• [deleted]

I thought it might be useful to restate once more the topic of the forum. ;-)

My claim is that we need a fundamentally new formalism for modeling the physical reality of expanding universe.

Why? Because there is nothing in the conventional math. which would allows us to come to grips with such process of expansion that is accompanied by the ceaseless CREATION OF QUALITATIVELY DIVERSE NEW 'STUFF'. No existing concept of space can offer any help in this respect (and, frankly, I am somewhat surprised at how this situation has been overlooked).

I also would like to discuss some proposals for dealing with such process (including my own). Thus, we can address the wish, mentioned in one of my posts, by Frank Wilczek that "more meat to be put on inflation", including "structure" and "mechanism".

    6 days later
    • [deleted]

    Lev,

    I am disappointed, as I know you must be, that the topic hasn't generated the kind of interest that (at least I think) it deserves.

    Suppose the question were framed:

    Does there exist a computable non-numeric representation of evolving novel forms that accurately describes the evolving physical world?

    Then suppose that rather than assuming the positive, we try to rule it out.

    I'll ask first: what do we mean by "computable?"

    Tom

    • [deleted]

    Tom,

    Let's be patient and wait (after all it's summer), and let's also be optimistic about it. ;-)

    Thanks for your continued interest! I hope you will stay with the topic.

    • [deleted]

    Here is yet another summary of our topic. ;-))

    As I stated above, in contrast to the line of generalizations of the concept of 'space'--reals, vector space, metric space, topological space--we have absolutely no concept with which to start the corresponding line of generalizations for the concept of 'evolving' space. And there are perfectly sensible (formal and informal) reasons for this situation: the present mathematics has developed in such a way that it is not 'equipped' to deal with evolving structures, except by means of formulas and sequences. But those cannot deal with the underlying mechanisms responsible for the structural 'evolution'. I submit that it is the ubiquitous spatial/ point representation that, on the one hand lies at the foundation of all math. concepts, and on the other hand is standing in the way of the new formalism which can adequately deal with the evolving structures: since the 'point' cannot evolve, it must be replaced by some dynamic/evolving structure, which requires complete rebuilding of mathematics as we know it. Evolution of the universe is about creation of novel structural entities, and such entities cannot be built out of non-structural entities, i.e. 'points'.

    Of course, the ease with which it became possible to add adjective "evolving" has partly to do with the light hand of Darwin and the modern biology. But if Darwin, as a non-technical fellow, can be forgiven for this, in mathematics and physics such attitudes are standing in the way of real progress, which, by the way, would also have a transforming influence on biology itself.

    The hypothesis, which would be interesting to discuss, is that 'space' (and its 'content') is being incrementally instantiated on the basis of the more basic informational mechanism, which builds the space based on the relational/structural information captured in the structural "event" (see informal introduction in my essay). In particular, such event has sufficient information as to where to attach the space 'patch'.

      • [deleted]

      Lev,

      Ever since being introduced to your work, I have wondered if I could be persuaded that a more fundamental structure than the integers underlies the idea of order. I was taken by your coinage, "struct", and its description, almost immediately. Structs seem to fit naturally with the kind of "black box" relation that characterizes a system of components evolving at different rates (like the Ashby/Bar-Yam multiscale variety)*; the internal evolution of the black box is unavailable, but the time dependency of the network forces a visible relation among hubs of coordinated activity**, such that even though the system state shows little change in the aggregate of elapsed time, at any two particular adjacent time measures, the locations of central hub activity may differ radically. (Cf. Gould-Eldredge punctuated equilibria^ for a connection to evolutionary biology, and self-organized criticality^^ in the extended model of evolution.)

      If black boxes are structs and structs are nodes, network vertices are time paths, which leads to the important conclusion that you and I share: time is identical to information. In such a network, information is physical (quantum information)accounting for dynamic activity. In other words, the time we measure is independent of the internal "black box" time; the struct is self contained and independent of the network and only enters via a time-dependent relation of measured quantum information.

      I understand the lack of evolutionary potential in your "non-structural point." However, what always hangs me up when I engage with your work, is that points of the complex plane are not "non-structural." Points are analyzed as lines in complex analysis, and the complex plane compactified with one point at infinity (Riemann sphere) _does_ give us space and content; i.e., the algebra is closed and the space has dimension 2. From the chaotic field of non-ordered complex numbers, we do get ordered relations in real time and space, from analysis on the Hilbert space. I still don't grasp what in your concept would obviate such a mathematical approach.

      Tom

      *Bar-Yam, Y. [2003] "Multiscale Variety in Complex Systems," NECSI Technical Report 2003-11-01 (Nov.)

