# Smolins 3 roads: new logic

I finally started to read Smolin's Three roads to Quantum Gravity and only read the first two chapters so far. It doesn't contain any math, but it does seem to present a particular choice of reasoning on howto make progress on the matter, which I think is interesting in it's own because it may be a valuable guide in the world of theories and on a very early stage in the reasoning, it may hint us about flaws in reasoning.

I am not sure if anyone else is interested in such things but I will give it a try. My aim is to see if the logic of reasoning used in science can have any constructive outcomes.

In chapter 2 Smolin argues that that classical logic, that there is an objectivity to the notion of true and false, is not well designed for the task of quantum gravity. One of the reasons is that due to limited information of each observer (no observer can hold compelte information about everything in the universe at once), and prescription to establish truth or false, would be observer-dependent.

I agree with that.

But then Smolin seems to argue that a measure ofthe rationality of actions/decisions can be construced without the use of an "superobserver" knowing everything at all times. He says it's enough to assume that the observers are honest, and argues that in that way, two observers facing "the same information" will always make the same decision.

This makes me suspect, and I am curious to se how he builds onto this later in his reasoning. The problems I see is the feedback, that also "logic of reasoning" of a particular observer is evolved in the observer history. So it could still be that different observers facing the same information, responds differently, becase the very notion of "logic of reasoning" is different.

This is what I see as the basis for backgroudn independence at a fundamental level. There seems to be a feedback and self-reference between the way information is processed, and the evolution of the logic of information processing.

The reason I find common language analysis of very simple things interesting is that, I think differences in reasoning does have implications when you choose the mathematical formalism later. And at the later stages there is such much details and baggage that it's hard to analyse. Defects in the line of reasoning will propagage throughout the entire constructions.

/Fredrik

new logic -> topos theory?

Perhaps Smoling will argue later in the book but, he mentions something that the topos theory formalism is a formalism that naturally resolved the issue of the new logic.

Set aside the abstract definition of topos theory as a mathematical subject, is anyone aware of the logic that Smolin implies exists - that topos theory formalism, somehow would naturally emerge as the natural solution to the problem of replacing classical logic in the context of modelling reality?

Is there some paper where this reasoning is lined out explicitly in some way? And how is this exploited to constrain the approach? ie what are the constraints of the topos formalism when applied to strategies?

/Fredirk

A Topos Foundation for Theories of Physics

As many times before Baez appears to have made some nice summaries!

http://math.ucr.edu/home/baez/topos_physics/

which contains the following papers

(1) A Topos Foundation for Theories of Physics: I. Formal Languages for Physics
-- http://arxiv.org/abs/quant-ph/0703060

(2) A Topos Foundation for Theories of Physics: II. Daseinisation and the Liberation of Quantum Theory
-- http://arxiv.org/abs/quant-ph/0703062

(3) A Topos Foundation for Theories of Physics: III. The Representation of Physical Quantities With Arrows
-- http://arxiv.org/abs/quant-ph/0703064

(4) A Topos Foundation for Theories of Physics: IV. Categories of Systems
-- http://arxiv.org/abs/quant-ph/0703066

Judging from the titltes, theis sounds interesting enough that I have to put Smolins book aside and at minimum skim these papers.

/Fredrik

This is somewhat interesting! just skimming the first paper... to mention one thing a new formalism where "the law of excluded middle need not hold" is intuitively plausible to me. It is in line with my thinking that there is always an uncertainty in the microstructure itself. Because the microstructure (beeing the discrete basis for the analogy of the continuum probability space) is in my thinking itself a sort of state in a series of inductions.

I'll keep reading later when I ahve more time

/Fredrik

In chapter 2 Smolin argues that that classical logic, that there is an objectivity to the notion of true and false, is not well designed for the task of quantum gravity. One of the reasons is that due to limited information of each observer (no observer can hold compelte information about everything in the universe at once), and prescription to establish truth or false, would be observer-dependent.

I don't get that : if one observer would have limited information, he or she could say ''I don't know'' :-) BTW, the rest you say is true in classical GR too and classical logic works impeccably there.

But then Smolin seems to argue that a measure ofthe rationality of actions/decisions can be construced without the use of an "superobserver" knowing everything at all times. He says it's enough to assume that the observers are honest, and argues that in that way, two observers facing "the same information" will always make the same decision.

There must be plenty of dishonest people out there :-) Could you tell me what physical operator measures the honesty/dishonesty of a person? What you say is not even true in standard QM where there is no reason why a person facing the state |cat dead > + |cat alive > decides to see a dead cat :-)

You might want to ask yourself what such philosophy implies in the context of Ockham's razor...

I don't get that : if one observer would have limited information, he or she could say ''I don't know'' :-)

Yes, but one problem with that thinking is that then we don't know anything. "I don't know" is not a very constructive action. If we don't know, as is always almsot the case, we gamble. I think one can argue that, to not gamble (to not bet), is not free of risk either. It is also a choice of action.

So those players who consistently refuse to take any risks whatsoever, are IMO doomed!

What you say is not even true in standard QM where there is no reason why a person facing the state |cat dead > + |cat alive > decides to see a dead cat :-)

Maybe I made a different interpretation that you on this :) One does of course not "choose" the see a dead cat of course. The choice is to ask the question: is the cat dead or not. To fire the question may be a risk. The consideration is that perhaps may ask another question instead!

The answer is part of the unpredictable feedback, it's part of the game. Then the next choice is, once you for example found out that the cat is dead - what do you do about it? What do you learn from this new valuable data? :) How do you choose respond to a given answer? What response pattern is of highest utility to You? Of course, we don't know that either :) So we gamble again, the action rules are also evolving... and one would imagine that bad actions are not preseved since they self-desctruct.

/Fredrik

Smolins argumentation is not crystal clear to me, and it is still in the early chapters... but I got the feeling that what he means is something like that any two observers will respond to the information that the cat is dead in the same way. That there is somehow a objectively logical action, that is the rational response to this input if the observer is beeing "honest" about what he sees.

But in that case, I disagree with that. Which was my point. But OTOH I am not totally sure that is really what Smolin means. It's early in the book, and it's difficult to express things uniquely.

My view is that the observers actions isn't always "rational", because it's difficult to define the measure of rationality. Instead I see it a way where progress is close to unavoidable. The actions that survive are those which are self-preseving, which means that they have to be in some kind of harmony with their neighbours. (Here I'm thinking of abstract physical systems interacting, not humans).

And perhaps an analysis of this logic, will reveal interesting things. I would expect the rational view to emerge in equilibrium - defined at some level of the actions, where local agreement on rationality exists.

