Essay Abstract

This essay is a less technical account of recent results announced by the author. The starting point for our considerations is a collective of agents which has been exposed to ``The It'' of external events. These events are used by the collective to construct a family of statistical models which depend on continuous fitting parameters. From this premise, we show how to recover ``The It'' of classical gravity and a theory of strings from ``The Bits'' of stable inference schemes by the collective.

Author Bio

Jonathan Heckman is a theoretical physicist in the high energy theoretical physics group at Harvard University.

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Jonathan,

As a layman I appreciate your attempt at simplifying a rather complex subject. While I emphasize Information over Substance somewhat in my own essay, I must agree that they are co-creative entities and one w/o the other is somewhat superfluous (as I think Bohm also believed even while emphasizing Information much of the time).

In regards to this statement:

"A major bottleneck in even getting started with the study of quantum gravity

is that there is no sharp definition of a "local observable".

Again I am a layman and not that well-informed, and I'm not disagreeing w/ your statement in the slightest, but hasn't the major stumbling block of quantum gravity (as well as string theory) been in reconciling the theories w/ a dynamical space-time background as postulated by GR?

Regards,

John

    I read your essay rather quickly last night in a first skim reading. Of course I need to read it in greater depth. I think your approach is very interesting and it is in line with the quantum Bayesian model approach. Further, Wheeler's "It From Bit" idea is that an observer "constructs" reality from a series of measurements that are similar to a process of "20 questions." In that way the observer updates the Bayesian prior and iterates the process.

    Of course with general relativity we have a funny matter of there not being a preferred time slicing of spatial surfaces from which one can define probabilities that are normalized. This in a Born theorem perspective, for the expectation of an observable O there exists a corresponding probability, a difficulty with defining eigen-values such as energy. Some analysts of course introduce pseudo-tensors and the like to try to avoid these matters. Of course that adulterates the covariant properties of spacetime or what one observes in spacetime. The curious result is that the evolution of a quantum system bewteen an initial and final spatial surface can be inequivalent for different choices of time slicing between these "endpoints" in the path integral.

    The amplitude computed in a path integral is a summation over 3-metrics g

    Z = ∫D[g]e^{iS(g)},

    where a standard method is to Wick rotate the phase e^{iS(g)} --- > e^{S(g)}. This is a way to get attenuation of high frequency modes, and it is a "bit of a cheat," though at the end one must recover the i = sqrt{-1} and "undo the damage" for the most part. This phase then becomes e^{-GM^2}, which illustrates how the action and entropy are interchangeable. The integral measure is the size of the phase space of the system ~ exp(S). The amplitude is then on the order

    Z ~ e^{S}e^{-S} = 1.

    This holds universally no matter how large the black hole is. This might have some implication with your work from eqns 14 to 19. I need of course to read your essay in greater detail.

    In general your essay appears to be one of the better essays posted here. I'll write in greater detail in the near future.

    Cheers LC

      Doctor Heckman,

      I found your essay to be superbly written. You are clearly a man of your word. You promised us a less technically written essay on a subject you are an expert in and you delivered on your promise. I am a creaky old realist, yet I had no trouble reading the essay.

      There is one ironic sentence in your essay that caused me to laugh out loud. You wrote: "In statistics, this is commonly referred to as the Fisher score for the statistics. In my essay BITTERS, I maintain that all abstract statistics are unrealistic because only real unique exists, once.

        Dear Jonathan Heckman,

        I enjoy reading an essay that gives me a totally new perspective and yours gave me several! I recently studied ET Jaynes "Probability Theory: the logic of science", but I do not recall seeing the geometric approach to statistics, which I find very interesting.

        I also found very interesting the production "out of almost nothing" of the statistical mechanical partition function, with the number of sampled events playing the role of an inverse temperature N-> 1/T. That's food for thought.

        The brief perspective on Feynman path integrals and Euclidian space was also a fresh view as was adding prior beliefs as an analog to potential energy. Your analogies reach very far, even to an energy-based analogy of the collective powerful enough to "suppress dissenting opinion", a very relevant topic these days.

