTE |
| Then you aren't talking about either statistical mechanics nor thermodynamics. |
This is 100% correct. The claim is that this is a definition of how to relate information content to physical systems, not that this is about statistical mechanics or thermodynamics.
However, many earlier authors HAVE made this connection. If we are discussing these earlier authors, then we will refer to those concepts.
Also, there is a common lay understanding that statistical mechanics means we are moving to a more probable configuration, and thus all concepts of probability fall into this conceptual framework. For this reason, it will be necessary to bring up this topic to distinguish it from the topic at hand (the objective probability of the physical system).
The burden has been on you not to tear down Jaynes, but to build up your own useful, predictive and comprehensive theory of some realm of phenomena and then by virtue of the proven superiority of your theory's usefulness over that of all other theories which cover that realm of phenomena will Jaynes' stature diminish.
It is instructive to compare Jaynes theory to my own, and it would be instructive to consider other information theoretic theories as well. I don't think Jaynes stature will diminish any- he is one of the most preeminent statisticians who has ever lived. However, that doesn't mean he has the final word on every topic which he has laid eyes on. There is always room for improvement of our understanding of the world, especially where there are special frames of reference being introduced which break our ability to comprehend the underlying nature of things.
QUOTE
Instead you attack his use of technical labels even though he is entirely technically correct and as of yet, you show no comprehension that he is correct in word choice or that the axioms of probability are not influenced by the use of probability.
I am not attacking his use of labels, I am attacking his use of concepts. Please read through a couple of the responses here to see what this means. In the last response here, we can see that Jaynes theory as applied to a generated symbol stream is contingent on our ability to resolve what those symbols are. In the objective probability theory, the information content is not dependent on our ability to resolve them.
So let us suppose there is a stream of symbols being handed from one computer to another. My claim is that the information content of these symbols does not change on our ability (as an external agent) to perceive what they are. Jayne's view would be that it does change- because the information content is dependent on our lack of knowledge of them.
I believe he IS correct in word choice- for what he is trying to measure. This is like the circumference versus the height. I do not object to someone measuring the circumference. I object to not acknowledging that the height exists. Jaynes is measuring the circumference. he does this perfectly, articulately, and with the correct word choice and based on the axioms of probability. However, there exists another way to consider things, which is being proposed here.
QUOTE (->
| QUOTE |
| Instead you attack his use of technical labels even though he is entirely technically correct and as of yet, you show no comprehension that he is correct in word choice or that the axioms of probability are not influenced by the use of probability. |
I am not attacking his use of labels, I am attacking his use of concepts. Please read through a couple of the responses here to see what this means. In the last response here, we can see that Jaynes theory as applied to a generated symbol stream is contingent on our ability to resolve what those symbols are. In the objective probability theory, the information content is not dependent on our ability to resolve them.
So let us suppose there is a stream of symbols being handed from one computer to another. My claim is that the information content of these symbols does not change on our ability (as an external agent) to perceive what they are. Jayne's view would be that it does change- because the information content is dependent on our lack of knowledge of them.
I believe he IS correct in word choice- for what he is trying to measure. This is like the circumference versus the height. I do not object to someone measuring the circumference. I object to not acknowledging that the height exists. Jaynes is measuring the circumference. he does this perfectly, articulately, and with the correct word choice and based on the axioms of probability. However, there exists another way to consider things, which is being proposed here.
My appointed duty is to educate you in your failings and to otherwise improve the quality of the board as a whole, so to begin with I have to parse your claims which rest only on your own self-declared authority.
I look forwards to being educated.
QUOTE
You make this harder than would be necessary, because of the unscientific nature of your lack of specific citations and to the complete lack of definitions and argument.
This is similar to your initial comment placed in the initial post- by not referencing specific phrasing in Jaynes paper, you condemn the entire concept. Thus, you place me in the position of having to guess what you need to know, and condemn me for not guessing ahead of time. If I don't guess this, then I clearly have no idea what I am talking about. I think this represents a solipsistic view of reality on your part, but I will do my best to guess what you are thinking to avoid your harshness.
I will attempt to come up with some better citations and increase the definitions and argument. these are certainly legitimate valid points. However, we are not a peer reviewed journal here, so the standards are perhaps a bit lower, but if they are so low that we have no references at all then it is too low. At the time when I pass "newbie" status and can put in links I hope to put in many. I appreciated your linking to the Jaynes paper actually, and referred to it as an act of respect, not of demeanment, I am sorry you took it negatively.
However, you must expect that in the first post attempting to gain attention to itself, it would be difficult to make it both self effacing and also gain the interest of the reader.