      **Braha, D. & Bar-Yam, Y.[2006]. "From Centrality to Temporary Fame: Dynamic Centrality in Complex Networks." Complexity vol 12, no 2, pp 59-63

      ^Eldredge, N., & Gould, S. J. [1972]. "Punctuated equilibria: an alternative to phyletic gradualism." In: Models In Paleobiology (Ed. by T. J. M. Schopf). Freeman, Cooper and Co.

      ^^Bak, P. [1996]. How Nature Works: The Science of Self-Organized Criticality. Copernicus.

      • [deleted]

      "I understand the lack of evolutionary potential in your "non-structural point." However, what always hangs me up when I engage with your work, is that points of the complex plane are not 'non-structural.' "

      Tom,

      Points of the complex plane, or of any vector space, are just these, points. They can be algebraically decomposed via other vectors, that's true, but this decomposition is not unique and hence cannot really be called structural in the temporal sense:

      11 = 2 plus 9 = 7 plus 4 = 5 plus 6 etc.

      We have no (temporal) information on how number '11' (or any vector in a vector space) was *actually* formed.

      Also remember set theory (set = collection of points) as the foundation of mathematics.

      For temporal/formative information to be present in the object representation, you need a fundamentally new representational formalism, hence our ETS.

      • [deleted]

      Lev,

      We're on the same page. I dealt with that issue of decomposability in my NECSI ICCS 2006 paper here specifically in section 5.0.

      I do not rely on the set theory of classical mathematics. A time dependent complex network method frees us of that constraint.

      Tom

      • [deleted]

      Tom,

      I'm afraid you missed my main point: the formative/temporal information must be explicitly present in the representation and not put into it in some artificial manner. Of course, even with numbers, instead of '11' one can write '2@9' but this simple trick does not addresses the typical physical situation when a single event is followed by (i.e. directly connected to) several immediately consequent events each of various structure. By the way, graphs (with nodes and edges), as well as strings, are not such temporal representations.

      You really need some new, temporal, form of representation. The point is simple but strong mental habits prevent most from seeing it: math. does not really deal with non-numeric representations.

      • [deleted]

      Okay, Lev, even if I am willing to suspend judgment on everything I know about numbers, points, lines, planes -- I would still not understand why a "... new, temporal, form of representation" would be less "artificial" an imposition than converting points, lines and plane to "chairs, tables and beer mugs" as Hilbert put it.

      Why would not a topological quantum field theory satisfy your requirements? After all, if time is identical to information, exchange of quantum information over topological manifolds would reveal, but not determine, the object representation.

      Tom

      • [deleted]

      Tom,

      When I speak of "representation", I'm talking about the form of data representation in science.

      Any field theory or, for that matter, *any* current physical theory still relies on numeric measurements, while I'm suggesting non-numeric "measurements".

        • [deleted]

        Lev,

        Isn't an ordered structure what "measurement" implies? Then, isn't temporal order fundamental? And doesn't numerical order follow from temporal order?

        I think about Brouwer, who called mathematics "a languageless activity of the mind." That same Brouwer allowed that doing mathematics entails "a move of time ... a twoity."

        The twoity you seem to suggest is the independence of semantics and syntax, and I agree with that -- a congruence of semantics and syntax would seem to imply meaning -- yet how does such meaning differ from that we find in the congruence, e.g., of identical geometric angles?

        Do understand that I am not asking these questions to be contrary -- there is so much in your concept that I find agreeable. I am just looking for a handhold that would obviate numerical representation of physical phenomena, and I haven't found it yet.

        Tom

        • [deleted]

        Tom,

        I'm quite comfortable with any question. ;-)

        I came to ETS formalism very gradually, trying to model inductive (biological) processes, which I and many other consider central to unlocking the nature of biological information processing: How is an object represented in order to be able to 'recognize' later another object that belongs to the same class of objects. This led to the search for the concept of structural representation: conventional numeric representations are not rich enough for the purposes of induction.

        I guess the 'easiest' way to approach ETS is the direct way: think now of the generalized measurement process in which numbers are replaced by their structural generalization, structs. A numeric/spatial measurement is based on the repetitive application of the same "stick", while the result of ETS measurement is a struct also obtained during the interaction with the corresponding object/process (all objects are, in fact, processes) . Of course, the conventional measurement is a very special case of ETS measurement.

        • [deleted]

        Thanks, Lev.

        This gets me the closest yet, to understanding your research program. As a student of complex systems, I grasp the terms of a recognition algorithm, and I have always been impressed, as you know, with the power of structs to generalize relations to this extreme degree.

        Scale has got to play a role here, though. Consider an infinitely self similar set. One does not measure with the "same stick" across different scales; scale, in fact, determines the stick one chooses -- a jagged coastline may be of infinite or finite length. And surely the Mandelbrot set is also a process as well as an object, which evolves according to a simple algorithm into an exceedingly complex form.

        Anyway, may I make a suggestion to narrow this discussion a bit, and also accommodate your emphasis on biological processes? An important unsolved problem in both biology and computation is that of protein folding -- could we possible focus on an ETS strategy toward that singular case?