Edit: So perhaps the most "stable abstraction" here is the emergent rationality. But the rationality is never certain. Specifying the action is analogous the the physical action, it determines the response pattern of the system. But if there is no such level at which there is a truly fundamental, universal action... then perhaps this is the wrong way of asking the questions? Maybe the actions themselves are always in motion too? What kind of formalisms does that lead to?

/Fredirk

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Yes, but one problem with that thinking is that then we don't know anything. "I don't know" is not a very constructive action. If we don't know, as is always almsot the case, we gamble. I think one can argue that, to not gamble (to not bet), is not free of risk either. It is also a choice of action.

So those players who consistently refuse to take any risks whatsoever, are IMO doomed!

Funny, I was just giving you a simple example. In reality, a scientist would find out a few "simple" principles, compute trough a particular setup and calucate the probability of some particular answer getting out. Now, scientific discours consists of using well tested principles or at least those which confirm a lot of data with an incredible accuracy (and yes we do assume that measurement apparati do not lie :-) ) or at least deeper new axioms which lead to the former. Despite of lots of debate and intensive work ''I don't know'' is a phrase which sometimes expresses a deep knowledge and humility about the adequacy of such process.

Maybe I made a different interpretation that you on this :) One does of course not "choose" the see a dead cat of course. The choice is to ask the question: is the cat dead or not. To fire the question may be a risk. The consideration is that perhaps may ask another question instead!

I was merely saying that even if two different observers have the same information they can still draw different conclusions and since indeed, he does not choose to see the cat dead, it is difficult to understand how he could call the other person dishonest.

In reality, a scientist would find out a few "simple" principles, compute trough a particular setup and calucate the probability of some particular answer getting out.

Yes and I think is the interesting part. Implicitly I guess you here assume that this probability, is used as a basis for making decisions? or?

What is the utility of computing a probability?

Then, one asks, how do we know wether the probabilitiy is correct? One way of imagining is to repeat the situation an inifite times and get statistics. But that isn't realistic. For particle experiments it is, but hardly for cosmological scale things. Yet, there seems to be an utility to compute the probability?

So if we can't verify in advance if our computer probabitliy is correct, then is there another way to verify it? could there somehow be a more or less unique law of inducing an "expected probability" based on current information? Then the correctness would be a matter of correct induction. So one can imagine that the correctly expected proability, is in violation with what the future shows. How is such a situation handles constructively from the point of view of a theory builder? And how does the computational scheme for these probabilities revise, in the event that the future data is in disagreement with the original guess?

If you think this is silly questions, then note the context in which I ask this. I am trying to understand the meaning and utility of physical law, and what the physical basis for that is. There is a strong case of self-reference here which is what makes this complex. But given this problematic situation, what is the best way forward?

/Fredrik

Yes and I think is the interesting part. Implicitly I guess you here assume that this probability, is used as a basis for making decisions? or?

What is the utility of computing a probability?

Euh, such questions are all well answered within statistics, it is called hypothesis testing and it is used in economics every day to determine parameters of probability distributions.

Then, one asks, how do we know wether the probabilitiy is correct? One way of imagining is to repeat the situation an inifite times and get statistics. But that isn't realistic. For particle experiments it is, but hardly for cosmological scale things. Yet, there seems to be an utility to compute the probability?

Ok, so we agree that for particle physics this makes sense. Right, for cosmology you use a reasoning called extrapolation. That is: we know that the dynamics on the large scale should be an effective theory obtained by a renormalization procedure applied to the well tested microscopic theory. There is of course always the issue of the state of the universe (or initial data if you like classical theories), but that is a problem for ANY cosmological theory. Therefore, we should only be concerned about the dynamics and extrapolation severly limits the acceptable number of approaches. Now, even within this class, you have a selection procedure called ockham's razor which states that the fewer assumptions a theory requires, the more constraints your theory imposes on the physical universe, the easier the explanation of some phenomena occurs, ... the better is your theory. Of course these criteria are not satisfied uniformly for most proposals, and that is where the disagreement begins. But a theory which does not explain the (why of the) matter sector, has no classical limit, a prospect towards some unique microscopic dynamics ... is not even wrong.

A good way forward must for sure keep contact with well known and accepted physics and at the same time may scatter may upheld beliefs. People did not accept Einstein in the first place because he came up with the equivalence and covariance principle, but because the first thing he did was to show that the Newtonian limit of GR existed and to show that his theory made new predictions. The latter principles only became important later on although for him, they were the guidelines to this kind of physics. So, I do believe in theories of principle, but you have to choose them wisely and make contact as quickly as possible with the well known laws (even if such reasoning makes plausible extra assumptions).

Therefore, starting by throwing away the queen of science - that is logic - does not appear very fruitful to me.

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Therefore, starting by throwing away the queen of science - that is logic - does not appear very fruitful to me.

Careful, I appreciate your comments. To make sure I understand you right and what the focus is here.

Are you effetively questioning Smolins initial note that a prescription to establish truth or false, would be observer-dependent?

I am not throwing away logic in favour of madness or chaos, I am just suggesting that if we are to see it from a realistic view, the procedure, say the logical line of reasoning, that deduces the value true or false, are IMO is a physical process, and whatever is evaluating this truthness can't be anything but a part of the universe subject to the same issues as everything. To ignore an apparent issue, is not logical to me either.

I rather think that taking a too idealistic view of this, may inhibit a more fundamental awareness.

Just for the perspective what is your personal take one these things?

/Fredrik

Are you effetively questioning Smolins initial note that a prescription to establish truth or false, would be observer-dependent?

I do not know that this sentence - which is very vague and rich in grotesque words - has as originator Smolin. In this thread, Careful is talking to Fra and if Fra has no ideas himself and is merely interested in who is presumably saying what, then he or she should go in political and social sciences and as such is located in the wrong forum. What I do believe is that in science, you have to make the assumption that many circumstances in which measurements are about to take place are more or less identical and should therefore lead to a huge majority of consistent answers unless you have some very strong theoretical arguments and model to show otherwise or unless experiment forces you to consider that something else is going on (as was the case for the double slit experiment in quantum mechanics). If this were not possible, then science would degenerate into some postmodernistic blah blah. Now, the very concept of observation has always been delicate, since our theories are at the same time describing our observations while the observer itself should also satisfy the same theory: you cannot question that simple premise since other observers in the universe should make more or less the same theory and those will describe your physical movements. Now, the way you can decide about the best theory is by looking at phenomena which excludes both of them, using the same measurement apparati - there is no room for subjective interpretation here since experience shows that almost everyone agrees upon these facts. Therefore the physical laws should be constructed as such. Assuming that the very physical laws would leave the possibility for perception to differ in different universes effectively adds an infinity of degrees of freedom to your theory and is therefore an ideal victim for Ockham's razor.

