Jochen

"I think that in a sense I want to do away with any reference, and leave as a foundation to an ontology only those kinds of facts I have termed 'relative'---those which, if there were a reference, would be definite"

First you cannot do this, there is always a reference. Second, you are maintaining a reference anyway, and re-labelling it as facts which have a certain attribute and are therefore definite (ie facts). But that is the whole point of science. So the real question is, in the context of our physical existence what constitutes a fact?

Judging the validity of that statement has nothing particularly to do with time. Although none of the statement is that specific, it involves the concepts of rain, in a spatial position, at a time. The validity of that statement therefore depends on that event having occurred as depicted, ie what constitutes 'rain', where was 'here', and when was 'is'.

Your point in respect of the rainbow is incorrect. The actual spatial location of the rainbow does not alter. Its relative spatial location does, obviously, because its actual spatial location is being expressed with respect to a different spatial location.

The point is that everything can only be identified by comparison and the identification of difference. Which necessitates a reference. And in order to ensure comparability of outcomes, consistency of reference must be maintained.

Probably the simplest way to respond to your next paragraphs is to point out that A, B, C are not A, B, C subsequently, they are something else. Because you said "then". The only way A, B, C could still be A, B, C, then, ie at a different time, is if a) nothing about them ever alters, b) nothing has altered in the duration being considered, c) the physical attribute being considered has not altered (although this is not really a condition because the entity is therefore different).

To illuminate this point here are three introductory paras to another paper of mine:

1 Distance is an artefact of physically existent entities, it being a difference between them in terms of spatial position. Existence necessitates physical space, but that can only be assigned via entities. So distance can only involve entities which exist at the same time. And they can only exist in one physically existent state at a time.

2 Therefore, any given distance is always unique, since it reflects a definitive physically existent circumstance at a given time. The notion which presumes there could be varied results when quantifying it, either in terms of space or duration, is a fallacy. Whatever the measuring methodology, there can only be one outcome.

3 Unless this is understood, a problem arises when distance is expressed conceptually in terms of duration. The concept being that it can be measured as the duration which would have been incurred had any given entity been able to travel along it, either way. But this is not possible, because there is no duration available during which that can actually happen, so it must be understood that there is no duration, as such. That is, the result is just an alternative expression to, and the equivalent of, a specific spatial measure. Misunderstanding this leads to the flawed application of the equation x = vt.

Another general response to those paragraphs would be to point out that a) what we observe (ie receive) is a physically existent representation of the reality (eg light), not the reality, b) observation/measurement can have no effect on physical existence, because it occurs after that.

Paul

I have little time right now, so I'll just respond to two points briefly:

First, how is the absolute position of the rainbow defined? There is no thing in the world that corresponds to the rainbow that has any definite location, as far as I can see. It's not the case that if observer 1 sees the rainbow as point x, and observer 2 at point y, each one is more right than the other: their perception is both equally valid.

And as for the Kochen-Specker example, we can get rid of the contentious 'then': rather than measuring first one, then the other observable, you can measure them simultaneously.

We have different opinions but also some common ground. My position is basically platonic. Many structures in mathematics seem to be interesting because they have physical counterparts, especially euclidean geometry and combinatorial problems, but I think mathematicians would have been interested in most such things even if they lived in a non-geometric universe. One observation that supports my view is that many mathematical concepts were invented by mathematicians before their importance in physics or practical applications was known, e.g. complex numbers, non-euclidean geometry, group theory, prime numbers even. Other concepts originally inspired by physics have been used by mathematicians to prove theorems that were originally stated without any reference to applied maths.

However, I do not agree with the assertion by Tegmark that "in those [worlds] complex enough to contain self-aware substructures [they] will subjectively perceive themselves as existing in a physically 'real' world" You mention the novel "Permutation City" which as you know has a relationship to my earlier ideas about permutation symmetry over spacetime events. In that book in the end the simulation into which they copy themselves becomes real even though the computer stops running. I don't agree with this and if I understand you correctly I dont think you agree either because the simulation loses contact with the physical world. Tegmark would presumably disagree with us and agree with Egan.