        In short, your essay provided many fresh insights that I very much savored. I hope you will read my essay and comment. I am still not a fan of string theory, but I'm grateful for the new views you provided. You may not buy all of my conclusions, but I think you will find fresh perspectives.

        Good luck in the contest,

        Edwin Eugene Klingman

          Dear Sir,

          Your essay not only points to your great intellectual acumen and capacity to think out of box, but also provides a cogent reason for the present maladies of science. Mathematics explains only "how much" one quantity accumulates or reduces in an interaction involving similar or partly similar quantities and not "what", "why", "when", "where", or "with whom" about the objects involved in such interactions. These are the subject matters of physics. But over dependence on mathematical modeling and prior belief on the "established theories" to look for probabilities is making physicists more and more dependent on results of observation by Engineers to modify or tentatively extend the existing theories leading to development of many contradictory branches, while leaving many aspects unexplained or even unexplored. Because of your independent thinking, we provide you some inputs that can be extended further.

          To substantiate our above statement, we give one example about the unexplained questions relating to the strings. Given the measurement problem of quantum mechanics, what happens when a string is measured? Does the uncertainty principle apply to the whole string? Or does it apply only to some section of the string being measured? Does string theory modify the uncertainty principle? If we measure its position, do we get only the average position of the string? If the position of a string is measured with arbitrarily high accuracy, what happens to the momentum of the string? Does the momentum become undefined as opposed to simply unknown? What about the location of an end-point? If the measurement returns an end-point, then which end-point? Does the measurement return the position of some point along the string? (The string is said to be a Two dimensional object extended in space. Hence its position cannot be described by a finite set of numbers and thus, cannot be described by a finite set of measurements.) How do the Bell's inequalities apply to string theory? And so on.

          You have correctly described the Bayes' rule of statistical inference with the notion of prior belief, but left out other interpretations after hinting about them; probably you did not consider them as important. But if we interpret inference as the processing of the fresh input in the memory of an agent or by the collective, we have to admit that it is not restricted only to probability, but is a certainty - a notion of being able to repeat an experiment with arbitrary precision - though the degree of its accuracy or the proximity of the outcome to the universal or true distribution depends upon the memory content. An arbitrary command to a computer will prove this. Only conscious actions can change it or give the distribution a 'jolt' as you describe it. Because in cognition, it may be a specific choice of prior beliefs (data bank); but it will be with the sheen of more objectivity due to the notion of causality. From the input, we may be able to predict the outcome or from one input, we may derive other connected outputs. Many aspects of perception have been discussed in our essay "Information Hides in the Glare of Reality" published on May 31.

          Your description of collective inference is akin to reductionism. There is a story of six blind men, who went to "see" an elephant. Each one touched a specific part in such a way that they covered the whole body of the elephant. When their descriptions are compiled, it did not make any sense, though their individual descriptions were authentic. The reason is each was describing his perception as that of the elephant - which was their prior belief - without referring to the sequence of his body like in a jigsaw puzzle. It is like your description of the visit to Hawaii. Regarding your agents model, sample this limerick:

          There was this young lady from the West.

          Who thought her husband an unfaithful pest,

          For, he and her li'l son Tyke,

          Look so apart and hardly alike,

          And the divorce court is trying out a Hypothesis test! (joking only).

          Your description of perturbation includes both 'change of mind' as well as the uncertainty induced by the interaction with the field. While the first is a conscious action, the last is mechanical action. Thus, there is no wonder that "the number of fitting parameters is no longer an unconstrained number" - as you put it.

          In our essay, we have raised some very important and interesting issues related to physics. You are welcome to comment on those.

          Regards,

          basudeba

            Dear Jonathan,

            Edwin Klingman referred me to your essay. Quite interesting. I wonder if Leibniz's "monads" that I dwell on in my essay can serve as one of the possible "agents" you mentioned. If so, can you say a few words why not?

            Then, in your paper I didnt quite get what the two alternate states, designated 0 and 1 will be, since 'bit' is just short for binary digit.

            Best regards,

            Akinbo

              Dear John,

              Thank you for your message.