It is not because something bewilders you, that you have to take an easy way out and go on the metaphysical tour. Note that this has nothing to do with my comment about the braids in another thread; these comments stand even in the case of MWI like interpretations.

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Hi Fra … Careful!
May I join the discussion? I might add a different prospective?
Fra
The reason I find common language analysis of very simple things interesting is that, I think differences in reasoning does have implications when you choose the mathematical formalism later. And at the later stages there is such much details and baggage that it's hard to analyse. Defects in the line of reasoning will propagage throughout the entire constructions.
I would agree!
It is in line with my thinking that there is always an uncertainty in the microstructure itself. Because the microstructure (beeing the discrete basis for the analogy of the continuum probability space) is in my thinking itself a sort of state in a series of inductions.

Let’s not bring the cat into the discussion. Is it possible to determine if the “laws” that are observed at the macro/classical level are the same at the sub atomic level.
Uncertainty would then be base on the “laws of nature”.

In a few words …. Is this what we observe?

Classically, or at the macro level, two objects can be only be placed beside each other. Two objects cannot occupy the same location/position at the same time. Continuity.
At the molecular level, two molecules/objects cannot be placed beside each other. Crystal structures of atoms.
At the atomic level, two atoms/objects cannot be placed beside each other. Nucleon structures. Quarks structures are confined.

Now … into the unknown … (for me)

At the quark level, do we have any evidence that there is a “minimum length”. Do we have a cause for confinement? Do the quarks behave classically? Can they be placed beside each other? Can they occupy the same position/location at the same time?
Can a quark occupy two locations/positions at the same time?
=========

May I join the discussion? I might add a different prospective? ...
Is it possible to determine if the “laws” that are observed at the macro/classical level are the same at the sub atomic level.

Are you joking? :-) If you are truly interested in questions about the scientific method, you will find two excellent columns over here http://motls.blogspot.com/

Stop pushing ... I'm gone!

Careful, thanks for the contribution but I choose not to comment further because I can't relate to your comments in the intended context. My feeling though is that you either are making fun of the discussion or aren't appreciating the questions or maybe it's because of my poor way of posing them or not I don't know. Either way it's not interesting to I'll drop that.

Fra said:
It is in line with my thinking that there is always an uncertainty in the microstructure itself. Because the microstructure (beeing the discrete basis for the analogy of the continuum probability space) is in my thinking itself a sort of state in a series of inductions
Let’s not bring the cat into the discussion. Is it possible to determine if the “laws” that are observed at the macro/classical level are the same at the sub atomic level.
Uncertainty would then be base on the “laws of nature”.

In a few words …. Is this what we observe?

Hello Jal, I have no idea what the cat had to do with this in the first place.

I don't understand the follow-up reflection, but what I have in mind suggest that the "laws" themselves aren't the same but they are related in feedback between dynamics of the microstate and the microstructure itself. And this feedback might be able to formulate as and induction principle that may also be subject to change, but less so. But this is immature conceptual ideas only. I am working on finding the formalisms for this, but it's not yet mature and definitely not anyting standard so it's not something that's appropriate to discuss here. (But for sure, my starting points are not continous structures, I start with notions of distinguishability in the context of an observer - which impliticlty replaces the probability space with a discrete microstructure. The continuum approximation is recovered as the information capacity -> infinity. Actions are treated combinatorically, but the difference is that the action is part of the mictrostructure. So the action/logic is evolving along with the microstructure.) My starting point is that of reasoning, and my fundamental idea is that there is a strong connection between reasoning and the laws of physics themselves.

The seleciton of formalism that realises the idea is the motivation for the thread. In particular I was looking into some thinking of Smolin.

I'll try to read up on those papers later and keep reading Smolin.

/Fredrik

I read Three Roads recently and is a bit of an odd book. It is a lot like Penrose's Road to Reality in that it has a lot of little divergences where Smolin takes up a speculative idea and takes it in some direction for a few pages-- but then moves onto something else without actually arriving anywhere, and does not take the idea up again. Although these divergences are a lot of the time more interesting than the text's main thrusts, it makes it kind of difficult to discern exactly what it is the author thinks. The whole "everything is relative" theme is kind of like that, but:

But then Smolin seems to argue that a measure ofthe rationality of actions/decisions can be construced without the use of an "superobserver" knowing everything at all times. He says it's enough to assume that the observers are honest, and argues that in that way, two observers facing "the same information" will always make the same decision.

So, as I understood what he was saying in Three Roads, Smolin's general argument seemed to be something slightly different-- not that our reasoning "can" be constructed this way, but that it must be constructed this way. I.E., we have no choice, because of the logical difficulties of discussing relative theories like QM in an absolute way, and because of the impossibility of performing any experiment from the "superobserver" position. Smolin seemed to be of the opinion that whether or not we want to find a way of discussing physical theory in a purely relative fashion, we have to find some way to do so or we will never get any sensible results out of cosmology. I don't think he really comes to a conclusion in this book about what that way is.

Anyway to me the important application of this idea in Three Roads actually wasn't the topos bit near the beginning but actually later on, when Smolin gets into an extended exploration of various things related to the holographic principle. In this part of the book Smolin seems to be providing a solution to the "how do we do this?" question: If you have two observers in a relational theory, you cannot objectively or meaningfully define the state of either observer-- but you can rigorously define and reason about the boundary between those observers. Smolin talks about defining sort of "surface areas" (? so to speak...) between regions in space, and goes on quite a bit about the idea that the information flowing across this boundary actually fully specifies what is happening on either side (though his main focus in doing so is on black holes and the Bekenstein bound). The overall argument, then, seemed to be that since the state of individual observers is not real or at least fuzzily defined, we should just ignore the observers and concentrate on the boundary as the "real" thing for purposes of constructing our theories.

To me this approach of using the holographic principle as the solution is actually somewhat familiar, since it is analogous I think to the reasoning in gauge theory-- local states are arbitrary and inaccessible, therefore we ignore the local states and treat our mechanism for translating between local states as the fundamental object. Right?

