Hector nice essay.

From an artistic perspective, I view the behavior of the universe as a reproductive system. Interesting enough, if you view a reproductive system as a set of random events, or you view it as a predictable (algorithmic) set of events, the resulting distribution is pretty much the same in either case.

That is the link to the Fibonnaci series I elude to in my essay. Check it out if you get a chance at http://fqxi.org/community/forum/topic/893.

Good Luck

Pete

    Dear dr ZENIL,

    Your essay is very understandable and readable, but I dont see the universe as a computer, I quite understand that humans created this machine and for that they had to design a way in which this machine really could make computations, these computations resulted in images and sounds that our senses sight and hearing could interprete as a virtual reality, the point is still the same it is "to be or not to be", the virtual universe we are creating out of the zero's and the one's is just ONE possibilllity that we have as mankind to CREATE, as I put it in my essay when we are in the possibillity to create a consciousnes that exists in this virtual reality we move one step further in the understanding of our own consciousness, this new consciousness however has all the restrictions of the DIGITAL essence, it is a second hand reality from our point of vieuw.

    Analogue may also mean ONE, the continuity of the whole, not made of two units, when science will be able to construct a quantum "computer" there is a infinity of superpositions to choose, and all the answers of all the possible questions are in facto "present" even when he is not connected to the electricity, we can see that as a ONE, for achieving that we have to bring back choices to one...

    kind regards

    Wilhelmus de Wilde

      Hello, Hector

      Thanks for a well-written essay, which I read with keen interest. I like your (French!) style of clear analysis and expression. The strategy of comparing the evolution of patterns in nature and in computer programs seems very promising. I do have some comments about certain passages, and would like to know your response to them.

      "Lossless compressibility" [p9] may apply perfectly to a pattern that is already defined (like files in your computer), but only imperfectly to natural patterns (data from observations). Your result that "most empirical data carries an algorithmic signal" seems simply to restate the fact that there are evident patterns in the world. I cannot take this to mean, however, that the world in itself is pure ordered pattern, fully accountable in a set of algorithms. That seems too great a leap. Am I missing something?

      [p5] You say that "Producing random bits in a deterministic universe...would actually be very expensive..." But isn't this an argument AGAINST determinism? Perhaps nature cannot be forced into a mold that defines it either as deterministic or as non-deterministic. This could be the case if 'determinism' is actually a purely logico-mathematical concept and not ascertainable as an ontologically physical reality. The meaning of 'determinism' may be nothing other than logical implication (computability). We are free to project this upon nature, but isn't it really our own invention? Similarly, we are free to imagine the universe as driven by simple algorithms (after all this works to some extent!). The really interesting thing, to me, is our apparent human need to know what the universe is in itself, in ultimate terms, apart from simply understanding what knowledge is (or can be) for us. Perhaps it is human thought that is driven by simple algorithms!

      [p4] From an engineering point of view, "what makes a cup a cup" is information; but from a physics point of view, what makes a cup a cup is structure. They may seem to coincide in the cup, which is an artifact, more than in the case of the human body, which is not. Information is effectively a set of instructions to the engineer to build the cup (a program). No engineer, however, knows how to build a human body or any natural thing. (The cup too--as a physical thing rather than a conceptual thing--is made of natural materials.) Such knowledge presupposes a blueprint from which to construct the natural entity. But a natural thing does not come with a blueprint, and anything looking like its blueprint is actually a product of an analysis that can never be assumed complete or exhaustive. The natural thing is found, the simulation (and the information behind it) is made. I suspect this applies to atoms as well as cups.

      [p5] You say "if information is even more fundamental than the matter of which it is made and the physical laws governing that matter, then the question of whether these effects violate physical laws may be irrelevant." That is a big 'if'! The very question to be decided! It would undeniably be convenient if natural reality were fundamentally "informational", but that does not make it so. In the medieval world, violation of physical law was similarly irrelevant, because an omnipotent God was ultimately the cause of everything, including natural law and miracles!