              To clarify the statement about ``stumbling blocks'', I think you are referring to the issue of background independence in a candidate quantum theory of gravity. This is actually closely related to the issue I mention in my essay. Part of this has to due with the fact that in classical gravity, there is a redundancy in our description, which is captured by the diffeomorphisms of the geometry. However, once we pick a preferred point to construct our off-shell quantum observable, we have eliminated this redundancy, i.e. ``broken'' the diffeomorphisms. This is acceptable to do provided gravity is not dynamical: It is simply a choice of convenient coordinate system. However, once we make gravity dynamical, fixing such a choice is no longer consistent, since we have now eliminated fluctuations of the spacetime. For further discussion, you might find the discussion in section 2.1 of the following paper helpful:

              http://arxiv.org/abs/0704.1814

              I should also mention that in some favorable situations, it is possible to say a great deal more. For example, in string theory some cases are understood where the interior spacetime geometry fluctuates, provided the boundary geometry of the spacetime is not allowed to fluctuate. Examples of this type include the AdS/CFT correspondence: The interior of the asymptotically Anti de Sitter spacetime geometry can freely fluctuate, but boundary conditions must be imposed. String theory in asymptotically flat space is another example: Everything is packaged in terms of the boundary data of incoming and outgoing

              scattering states, no reference to an interior spacetime geometry is needed. However, these cases require some special behavior for the asymptotics of the geometry.

              Indeed, part of the aim of my contribution is to ask whether we can move away from these idealized situations to more general spacetimes. In this vein, the idea is to introduce a notion of an approximate observable which works more generally.

              Best Regards,

              Jonathan

              Dear Lawrence,

              Yes, I agree that my approach is roughly in line with what Wheeler proposes, though I think the details deviate from his case. Further, I do not see a way to go purely from informatics to physics (as I mention in the Introduction).

              Thanks also for your comments on the essay. I look forward to further discussion.

              Best Regards,

              Jonathan

              Dear Joe,

              I am happy to hear that you found the essay readable. I hope you found it enjoyable as well.

              With regards to your viewpoint that only ``real unique exists'', I would agree that this is a position which is hard to directly refute.

              In my own considerations, however, I found this to be a difficult starting point. Without the use of statistical inference, I do not see how we can conclude anything about an external world. It is indeed an assumption I am making that there is a notion of an external world which we can only access statistically. Without statistics, I find it hard to make progress on questions pertaining to the natural world.

              If one foregoes the use of statistical reasoning altogether, then I worry that one would be subject to various potential pitfalls. For example, is there something more to a ``real unique'' other than sensory perception? If not, one can concoct various solipsistic attitudes which make no reference to the external world at all. A classic example is to take the extreme position that one is a brain in a jar, and is being exposed to electrodes which generate appropriate sensory data. A sufficiently contrived set of sensory data could mimic any ``real unique'' from the external world. However, if one allows for statistical inference, then this supposition becomes increasingly contrived

              as the experiment is repeated sufficiently often.

              Best Regards,

              Jonathan

              Dear Edwin,

              Thank you for your positive comments, I am glad you found something to enjoy in my essay. I too was quite struck with the connection to statistical mechanics which Vijay Balasubramanian found. It was one of the starting points for my own thinking on the topic.

              When I have time I will read and comment on your essay.

              Best Regards,

              Jonathan

              Dear Basudeba,

              Thank you for your detailed questions and comments. I fear that answering all your questions on strings would consume too much time for both of us, but there are some general points I hope I can address.

              First, strings keep intact the structure of quantum theory. However, there can be more generalized types of uncertainty principles in quantum systems, which are straightforward to realize in string-based systems. To give an example, in some regimes of validity, strings in a background flux can lead to a non-commutative geometric structure. This generalizes the Heisenberg uncertainty

              relation to relative uncertainty in knowing two positions, or a position and a time to arbitrary accuracy.

              With regards to the need for consciousness of the agents to enact a ``jolt'', I do not think consciousness is actually necessary. Consider for example a probabilistic machine which has been trained on a data set. This can receive a ``jolt'' when it receives instructions to flip a coin. Also, I would count a D-instanton as an agent, and this has no semblance of consciousness (as far as I know).