What is confusing to me about this bit-- as with much of Three Roads-- is that I have trouble connecting Smolin's apparent conclusion here with what Smolin himself did afterward, forcing me to question to what degree the conclusions are particularly useful (considering even the author did not in the long run really find a use for them). Smolin presents a compelling argument in Three Roads for the importance of the holographic principle-- and if one looks at Smolin's papers from the 2000-2001 period (when I assume he would have been writing Three Roads) one finds a LOT of holographic related work!-- but to my knowledge he did not significantly work with the holographic principle afterward. In fact the only really recent work in my (limited!) understanding of QG research to seriously apply holographic reasoning of the kind Smolin seems to be arguing for is occurring in the String camp (I am specifically here thinking of the ongoing work on AdS/CFT).

Of course, Marcus tends to argue that Smolin is not really relevant to LQG today as regards cosmology (and recently seems to have expressed that Smolin may be in his recent work wandering away from LQG altogether), and I believe he has said a few times that Ashtekar's camp in particular are the people to look at if you want to know what's happening with LQG as applied to cosmology. The topos/holographic arguments in Three Roads, it seems to me, were quite specifically about cosmology (since it is only on the cosmological scale that we really lose the ability to select a preferred "superobserver"), so it is unsurprising that if Smolin lost interest in cosmology he'd not be following up on his cosmological ideas. So perhaps this would be a good point to pick Marcus's memory banks on-- has the holographic principle turned out to be a useful tool for modern loop quantum cosmology for those who are working in the field today? What about, for that matter, topos?

marcus
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Of course, Marcus tends to argue that Smolin is not really relevant to LQG today as regards cosmology (and recently seems to have expressed that Smolin may be in his recent work wandering away from LQG altogether), and I believe he has said a few times that Ashtekar's camp in particular are the people to look at if you want to know what's happening with LQG as applied to cosmology. The topos/holographic arguments in Three Roads, it seems to me, were quite specifically about cosmology (since it is only on the cosmological scale that we really lose the ability to select a preferred "superobserver"), so it is unsurprising that if Smolin lost interest in cosmology he'd not be following up on his cosmological ideas. So perhaps this would be a good point to pick Marcus's memory banks on-- has the holographic principle turned out to be a useful tool for modern loop quantum cosmology for those who are working in the field today? What about, for that matter, topos?

I don't say not RELEVANT. I dont criticize the directions Smolin has been exploring recently or deny the possibility that he might be right and they might bear fruit. People (especially the string-minded when only half-aware of what goes on in the nonstringQG community) often treat Smolin as a representative or icon of the competition. As if he symbolized it. His work is definitely not typical and I always want to emphasize that. It's not a value judgment.

If someone is organizing a big international conference, they will get Ashtekar to speak on quantum cosmology. they will get Rovelli to speak on the current state of putting together spinfoam LQG with the older canonical LQG----now LQG has become a fusion approach and Rovelli has the largest group working on that.
Or they might get Thiemann, or Freidel. But they wouldn't get Smolin!
That is neither good nor bad it is just how it is. Smolin has always scouted out where the mainstream hasn't ventured and tries new things and gets others to try new things.

Now what I've said just now is basic and rather superficial. I notice you are making a penetrating analysis (involving things I don't know much about, like topoi) and hoping that I can fill in. Unfortunately I must disappoint you. I can't fill in the gaps in this case, and I hope some others will be able to.

I have to say that even though Ashtekar (and Bojowald too) exemplify the LQC mainstream---turning out the quantum cosmology grad students and computer modeling and research papers----Smolin has been voicing some very interesting IDEAS about cosmology. So you can't ignore him or count him out in that area either. He tends to go after fundamental question, as you pointed out, like What are Laws as contrasted with initial conditions? How can we have quantum mechanics if there is no classic observer of the whole universe? What could be the deterministic ground that undeterministic quantum phenomena arise from? What is the deeper ground that space and matter and laws arise from? Why these numbers and not others? I am certainly getting it somewhat wrong and misrepresenting---but you know the kind of question I mean.
That is a valid part of cosmology too, just as much as the more practical computer models of the big bounce they run at Penn State and some insight into the basics there might be a key to unlock stuff. But it's not the LQC mainstream, is all.

Let's look at the papers these people have written recently, say since 2005, and see if we can find some direction signs. My impression is that Three Roads is a fascinating book but it was written back in 2001 (correct me if I'm wrong). So it wouldn't give the latest clues as to the directions these people are taking.

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marcus
Gold Member
Dearly Missed
To refresh my memory with concrete specifics, I fetched a list of Smolin's preprints from the past 24 months (excluding papers from May 2006 and earlier). There are these 8. BTW it looks like he was in at the start with Wan on 4-valent braid matter (maybe in fact got him started on it)

1. arXiv:0804.0037 [pdf, other]
Title: Particle Identifications from Symmetries of Braided Ribbon Network Invariants
Authors: Sundance Bilson-Thompson, Jonathan Hackett, Lou Kauffman, Lee Smolin

2. arXiv:0803.2926 [ps, pdf, other]
Title: Matrix universality of gauge and gravitational dynamics
Authors: Lee Smolin
Comments: 21 pages, no figures, corrected version, references expanded

3. arXiv:0712.0977 [ps, pdf, other]
Title: The Plebanski action extended to a unification of gravity and Yang-Mills theory
Authors: Lee Smolin

4. arXiv:0710.1548 [pdf, other]
Title: Propagation and interaction of chiral states in quantum gravity
Authors: Lee Smolin, Yidun Wan
Journal-ref: Nucl. Phys. B 796 (2008) /1-2 pp 331-359

5. arXiv:hep-th/0612185 [ps, pdf, other]
Title: The status of cosmological natural selection
Authors: Lee Smolin

6. arXiv:astro-ph/0611695 [ps, pdf, other]
Title: Holography and the scale-invariance of density fluctuations
Authors: Joao Magueijo, Lee Smolin, Carlo R. Contaldi

7. arXiv:hep-th/0611197 [ps, pdf, other]
Title: Quantum Graphity
Authors: Tomasz Konopka, Fotini Markopoulou, Lee Smolin

8. arXiv:quant-ph/0609109 [ps, pdf, other]
Title: Could quantum mechanics be an approximation to another theory?
Authors: Lee Smolin

It looks like one thing he does is get people started on stuff. Like getting a group started on the whimsically named "graphity" research line. And then they go on with that and he gets another group started on braid matter. And they go on with that while he gets busy thinking of something else to start. (though retaining an interest in what's already in progress)

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I read Three Roads recently and is a bit of an odd book. It is a lot like Penrose's Road to Reality in that it has a lot of little divergences where Smolin takes up a speculative idea and takes it in some direction for a few pages-- but then moves onto something else without actually arriving anywhere, and does not take the idea up again. Although these divergences are a lot of the time more interesting than the text's main thrusts, it makes it kind of difficult to discern exactly what it is the author thinks.