QUOTE (->
| QUOTE |
| You make this harder than would be necessary, because of the unscientific nature of your lack of specific citations and to the complete lack of definitions and argument. |
This is similar to your initial comment placed in the initial post- by not referencing specific phrasing in Jaynes paper, you condemn the entire concept. Thus, you place me in the position of having to guess what you need to know, and condemn me for not guessing ahead of time. If I don't guess this, then I clearly have no idea what I am talking about. I think this represents a solipsistic view of reality on your part, but I will do my best to guess what you are thinking to avoid your harshness.
I will attempt to come up with some better citations and increase the definitions and argument. these are certainly legitimate valid points. However, we are not a peer reviewed journal here, so the standards are perhaps a bit lower, but if they are so low that we have no references at all then it is too low. At the time when I pass "newbie" status and can put in links I hope to put in many. I appreciated your linking to the Jaynes paper actually, and referred to it as an act of respect, not of demeanment, I am sorry you took it negatively.
However, you must expect that in the first post attempting to gain attention to itself, it would be difficult to make it both self effacing and also gain the interest of the reader.
As you see the OP has confused subjectivism with unconstrained subjectivism with maximum entropy subjectivism.
I think you have a good point here. I did not refer to any other authors, but piled them altogether. In piling them altogether, I slurred the concepts which are distinct. Hopefully if I get a chance to compare and contrast other authors, a claim can be made there is a similarity between their views which may be encapsulated by the word "subjectivism" but I haven't made that point clearly at all at this time, and probably would be better served by some other term.
I appreciate your attempt to understand this- don't get me wrong- I think you get this better than any other poster so far.
To consider the information content of our physical world (or subsets of it) it will be helpful to consider the information content of some very very simple mathematical objects. By understanding these, we can work towards building up mathematical objects which come closer and closer to representing our actual physical universe.
A good place to do this is in the world of cellular automata. For those interested in reading more for background, please try:
Cellular Automata and Complexity: Collected papers by Stephan Wolfram
A New Kind of Science by Stephan Wolfram
Stephan Wolfram is convinced that the physical world is a cellular automata. However, he primarily considers deterministic cellular automata. This does not correspond with the actual physical world with regards to quantum mechanics. It isn't clear why he does not address this deficiency of his model. Wolfram is not the first to consider the universe as a cellular automata, earlier writers such as Edward Fredkin have written extensively on this subject.
Here, we are interested in exploring nondeterministic cellular automata to understand their information content.
A cellular automata is a discrete mathematical process, normally consisting of a grid of cells which have states. Rules govern how one state of the cellular automata change through time to the next state.
For our first system to consider, it will be an infinite cellular automata with a center cell, with the center cell in the on state, all other cells in the off state. At each time interval, with a 1/3 probability, that on state will either move to the left, stay still, or move to the right.
This then becomes a random walk- the cell will drift to the left and the right, randomly walking around. At time zero there is a 100% probability it is in the center square. After time unit 1, there is a 1/3 probability it is in x(-1), 1/3 in x(0), and 1/3 in x(1), where the parenthesis indicate the cell index.
After time unit 2, there is now the following probabilities:
x(-2) 1/9
x(-1) 2/9
x(0) 1/3
x(1) 2/9
x(2) 1/9
So after time N, we can observe the cell and then come to a determination of the information content of the state, as -log(p(x(i)))
A few things to note in this simple example:
1) Some states, such as the center, are more probable than other states, such as being located near the edge.
2) Some states, such as x(3) are impossible to reach given the rules of the system at specific times at time 0 and 1 this is not reachable. But later, it becomes a reachable state.
3) The history of the cells motion does not inform the probability of the present position (it does not matter if it went left then right, or right then left), what informs the probability is the aggregating probability.
4) The probability of a specific state must be measured relative to an earlier state. In this example, we are considering against the state at time interval zero. If we were to consider the probability between time 1 and time 2, we would need to examine the probability at time interval 2 relative to time 1, not relative to time 0.
Let us immediately bring this to bear on our physical universe to compare and contrast
1) Some states are more probable than others in the physical universe.
2) Some states are impossible to reach given the rules of the system. For example, gravity dictates the large scale motion of objects in gravitational fields. This dictates that many states are simply unavailable to the future of the system as a potential reality, even if they are imaginable (such as Mars teleporting to the far edge of the solar system).
3) The probability for a state of the universe at the present time, is given by adding up the amplitudes for all the histories that end with this state.
4) It is meaningful to consider the information content of real physical systems relative to earlier states that are not the start of the universe. For example, if you build a device for amplifying quantum randomness, you can consider the information content of a later state given the initial state of the apparatus.
If we wish to understand the information content of the entire universe we still have a long ways to go, but this sketches out the initial ideas.