      [p8 re: "DNA construction] I think it is unfair to dismiss the interaction with environment as not a "true random function operating on the DNA". What is a 'true random function'? Even by a mathematical definition, one cannot prove randomness. How then to apply this to the real world? Perhaps we can say no more than that DNA construction, like the evolution of the universe as a whole, involves an interplay of predictable and unpredictable factors.

      Thanks again and best wishes,

      Dan

        Hello Dan,

        Thanks for your kind comments. Here are my answers to your interesting questions:

        You say:

        ""Lossless compressibility" [p9] may apply perfectly to a pattern that is already defined (like files in your computer), but only imperfectly to natural patterns (data from observations). Your result that "most empirical data carries an algorithmic signal" seems simply to restate the fact that there are evident patterns in the world. I cannot take this to mean, however, that the world in itself is pure ordered pattern, fully accountable in a set of algorithms. That seems too great a leap. Am I missing something?"

        You are not missing anything, you make a fair point. That, as you say, may be the case. Ii find, however, interesting the fact that this 'algorithmic signal' seems to be present everywhere and that it can actually be quantified. There is a researcher that takes your point to the extreme, that empirical data sets are algorithmically random, you may be interested (although I cannot agree with his conclusions):

        James McAllister's 2003 article, "Algorithmic randomness in empirical data" Studies in History and Philosophy of Science Part A 34 (3):633-646.

        See also a strong reply:

        Charles Twardy, Steve Gardner & David Dowe (2005). Empirical Data Sets Are Algorithmically Compressible: Reply to McAllister. Studies in the History and Philosophy of Science, Part A 36 (2):391-402.

        You say:

        "[p5] You say that "Producing random bits in a deterministic universe...would actually be very expensive..." But isn't this an argument AGAINST determinism? Perhaps nature cannot be forced into a mold that defines it either as deterministic or as non-deterministic. This could be the case if 'determinism' is actually a purely logico-mathematical concept and not ascertainable as an ontologically physical reality. The meaning of 'determinism' may be nothing other than logical implication (computability)."

        Yes, if a deterministic universe were able to produce true random bits that would be an argument against determinism if I were ready to accept that that actually happens (as Quantum Mechanics may imply). If I consider this possibility is only to explain that classical mechanics implies a deterministic universe yet quantum mechanics is supposed to be a source of free randomness which is one of the deepest contradictions between these two mainstream theories. I only point out that if the universe is deterministic as one may believe (as I do), then there is this fundamental incompatibility.

        You say:

        "We are free to project this upon nature, but isn't it really our own invention? Similarly, we are free to imagine the universe as driven by simple algorithms (after all this works to some extent!). The really interesting thing, to me, is our apparent human need to know what the universe is in itself, in ultimate terms, apart from simply understanding what knowledge is (or can be) for us. Perhaps it is human thought that is driven by simple algorithms!"

        Yes, it might be a projection, or even a mirage. But when a mirage works well (i.e. seems to explain and predict something) we use to call it a scientific model. I think it is fair to think that the world is based in simple rules if it turns out that, as it seems to be the case, it is comprehensible in a large extent with simple models of the world (including current scientific theories governed by simple formulae). If these simple rules turn out to produce the complexity we see around I think one can safely assume that they may be the responsible for the organized complexity in the world. It could, of course, be the case, that nature is fooling us making us to believe that rules are simple but actually are very complicated, looking only simple at the surface.

        "[p4] From an engineering point of view, "what makes a cup a cup" is information; but from a physics point of view, what makes a cup a cup is structure. They may seem to coincide in the cup, which is an artifact, more than in the case of the human body, which is not. Information is effectively a set of instructions to the engineer to build the cup (a program). No engineer, however, knows how to build a human body or any natural thing. (The cup too--as a physical thing rather than a conceptual thing--is made of natural materials.) Such knowledge presupposes a blueprint from which to construct the natural entity. But a natural thing does not come with a blueprint, and anything looking like its blueprint is actually a product of an analysis that can never be assumed complete or exhaustive. The natural thing is found, the simulation (and the information behind it) is made. I suspect this applies to atoms as well as cups."

        But a blueprint is a description which tells someone (if not you then nature) how to build something. The claim that only information makes a cup a cup rather than a human being is because both human beings and cups are made exactly of the same elementary particles and it is nothing but the way they are arranged that make one or the other. But let me know how that could be wrong from a purely materialist point of view.