Hello Coin! Thanks for joining. That sounds familiar.

So, as I understood what he was saying in Three Roads, Smolin's general argument seemed to be something slightly different-- not that our reasoning "can" be constructed this way, but that it must be constructed this way. I.E., we have no choice, because of the logical difficulties of discussing relative theories like QM in an absolute way, and because of the impossibility of performing any experiment from the "superobserver" position.

Right, "must be", might makes more sense to me in one way, but I choose "can" to attract those that may disagree too in discussing :)

In this part of the book Smolin seems to be providing a solution to the "how do we do this?" question: If you have two observers in a relational theory, you cannot objectively or meaningfully define the state of either observer-- but you can rigorously define and reason about the boundary between those observers. Smolin talks about defining sort of "surface areas" (? so to speak...) between regions in space, and goes on quite a bit about the idea that the information flowing across this boundary actually fully specifies what is happening on either side (though his main focus in doing so is on black holes and the Bekenstein bound). The overall argument, then, seemed to be that since the state of individual observers is not real or at least fuzzily defined, we should just ignore the observers and concentrate on the boundary as the "real" thing for purposes of constructing our theories.

I'll have to come back to this, I am stil in the early parts of the book :) But the boundary issues is definitely interesting. I have to admitt that when I think of that I currently think in more abstract terms, rather than an actual space or spacetime boundary. I think in terms of information boundary, where this surface is more like an abstract representation of the communication channel between the observer and "the rest" (the environment as I like to call it). And even from the abstract perspective, the communication channel does bound the interior, and I think it will be interesting to compare this to the application of blackhole information issue. Instead of area and mass, one can talk about information capacity and channel capacity. I think the abstracted version is easier to understand and I like to think it's more general. I definitely make a close association between an observer, and a blackhole. But that's further ahead.

local states are arbitrary and inaccessible, therefore we ignore the local states and treat our mechanism for translating between local states as the fundamental object. Right?

You're probably right on what he thinks, and it sounds terribly much like rovelli's relational QM argumentation.

That some kind of objectivity is recovered in the connection/transformation/relational between subjective views. Ie. objectivitiy is recovered from the subjectivity, by means of the relations. So that's how we can have it observer relative, and still objective relation. That is slight, but if the idea is to be taken litteraly in a static sense, then it seems to have the same "flaw" as the previous reasoning. I have difficulty in seeing that this solves the problem. The relation itself is again bringing the ideas to an superobserver or background.

The way I picture this, the relations themselves also need to be perceived by an observer again keeping a self-reference. My tentative idea to solve this is to consider a induction, and the induction FLOW somehow relates to local time evolution. But there are many details yet to figure out.

In my thinking I expect the idea of objective relations, connecting subjective information to be emergent. So it does make sense to me, I just think there is still a subtle level of feedback missing. I love Rovelli's book up until this point... then I simply don't quite understand his logic. Perhaps Smolin is similar.

About topos theory: I have absolutely no prior experience with this at all, and I tried to skim

(1) A Topos Foundation for Theories of Physics: I. Formal Languages for Physics
-- http://arxiv.org/abs/quant-ph/0703060

last night, and it is clearly having a high level of abstraction which I haven't idenfitied yet. Something is appealing with it, but I could be mistaken. I probalby need to read this again and think about it. The basic motivation as argued in the paper for coming up with a new formalism is one I share, but at least on the first reading I failed to see why topos formalism is the best solution. It seems to be strongly mathematically guided. I need to read more on this to be able to sensibly comment.

/Fredrik

Chronos
Gold Member
That piqued my curiousity. I believe it safe to say quantum entities rarely, if ever, behave 'classically': hence the term 'quantum weirdness". Their ability to occupy multiple states simultaneously is an example [e.g., wave-particle duality].

He tends to go after fundamental question, as you pointed out, like What are Laws as contrasted with initial conditions? How can we have quantum mechanics if there is no classic observer of the whole universe? What could be the deterministic ground that undeterministic quantum phenomena arise from? What is the deeper ground that space and matter and laws arise from? Why these numbers and not others?

These questions is part of why I like Smolin's thinking.
These are good questions. I don't see how we can not ask them.

/Fredrik

Their ability to occupy multiple states simultaneously is an example [e.g., wave-particle duality].

Smolin briefly associated the origin of the superposition principle as possibly explained as a point of view. This is closely related to my own thinking still in progress. I think this can be formalised quite strongly and that there is an utility in superposition and that the superpostion can be understood as transformations in the observers view. It may be possible to argue that superposition is more efficient, thus the superposition is part of the relation between observer and observed. There might be a selection for observers reflecting the superposition of information. So that there might be a sort of bayesian argument for superposition without assigning a microstructure to the environment like is done in decoherence approaches.

So that the rule of addition of information as per the superposition, can be transformed into the ordinary probability rule of adding events byt transforming the information itself - which represents an internal transformation of the observers microstructure. But this can't be a unitary transformation, and this is where the time flow comes in IMO. Releasing the worthless information in favour of enriched information is my association. Here it's tempting to associate to radiation. Unless the systems getting more and more excited, the steady state required release of information in favour of new. The decision of the microscopic action rules I picture are what information that is to be considered least useful, so what we can release. Ideally this would be random information and contain no useful information, but that's judged to the observer himself.

/Fredrik

I finished the first part of the book last night. That part of the books seems to serve the purpose of spawning reflection in a particular (IMO plausible) direction, but without beeing very specific at all. So there where no overall constructive outcomes in the first part of the book IMO except for possibly inducing a state of mind in the reader for the later parts. It will be interesting to see what comes next.

/Fredrik

Here is what I consider to be a key question in the context of the new logic. I don't know exactly in what book or paper Smolin asks this but Marcus listed this question.

What could be the deterministic ground that undeterministic quantum phenomena arise from?

This asks what could the deterministic basis for underterministic phenomena be.

But another prior question is: Do we even need a deterministic ground in the universal sense? Can we do without it?

It seems the answer to this, may be reflected in the strategy one implements.

/Fredrik

That some kind of objectivity is recovered in the connection/transformation/relational between subjective views. Ie. objectivitiy is recovered from the subjectivity, by means of the relations. So that's how we can have it observer relative, and still objective relation. That is slight, but if the idea is to be taken litteraly in a static sense, then it seems to have the same "flaw" as the previous reasoning. I have difficulty in seeing that this solves the problem. The relation itself is again bringing the ideas to an superobserver or background.