My reasoning is that this was just one version of the simulation and it was being simulated everywhere, in the rock or the wall as you cited from Putnam and Searle, or in the dust as Egan put it. Some simulations would have small differences so which ones would the copies experience? There is nothing to hold their experience to the original algorithm. How then can any copy be aware, and isn't our own consciousness just a program running on wetware?

My solution is that what counts is universality. The features of mathematics that have most intrinsic interest are those that come from universal behavior of complex systems. They appear in many different places and that makes them useful and interesting. I think if you take the grand ensemble of all possible mathematical universes then there is a universality of behaviour that in some sense dominates the ensemble, like the laws of thermodynamics but more general. This is what determines the actual laws of physics and awareness is only possible through contact with that physical system. It seems to me that you and I therefore arrive at a very similar conclusion about awareness, even though we start from almost opposite philosophical positions. Do you agree?

Yes, I think there's definite common ground. I'm also very interested in what I call 'ensemble theories of everything', one example of which is Tegmark's, another Schmidhuber's ('Algorithmic Theories of Everything), and perhaps also the recent and intriguing work by Lloyd and Dreyer ('The Universal Path Integral'). But one worry I think these proposals must address is the issue of triviality: if your explanation is consistent with everything, it explains nothing. This is why I can't really get on board with the extreme form of Tegmark's mathematical universe: one could postulate such a hypothesis basically no matter what. I'm not even talking about falsifiability; it's just that simply saying 'everything exists' is not a good explanation for our observations.

This is essentially what leads me to search for a nontrivial implementation relation, i.e. for a way, given a physical system, to constrain possible computations that can be attributed to that system, for instance. The scenario in which the simulation shuts down and is nevertheless carried on in the dust essentially corresponds to a trivial implementation relation: everything computes everything, so every computation occurs *somewhere*. Like you, I find this dissatisfying. It would also lead to a complete dissociation between the computational and the physical: your dripping faucet could be seen as computing universes, the square root of pi, or the precise number of licks it takes to get to the center of a tootsie pop---absolutely anything at all.

By universality, do you mean computational universality, or universality in the sense of a system's behaviour becoming independent of the detailed microphysical details? Because I have been looking at computational universality specifically, but I think the notion is still too broad: very simple systems are universal, and thus, can in principle simulate any given Turing machine, again leading to a version of the above worry. So I've begun trying to find a criterion (a kind of 'informational equivalence principle') that sort of uses a quantification of the information content in a computation in order to determine what computations can usefully be attributed to a physical system, the idea here being that if the information content of the computation greatly exceeds that of the system, in order to get the computation out, you sort of have to put in more work than is done by the system itself---so that the computation is not really performed by the system after all (like in my example where a code maps the symbol @ to the complete works of Shakespeare---you need something equal in information content to the complete works of Shakespeare in order to extract them from @, so the symbol itself plays really only a nominal role in the production of all this information).

Jochen

"First, how is the absolute position of the rainbow defined?"

It cannot be. We cannot know the absolute position of anything. Only its relatyive spatial position with respect to anything within our existentially closed system The observer's are each valid in respect of observer vis a vis rainbow. But if you want to know the position of the rainbow with respect to both observers then you need another reference.

Re your second point. Ohysical existence only occurs in one definitive physically existent state at a time. So if state A & state B exist at the same time that is fine. I am leaving aside the practical difficulyies of measuring such. But one should start with how reality must occur, then try and resolve any problems we get as a result. Not construe a constitution for reality which fits our abilities.

You need to read my essay

Paul

Computability is one form of universality where there are lots of ways to define "computable" and none that is the best, but they are all equivalent. Actually that is not quite true. If I define computable to mean something I can compute on my PC then that is limited by the memory capacity, but taking all possible finite computers together there is a limiting case where memory is not an issue.

A similar thing happens in critical phenomena where you approach a critical point and renormalise as correlation lengths grow to get a theory which does not depend on microscopic details. This is another form of universality, as is chaos theory.

