Hello Efthimios,

Good question. What I claim, and the reason I believe my model is stronger than claiming directly that the world is digital, is because in my view one doesn't have to presume discreteness as a basic assumption of the world. One starts asking how the universe looks like in terms of the distribution of patterns in the world. Then one can conclude either that the world is...

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Hello Efthimios,

Good question. What I claim, and the reason I believe my model is stronger than claiming directly that the world is digital, is because in my view one doesn't have to presume discreteness as a basic assumption of the world. One starts asking how the universe looks like in terms of the distribution of patterns in the world. Then one can conclude either that the world is digital because it looks like so (or does not), or that it is algorithmic (in the digital sense) even if it is not digital, case in which I argue we have no reasons to think it is not digital. We provide some evidence in favor of the resemblance between empirical and digital datasets and means to continue the investigation (investigation that has already provided some applications by the way, such as the calculation of the complexity of short strings where compression algorithms use to fail).

You may also mean that the world could be algorithmic in other different sense, in an analog fashion (in the sense of being carried out by an analog computer) and still remain algorithmic. It could be, but so far we have had a hard time trying to define analog computation, at least in feasible terms, and our best model to understanding the world has turned out to be digital (Turing) computation. This is why I focus on discussing the way the world seems to unfold and whether it may do so in one or another way. Our claims are supported by statistical results (statistics are not proofs though), and we found that patterns in the real world and the digital ones, that we simulated, seem to be distributed alike.

Among the things I argue in my essay is that the world would have greater chances to look random (or more random if you prefer) if it were analog. If one throws digits into the air of an analog (infinitely divisible) world and if this hypothetical world allows 'true' (indeterministic) randomness unlike in a digital one, then one would expect every digit to be like the digits of a Chaitin Omega (see definition in the Appendix of the essay), this is a number that is random by definition under our standard model of computation. You can perform the same thought experiment with a real number line and see that chances of picking a random number among all numbers, in a finite interval, is 1, that is complete certainty that you will pick a random number. Yet we don't experience that in our everyday life, but quite the opposite. Chaitin has proven that one cannot calculate most digits of an Omega number (for some Omega numbers not even a single digit), so in a world where random numbers persist, things might just have greater chances to look like Chaitin Omegas. The fact that we can do science in this world seems to be an indication favoring that this is not the case.

You are right, it is very interesting how physical models based on mathematical theories assume continuous variables, yet when one solves the equations of, let's say general relativity to take the example you mention, the model becomes algorithmic in the strict digital sense, either by the mechanistic way in which equations are solved by hand, or literally when solved by a digital computers. The algorithmic view might turn out to help as a shortcut to understanding the digital nature of the world without having to assume it at first.

Sincerely.

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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...

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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

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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...

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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.

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Dear Dr. Hector Zenil,

The professional scientists often send fantastic essays to our contest just because this contest is encouraging people to share with others to trigger interesting discussions. We do not write holy papers so it needs revision. Thus, even if your essay may have errors, it is not a catastrophe.

1) You write: ''a particle may have these properties only when...

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Dear Dr. Hector Zenil,

The professional scientists often send fantastic essays to our contest just because this contest is encouraging people to share with others to trigger interesting discussions. We do not write holy papers so it needs revision. Thus, even if your essay may have errors, it is not a catastrophe.

1) You write: ''a particle may have these properties only when interpreted from outside, a particle only has mass when measured related to other matter''. a) There are huge, cold clouds of gas and dust in our own galaxy. These particles are very cold and practically do not interact one with another. Meanwhile these clouds have gravity that influences the motion of planets, stars and even galaxies. It is a proof that the particles have mass even if they do not interact with each other or measuring devices. Thus, your statement is wrong.

b) There is a huge number of neutrino which is able to pass through ordinary matter almost unaffected. Neutrino practically do not interact with matter but their gravitation influence the motion of planets, stars and even galaxies; It means they carry information about their mass even when they don't interact with matter.c) If you mean gravitational interaction, then your statement also is wrong - particles interact gravitationally always. Thus, since particles carry information (about mass) without interacting, your statement is erroneous: ''But at the lowest level, the most elementary particles, just like single bits (the Shannon Entropy of a single bit is 0), carry no information when they are not interacting with other particles''.

2) ''the universe is capable of performing digital computation''. This statement also is wrong; it contradicts quantum mechanics and Black Hole physics. The same error I found in T. Bolognesi's essay and you can see my arguments on his page.

3) ''the lossless compressibility of data is in any sense an indication of the discreteness of the world''. This statement is completely senseless as I shown in my above post.(Programmers may tell us about the nature of the Universe by performing an analysis of the compressibility of mp3 files).