        You say:

        "[p5] You say "if information is even more fundamental than the matter of which it is made and the physical laws governing that matter, then the question of whether these effects violate physical laws may be irrelevant." That is a big 'if'!"

        Of course that is a big 'if', I would only dare to say so in a foundational question essay. Notice, however, that several authors think of information as more fundamental than physics itself. And it is a common practice in science to find all the time more fundamental structures on which previous ones were lying on. I don't have may troubles seeing information as more fundamental than matter but of course some may disagree (as they do, such as e.g. David Deutsch).

        "The very question to be decided! It would undeniably be convenient if natural reality were fundamentally "informational", but that does not make it so. In the medieval world, violation of physical law was similarly irrelevant, because an omnipotent God was ultimately the cause of everything, including natural law and miracles!"

        Right, but I don't think we are going backwards, replacement of explanations that were once laws before is a common practice, if not the goal, of science, and the replacement seems to have a direction in the form of models that explain more and more phenomena and have greater prediction power. Of course saying that the world is something won't make it that something, but when you find that something smells, looks and behaves as something one can be persuaded that it is this something. In this case, it seems clear that information is, in the worst scenario, something as fundamental (even if it is a worldview and not necessarily an ontological truth) as other variables in the physical world (matter, energy). Whether this is the case or not we will see or we may never know. Notice, however, that many physicists have jumped to similar conclusions even if they are treated differently, by giving the concept of symmetry (that you may see as information or an abstract mathematical object) a foundational role for even predicting the existence of new particles, that so far has been quite successful.

        "[p8 re: "DNA construction] I think it is unfair to dismiss the interaction with environment as not a "true random function operating on the DNA"."

        It is a generalized agreement that the macro world is fully deterministic and does not produce indeterministic randomness, so mutation may be only truly a random process if based on quantum mechanics based on current physics.

        "What is a 'true random function'? Even by a mathematical definition, one cannot prove randomness."

        When I write true random function I mean a function capable of producing truly independent random bits just as predicted by the mainstream interpretation of QM.

        Thanks Dan, very interesting questions.

        - Hector

        Thanks Pete. Vey nice and Interesting essay, I like your artistic point of view.

        I discuss a bit the relationship of an object vs. its pictorial representation in this paper (in joint with Delahaye and Gaucherel) that you may find interesting as related to the concept of physical complexity:

        Image Characterization and Classification by Physical Complexity, available online at http://arxiv.org/pdf/1006.0051

        Best regards.

        Dear Peter,

        Thank you for sharing and for your encouragement.

        The claim that only information makes a cup a cup rather than a human being is because both human beings and cups are made exactly of the same elementary particles and it is nothing but the way they are arranged that make one or the other. But let me know how that could be wrong from a purely materialist point of view.

        Sincerely.

        Dear Edwin,

        Interesting comments. I agree with you on some points, I hope to find time soon to elaborate further and give you a more proper answer.

        Thanks for your kind words.

        Sincerely.

        Rafael,

        Thanks for your comments. You are right that I didn't jump to making claims on what the universe may be truly made off, or whether it may turn out to be digital or not. I prefer to leave the readers withdraw that conclusion by looking that an algorithmic world would not really need to assume but the kind of digital computations. Yet, my view is compatible with an analog algorithmic world. I explain, however, why I think that may not be the case, because it would look more like the uncomputable (truly random in the strictest mathematical sense) digits of a Chaitin Omega number rather than the more ordered digits of the mathematical constant Pi, random-looking but deterministic and plenty of algorithmic structure, as I think may be the case of the real world.

        I don't think most people think that the universe is digital by the way it unfolds, I think this is a rather different view of mine, or if not a novel view a novel statistical treatment based in an empirical distribution and the concept algorithmic probability undertaken in my research project. Yet, I don't conclude from there that the world is digital, even if I (as do the results) suggest that there is no need to think it is analog.

        Sincerely.