In the "ensemble theory of everything" perhaps something happens where one particular form of universality is more common than anything else in the ensemble so it simply dominates.

This might happen in the Lloyd-Dreyer universal path integral for example. If something dominates in this way it solves the issues about very specific crazy models because they dont really contribute anything. It is the much bigger collection of complex models in the ensemble that matter. Anything that is not close to the universal behavior has measure zero contribution relative to models that cluster around the universal point.

Now the Lloyd-Dreyer path integral is a quantisation and the path integral itself could be a computable structure, so it should have been in the original ensemble and in some sense gets quantised again under the path integral. I conjecture that this structure actually dominates the path integral in which case it is a structure which when quantised leads to itself. This is also what you get when you use multiple quantisation ad infinitum, you get the picture.

Of course that is ridiculously speculative but it is not inconceivable that some such argument could be made concrete. This would require defining what it means for two models to be close or equivalent which is one reason why category theory might be relevant.

I agree with you that there's no well-defined 'actual spatial position of the rainbow'; however, I'm somewhat puzzled, since in your previous reply you said: "The actual spatial location of the rainbow does not alter.", which appears to presuppose there is such a thing...

Regarding the position of the rainbow with respect to both observers, I again don't think there is such a thing: each observer observes the rainbow in a different position, and these observed positions are all we can meaningfully talk about. I consider, in a way, the set of all possible observed positions of the rainbow: these are my relative facts (or rather, this is one relative fact: the position of the rainbow relative to the observer). Any given observer then picks out one particular 'actual' fact.

About the Kochen-Specker theorem, I think you don't quite appreciate its force: it is simply an investigation regarding what follows from statements such as 'physical existence only occurs in one definite physically existent state at a time', and finding these consequences---the independence of certain observations from the context of these observations---to be inconsistent with observation.

The connection you mention between computational and critical universality is something I've thought about a bit, but never was able to carry it beyond some vague feeling of 'there might be some relation'. I guess you're right to connect it to chaotic phenomena: there's the notion of 'edge of chaos', where systems show nontrivial emergent behaviour. Hmm, maybe one could connect the two via Wolfram's class 4 cellular automata? The conjecture then would be that every class 4 system---every system on the 'edge of chaos'---is a system showing both critical and computational universality, thus linking the two.

As for your other speculations, I think that maybe I'm thinking in a broadly similar direction: my own idea is that what's invariant across all such phenomena should be the way information travels from one system to another, or the laws that govern this information exchange. Because when you think about it, no matter what the details of the microphysical implementation are, you'll always have to somehow inform the behaviour of a system about the behaviour of other systems. And (a natural conjecture for somebody with a background in quantum information, perhaps) this information exchange is described by quantum mechanics (which is where, if that's right, one could take advantage of Weizsäcker's or more recent ideas linking quantum information to 3-space, and things like that).

So, matching your ridiculously speculative ideas with my own, there might emerge a broadly similar picture: the information exchange between two systems, if governed by quantum mechanics, is intrinsically probabilistic, and in some 'large' limit, maybe the crazy possibilities have a small enough meassure to be ignored...

But I hear the ice creaking beneath me, so I'll better return to more serious work for the day.

These vague ideas help point in certain directions but my focus is on ways in which purely algebraic structures can lead to geometric ones. It would be nice to have an answer in my lifetime so I will happily accept the hypothesis that multiple quantisation solves the path integral over the grand ensemble of theories and see where I can go with that.

I like the group field theory approach to forming spin metworks because it gives a manifold from an group by a process of quantisation. It has to be extended to higher dimensions and to manifolds with matter content too. That is not going to be a simple generalisation.

The information angle seems to have some baring on this. The relation between redundancy of information and redundancy in gauge theories seems useful and perhaps your ideas about information transfer also relate to something algebraic such as invariants as you mentioned.