        Tom

        Dear Lev and Tom,

        This looks like an interesting topic, if I understood it, but several points leave me confused.

        When Lev says "representation", this typically implies some sort of graphical picture or map. Yet he states that "...graphs (with nodes and edges)... are not such temporal representations. So are you foregoing all graphical (i.e., visual) representations?

        Lev states, "we have no (temporal) information on how number '11'...was formed. What does this mean? Using logical circuitry I can create a counter to generate *ALL* integers (with appropriate carry extensions) and also build adders and subtractors. They are generated in numerical order that can be interpreted as temporal order. What exactly is the problem?

        Tom says, "...isn't temporal order fundamental? And doesn't numeric order follow from temporal order?"

        Eons ago, in physics lab, we attached a weight to a paper tape, running between two electrodes and the spark 'marks' recorded 'measurements' of acceleration on the paper. if I now add simple counter circuitry to encode the marks (as binary integers) then I have integer marks, existing as spatial order, that we can interpret as temporal order. Where is the problem?

        Lev then states, "...I'm suggesting non-numeric "measurements"." What does this mean?

        Thanks for any explanation,

        Edwin Eugene Klingman

          • [deleted]

          Hello Edwin,

          1. "When Lev says "representation", this typically implies some sort of graphical picture or map."

          Please note that yours is not a formal meaning of the term 'representation': the formal meaning has to do with the formalism chosen to represent data.

          2. "Lev then states, '...I'm suggesting non-numeric "measurements".' What does this mean?"

          This is the case when you represent your data not by numbers but by some (preferably properly formalized) entities other than numbers. Note that "graphical pictures or maps" are not properly formalized entities that can be reliably manipulated for the purposes of "data processing" (in the same sense as we 'manipulate' numbers). So far, in science, this has not happened yet, but there are important reasons for moving in that direction.

          • [deleted]

          Tom,

          In ETS, "scales" (i.e.'stages') are handled very naturally, via the concept of 'transformation', which allows to shrink most large structs at he next stage.

          Also, although I would be more comfortable to talk biology, I believe it's not about comfort. ;-)

          I would like to make at least some small headway in physics: physics began essentially with dynamics but ETS is about structural representation. So I would like to understand at least some connections between an object viewed/represented as a process and its motion in space. I have some very preliminary ideas.

          Lev,

          Thanks for the answers. Since you stated that you are comfortable with questions, I'll continue.

          Are you saying that your 'structs' cannot be represented graphically?

          And would you attempt to explain about "(temporal) information on how '11'..was formed."?

          Edwin Eugene Klingman

            • [deleted]

            1. "Are you saying that your 'structs' cannot be represented graphically?"

            Edwin, let's not confuse their *pictorial depictions* with their formal definition (see our main paper, p.29).

            2. "And would you attempt to explain about "(temporal) information on how '11'..was formed."?"

            I'm simply following the the temporal spirit of Peano definition of natural numbers (and, of course, more generally, the concept of struct).

            For example, '11' could have been obtained as '7' "followed" by '4', which is different from '2' "followed" by '9'. But when you look at '11', you can't see which temporal sequence of events produced that struct (in primitive cultures, one new what was going on simply because you had to make knots on the rope, or notches on a stick, or find the right number of stones) . And this is a general problem with all conventional mathematical representations (since they are not temporal).

            A temporal representation (such as struct) is not only more accurate but is also much richer, simply because it allows for the existence of qualitatively different events, which of course we have admitted in physics (e.g. qualitatively different particles).

            • [deleted]

            Lev,

            I read a newspaper story here in Detroit, concerning a giant T-shirt that public school teachers had made to adorn the "Spirit of Detroit" sculpture downtown.

            Accompanying the story was a picture of the shirt all spread out, with a caption that began "Up to 300 yards of material were used ..."

            "Up to"? I imagine that the caption writer was working from an earlier press release that estimated the amount of material needed. But here is the actual shirt, all constructed. If all the information we have is in the picture and caption, the shirt may have anywhere from a fraction of a yard to 300. If it has 300 plus a fraction, however small, the narrative that was true, before the shirt was made, is false after the shirt is made. If it is important to know (obviously, in this trivial example, it isn't, but the principle still applies) we measure the material to the best of our technical ability. Perhaps there are weather conditions that cause it to shrink or expand, so we may decide on either an average or a median measure under varying conditions. After all said and done, we declare the account of the event true or false, but not both. Wait, though - this account was written _after_ the shirt was constructed, and one would think that it has a definite value, a "real" outcome. Yet, even though the outcome has already been determined (the shirt is made) and its representation (photo & caption) exist simultaneously, our knowledge of the state of the shirt is in limbo until after the event and its representation are reconciled by measurement. There is only one right answer.

