Thanks, Joe. So many essays to read, not nearly enough time. I hope I have the requisite understanding to give you some good feedback. Any thoughts on Digital Physics?

Jon

Thanks for the response, Gary.

I'm not sure if you could actually have a continuous universe that was finite. I assume you are imaging a continuous universe that is bounded, say by the observable universe or something similar. A math analogy: You might say that the interval of real numbers between 0 and 1 is continuous and finite, but I would say that you have the infinite in the form of the infinitesimal because you implicitly believe in infinite precision non-computable real numbers when you believe in the continuum. Infinite precision non-computable real numbers are what make up the continuum in a mathematical sense.

A discrete universe would rule out a continuous wave, just like a computer couldn't actually contain the infinite amount of information needed to represent every point on a curve... although it could contain the finite algorithm to generate the wave to any desired level of accuracy... It just can't contain the non-compuable, which is what makes the continuum the continuum.

Jon

Thanks for the response, Gary.

I'm not sure if you could actually have a continuous universe that was finite. I assume you are imaging a continuous universe that is bounded, say by the observable universe or something similar. A math analogy: You might say that the interval of real numbers between 0 and 1 is continuous and finite, but I would say that you have the infinite in the form of the infinitesimal because you implicitly believe in infinite precision non-computable real numbers when you believe in the continuum. Infinite precision non-computable real numbers are what make up the continuum in a mathematical sense.

A discrete universe would rule out a continuous wave, just like a computer couldn't actually contain the infinite amount of information needed to represent every point on a curve... although it could contain the finite algorithm to generate the wave to any desired level of accuracy... It just can't contain the non-compuable, which is what makes the continuum the continuum.

Jon

Jon,

You should exchange comments with Akinbo Ojo if you have not already done so.

Now I understand what you mean. I will maintain that I think it is finite - as demonstrated by the Hubble Bubble. I will also state that I think it is continuous. My justification for this is that the electron is considered to be a point particle.

Essentially, I am an Aether believer. The fact that electrons are viewed as a distribution around a proton to me indicates that the vacuum is the source of the electrons and they simply rise up as needed due to the presence of a proton ... Basically, I think the electron is a vibration of the vacuum.

I don't think the universe needs to compute anything ... it simply is.

Best Regards and Good Luck,

Gary Simpson

    Jon; some new comments on my Essay Forum might interest you. Or maybe just start there with some pressing questions? (Remembering that the maths is not difficult.)

    With best regards; Gordon Watson: Essay Forum.

    I give you a mathematical argument and you come back with the Hubble Bubble!? :) I don't even know how that relates, partially because I had never heard of it, and partially because my skimming of Wikipedia didn't give me too much insight. I sort of get your point with the point electron, but I would say that if you inspect these models that you think are accurate representations, you have to decide whether you believe if any continuous thing that the models represents is always fully formed (infinite) or if they are generated from a calculation done using the model (finite). Again, a wave equation or distribution is fine from a digital perspective if things are only discretely generated into existence, but if they exist always and continuously, I think you have the infinite on your hands.

    Anyway, I have talked with Akinbo, but he didn't convince me that I couldn't have movement in a digital universe, although I did enjoy his essay. (see our discussion above) Long live digital physics:)

    Hubble Bubble ... yes. It is the observable universe. It is everything within a radius of roughly 13.8 billion light years. My argument is why should I believe there is anything outside of that? The standard thinking is that we cannot be at the center of the universe and therefore the observed expansion must be the same everywhere. The reason for following that line of thinking is that scientists do not want to make the same mistake of geo-centrism made prior to Copernicus. I will reply that what is observed does not require that we be at the center. It only requires that we are moving slowly compared to those objects at the edge of the visible universe. This points out the essence of the math vs physics question. Observation has been replaced by speculation ... even good and reasonable speculation is still speculation.

    Best Regards and Good Luck,

    Gary Simpson

    4 days later

    Dear Jonathan,

    Thank you for pointing out your interesting video. Did you submit it at the FQXI video contest?

    There is some form of determinism-geometry-topology-algebra that underlies the observables of multiple qubits. This has been my topic with collaborators for the last 10 years. Also the structure of primes plays a role, there are a few references in my essay that, I admit, may not be so easy to read in a single shot.

    Good to have your essay that provides a different taste to the contest.

    Best,

    Michel

      Jonathan,

      At last a serious attempt to comprehensively tackle an important and potentially dead boring subject in a way guaranteed to keep the reader awake and wondering what planet he's on. Quite brilliant. When does it go on general release?

      Can I assume you saw my own video? a full length feature film on how the whole universe works, blue shifted to gamma to compress to a 9 minute run time?

      (if not; How universes work in 9 mins. ).

      Thanks for your nice comments on my string. perhaps you or a friend can tell me if you understood my essay, video and quasi QM papers, and if so explain them to me in words or pictures of any number of syllables but without using dodgy manipulation of ancient Arabic symbols or Tarot cards? (I think those should come later).

      Real nice job.

      Peter

        Hi Michel,

        Thanks for the post. I did not submit the movie to the FQXi video contest since it is a feature length movie that I am trying to get into festivals and will eventually distribute. I guess I could have submitted the trailer, but I didn't think that it was relevant enough for the contest.

        I plan to look at the your essay more in depth sometime soon. Primes in physics is an interesting concept. Do you look at them statistically as the prime number theorem does, or deterministically as a sieve does?

        Jon

        Dear Jon,

        I enjoyed the quotes from Khatchig. I would love to see the movie. And the satirical abstract was very amusing, thanks!