I am not looking for something 3D or 4D specifically. I prefer to explore theories in any number of dimensions. I will look at the framework of field theories and worry about real physics later. The geometric process of dimensional reduction by compactification (Kaluza-Klein) would be related to taking an algebraic structure modulo some relations so it is a very natural process from an algebraic point of view and it enriches the physics on the geometric side.

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Jochen

"I'm somewhat puzzled, since in your previous reply you said: "The actual spatial location of the rainbow does not alter.", which appears to presuppose there is such a thing...

Yes, because the next sentence was: "Its relative spatial location does, obviously, because its actual spatial location is being expressed with respect to a different spatial location." And then another sentence is (in the next post, but something similar I said after that sentence without the caveat): "We cannot know the absolute position of anything. Only its relative spatial position with respect to anything within our existentially closed system".

Absolute refers to where (and indeed what, etc) it might 'really' be. Which we cannot know, or to be more precise, we can never know that what we do know is the 'absolute' truth, because there is always the possibility of an alternative. So this is irrelevant. The corollary being that we can know a definite something, ie the form of existence potentially knowable to us. And within that closed system the rainbow, or indeed anything else, exists independently of us in a specific spatial location. But we can only calibrate that, because we cannot externalise ourselves from the closed system, by comparison and the identification of difference, ie its relative special position with respect to something else.

It's all about context. And science is not in the context of every possibility we can conceive and believe in, it is supposed to be considering what is potentially knowable, which is underpinned by a physical process.

"Regarding the position of the rainbow with respect to both observers, I again don't think there is such a thing: each observer observes the rainbow in a different position"

Of course there is. The rainbow and observers are all independently physically existent entities. They therefore have, by existing, a definitive spatial location. We just do not know where 'exactly' it is. Only where it is with respect to something else. Is is the observers who are in different spatial relationships vis a vis the rainbow, not the rainbow which is 'altering' position.

Re your last paragraph. Observation and existence are different. Observation involves the receipt of a physically existent representation of the existential sequence (in sight this is light). Light travels, which takes time. So the timing of the receipt of that representation (ie which is not the reality anyway) is different, and after a delay, from the timing of the actual occurrence. This is where Einstein went wrong, because he had no observation, he conflated occurrence and observation (note his in the "immediate proximity" caveat 1905 Part 1), as he had no observational light (just a ray, or lightening, etc). Just a constant in order to calibrate distance and duration, which happened to be an example of light. It could have been anything. This error was counterbalanced by his failure to understand the reference for timing, because he followed Poincaré's flawed concept of simultaneity. In short: he shifted the real timing differential from the receipt of light, which fundamentally is a function of spatial relationship, to deeming it to be a characteristic of reality (ie relativity). Which is what you are doing with the rainbow. The fact that physical existence can only occur as a sequence, one state at a time, is a supplementary point(!).

Paul

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Guys

There can be nothing, vague, chaotic, uncertain, etc, etc about physical existence. In order to be existent (as we can know it, and this is science, not religion) there must be something in a physical state (what, why, etc, is for you lot to discover, I just do the easy bit!). And in order for it to occur in different states, there must be a physical cause which results in that different state. One state, the next different state, something caused that difference. It is all explainable, if we could 'bottom it out'.

The issue is about our ability to identify that, and not make up rules about how reality occurs in order to cover over our deficiencies.

When I was young (not that I'm that old) TV was quite new. Every now and then a message would show up saying: please do not adjust your sets we are having problems with the transmission.

Paul

But consider how a rainbow works: light from the sun is refracted and retroreflected in a rain drop; if it is incident on, say, an observer's retina, this creates a virtual image, which we call the rainbow. But this is not anywhere in the world: there is no physical object that conforms to the rainbow at any point in space. How then there should be some absolute location to the rainbow seems wholly unclear to me. At best, you could argue that there's a set of rain drops, each of which contributes one 'pixel' to the image of the rainbow; but even this set will be different for different observers.

And I hear your point that observation and existence are different; in a sense, that's what I'm all about: everything we know and can make contact with (though precisely how is a problem in itself) is observation. Hence, I try to only consider observation, making no statement about 'what really exists'. Of course, this is also exactly what Einstein did, asking himself what the world would look like if he rode on a rainbow, etc. (and the functioning of my GPS confirms to me daily the correctness of his conclusions, at least in so far as there is any correctness in science).