        Good afternoon (or the time you may read this post) Hector Zenil

        I did not at all want to offend you in my post, on the contrary you gave me a lot of reasons to continue for the search of understanding our universe and explainede very clear how the "technical" side of our community is searching for more knowledge.

        I would like to join to my post that in my opinion there is a difference between Intelligence and Consciousnes, with our total intelligence we can construct the LHC, but it is our consciousnes that asks always WHY, like a child that won't stop asking WHY, the HOW is the intelligence and the Why our consciousnes, the intelligence can be constructed by our (Turing)machines, but the consciousness untill now we could not reproduce so this is perhaps not a digital "substance", so not reproducable in the digital way (?), like a piece of art, you can copy it but the copy will never be the original.

        The way we experience "reality" is different for every one, but seems to be analoguefor a majority, (ana = from logos= reason) so the way our reason interpretes it becomes reality, but this also means that there multiple interpretations, from which the digital interpretation is only one.

        Perhaps my interpretation is not the one of a pure scientist like yourself, but I think that this is the richness of the rainbow of thoughts so beautiful expressed in this contest.

        I wish you a lot of luck (digital ?) in the contest

        and

        best regards

        Wilhelmus de Wilde

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        • Post #115

        Hi dear Hector you say "In any case, the main argument holds, that Pi is simpler to calculate by throwing bits that one interpret as instructions of a computer language, disregarding the language (or if you prefer rules), but it is much harder if you want to generate any number of digits of Pi by throwing the digits themselves into the air. This is because programs of Pi will be always short in relation to its expansion"

        Could you develop, it's relevant that...

        Regards

        Steve

        • [deleted]

        • Post #116

        because for a real understanding of the theory of numbers, the reals and the continuity and discretness .....it must have a difference between the physicality and its distribution rational, the infinity behind our walls.And the adds and infinities invented by humans due to some adds or mult.Now if we take this language, mathematical, as the computing, don't forget it's a human invention where we create codes of continuities, where sometimes the categories permits the synchro and the sortings. Of course it's a beautiful machine and its language is logic, but for the simulations, the laws can be changed and thus the conclusions loose the real uniersal sense. It's essential when we want really interpret our reality objective physical. I can for example simulate the mass of stars and planets, or BH , that doesn't mean it's real...there we return about a very beautiful work of Eckard about the axiomatization rational of our reals with a real unity, 1 and reals domains.All is there in fact,the 0,- and infinity aren't reazlly real in their pure number and its distribution, spherical.

        The language is the same because the maths are the maths but the reals are better than imaginaries ....the strings are a beautiful tool for the 2d picture , I prefer a spherical membran, oscillating and we can thus simulate the mass also,it's more logic, the programm just needs a little improvement inserting the number of the ultim entanglement of spheres.and their volumes from the main central sphere.In all case, the duality wave particle can be harmonized due to the proportions with mass.The strings were an idea, this idea can be universalized simply in the spherical logic in 3D.

        Dear Hector, could you explain me the algorythms, If I know the principle, I can invent several models of sortings and synchro.Could you explain me how is the base of computing , this language in fact is logic and mathematic,but what is an algorythm of sorting for example, you insert what the volumes??? Or a serie, ....in fact how I have the pictures here at home on my pc for example.

        Steve

        Dear Wilhelmus de Wilde,

        You didn't offend me at all. I appreciate your comments.

        Best.

        Thank you so much, Hector, for your thoughtful and patient replies. I haven't been able to access McAllister's 2003 article, but I did read the Twardy et. al. reply, which I think fairly refutes McAllister's claims when interpreted in narrow terms. However, I did read a more recent piece by McAllister (2009) "What do patterns in empirical data tell us about the structure of the world", from which I can see that he hasn't given up! His two main points there, liberally interpreted, seem to be (1) 'noise' is relative and may be mined for further pattern (signal), and (2) there is a sense in which 'pattern' is in the eye of the beholder. I would agree fully with (1), while acknowledging the usefulness of provisionally disregarding noise in pattern extraction. While I think he may go too far in his case for (2), there is something in the spirit of it that would certainly be useful should we ever have to confront alien scientists! In any case, it seems a wise proviso for human researchers to bear in mind.