            My point: As you make clear with the independence of semantics & syntax, the gulf between representation and truth is not bridgeable. A representation is neither true nor false; ergo, there is no numerical representation that can tell us the truth, so long as the truth is probabilistic.

            Trouble is, we know that measured truth _is_ probabilistic. One of the contributors to quantum theory (I forget whom) characterized quantum mechanics as "something somewhere is doing we don't know what." The measured is never certain enough, only good enough. We don't need to know true from false. Except ...

            For cosmological models.

            I think Brendan made a good call in naming this thread. It makes a difference, when considering the origin, whether we start with something or nothing. If "something," our problem is rather like botany or zoology -- naming particles and properties, identifying and studying the characteristics that demarcate one particle from another. If "nothing," our problem is one of structure itself--and that is structure without matter, because when we measure changes in the state of a system, it is always from mass points, never space points. We know how spacetime changes matter dynamics; we do not know (in fact, general relativity forbids it in principle) that matter changes spacetime.

            To a theorist, and particularly a mathematical analyst, matter is a contaminant in an otherwise perfectly symmetrical world. We want all our space to behave smoothly, on an infinitely flat plane, where we manipulate points and lines at will -- we are descendants of Euclid. If mass doesn't want to cooperate, we coopt mass for energy and spread it symmetrically over the plane. If we encounter enough curvature caused by physical effects, to be troublesome, no problem -- we add dimensions. The n-dimension distribution (generalized Poincare Conjecture) is massless, with average energy content zero.

            My own strategy toward this problem (my "time barrier" preprint linked earlier) is to give the vacuum an n-dimensional sphere kissing order in which time (information) is dissipative over n Euclidean dimensions. The math works out (by a purely algebraic method) to where the ordinary matter content of the universe (4.59%) becomes a probability 0.0459 that our universe has any matter content at all. (As a consequence, my model anchors probability theory to a length 1 continuous field in n-dimension space, with asymptotic approach to 1).

            As with the giant T-shirt, the result we get after observation (WMAP data) is consistent with the range of observation; i.e., 4 dimensions. The 4-dimension horizon, I have found, is identical to a 10-dimension limit of an n-dimension field.

            So--a numerical analysis _does_ get us "somewhere." My interest in your research, Lev, is that the numbers don't tell us what "something" is doing. The dynamics of structure must always add a " 1" dimension to account for our knowledge of change in the system. The classical dynamic system is 3 1. The added dimension is of course, time.

            We agree between us that time is identical to information. However, do we mean the same thing by "information?" I mean, quantum information bytes, physical information, i.e., the same as described by Jacobson-Verlinde. I think, by your definition of structs if I understand it, that we do mean the same thing in different terms--"pairs of primitives" correspond, do they not, to quantum information? It is understood, though, that the state of your structs is positive definite and not in superposition, and quantum state measure is replaced by struct dynamics. Which leads back to the main question:

            Something or Nothing?

            (1) If something, structs are the product of broken symmetry, evolution is top down, and cosmology is botany.

            (2) If nothing, structs are a primitive, self organized, dynamic relation between time and space, and evolution is bottom up.

            My program is compatible with structs IFF (2). In that context, 0 1 spacetime relates the n-dimension set to the measure function -- with your representation of the natural numbers in fig 12, pg 30, the connected dots representing evolutionary events and therefore dynamic results. I can see that these events can both structure and decompose structs (according to the initial states of the structs) just as in biological evolution. Your definitions that follow imply novel structures from primitive representations, with a non-perturbative mapping.

            How am I doing so far?

            Tom

            Lev,

            I will look at your paper to try and understand your point of view of graphic depiction.

            But on the following:

            You say: "I'm simply following the the temporal spirit of Peano definition of natural numbers (and, of course, more generally, the concept of struct).

            For example, '11' could have been obtained as '7' "followed" by '4', which is different from '2' "followed" by '9'. But when you look at '11', you can't see which temporal sequence of events produced that struct (in primitive cultures, one new what was going on simply because you had to make knots on the rope, or notches on a stick, or find the right number of stones) . And this is a general problem with all conventional mathematical representations (since they are not temporal)."

            The basics of quantum electro-dynamics is the counter, the sum of creation and annihilation operators over a particle space. The basic logico-arithmetic circuit is the counter. It is basic because it gives rise to the integers *in order*. It is the physical implementation of Peano's axiom. Probably an infinite number of other logic circuits can be defined to produce any number of logical combinations of binary bits, but the primary ones that are useful are comparators, adders, and subtractors. The use of these to accomplish 2 plus 9 or 4 plus 7 are of no consequence and have nothing to do with the nature of time. I think the point about "(temporal) information on how '11'..was formed" is non-sensical and based on a misunderstanding of the nature of number in a physical universe that supports logic.

            Edwin Eugene Klingman