A few more points of interest on this very simple non deterministic cellular automata:
Some states (such as 10 units away from the center) are impossible at the start time, then become reachable but highly improbable, then eventually enter a "steady state" where their information content steadily declines as it becomes a more and more probable state.
I will argue this is similar in nature to an organism evolving into a specific niche through specific mutations in its DNA. The "target DNA" is unreachable for a long time frame, then becomes a potential but improbable DNA string, then eventually becomes a more probable DNA string (as a long history of mutational changes have made this a more accessible state to the entire genome of the species). This is leaping ahead a bit, but gives an idea of the practicality of understanding the information content of physical systems.
This simple cellular Automata also demonstrates a maximum speed of causality, a "speed of light" in this simple universe. If we consider the center cell being on, it can only traverse in each time unit one unit in either direction. Thus, the maximum speed of this cells motion is constrained by the laws of the system.
[Moderator: Suspended 10 days for posting no useful information or asking any valid questions.]
A good place to do this is in the world of cellular automata. For those interested in reading more for background, please try:
Cellular Automata and Complexity: Collected papers by Stephan Wolfram
A New Kind of Science by Stephan Wolfram
Stephan Wolfram is convinced that the physical world is a cellular automata. However, he primarily considers deterministic cellular automata. This does not correspond with the actual physical world with regards to quantum mechanics. It isn't clear why he does not address this deficiency of his model. Wolfram is not the first to consider the universe as a cellular automata, earlier writers such as Edward Fredkin have written extensively on this subject.
Here, we are interested in exploring nondeterministic cellular automata to understand their information content.
A cellular automata is a discrete mathematical process, normally consisting of a grid of cells which have states. Rules govern how one state of the cellular automata change through time to the next state.
For our first system to consider, it will be an infinite cellular automata with a center cell, with the center cell in the on state, all other cells in the off state. At each time interval, with a 1/3 probability, that on state will either move to the left, stay still, or move to the right.
This then becomes a random walk- the cell will drift to the left and the right, randomly walking around. At time zero there is a 100% probability it is in the center square. After time unit 1, there is a 1/3 probability it is in x(-1), 1/3 in x(0), and 1/3 in x(1), where the parenthesis indicate the cell index.
After time unit 2, there is now the following probabilities:
x(-2) 1/9
x(-1) 2/9
x(0) 1/3
x(1) 2/9
x(2) 1/9
So after time N, we can observe the cell and then come to a determination of the information content of the state, as -log(p(x(i)))
A few things to note in this simple example:
1) Some states, such as the center, are more probable than other states, such as being located near the edge.
2) Some states, such as x(3) are impossible to reach given the rules of the system at specific times at time 0 and 1 this is not reachable. But later, it becomes a reachable state.
3) The history of the cells motion does not inform the probability of the present position (it does not matter if it went left then right, or right then left), what informs the probability is the aggregating probability.
4) The probability of a specific state must be measured relative to an earlier state. In this example, we are considering against the state at time interval zero. If we were to consider the probability between time 1 and time 2, we would need to examine the probability at time interval 2 relative to time 1, not relative to time 0.
Let us immediately bring this to bear on our physical universe to compare and contrast
1) Some states are more probable than others in the physical universe.
2) Some states are impossible to reach given the rules of the system. For example, gravity dictates the large scale motion of objects in gravitational fields. This dictates that many states are simply unavailable to the future of the system as a potential reality, even if they are imaginable (such as Mars teleporting to the far edge of the solar system).
3) The probability for a state of the universe at the present time, is given by adding up the amplitudes for all the histories that end with this state.
4) It is meaningful to consider the information content of real physical systems relative to earlier states that are not the start of the universe. For example, if you build a device for amplifying quantum randomness, you can consider the information content of a later state given the initial state of the apparatus.
If we wish to understand the information content of the entire universe we still have a long ways to go, but this sketches out the initial ideas.
A few more points of interest on this very simple non deterministic cellular automata:
Some states (such as 10 units away from the center) are impossible at the start time, then become reachable but highly improbable, then eventually enter a "steady state" where their information content steadily declines as it becomes a more and more probable state.
I will argue this is similar in nature to an organism evolving into a specific niche through specific mutations in its DNA. The "target DNA" is unreachable for a long time frame, then becomes a potential but improbable DNA string, then eventually becomes a more probable DNA string (as a long history of mutational changes have made this a more accessible state to the entire genome of the species). This is leaping ahead a bit, but gives an idea of the practicality of understanding the information content of physical systems.
This simple cellular Automata also demonstrates a maximum speed of causality, a "speed of light" in this simple universe. If we consider the center cell being on, it can only traverse in each time unit one unit in either direction. Thus, the maximum speed of this cells motion is constrained by the laws of the system.
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