        In your reply you say:

        "I only point out that if the universe is deterministic as one may believe (as I do), then there is this fundamental incompatibility [between randomness and determinism]."

        My point is that the universe can only be deterministic if it happens to coincide perfectly with some formalism, for only such deductive systems are truly deterministic (i.e. the only meaning that can actually be assigned to causality is logical implication within some deductive system). In other words (to put it somewhat outlandishly), the universe can only be deterministic if it is not natural but artificial; conversely, if it is natural, it cannot be fully and finally mapped in any formalism. On the other hand, we are not in a position to say that it is fundamentally indeterministic either, since (mathematical) randomness cannot proven. This is why I wonder at the basic human impulse to assert a "truth of the matter" one way or the other, since it seems hopeless to establish that. I hope I am not trying your patience too much, but I would very much value your feedback to these ideas.

        You reply also:

        "But a blueprint is a description which tells someone (if not you then nature) how to build something. The claim that only information makes a cup a cup rather than a human being is because both human beings and cups are made exactly of the same elementary particles and it is nothing but the way they are arranged that make one or the other. But let me know how that could be wrong from a purely materialist point of view."

        While perhaps useful, I think it is a mistake to project human communication models upon nature. We should not assume that nature engages in some form of information processing or computation, along the lines utilized by human beings. We cannot assume that we possess the (complete) information involved in the structure of a natural thing, which is not made by us but found in an incompletely known state. In the sense hinted at by McAllister, the information is made by us, and we can never be sure how exhaustively (or correctly) it describes the real thing. We only know for certain the blueprints we literally make, not the blueprints we impute to nature.

        Thanks again for the clarity of your thinking and your willingness to respond.

        Dan

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        • Post #119

        The continuity rational seems lost in the pure confusions, why just because the reals are correlated witht he biggest rationality.The cotegorification of sortings in computing seems the cause, due to the adapted algorythms probably.That's why probably we have some bizare simulations.In logic a real turing machine seems rational, it can't simply be an irrational road simply.

        Dear Hector, you say"By definition, a continuum is a body that can be continually sub-divided into infinitesimal elements" I am not sure about that, really,that implies some confusions about the real meaning of the infinities.And the finite numbers! DEFINITING MASS FOR EXAMPLE.thus what is this fractilization, I think there is a little problem.A continuum is more than that,the time operator seems confound with the fractal of a body which is in logic finite in its pure newtonian fractalization.I can understand the difference with the 2d computing and the waves correlated with the fractal of this digit,a kind of unity...that permits the 2d forms ok but the strings aren't foundamental for our universe ,a spherical 3d sphere and the picalculus improved with a better fractal for the digit of this 3D sphere and its spherical membran forming all systems....if the rotations are proportional with mass and if the fractal is finite and precise in its decreasing of volumes.....3D spherical computer holographic .....a program of convergences will be easy, and after we can simulate correctly at my humble opinion, I AM PERSUADED THAT lAWRENCE CAN MADE THAT for the 3D holographic computer and its turing universality....the work of Pierce seems relevant about the real axiomatization , the caratheodory method also and the real proportionalities....the convergences seem easy between this 2d towards the 3D universal......the Mtheory is too weak simply ...3DSPHERES AND SPHERIZATION DEAR ALL .

        Regards

        Steve

        Our reasoning and empiri-cal findings suggest that the information in the world is the result of processesresembling computer programs rather than of dynamics characteristic of a more random, or analog, world.9

        Hector,

        This is a well-supported perspective, ably argued.

        My prejudice is that the above only proves humankind's approach to understanding reality but my argument tends to lack your many details.

        Jim Hoover

        Hi Hector

        You said; "The claim that only information makes a cup a cup rather than a human being is because both human beings and cups are made exactly of the same elementary particles and it is nothing but the way they are arranged that make one or the other. But let me know how that could be wrong from a purely materialist point of view."

        I think the word 'makes' is the key, as it implies causality. I must entirely agree 'information' may be a good word to describe the difference, but the whole gamut of my own thesis here is that, while we can 'describe' something from any viewpoint, description is once removed from the reality of something, as so well described by Georgina in the most foundational terms. Correcting only this seems to bring Occam's razor into action.