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Hi Jochen,

Very Interesting essay!

You wrote at the end of 4:

"In many worlds, both `the electron spin is up' and `the electron spin is down' are true; in the

relative-facts setting, only `the spin of the electron is (up/down) relative to the measurement

apparatus recording (up/down)' is true. A universe of relative facts is not a multiverse!"

I think there is one possibility that a universe of relative facts is a multiverse,

The possibility that the Big Bang produced fully symmetric and entangled anti-copy universes.

Then, there is at least one Charge Parity symmetrical anti-universe ( a mirror world) with equal time because all clocks over there are running (spinning) only in the opposite direction.

To make this a bit more redundant and symmetric, I propose that we live inside a 12 lobed dodecahedron raspberry shaped symmetric multiverse.

However then GOD PLAYS DICE with 12 entangled CP symmetric pinball machines where each pinball is instant connected to its anti-copy living in that other universe.

Perhaps we are even able to measure the number of these raspberry lobes if we are able to observe a definite number of neighbouring lobes in the CBradiation pattern, or even by repeating the well known Benjamin Libet experiments on reaction times and preplanning thoughts ( RPs) of test persons.

See attachments

Leo Vuyk.

http://vixra.org/author/leo_vuykAttachment #1: B.Libet_Preplanning_vs_Free_Will..jpg

    Philip, I generally try to keep as minimal as possible---so since three dimensions are all we can currently observe, that's what I'm trying to figure out (actually, that's not quite true---I'm fascinated by the apparent connection between the division algebras and the forces of the Standard Model, and in as much as the higher division algebras, the quaternions and octonions, are much more naturally connected to six- and ten-dimensional spacetime respectively, I've done a bit of thinking in that direction, too).

    I'm not very familiar with the group field theory approach, but I'd think that as far as getting geometry from algebra goes, noncommutative geometry has some interesting things to say (and of course, with my penchant for the division algebras, the recent foray into nonassociative geometry by Farnsworth and Boyle immediately caught my eye at least). About getting higher dimensions from GFT, with the close connection to spin networks, is that even possible? Generally, I thought that loop variables really only live in 4d space (though I've caught some papers by I think Thiemann generalizing them to higher dimensions out of the corner of my eye). But that stuff really is a bit out of my reach.

    Perhaps one comment about algebraically reducing the dimension to the observed 4: in an approach based on octonions, you'd naturally have the group SL(2,O) for spacetime symmetries, which is isomorphic to SO(9,1), i.e. the ten-d Lorentz group. Now it's always struck me as a curious (and perhaps deep) fact that if you 'fix' one of the imaginary octonions, you not only 'break' the automorphism group from G2 down to SU(3), but also SL(2,O) to SL(2,C), which is of course isomorphic to SO(3,1) (I think I probably got this from Baez). So we get the symmetries of spacetime as we know and love them, and the gauge group of the strong force. Now this maybe something like the large numbers (you mentioned them in the other thread): a cute coincidence that leads all too easily to premature conclusions. But I can't help wondering...

    -------------------

    Paul, to you, it seems to be axiomatic that there must be some underlying, fixed physical reality; however, our best theories appear to be telling us that this is not the case. Now, this as you rightly say is not sufficient grounds to abandon this assumption: however, these theories are, and continue to be, tested to greater precision than anything ever before. It is these experimental observations that are ultimately in conflict with the assumption of a fixed reality; every theory that should supersede quantum mechanics will include nonlocality and contextuality just as much, or else be experimentally not viable.

