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FQXi FORUM
April 24, 2017

CATEGORY: Is Reality Digital or Analog? Essay Contest (2010-2011) [back]
TOPIC: A Functional Virtual Reality by Efthimios Harokopos [refresh]
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Author Efthimios Harokopos wrote on Feb. 2, 2011 @ 09:43 GMT
Essay Abstract

If reality is analog, in the sense that there is an infinitely divisible spacetime, then relativity theory describes a macrocosm that is autonomous, deterministic and obeys locality. If reality is digital, in the sense that spacetime is granular, then quantum theory describes a microcosm with indeterminacy at the level of particle interaction. In an attempt to resolve the apparent contradiction between the words of relativity and quantum physics, we may attempt to answer a fundamental question about the nature of reality: is it analog or digital? I will assume in this paper that reality is fundamentally digital and then based on a modern version of the old doctrine of Cartesian occasionalism I will sketch a model of the world that allows both uncertainty and autonomy within the limits of physical laws. I will then outline an experiment that has the potential of falsifying the model.

Author Bio

Efthimios Harokopos received a BS and a MS from State University of New York at Buffalo and completed all the coursework for a PhD at Columbia University while working for AT&T and Bell Labs. He is an independent researcher in the field of philosophy of science.

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ioannis hadjidakis wrote on Feb. 4, 2011 @ 11:46 GMT
Is the experiment proposed occuring continously in our head? What I mean is that our brain is a huge biological compouter runing in its full capacity when it is not at rest. However, its output varies (according to our opinions) although inputs and rules of thinking are the same for everybody.

Regards, narsep

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Author Efthimios Harokopos replied on Feb. 4, 2011 @ 15:12 GMT
Hello Ioannis,

Actually the proposed experiment occurs in some forms continuously in the whole universe, not only in our brains. The objective is to set it up so that it may generate an error between expected output and actual output. This is the purpose of the nanoprocessor, in that it will enable us to run a very complicated algorithm at a very high rate and at the same time the experiment reference frame will be accelerated at high speeds. Now, although the basic experiment runs continuously in the universe, the specific setup is under conditions that may, I want to stress this "may", allow us to detect deviations from expected output.

All the best.




Rita wrote on Feb. 4, 2011 @ 18:17 GMT
This is intriguing. I didn't know that Descartes believed in a continuously recreated world. This sounds a lot like a computer generated virtual reality.

Can you explain the experiment a little more? Why are you suggesting moving the processor at high speeds?

Thank you.

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Author Efthimios Harokopos replied on Feb. 5, 2011 @ 10:29 GMT
Hello,

The basis for the experiment is derived from the proposed model, which in turn was based on a modified version of Cartesian occasionalism. The prediction is that if there is a mechanism that is the real cause of all interactions in the universe then it may have an upper operational limit locally. By locally, I mean over very short distances, like a few hundred meters. If the demand for coordination of motion locally exceeds what the mechanism can accomplish then we may be able to detect that. The setup I propose is a processor made up of nanoscale transistors, billions of them. Currently, fats processors are made of billion of regular transistors. Nanoscale transistors would allow more density. next, the processor is instructed to run a complex algorithm. This required a high degree of coordination in the movement of electrons in the nanoscale transistors according to a certain timing imposed by the processor clock. If in addition the processor is accelerated at very high speeds, it may be possible to detect deviations from the expected output of the program it runs due to the inability of the mechanism that coordinates all causes to properly achieve its objective. Accelerating the processor makes, supposedly, the job of the mechanism much harder.

The analog, which I did not state in the paper due to space limitations, is how the output of a digital camera is distorted when it is moved fast. The camera has no time to refresh its display and as a result it misses frames. If you know what it was supposed to record, when you look at the video you know something went wrong. In this experiment we know what the processor must output and if it does not, assuming the experiment was setup properly and there is no noise or other interference, then something is wrong at the local scale.

Please note that experiments in physics can only corroborate or falsify theories. Experiments cannot prove any theory to be a true representation of how reality works. The objective of physics is progress through falsification of new scientific theories. A scientific theory is one that generates predictions that can be tested. A physics theory that does not generate testable predictions is not scientific.

I hope I answered your questions.

All the best.




Vladimir F. Tamari wrote on Feb. 5, 2011 @ 11:55 GMT
Yasu Efthimios,

I did not follow all the arguments you put forward in detail, but was happy about various highlights of your paper. Yes Descartes had a highly original idea of an ether filling all of space, and his concept of (analog?) vortices as the cause of the propagation of light is somehow related to my Beautiful Universe theory of spinning analog nodes as building blocks of the universe. I too (and many others of course) disagree with Einstein's decision to make measurement absolute (c is constant) while creating a relative reality (flexible space-time). Why did Lorentz not defend his position more vehemently and save the ether and perhaps much else in physics besides.