              When I have time I will aim to read and comment on your essay.

              Best Regards,

              Jonathan

              Dear Akinbo,

              Thanks for your question and comments. I am not very familiar with Leibniz's theory of monads, so I will need some time to work through your essay before I can give a full response, and comment on your essay. As far as I understand, there is indeed some overlap between what I call an agent, and your use of monads.

              However, I think there are also some distinctions. For example, the notion of an agent allows for it to be itself composed of smaller entities, whereas a monad (as far as I understand it, please correct me if I am incorrect here) is taken to be the smallest component out of which other components can be built. To give an example, if we identify all the agents of the collective itself as another agent, then we might start anew with this collective as our ``basic building block of agents''.

              I think the most practical description may be one where we simply demarcate different regimes of validity for what we assign as an agent; as we move to bigger or shorter distance scales, what we identify with a practical definition of an agent may consequently change. Here is an example from physics: In QCD at high energies, a description in terms of free quarks is quite convenient. However, at low energies, the description in terms of quarks becomes rather cumbersome because the couplings between states are now quite strong. Rather, we instead have low energy excitations such as pions which are a more convenient description of some aspects of the low energy physics.

              With regards to your question about 0 versus 1, i.e. the ``bits'' of the agent, the assumption I start from is that information by the agent is measured in ``nats'' rather than ``bits'', since the agents make use of continuous fitting parameters. This should be viewed as the analog version of digital information.

              Best Regards,

              Jonathan

              Dear Dr. Heckman,

              I read your paper with great detail yesterday. I think your paper is certainly one of the more interesting ones in the lot. It is too bad that it is a bit far down the community rating list.

              The argument for a path integral based on p_t = p_g δy^I∂p_g/∂_y^I is interesting. This is a form of variational calculus as I see it. The variation is the parameterization between the true probability and the Bayesian prior associated with the "guess" p_g. The variation describes a metric ds^2 = G_{IJ}δy^Iδy^J which defines E(y) = ds^2. The quadratic term in the variation is substituted with

              δy^Iδy^J --- > h^{ab}(∂y^I/∂σ^a)(∂y^J/∂σ^b).,

              of course has the appearance of the kinetic energy term in the Hamiltonian (or Lagrangian depending on the signature of h^{ab}) for a string. It the parameter σ --- > (σ, τ) the two dimensional flow (conformal flow) is on a string world sheet. This enters into a partition (path integral) of the form sum e^{-E(x)/T}.

              The variation appears to be over microstates. If the p_t is close to the p_g then E(y) is small and this variation is over a set of states in a coherent set c. The evaluation of Z(A_col|E_col) is an overlap of the form

              (x|Ψ) = ∫_cδx' e^{-iS(x')}(x'|Ψ).

              The evaluation is over a set of states that are fine grained. This is probably only applicable over some local region in the entire parameter space. A region outside this region is less amenable to this sort of analysis. This local region defines a region of a saddle point integration. The action near this fixed point is then expanded by y^I as

              S[y] = S[y_0] (1/2)(&^2S[y_0]/&y^I&y^J)&y^I&y^J

              = S[y_0] (h^{ab}/2)(&^2S[y_0]/&y^I&y^J) h^{ab}(∂y^I/∂σ^a)(∂y^J/∂σ^b).

              The action then contains a term corresponding to the KE for the above Hamiltonian or Lagrangian. A saddle point integration gives

              |Ψ) = ∫_c δσ sqrt(δ^2S[y_0]/δy^Iδy^J)^{-1} e^{-iS(σ, y_0)}

              over the coherent set C with a fine grained set of states with S(σ, y_0) the form above or in equation 18 in your paper.