        Linguistic semantics apart, information is the difference in superposed wave patterns, causality is the interaction of it, and only allowed by qauntization. Therefore if either waves or particles were removed we'd be in the proverbial!

        Do have a look at this easy read paper, with photographic evidence, if you're interested in the entertaining logical extension; http://vixra.org/abs/1102.0016

        Best wishes

        Peter

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        • Post #122

        Dear Dr. Hector Zenil,

        Since it is a ''leading essay'', I must check it for consistency; I hope to find the novel ideas in physics and clear proofs about the nature of the Universe. The essay seems to contain two separate stories about the origin of the universe and the algorithmic nature of the world. Since it is an contest about the nature of reality, let's begin with the proofs about the nature of the world: ''One may wonder whether the lossless compressibility of data is in any sense an indication of the discreteness of the world''.

        It is a completely senseless ''proof''. Now we can close all Physics' laboratories because we can find all fundamental information about the Universe by help of programmers and computer specialists. Programmers can tell us if gravity is analog or digital after a careful analysis of the compressibility of mp3 files. Dear Hector, please tell us more about discrete spacetime (spatial atoms) or a fundamental length scale by analyzing the compressibility of data. His further reasoning also is senseless: ''An analog world means that one can divide space and/or time into an infinite number of pieces, and that matter and everything else may be capable of following any of these infinitely many paths and convoluted trajectories''. You cannot divide space and/or time into an infinite number of pieces because it is forbidden by Heisenberg uncertainty principle. If you try to penetrate in a very small region of space, you need more and more energy. Therefore it is no sense to speak about the lossless compressibility of data because we can find the same answer by analyzing the Heisenberg uncertainty. Moreover, I can say that since the computer programs are digital, it is an indication that the world is digital. This statement is absolutely equivalent to Hector's statement about compressibility of data, therefore we both ''deserve'' the same prize.

        Let's analyze the rest of Hector's essay: Everything out of nothing. The main problem in the cosmological theories which claims that the Universe started from nothing is to explain how a matter can appear from nothing. I don't see any solution for this problem in your essay. Why Hector use the title ''Everything out of nothing'', if he is not able to explain this problem? He writes: the universe began its existence as a single point; When the universe had cooled to the point where the simplest atoms could form'' - it are the old statements from the Big Bang theory. Thus, the first part of essay does not have any novel ideas, it is a story about Big-Bang-like theory.

        Let's analyze his statements about the algorithmic nature of the world. Dear Hector, please show us an algorithm for the free motion of a particle and Heisenberg uncertainty. Since you state that the universe is capable of performing digital computation, please show us how this imaginary computer can process motion of a particle and Heisenberg uncertainty. To process the motion of a particle, this computation must know the complete information about position and momentum before events occurs. In this case you should accept that your theory contradicts quantum mechanics.

        I can show you a place where the digital computation theory is wrong: 1) At the center of a black hole lies a gravitational singularity, a region where the spacetime curvature becomes infinite. Thus, at the center of a black hole a digital computation is not possible because spacetime curvature becomes infinite. You see, there are places and phenomena which exist without need in the digital computation. Since I found at least one place where the digital computation can not exist, it is a proof that this theory is wrong.

        Another flaws in Hector's essay: ''But at the lowest level, the most elementary particles, just like single bits, carry no information when they are not interacting with other particles''. It is an erroneous statement; even if a particle is born, one carries information about his kind, mass, charges and so on.

        Conclusions: The main conclusion of the essay about the nature of reality is absolutely senseless and unconvincing; I found neither proofs about the nature of the Universe nor novel ideas in this essay. The statement about computational nature of the Universe is very doubtful and contradicts quantum mechanics.

        It is a crime against humanity and science to support the false theories. There are advanced theories supported by nobody because all money is absorbed by false theories. The human race will NOT survive the next thousand years without teleportation and true Science.

        Sincerely,

        Constantin

          Dear Hector,

          I've made some progress with my novel idea of a helical screw in empty space as a model for the graviton. I've posted in another two leading essays so I'll copy and paste it here.