        Best wishes in the contest,

        Cristi

          Dear Jonathan,

          I like your thought provoking essay. I would like to comment on one of your Dedekind cuts where you say " Show me one place where

          infinity exists in the natural world! Show me one infinite or continuous process!" Isn´t the total seconds of the Universe and infinite amount? or do you think that because everything is finite, the Universe must recollapse in a singularity in the future such that no observer can experience an infinite amount of proper time?

          Kind Regards,

          Yafet

            Dear Jonathan,

            I did not see your above reply until just now. I revisited your blog to bring to your attention an essay by Tommaso Bolognesi which I thought you might enjoy because it has something of a movie script quality to it.

            Now to answer your questions:

            "Are you saying that you think light cones should really be depicted as warped images instead of perfect cones?"

            No, I am saying that, in my view, the boundaries of lightcones should properly not be considered regions of spacetime. To give a somewhat misleading analogy, a zero-dimensional point cannot be considered a "region of space" because it cannot contain any objects in space.

            Where the analogy is misleading is that Euclidean space has only one kind of object that is characterized by the fact that every neighboring point is separated from its center by zero distance: A zero dimensional point; but Minkowski space time has two: A zero-dimensional point and the boundary of a light cone. In this sense, the latter is a second type of "point- like object" for which we, who intuitively perceive ourselves as inhabitants of a 3D Euclidean space have absolutely zero intuition, and this is the reason, I think, that this has not been yet recognized.

            If you accept that the boundaries of light cones are not regions of spacetime, then logically things which are constrained to exist only there, like photons, cannot be said to exist in spacetime. That special relativity gives us hints that this is indeed the case, starting from the fact that no spacetime observer can transform to a photon rest frame, was essentially what my vixra paper referenced above was driving at. Again, ultimately I think it will take a mathematical proof that the topology of spacetime really is intrinsically different from the topology of Euclidean space to convince others that this is the case.

            "If so, that sort of makes sense in a world where matter warps spacetime... unless the warping of space and time perfectly offset each other so that the light cone looks normal for any object, whether it is near massive bodies or not. (I feel like my understanding is not right, so forgive me if I am off base)"

            You are forgiven;) usually what people mean by the "warping" of space and time is that there are coefficients (and sometimes more involved combinations of terms) for the space and time terms different from the constant 1 (in Cartesian coordinates) which modify the metric relations at particular points. Importantly, these metrics are never expressed in such a way that the spacetime interval gains a coefficient different from 1 , because it is the invariant quantity, whereas space and time are separately not invariant. But even if you changed the coefficients of the space and time terms so that it would become equivalent to multiplying the metric interval by a coefficient not equal to 1, which amounts to scaling it, it would still be the case that ds=0 describes the boundary of a lightcone.

            "I will try to respond to some of your explanations that you offered on your page to some of my questions, but I do remember thinking that some of it was a little over my head. Oh well, maybe I'll google some stuff and try to understand it a little better."

            Well, I appreciate your interest in my ideas, if you have any questions let me know, you can also email me.

            Best wishes,

            Armin

            Dear Jonathan,

            My most recent paper is very close to Riemann idea of counting the primes statistically and of course connects to Riemann hypothesis (RH).

            http://xxx.lanl.gov/abs/1410.1083

            Also

            http://xxx.lanl.gov/abs/1103.2608

            (in particular the Hardy-Littlewood function and RH, and a connection to qudits)

            Michel

            Thanks for reading my essay, Yafet.

            Even if there won't be a big crunch, I think there should be a distinction between actual infinity and potential infinity. I think you would agree that we would never reach a point where we could say that an infinite number of seconds had passed sinced the big bang, right?

            Jon

            Thanks for coming back, Armin. And thanks for pointing me in the direction of Tommaso's essay! Besides being an entertaining way of presenting the ideas, Tommaso's story also has a lot of themes that are very similar to ideas presented in Digital Physics, so it's nice to see some people thinking along the same lines as the main character in the movie.

            Your talk of how a point-like boundary of a light cone does not really exist in our universe reminds me very much of digital physics in the sense that you cannot have infinite precision objects existing in digital physics. Everything should be either inside the cone or outside. Would you say that you don't believe that the continuum exists in space or time or spacetime?

            Jon

            Thanks, Cristi!

            I'm glad you found the satirical abstract amusing... subtle, heretical, mathematical humor doesn't always go over well:)

            I hope you get to see the movie sometime soon!

            Jon

            Hey Peter.

            I'm glad "Digital Physics" is something you've been waiting for. I hope it keeps people awake:)

            I didn't see your video, so thanks for sharing it. I'm going to have to google some stuff before I try to take it in again. Are you familiar with Roger Penrose's [link:www.youtube.com/watch?v=hAWyex1GKRU]twistor model?[link] I'm not sure if this relates to your video, but the visualization's of your video did remind me of his talk.

            Jon

            Hi Jon,

            I think our way of conceptualizing whether spacetime is continuous or not is shaped very strongly by our intuitions, which however mislead us into perceiving our existence to be in 3-D Euclidean space plus time. But once you accept that there are two kinds of "point-like" objects in Minkowski spacetime, then this has to be taken account when considering the answer to your question.

            I believe the answer is that spacetime is continuous in terms of ordinary zero dimensional points, just as in the mathematical model (This implies, in particular, that all the spacetime symmetries are preserved, or, in some sense, fundamental). On the the other hand, lightcones are already characterized by discontinuity by virtue of how they separate time-like regions from space-like regions in certain directions (namely those which require crossing v=c either from below or from above).

            My idea about spacetime emerging from areatime might at first give the impression that it requires spacetime to be discontinuous with respect to the former, but I think that is not necessary because I take the "substrate" from which the emergence takes place, or, in other words, the limit in which spacetime vanishes, to be the boundary of the lightcone (which brings me back to the point of my previous post).

            I hope I could make things a little clearer.

            Armin