''Finally, most if not all of my essay is based in hard science'' - it proves nothing; the SM is a mathematical model only that can compute only but explain nothing. Please try to explain inertia, mass and the curvature of spacetime by help of your ''hard science''. Your ''hard science'' may fall during next 10 - 20. Pay attention how many doubtful essays you see in our contest - the same situation is everywhere in the Physics. About 70 percents of theoretical papers in physics are wrong. An example is your theory based on ''hard science'' which contradicts quantum mechanics and Black Hole physics. If your theory is true then quantum mechanics and Black hole theories are wrong and vice versa. Since astronomers found evidence for Black Holes, but I don't see observable evidence for the algorithmic Universe, we conclude that your theory is false rather than first two theories.

Sincerely,

Constantin

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Dear Sir,

You have raised a very important question. We have discussed it below the essay of Mr. Ian Durham. Here we reproduce it for you.

The latest finding of LHC is that the Universe was created from such a super-fluid and not gases. The confined field also interacts with the Universal field due to difference in density. This in turn modifies the nature of interactions at...

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Dear Sir,

You have raised a very important question. We have discussed it below the essay of Mr. Ian Durham. Here we reproduce it for you.

The latest finding of LHC is that the Universe was created from such a super-fluid and not gases. The confined field also interacts with the Universal field due to difference in density. This in turn modifies the nature of interactions at different points in the medium (Universal field).

A force can act only between two particles as only a particle can influence the field, which in turn can be experienced by another particle. If the external force of the field is more than the confining force of the two particles, then the two particles break up and join to form a new particle. We call this “sambhuti”. In the opposite case, the two particles experience the force without being internally affected. The force acts between the centers’ of mass of each treating each as a point particle. We call it “bibhuti”. This second category of relationship, which we call “udyaama”, is known as gravity. Since it stabilizes the two bodies at the maximum permissible distance between them depending upon their respective masses, we call it “urugaaya pratisthaa”. For reasons to be discussed separately, this is possible only if gravity is treated as a composite force.

The first category of forces, which are interactions between two bodies, acts differently based on proximity-proximity, proximity-distance, distance – proximity and distance – distance variables. We call these relationships “antaryaama”, “vahiryaama”, “upayaama” and “yaatayaama” respectively. This interaction affects the field also inducing various local disturbances. These disturbances are known as “nitya gati”, “yagnya gati”, “samprasaada gati” and “saamparaaya gati” respectively. Any particle entering the field at those points feels these disturbances, which are known as the strong nuclear interaction, weak nuclear interaction, electromagnetic interaction and radioactive disintegration respectively. Thus, you can see that gravity belongs to a completely different group of forces and cannot be integrated with other fundamental forces of Nature in the normal process. Yet, it has a different function by which other forces can be derived from it. We will discuss that separately.

According to our theory, gravity is a composite force of seven forces that are generated based on their charge. Thus, they are related to charge interactions. But we do not accept Coulomb's law. We have a different theory for it. We derive it from fundamental principles. We will discuss it separately.

According to our theory, all particles are locally confined fields. This confinement takes a three fold structure for the particle - center of mass or nucleus, extra-nuclear field and the confining orbitals. If we take into account the external field with which the particle interacts, it becomes a four-fold (3+1) structure. The particle interacts with the field in two ways. If the internal energy distribution cancels each other with a little inward pull, then it behaves as a stable particle. Thus, all particles can be described as composites that exhibit two types of charges: that which pushes out from a central point and is described as positive charge and that which confines it and is described as negative charge. Where both are balanced, it is neutral charge.

We have derived theoretically that the charge of proton in electron units is not +1, but +10/11. Similarly, the charge of neutron is not 0, but -1/11. This makes the atom slightly negatively charged. This excess negative charge is not experienced out side as it is directed towards the nucleus. It is not detected during measurements due to the nature of calibration of the measuring instrument. But it is released during fusion and fission.

The confinement described above takes place where the external field dominates to confine the particle. Here the particle becomes negatively charged. In the opposite case, the particle becomes positively charged. The particles are classified as positively charged or negatively charged according to whether the external field dominates over confinement or the confined force dominates over the local field. Since equilibrium is inherent in Nature, in either case, the particles search for their complements to become full. The less negative part of the proton (since it is +10/11, it has -1/11 negative charge) seeks to couple with the electron to become -1/11. This makes hydrogen atom highly reactionary.

The combined charge of proton and electron (-1/11) seeks the neutron since it has an equal charge. Thus, the opposites do not attract and same charge does not repel. It is not the opposite either. The charge interaction can be of four types:

positive + positive = explosive. That is seen in fusion reaction.

Positive + negative (total interaction) = internally creative (increased atomic number)

Positive + negative (partial interaction) = externally creative (becomes an ion and interacts with other particles.)

Negative + negative = no reaction. They co-exist.

For further clarification, kindly write to: mbasudeba@gmail.com.

Regards,

basudeba.

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