              I now define a differential form d = (dy^I)δ/δy^I and evaluate terms of the form (Ψ|d|Ψ) and (Ψ|d*d *dd|Ψ), where the last is an evaluation of a Laplacian, with * = Hodge dual star operation. This becomes an evaluation of Morse indices. I can maybe go into this with greater detail later. This post is already getting a bit long and complicated. I did some analysis last night and found this sort of theory lends itself to a Morse theory or Floer cohomology theory of quantum numbers. The manifold physical states may have a nontrivial topology with coherent sets at regions near fixed points. The evaluation of these integrals, path integrals or partition functions can now describe quantum tunneling or transitions between fine grained states.

              The agents are a sort of chain of states. An elementary form would be a set of qubits or quNits, where a 1-dim case is something like the Ising model in 1-dim. P. Gibbs has a paper that expounds on this in this essay contest. In my papers, more within a technical supplement section, I also discuss a chain of this sort for S-matrix.

              Cheers LC

              Dear Sir,

              We have clarified earlier that we are raising these issue only with you because of your independent thinking. Hence kindly bear with us some more.

              We raised those points on strings only to highlight how quantum physics is sprawling uncontrollably instead of consolidating itself. But has anyone "seen" a string? We have seen pictures of "foams". But has it been discovered in a laboratory or is it simply the Artist's impression? Something that is built upon imagination cannot be physics. True, modern research is based on hypothesis and modelling. But it has to be backed up by physical evidence of its existence within a reasonable time. Unfortunately, we go on building "theory" in an incremental manner based on "established theories", even though such theories are never experimentally established. One example is the extra dimensions, which has not been experimentally established even after more than a century. But still we build theories on such fantasy. How long we will continue like this?

              Regarding consciousness, you have brought out an interesting point. You say: "Consider for example a probabilistic machine which has been trained on a data set". Who built the machine and who trained it? It must be a conscious agent. It "can receive a "jolt" when it receives instructions to flip a coin". But any "intelligent machine" is a GIGO - garbage in garbage out! It can't act beyond its programming. It can't solve problems it has not been programmed for. The flipping of a coin can only describe a probability. But the universe is not a probability - it is highly ordered. Who ordered that?

              Regarding D-instanton, we leave it for the time being, as we would like discussing the basics leading to the present theory. We find some problems with the application of Riemannian geometry, which was developed to solve the problem of curvature of hot metal plates when they were heated. We question its application in physics without considering all of its implications. Then we question the identification of direction and dimension as interchangeable, which we have discussed in various threads here.

              What we propose is to rewrite physical theories based on presently available data instead of continuing with modifying earlier theories, because in most cases, it has gone beyond recognition and mostly built upon fantasy foundations. Why scientific papers can't be written precisely defining everything as we have done in our essay:

              "INFORMATION HIDES IN THE GLARE OF REALITY by basudeba mishra:

              http://fqxi.org/community/forum/topic/1776"?

              Regards,

              basudeba

              6 days later

              Jonathan,

              I decided to check in on your essay area. I'm sorry to see it lagging a bit. I gave you a 10 when it first showed up, but unfortunately that might not have been enough.

              If you read my essay the first part of this is an argument that nature can't be completely mapped into some formal systems, such as an algorithm that processes bits or qubits. My argument is in line with David Hume's argument against the naturalist fallacy. I agree that nature can't be codified completely in an axiomatic-information form.

              Cheers LC

              Jonathan,

              If given the time and the wits to evaluate over 120 more entries, I have a month to try. My seemingly whimsical title, "It's good to be the king," is serious about our subject.

              Jim

              7 days later

              Jonathen,

              Excellent job, and interesting subject. Your smooth easy to read style is also something I can only aspire to.

              Starting at the finish; Extra point as I'm a Wittgenstein fan. Then a bonus for "...may remain forever shrouded in the murk of statistical noise."

              I'd like to suggest that statistics may perhaps be missing a trick, and indeed hiding the solution to the noise. You earlier refer to the; "three competing demands: Accuracy, Simplicity, and Stability."

              What if there was another? What if there was a parameter the data set used in the analysis omitted? Like perhaps some 'hidden dimensions' in a hidden 'layer' of phase or sample space not studied? We may then call the demand 'Scope'. The scope may then include significant 'noise'.