Three things comes out to me as apparently inconsistent from the point of view of clean reasoning.

1) The above issue, in short that subjectivity or "apparent inconsistencies" in general, are resolved by considering the existence of objective relations between the former.

2) The epistemological measurement ideals, that all information is acquired/measured.

3) The idea that there is a limit to the information that can be encoded in any region or system, and hence in any observer.

The issue I have is that the "trick" in (1) increases the information capacity, if the relations are to be considered physical, then information about them must be acquired, right? IMHO, (2) and (3) suggest to me at least that (1) can not be a final solution - something is still missing. And to me the closest way out seems to consider a hierarchy of drifting relations, where the flow that generates this drift is related to time flow. What stops it from beeing an infinite hierarchy should be exactly (3) - it would not fit. That's just an idea of course, there may be another solution.

I'm not sure what others think of this, but these type of things is what bugs me.

/Fredrik

But then Smolin seems to argue that a measure ofthe rationality of actions/decisions can be construced without the use of an "superobserver" knowing everything at all times. He says it's enough to assume that the observers are honest, and argues that in that way, two observers facing "the same information" will always make the same decision.

I think this is wrong, and that has nothing to do with honesty. A real observer cannot even know both his own position and velocity unless he is infinitely massive, because the commutator

[x, v] = i hbar /M

vanishes only if hbar = 0 or if M = infinity. It seems obvious to me that an implicit assumption about an infinitely massive observer is problematic in the presence of gravity, e.g. because the observer would interact with gravity and immediately collapse into a black hole.

It seems obvious to me that an implicit assumption about an infinitely massive observer is problematic in the presence of gravity

If we associate here inifinite mass ~ infinite confidence in your priors, then I agree completely, it doesn't make sense to me either. This is why I doubt that we can find a deterministic basis at all. We can speculate that there is one, but a real observer can never see it. But such reasoning is not appealing to me, it seems to consider the modelling itself to not be constrained by nature itself. I think a consistent reasoning must itself be subject of the same principal constraints. This is what to me is the motivation for a "new logic".

Of course I can only guess what Smolin means, but it seems to me he somehow argues along some line where the objectivity is there, but it's hidden from a real observer in line with say GR where the manifold and the geometry somehow represents the connection between observers, but the real observer still doesn't observer this. But that view is what I find weird. It's like there are two observers. The theoretical physicists (the model) who seems to think he are under no constraints, and the observers. IMO, there is only one realistic view and that's the inside view.

/Fredrik

I've been distracted by worktrips so I haven't been reading anything for a few days. Now I'm starting to get to the later parts of the book. I keep getting the similar feeling as when I read rovelli's and penrose books. It's the reflection of the nature of spacetime that appears to not depend on the observer. I am trying to figuure this out. I perceive this as somewhat like inconsistent reasoning. But maybe I haven't understood the idea yet. They argue clearly about the relational nature of this, but at the same time, at some level in the reasoning the reasoning itself does not seem to reflect same ideal. I would like to implement the relational ideal also to the reasoning itself.

The last time I tried to read rovelli's and penrose book, what might have made sense to me was to consider the observers microstructure to be represented by something like a spin network, and the spinfoam would result from the uncertainty of the spin network itself which drifts in time. And in this sense the spin network as beeing the observers microstructure would be somewhat like a relative image of the environment. So it would only indirectly represent the external space. But the more I read in the books, it seemed this is NOT how they think of this. What i am thiniking woudl somewhat related well to the holographic principle or a version of it in the senes that inside the observers microstructure, the model of the environment "lives". It's like an inverted image. And thus I picture that the "reasoning that takes place" is all relative to the logic of this observer.

It would be beuatiful if I could understand the spin network thinking from this angle. It seems clear that this is at least not how they seem to think of it, but that's not to say that it can't be compatible with it.

Edit: A simple illustration of the inverted pictures is to consider two almost dual views. Consider an observer (think of him as a sphere) embedded in an environment. Then the observers reasoning and view of the environment is constrained to this microstructure. The surface in between them represents the communication channel. This is like the small guy looking out into the world, or earthbased observers probing the distance parts of the universe.

The other picture is if we turn this around. If the environment, is seen as an observer and tries to probe this little sphere. Not too unlike what we do in particle experiments. Then the observers is relatively speaking almost infinitely massive relative to the observed object.

Unless this logic is unified it is not surprising that the models from particle physics and those from cosmology doesn't mix smoothly. But I think issues are visible already at the level of reasoning.

/Fredrik

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Marcus, re your earlier post: Thanks, sorry if I misinterpreted you!

So, my last post in here basically ignored Topos, and Fra seems to be a little confused in some of his posts trying to tackle the subject, so I would like to go back and try to say something about that. I apologize if anything I'm about to say here is just repeating things people already know.

About topos theory: I have absolutely no prior experience with this at all, and I tried to skim

(1) A Topos Foundation for Theories of Physics: I. Formal Languages for Physics
-- http://arxiv.org/abs/quant-ph/0703060

last night, and it is clearly having a high level of abstraction which I haven't idenfitied yet. Something is appealing with it, but I could be mistaken. I probalby need to read this again and think about it. The basic motivation as argued in the paper for coming up with a new formalism is one I share, but at least on the first reading I failed to see why topos formalism is the best solution. It seems to be strongly mathematically guided. I need to read more on this to be able to sensibly comment.

/Fredrik

I don't know if this will help, but let me take a shot:

First off, for purposes of what Smolin is talking about, the important thing is not topos theory. It is topos logic. So it would not surprise me that if you started looking up information on topos, you wouldn't see anything that seems specifically relevant to the point Smolin is making about kinds of logic.

What I mean by this: Topos are actually just a mathematical construct from category theory. Topos theory is all about the behavior of this construct. (Category theory is an aggressively abstract subject, and it has its own extremely insular and peculiar vocabulary, so if you look at material on Topos theory by itself you will probably be quickly overwhelmed by the sea of weird category-theory terms and the lack of any immediate connection to application...) Topos logic, on the other hand, is one particular application for which this mathematical construct is useful (although it may not always be called "topos logic" specifically). As far as I know logic is one of the main uses, if not the main use, of topos; but it is not guaranteed that material on topos will be particularly useful to understanding Topos logic.

Okay, so what's Topos logic and why do we care about it in the Physics context? Well, let's look at the place where Topos first shows up in Three Roads:

The mathematicians, it seems, were not aware that they were inventing the right form of logic for cosmology, so they called it other names. In its first forms it was called 'intuitionalistic logic'. More sophisticated versions which have been studied more recently are known collectively as 'topos theory'.