Your proposed experiment made me think of two things: Could you not set it up in such a way so as to make use of some sort of moire effect? This effect relies on two screens seen slightly apart (hence one is seen slightly smaller) , creating fringes much larger than the wires of either screen. Do not ask me how this can be implemented when the 'wires' are the tiniest elements of reality!

The other thing is that the iphone and similar devices have no shutter and when set in motion while taking a picture the result is unexpected as explained here perhaps in a similar way that your moving sensor would work? Cheers

Vladimir

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Author Efthimios Harokopos replied on Feb. 5, 2011 @ 21:55 GMT
Yasu (Hello) Vladimir,

Thanks for your remarks. As far as special relativity, I belong to the group of those who think that the constancy of the speed of light is necessary in order to make the theory consistent and that Einstein was correct in inventing it. The issue is whether the theory is a true description of how reality operates. I cannot answer this question until we know something more about the nature of reality. I tend to think that special relativity although very consistent mathematically and in its predictions cannot be a true theory of reality but you can never know. Maybe life is a movie and everything, including writing this post, was predetermined at the time of big bang.

As far as the moire effect you mentioned, this is a very interesting thought and there have been some experiments already to determine if spacetime is digital using light coming from distant stars. These experiments have been somewhat controversial. But I have to think more of your suggestion.

All the best.



Author Efthimios Harokopos replied on Feb. 5, 2011 @ 22:08 GMT
Vladimir,

I forgot to comment on your iphone remark.

This effect was only an analogue I used. The iphone and in general all devices with digital cameras have a limitation in refreshing their screens because of the algorithms they use. In my experiment then, the iphone would be reality and my processor would be the image to capture, which is moving at high speeds and has known details. Thus, the sensor you mentioned is reality itself and the image is the experiment. I hope I explained this better this time around.

Cheers.




Vladimir F. Tamari wrote on Feb. 6, 2011 @ 13:54 GMT
Efthimios,

SR was an imaginative and elegant solution to the ether 'problem' However if it is assumed that all matter and the vacuum is electrical as Hertz theorized, that allows for an absolute space and time with variable speed of light. And it greatly simplifies GR (which is now dependent on SR) to a question of local density or potential of space. Such space refracts geodesics like a mirage would.

In my original Beautiful Universe Theory (reference 48 in my present fqxi paper) I have proposed an experiment to test the ordered texture of the universe. It is based on a standing wave of strong electromagnetic radiation in vacuum. A second wave is shone normal to it. If it acts like a diffraction grating it means the vacuum has this crystal-like structure. Two parallel standing waves can produce a moire pattern, I suppose.

The iphone example is just to show how an instrument can be used to distort reality. You have a specific idea - maybe a sketch will help explain it further. I feel your sensor may be like a filter moving to intercept elements of the digital world - like a baleen whale swimming through a school of tiny fish? Cheers

Vladimir

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Author Efthimios Harokopos wrote on Feb. 6, 2011 @ 16:01 GMT
Vladimir,

I agree with you that an ether-based theory with absolute background and universal time and SR are experimentally indistinguishable. This is understood in the circles of Relativity theory. I believe that Einstein's thesis was that the ether is not required mathematically. I also agree that this mathematical solution leads to metaphysical commitments, as I state in my paper, that are maybe unacceptable. I like your experiment. I think you may have something there but I must admit I do not know a lot about the moire affect in the context your employ it. I must do some more reading in this area. However, this is a reference to work of Richard Lieu who claimed that in similar experiments he found no evidence of a granular space:

http://iopscience.iop.org/1538-4357/585/2/L77

Furthermo
re, in Italy, Fabio Benatti and Roberto Floreanini proposed using atom interferometers to search for granularity of space, by separating and then recombining two beams of precisely synchronized neon atoms. When the beams merge they form an interference pattern. I was not able to find the reference for this experiment.

Best regards-




basudeba wrote on Feb. 7, 2011 @ 07:50 GMT
Dear Sir,

You begin with the premise that relativity deals with analog and quantum theory deals with digital descriptions of the Universe. In our essay, we begin with the premise that there is no consistency between the various interpretations of quantum theory and that there is no unanimity about what constitutes reality. Each branch of quantum theory comes with its own interpretations,...

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Author Efthimios Harokopos replied on Feb. 7, 2011 @ 08:39 GMT
Hello,

This is an excellent link regarding the experimental basis of Special relativity:

http://math.ucr.edu/home/baez/physics/Relativity/
SR/experiments.html

As fas as the various interpretations of quantum theory, to which I make reference in my paper, they do not lead to different experimental predictions but only to different ontological commitments. Thus, the problem with the different interpretations is only philosophical.

if you are more interested in Zeno's paradox I suggest you read the references in my paper. The fundamental premise in Zeno's paradox, as Barnes demonstartes in an extensive treatment, is that "nothing can perform infinite tasks". If you are to resolve the paradox, you must first prove this fundamental premise false. I cannot see how your velocity function does that. Maybe you can explain this further.