          On day-by-day thinking about the novel idea of a mechanical Archimedes screw in empty space representing the force of gravity by gravitons, I have deduced an explanation for the galaxy rotation curve anomaly.

          The helical screw model gives matter a new fundamental shape and dynamics which the standard model lacks imo. This non-spherical emission of gravitons is in stark contrast to the Newtonian/Einsteinian acceptance that "all things exert a gravitatinal field equally in all directions". This asymmetry of the gravitational field allows for the stars to experience a greater pull towards the galactic plane, due to their rotation giving more order to the inner fluid matter of the stellar core. Both the structure of the emitter and the absorber of the gravity particles is important. It also has implications for hidden matter at the centre of the galaxies..

          I've given the idea some more thought and come to the conclusion that the stars furthest from the galactic centre must have a more 'bipolar nature' than the matter of stars of the inner halo presumably. This is the reason they have wandered towards the galactic plane whilst the halo stars have not. The outer stars' configuration means they experience a greater interaction with the flux pattern of the graviton field. Are the stars of the outer arms simply spinning faster?? We are on the outer edge of a spiral arm and so this would fit with this hypothesis. Our sun could have spin which is higher that that of the average halo star. This relationship between spin and distance from the galactic centre is a fundamental feature which ties in with the suggested mechanism of their creation.

          All that is needed is an additional factor of stellar spin speed as well as it's mass and distance from the galactic centre. The relationship should then give calculated values which match those of the observed.

          Best wishes,

          Alan Lowey

          Constantin,

          Thanks for your comments. I find difficult to address your arguments agains my essay one by one because I think there is a misreading from your part at several levels but I will do my best to address some of the most fundamental.

          I can say, as I said before, that nothing in my essay is pretending to be a mathematical (or even physical) proof, it is statistical evidence in favor of a personal worldview (and an original research as acknowledged by my peers upon publication of my work in books and journals). I'd also like to tell, again, that I'm not even jumping to the conclusion that the world is digital but rather algorithmic, the reader can then jump to the digital hypothesis using Occam's razor, if they wish.

          I think I also clarified that my definition of the continuum is limited and I can acknowledge that you make a fair point, it is as limited as it was the space to talk about it in this contest. I could unpack more about the continuos case, but my main concern and what I stand for is that there is not even a general agreement of what continuity might be, while for the digital case the consensus is almost unanimous, both intuitively and formally in some extent.

          Concerning whether an elementary particle carries information, you say it carries its mass, size and so on. I do not agree, a particle may have these properties only when interpreted from outside, a particle only has mass when measured related to other matter, it has a location only when fixing an external framework, and it has a size only when compared to other things. The particle by itself, from my point of view, does not store any of these parameters in itself, and it is only when interacting with others that this information is possible chaining itself into other processes (this makes more sense if seen under my algorithmic view, because it is processes that gives the algorithmic sense to the world in my view).

          I see you are re-using your argument against Tommaso Bolognesi's essay regarding your claim that "At the center of a black hole lies a gravitational singularity, a region where the spacetime curvature becomes infinite. Thus, at the center of a black hole a digital computation is not possible because spacetime curvature becomes infinite." From it I guess it is you who claims to hold a proof that the world is analog, or at least that it is not discreet. Unfortunately, I don;t think the claim will convince most researchers, including me, simply because not knowing what happens inside a black hole doesn't rule out anything, but specially because physics as we know them are also inapplicable inside a black hole and scientists do not throw their theories away. But again, I'm not even standing strongly in favor of the digital hypothesis as I'm doing for the algorithmic case.

          Finally, most if not all of my essay is based in hard science, particularly the mathematical theory of information and computation, except for my particular worldview that this contest is encouraging people to share with others to trigger interesting discussions.

          I find difficult to argue against claims such as: "There are advanced theories supported by nobody because all money is absorbed by false theories [link inserted to your own work]. The human race will NOT survive the next thousand years without teleportation and true Science."

          I will let others judge by themselves, but it is always a risk to tag science as 'true' science, specially when arguing against someone else theories in favor of yours.

          Thanks for sharing.