              In the EPR case, let's say Dr Bertlemann has drawers full of green and red STRIPED socks, each different proportions of red and green, but all pairs adding up to the same. Using 0,1 we only ask; red, or green?. So called 'weak measurement' (really strong statistics) will then find nothing else but red/green. A pair of roughly equal r/g socks may give a 50:50 return, yet if we also asked 'how' green/red? both Bob and Alice might also find a local Bayesian cosine distribution around an 'orbit'. I find they do in my essay, and that John von Neumann agreed, as indeed did Bell resolving the paradox.

              My essay builds a multi component ontological construction suggesting a consistent physical model, invoking Malus' Law but also proposing a new law in line with Joe's uniqueness proposal above. That then proves more useful than you have yet found.

              I'd be delighted for your views if you can find the time to read it. Bill McHarris's essay on nonlinearity and chaos theory is also worth reading, and I believe others, including Gordon Watson's mathematical model are consistent.

              But well done for yours, which I have down for a top mark when coming to score as I think it's greatly undervalued.

              Best of luck.

              Peter

              4 days later

              Dear Jonathan J Heckman:

              I am an old physician, and I don't know nothing of mathematics and almost nothing of physics, but after the common people your discipline is the one that uses more the so called "time" than any other.

              I am sending you a practical summary, so you can easy decide if you read or not my essay "The deep nature of reality".

              I am convince you would be interested in reading it. ( most people don't understand it, and is not just because of my bad English). Hawking, "A brief history of time" where he said , "Which is the nature of time?" yes he don't know what time is, and also continue saying............Some day this answer could seem to us "obvious", as much than that the earth rotate around the sun....." In fact the answer is "obvious", but how he could say that, if he didn't know what's time? In fact he is predicting that is going to be an answer, and that this one will be "obvious", I think that with this adjective, he is implying: simple and easy to understand. Maybe he felt it and couldn't explain it with words. We have anthropologic proves that man measure "time" since more than 30.000 years ago, much, much later came science, mathematics and physics that learn to measure "time" from primitive men, adopted the idea and the systems of measurement, but also acquired the incognita of the experimental "time" meaning. Out of common use physics is the science that needs and use more the measurement of what everybody calls "time" and the discipline came to believe it as their own. I always said that to understand the "time" experimental meaning there is not need to know mathematics or physics, as the "time" creators and users didn't. Instead of my opinion I would give Einstein's "Ideas and Opinions" pg. 354 "Space, time, and event, are free creations of human intelligence, tools of thought" he use to call them pre-scientific concepts from which mankind forgot its meanings, he never wrote a whole page about "time" he also use to evade the use of the word, in general relativity when he refer how gravitational force and speed affect "time", he does not use the word "time" instead he would say, speed and gravitational force slows clock movement or "motion", instead of saying that slows "time". FQXi member Andreas Albrecht said that. When asked the question, "What is time?", Einstein gave a pragmatic response: "Time," he said, "is what clocks measure and nothing more." He knew that "time" was a man creation, but he didn't know what man is measuring with the clock.

              I insist, that for "measuring motion" we should always and only use a unique: "constant" or "uniform" "motion" to measure "no constant motions" "which integrates and form part of every change and transformation in every physical thing. Why? because is the only kind of "motion" whose characteristics allow it, to be divided in equal parts as Egyptians and Sumerians did it, giving born to "motion fractions", which I call "motion units" as hours, minutes and seconds. "Motion" which is the real thing, was always hide behind time, and covert by its shadow, it was hide in front everybody eyes, during at least two millenniums at hand of almost everybody. Which is the difference in physics between using the so-called time or using "motion"?, time just has been used to measure the "duration" of different phenomena, why only for that? Because it was impossible for physicists to relate a mysterious time with the rest of the physical elements of known characteristics, without knowing what time is and which its physical characteristics were. On the other hand "motion" is not something mysterious, it is a quality or physical property of all things, and can be related with all of them, this is a huge difference especially for theoretical physics I believe. I as a physician with this find I was able to do quite a few things. I imagine a physicist with this can make marvelous things.

              With my best whishes

              Héctor