Regards



basudeba replied on Feb. 7, 2011 @ 13:36 GMT
Dear Sir,

We have refuted the experimental basis of of relativity in our post below the essay of Mr. Castel. Since it is very long, we are not reproducing it here. You may refer to that and refute if you wish.

Since the various ontological commitments of the different interpretations of quantum theory are not fully integrable to a common approach, this aspects needs to be examined at length.

We do not want to know more about Zeno's paradox, we refute it. We have shown that the fundamental premise is false. Regarding velocity function, we cannot see how does it validate Zeno's paradox, but we have the answer, which we have discussed in our post below the essay of Mr. Perez and others.

Our only intention is to find out the truth and not score points. Kindly forgive us if any of our comments appear harsh. After all palatable benevolence is a rarity.

Regards,

basudeba.

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Author Efthimios Harokopos replied on Feb. 7, 2011 @ 15:57 GMT
Hello,

You wrote: "We have refuted the experimental basis of relativity in our post below the essay of Mr. Castel. Since it is very long, we are not reproducing it here. You may refer to that and refute if you wish."

You mean you have refuted the work of thousands of credible scientists in many laboratories and universities around the world in the past 60 years in a reply to a post?

I hope this is just a joke. I take it that way, no offense.

Regards and good luck to you.




T H Ray wrote on Feb. 7, 2011 @ 19:25 GMT
My two favorite essays in this competition both have to do with virtual reality -- yours and Brian Whitworth's. Though the essays are only loosely related, because of differences in definition, the overarching idea that we cannot differentiate "reality" from "process" _in principle_ is one that deserves a lot more attention than it gets, IMO.

For myself, I long ago decided that metaphysical realism (Popper) is the correct substitute for "physical" notions. We can't know what's physical in any objective sense, yet we can know how to reconcile theory with result on something resembling Tarski's correspondence theory of truth, from which Popper drew much of his philosophy.

I think your proposed experiment may not be Popper falsifiable, however, because I don't see a way to show that the program potentially halts. To illustrate, consider how Popper demonstrated hypothesis testing by reformulating two number theory conjectures (still unproven) that are closely related: The Goldbach Conjecture and the Twin Primes Conjecture.*

Popper called the Goldbach Conjecture true if G: for every natural number x > 2, there exists at least one natural number y such that x + y and (2 + x) - y are both prime. The Twin Primes Conjecture is true if H: for every natural number x > 2, there exists at least one natural number y such that x + y and (2 + x) + y are both prime.

Neither G nor H are verifiable, but G is falsifiable and H is not. Your proposal as I read it falls into the H category; i.e., I think at best you could only conclude that the quantum configuration space cannot be mapped onto the physical space (which in your case amounts to a universal Turing machine) without a nonlocal model. Bell's theorem already informs us of that. If Chaitin's number Omega is the halting probability of a universal Turing machine (and I think it is) then there is no possible falsfication. (G potentially halts when an iterated calculation hits a counterexample). If you want to read a more formalized treatment,my ICCS 2006 paper goes into it.

Thanks for a really thoughtful, well organized and well argued essay. (Though you might have found a spell checker would improve it.)

Tom

*K. Popper, 1983. _Realism and the Aim of Science_.

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T H Ray replied on Feb. 11, 2011 @ 15:55 GMT
Efthimios,

The point I was trying to make is that the halting probability of a program with choices among a continuous range of variable values is zero. That's the difference between the + sign and the - sign in Popper's hypothesis testing criteria.

So even if your program is a finite state (Turing) machine with infinite processing capacity, there is no possibility that any finite...

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Author Efthimios Harokopos wrote on Feb. 7, 2011 @ 20:50 GMT
Hello Tom,

Thanks for your comments and the reference. I find them very important and they amount to more homework for me.

You are correct to point out that there is a possibility that the experiment may not be falsifiable. However, this is the situation: We know that the program halts when there is no motion. What we are looking for is errors when motion takes place and/or the program becomes more complicated. I am not a mathematician and I cannot describe the difference in a more rigorous way. There is an additional assumption about reality that goes beyond mathematics and it is that of an upper limit in the local processing capability of a mechanism that generates a virtual reality. If the mechanism has infinite processing capacity then you are correct, this is not a falsifiable experiment. But if it does not have infinite capacity, it is falsifiable. The only way to find out is by trying it. If the result is negative (no errors), nothing can be concluded. If the result is positive, then that can only corroborate the virtual reality hypothesis. It will certainly mean something, although not conclusive.