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    Hi Leo, thanks for your comments and for finding my essay interesting. You make great leaps and bounds in your reply, and I'm unable to follow you at that speed (I've always been a bit of a slow one), so I'm not sure I can cogently reply to them... In general, I'm not a particular fan of multiverses: in particular, I have never seen the term 'universe' defined well enough in order to judge whether there's one or more of them around. It might sound facetious, but, you and me, are we in the same universe? There's things that definitely exist in your universe, but not in mine: your thoughts, feelings, experiences, etc. Furthermore, you have been influenced by events that I have not yet come in causal contact with, i.e. our past lightcones do not overlap---our celestial spheres differ. Then, you experience everything in the world from your unique vintage point---an experience I never could share.

    So in the end, what makes a universe? I couldn't claim to know. And much less so in the case of any supposed multiverses.

    Just posting to say that the above was me---I must've gotten logged out somehow.

    Jochen, you have a good collection of references at your fingertips. I had not seen the non-associative geometry development. There are connections between necklace Lie algebras and non-commutative geometry http://arxiv.org/abs/math/0010030 but I am not chasing that angle. The division algebras are also interesting. The relationships to dimensions are important and probably part of a bigger picture, but I am skeptical about connections to the low energy gauge groups. I think if we knew how much physics there was between 1 TeV and the Planck scale we would laugh at the idea.

    With all these interconnected threads the trick will be to find which part is the key concept after which everything else will fall into place. The combinatorial necklaces that are associated with Lyndon words are also related to irreducible polynomials over finite fields which are in turn related to cyclic linear codes and exceptional structures such as division algebras, exceptional groups and lattices. My goal is therefore to understand the Necklace Lie algebras first and then see how these exceptional structures appear within them and how that relates to special properties of different dimensions. Of course the whole program is ambitious and I have no idea if I know enough mathematics to make any progress even assuming there is really something to discover, but it is all fun to think about.

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    Thank you Jochen,

    i realize that my proposals for the idea of a Big bang symmetry and that you and I are dealing with one or more other you's and I's living in an anti matter universe coupled by instant entanglement is too much to grasp.

    sorry.

    Jochen

    How the rainbow works, and that it just happens to involve light, is irrelevant. It is a physically existent entity. This argument has the structure of Einstein where there is always some form of light, but it is actually just a constant, which happens to be light (eg lightening on his train). Indeed, this always happens. Turn to Cox & Forshaw, a good explanation of the argument, and there we have a clock that is a light beam. The light entity is a constant against which to calibrate duration and distance, not observational light.

    Whatever the entity, to observe it involves an interaction between it as the existent sequence progresses, and something else, which creates a physically existent entity that is representational of it, ie observational light. This then travels, and some of it interacts with eyes.

    Put another way, the rainbow is not inside people's heads. As you then say, because it is to do with water and light.

    "everything we know and can make contact with (though precisely how is a problem in itself) is observation"

    No. Everything we could potentially know is determined by all the sensing systems of all sentient organisms. Which would include an alien if he/she landed here and explained a new sensory system to us. And that encompasses hypothesising so long as it is effected in accordance with the operational rules of the sensory system it is supplementing. Because, obviously, not everything can be sensed directly, therefore it is perfectly legitimate to establish what could have been so had some identifiable problem not prevented it. But this does not involve belief, which is the assertion of reality on the basis of no experienceability whatsoever. In other words, physical existence is whatever we can potentially know as enabled by the physical processes (which are part of physical existence) which feed the sensory systems, or hypothetical equivalents.

    "Hence, I try to only consider observation, making no statement about 'what really exists'."

    Indeed. But leaving aside the point that it is more than just observation, direct or indirect, if you do not start with the premise which corresponds to the form of existence we can know, then you are likely to be considering alternatives (ie what possibly really exists), albeit inadvertently. It is considered intellectually correct to presume physical existence as an abstract concept, ie presume nothing. But it is not abstract, generically it has a definitive form and modus operandi.

    Einstein did not do this, please find me an example of actual observation, ie where there is observational light and it is being received. You can't. In the AB example it is a ray of light, in the train there is another ray of light (which takes the place of the man walking-which it does not) and there is lightening.

    To try and settle the Einstein 'angle', I will post on my essay site the first 24 paras of another paper. This is only 4 pages and is easy to read, it gets slightly more complex after that.

    Paul