This, and the reference to topos in "Trouble with Physics", show up only very briefly and mostly consist of references to other people's work, so I am going to conclude Smolin himself is not very involved with Topos and he is just trying to call attention to work by Fotini, Isham etc. in this area which he considered important. But let's look for a moment at the thing that Smolin seems to consider important here about Topos: Its link to intuitionistic logic.

Intuitionistic logic is one of a series of nonstandard "formal logics" from the last century. When we are doing "formal logic" we say that is not enough to just write a proof that can be read by humans. Instead, we define a little symbolic "language", we define construction rules for creating sentences in this language, and we define rules for transforming sentences in that language into other sentences which are somehow equivalent. We then say that a logical statement is a sentence in the little language we've defined; and a "proof" is a series of transformations that transforms our premise sentence into our theorem sentence. The general idea is that a proof should be a completely mechanical thing, such that something like a computer could understand it and check its validity, with no room for human imagination or error.

It turns out that almost all of everyday mathematics, and almost any proof you can easily think to describe, actually reduces to "first-order logic", which is a formal logic of this sort. First order logic has symbols for things like "and" and "or" or "for every" or "there exists", and it has transformation rules that-- despite just being transformations on symbolic strings-- neatly encapsulate familiar logical principles like tautology or inference.

The interesting thing here is that you have other choices as to what to work with besides first order logic. You can create systems which are more expressive than first-order logic and contain first-order logic within them. You can also create systems where the rules are simply different. One of these is intuitionistic logic, which is distinguished by the absence of the "law of the excluded middle". The law of the excluded middle is an axiom of logic so basic that usually one would not even think to think of it as an assumption: If not true, then false. If you throw this assumption out, you can't do things like proof by contradiction-- you can prove something is "not false", but this does not prove that it is true!

So the idea here, as best I understand, is that when people started studying Topos-- a Topos is a special kind of Category-- they found that Topos work really well with intuitionistic logics. Basically Topos define a generalization of set theory ("Set", the category that encapsulates set theory, is a Topos, in the same way that grade-school arithmetic is a group.) and there is some sense in which topos "go with" intuitionistic logic the same way sets "go with" first-order logic. A better way of putting it might be that each different Topos prescribes a collection of objects with certain behavior, and each of these collections give rise to a different formal logic. By default, these formal logics are intuitionistic, but depending on which Topos you pick you can get logics with all kinds of different interesting and unusual rules.

This second bit-- about having a free choice of Topos-- is why Topos turn out to be really valuable to Isham&co who wrote that paper you link, because in doing quantum gravity they find themselves wanting to describe certain systems with unusual rules. Worse, they're not quite sure what rules it is they want. They think, for example, that quantum physics needs to be described using the complex numbers, but maybe at some point they'll have to revise that. So what they do is decide that whatever rules they pick, they will demand those rules have some specific Topos which they spring from. They assert that if you just pick Set for your topos you get classical field theory (which is actually kind of cool, since it seems to reify the idea that classical field theory is the most fundamental thing and more modern concepts of physics are generalizations of that fundamental basis). They also have a specified Topos which they claim produces quantum physics; and they seem to be claiming that if you have a description of a physical system which any one of these topos-based-theories acts on, you can just switch out one topos for another and compare directly how different theories would act on that single system.

One interesting thing is though that it looks like they are not promoting Topos as a practical tool but rather as a sort of foundation. It seems slightly unlikely that, were these Topos guys to have a breakthrough, you would actually wind up using the Topos directly in whatever theory that results; rather, someone would use Topos to define the axiomatic basis of the mathematical constructs that some theory uses, and then once the theory was defined everybody else would just learn to use the constructs that the Topos burped out. I think-- I could be wrong about this, maybe if you had a fully Topos-grounded theory then you'd be using Category-theoretic ideas directly to reason within the theory. But it seems like the main reason they are pushing Topos is as a tool for initially defining physical theories-- for specifying them, giving them a rigorous basis, and comparing them to other theories. This is why there is such a high level of abstraction-- because creating abstractions is precisely their goal. Of course, initially defining things is exactly what is missing in Quantum Gravity right now!

On that note there is something about this Topos stuff which is important to keep in mind:

Therefore, starting by throwing away the queen of science - that is logic - does not appear very fruitful to me.

The thing to remember here is that *topos logic is still a kind of logic*, and any topos-derived logic is a valid formal logic. It may be in some way different from the logic you are intuitively used to, but this is okay. We created formal logic to mimic what we might call "intuitive logic" (the name "intuitionistic logic" itself derives from a flamewar from the 1920s or so between Hilbert and some other people, over the question over whether it is more, or less intuitive to consider the law of the excluded middle a basic logic), but it can't be precisely equivalent to intuitive logic-- and really, we don't want them to be, since the entire point of formal logic in the first place was to restrict logic in such a way as to exclude the ambiguities and errors of human thought. So as long as you stick to the formalism, exotic logical systems are as trustworthy as the ones you would normally be using in physics, because even exotic logics correspond to some rigorous mode of thinking. Topos-based logic is not about "throwing away" standard logic but about expanding and enriching the ways in which we describe the logic we are using.

However, there is a cost here, and that is that because here we have divorced "intuitive logic" from our mathematics you cannot quite rely on intuition the same way you normally might. This is the important thing to remember-- formal logics like the ones we get out of Topos are pure math, they are formalisms, and so you can only say you are using these logics if you're actually doing the math. For example if you study a Topos-based logic you might be able to honestly say that truth values within the logic are in some meaningful sense "subjective" or "observer-dependent". For example in the quantum-alike topos Isham&co define in the second paper you can only extract notions of "true" or "false" by the use of a particular "truth object":

In the present paper, we use L(S) to study ‘truth objects’ in the topos. These are objects in the topos that play the role of states: a necessary development as the spectral presheaf has no global elements, and hence there are no microstates in the sense of classical physics. Truth objects therefore play a crucial role in our formalism.

There is a very clear sense in which 'truth objects' are analogous to observers; and since the truth values you extract will vary depending on the choice of truth object, we have just defined a mathematically rigorous system in which it is meaningfully the case that the truth of any given proposition is "subjective". However we have to remember that the word "subjective" here is really just a metaphor for some more complicated mechanical rule of interpreting truth values out of sentences. The metaphors can be very useful but they can also deceive-- this is always a little bit the case in mathematical physics, I think, but it will be even more of a danger with topos, because anytime Categories crop up you have REALLY diven into the deep end of the abstraction pool. So I think it may be important if one is to work with Topos-based logics to try to always try to keep a clear link between how you're thinking about the problem versus what the formalism says, and not let the metaphors and "intuitive" language take over your thinking.

Again, don't know if this is any help or not. I may go back and try to read the Isham papers in more detail, my understanding of category theory is very poor but I do know something about logic/formal languages so maybe I actually have a chance at understanding this one. :)

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In my initial skimming of Doering and Isham's first paper it was the exclusion of "law of the excluded middle" that attraced my attention. To me this has a an intuitive meaning, and the connection I see is to violation of unitarity. And to try to treat this at the deepest level of abstraction, rather than technical level is the right way to go IMO. Still I'm not a mathematician, so I have limited interest in mathematical reasonings which has to me, no utility.

A quickly identifiable issue with QM is exactly the definition of the logical operators. What exactly does (A and B) and (A or B) mean in the general case? In particular what does x and p mean. The obvious problem is that x and p are not cleanly in the same set (probability space). They are however related. I think somewhere in this reasoning, the superposition principle can be understood by different definition of logical operations.

I also see a close connection of "the logic of reasoning" and the physical action principles. I think the action forms, are somehow the physical basis, or at least analogous to the logic of reasoning. So I see the logic of reasoning as evolving long with whatever well call "states". Your comments on the connection between truth object and the observer is interesting! I will keep this in mind the next round I read the same paper and see if it helps me get it.

Now, wether topos logic is the right thing for this I don't know. But it spawned my curiousity, and Isham's paper poses many good questions that motivates the development of the topos thinking.

When I finished Smolin's book i will try to read up on this again.

/Fredrik

another reflection

It strikes me that there are similar structures of many formalisms...

For example standard logic one has "hard implications" such as A => B.
Or deterministic time evolution such as A(0) => A(t).

(Wether A are classical variables or quantum states makes no principal difference here. There is still a layer of deterministic logic.)

It seems the degree of truth in B depends on the confidence not only in the premise A, but also in the implication itself. Here the implications serves the purposes of logic of reasoning.

A implies B, as per some particular choice of reasoning. And in my thinking, the choice of reasoning is not obvious, and it is itself subject to change. Therefore uncertainties, applies not only to premises and conclusions under the flow of certain logic of reasoning, it also in my view apply to the logic of reasoning itself.

To understand this reflection, is similar to understand the "logic" behind how (A or (not A)) isn't necessarily true. It's a simplification. I would argue that this sort of softer logic, is more intuitive and realistic than the idealistic logic.

> They think, for example, that quantum physics needs to be described using the complex
> numbers, but maybe at some point they'll have to revise that. So what they do is decide
> that whatever rules they pick, they will demand those rules have some specific Topos
> which they spring from.

Hmm.. all the various papers I have ever read on trying to "explain QM superposition" under various names, quantum logic, consistency of amplitudes etc... all one way or the other sneak in the complex choice as and implicit assumption.

In what I envision, the dynamics of logic, should be able to explain from more first principles why the logic of superposition appears in nature. If I am about to guess about the topos talk I still don't quite graps, I would suspect from your expansion that what is challange here is to explain how different topos spontaneously evolve into each othe - ie. the "choice of topos"? must be a physical process.

Here I also associate to Smolins generic reflections of what the nature of physical law is, and what selects it. This is to me a special case of what is the nature/physical basis of reasoning (logic).

I am about to start section III of smolins book, so I want to finish it before I distract myself too much in reading up on topos. It seems to be embedded in alot of context, that I also need to read up on. My first impression are purely ituitive, based on what I "hope it its", if it is what I am looking for.

This is interesting stuff.

/Fredrik

It's fairly obvious whether or not this soft logic applies to reality. The answer is yes and no.

I read Smolins argumentation in favour of the weak holographic principle last night and I agree with what Coin mentioned in post #17 that so far this was the better part of the book.

The abstraction of observer and screen, and how the size of the screen can grow and shrink are pretty much a setting in which I feel good. There may be a need to dicsuss details and versions of the principle, but it's something that in my opinion provides part of a good starting point.

The complication is of course that the "screen" itself is also dynamical. It is at least the conclusion i've made from thining in terms of a microstructure. I picture the observer itself to be represented by a microstructure and I was trying to find the decomposition of internal degrees of freedom and the interfacing degrees of freedom. The latter would correspond the the screen. But as far as I can see there is internal equilibration processes that is transforming the surface and internal degrees of freedom. And my conceptual view of that is that it is like tradeoffs between distinguishable statements and confidence thereof. And in a given environment the observer will find that there is an preferred balance. So the observer can conceptually shrink his screen to gain more confidence in what he can distinguish. Or can can transform the confidence into a larger screen. But I figure this internal equilibrations are part of the time evolution.

I think this is a good focus, but there still seems to be quite some headache here due to the strong self reference. I didn't see so far that smolin offered any solution to this. Unless it's in the even later chapters.

I expect to see gravity emerge when one starts to consider the dynamics of the screen sizes. And Smoling refers to Ted JAcobsson who derived GR from the holographic principle and second law. That sounds like something to check.

I am particulary interested to see what entropy they use. My own thinking of this suggest that shannon entropy isn'y the right one because it's not usually relationally constructed.

Does anyone know which the key paper is? Strangely in the text he mentions Ted Jacobsson's famous paper but gives no reference. And googling he has alot of papers.

/Fredrik

A good quotes from the holography chapter.

"space is nothing but a way of talking about all the different channels of communication that allow information to pass from observer to observer. And geometry, as measured in terms of area and volume, is nothing but a measure of the capacity of the these screens to transmit information"

I would like to extend this to not only refer to ordinary "space". Also other things, other interactions of the standard model that is usually considered to be taking place IN spacetime, must also fit into this framework if it is to be satisfactory.

This suggests to me at least, that one fundamental rethinking of all this, would for a second forget about the notions space and time, and instead start to consider information: what to we seem to know, and how do we rate our confidence? Then as information is rational structured and processed, one would expect that structures would inevitable be emergent and perhaps here we can identify the familiar notions of dimensions, space and time, and hopefully all the known interaction phenomenology.

I associate here logic of reasoning with a particular observer, his strategy of taking actions. And in the information view suggested in this chapter there seems to be a connection with analysing *logic of reasoning in context* and analysing the laws of nature. Since like Smoling argues in this chapter at fundamental level, our world could be nothing but a game of a network of relative information processing. This is an idea I support 100% :)

/Fredrik