Thank you and best regards,

Efthimios




Vladimir F. Tamari wrote on Feb. 9, 2011 @ 03:09 GMT
Efthimios,

The ingenuous Lieu and Hillman paper you cited proves that there is no evidence for Planck-scale fluctuations in time and space. So far so good, but then it uses that result to say the ether does not exist. This is a very weak conclusion hinging on the assumptions that probabilistic effects are an inherent property of nature and not merely the result of macroscopic measurements and theoretical interpretation of what may be a very different physical reality at the Planck-scale, presumably the ether granularity level. I have suggested in my my original 2005 Beautiful Universe paper on which I based the fqxi essay, how probability can emerge as diffusion within an exquisitely ordered ether. Such an ether may exist and not contradict Lieu's result.

Atomic interference has been demonstrated, even for molecules, (which incidentally I now conclude in my above paper may be the result of the interference of the gravitational fields surrounding the particles). But how would that give any data for or against a much finer supposed granularity of space? It will be interesting to read the Italian paper if you find it thanks. BTW here is an interesting demonstration of moire patterns it may inspire something!

Good luck. Vladimir

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Author Efthimios Harokopos replied on Feb. 9, 2011 @ 08:22 GMT
Vladimir,

I do not like to post more than one link usually so this is the response to Lieu’s paper that attempts to rebut its claims:

http://iopscience.iop.org/1538-4357/591/2/L87/

Besides
the theory and the measurements, let us think about it in a more fundamental way:

If spacetime is granular, then what is there between the grains? There must be something because if there is nothing, then space is not granular.

If space is granular, then it is a virtual space.

Disproving the granularity of space is equivalent to preserving the autonomy of the world. In my opinion, it is now too late for that.

Cheers.



narsep replied on Feb. 12, 2011 @ 08:54 GMT
Dear Efthymios (and all),

I wonder if you have a look to my essay. In it there is an idea of "granularity" of space and how virtuality fits in between or "reality" fits in between "granular" virtuality.

Giving the oportunity, I would like to make clear what I meant in my previous responce to your experiment proposed. Human brain as a huge local computer working with its trementous capacity and following the same rules usually gives various results although the inputs are the same. Because all these different results can not be the "expected" answer this is an indication that there is a limit in the local processing capability. Whether this is THE upper limit I think we will not in a position to ever know as we will never manifacture a machine better than our own brain for the simple reason that its results will be interpreted as faulties.

Regards, narsep (ioannis hadjidakis)

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Author Efthimios Harokopos replied on Feb. 22, 2011 @ 15:06 GMT
Dear Ioannis,

In my paper, I framed no hypothesis about the specific structure of reality, whether analog or granular. As Newton said, "hypotheses that are not deduced from the phenomena, whether mechanical or occult, have no place in science, especially in experimental physics"

My essay was not about the ontology of spacetime. It was an effort to find a way of falsifying or corroborating the virtual reality conjecture. A virtual reality is generated by definition by a higher reality. I am not interested at all in specific proposals about possible ontologies. I began thinking this way long ago and soon I realized that unless those ontologies generate unique falsifiable prediction they are nothing more than metaphysical hypotheses.

I am not sure I agree with your comment about not being able to manufacture a machine better than our brain. I certain respects I believe this has been accomplished many years ago. The human brain is very limited in mathematical operations but very fact in pattern recognition. In my experiment I am looking at a nanocomputer running a complex math algorithm. Computers are orders of magnitude better in doing math than people, I hope we agree to that. If you do not agree, try asking the smartest people in the world to matrix multiplication of solve partial differential equations with split boundary conditions.

I cannot also discount the results of any experiments before they are performed.

Thank you for your comments.

E. Harokopos




James Putnam wrote on Feb. 11, 2011 @ 22:20 GMT
Dear Efthimios Harokopos,

I have just downloaded your essay. I will be looking for your support for:

"I will assume in this paper that reality is fundamentally digital and then based on a modern version of the old doctrine of Cartesian occasionalism I will sketch a model of the world that allows both uncertainty and autonomy within the limits of physical laws."

You begin with digital and sketch a model that allows for uncertainty. I assume that you mean that uncertainty frees us from a digital universe. I think that uncertainty does not free us from anything. If I have misunderstood your meaning, I will learn that from your essay. Thank you for participating.

James Putnam

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Author Efthimios Harokopos wrote on Feb. 12, 2011 @ 08:53 GMT
Hello James,

As a matter of fact I state the opposite that uncertainty is a feature of the digital word and determinism of the analog. I do not invent these, QM and Relativity say so, respectively.

In physics, as you know, every model we build is an assumption that must be falsifiable. Thus, regardless my personal beliefs about the nature of reality (I may have none as a matter of fact), I sketch the model of a mechanism continuously recreating a digital universe at single instants of time and I am trying to find a way to falsify it.

Someone else may come up with a different digital model and find another way to falsify it. You see, analog models cannot be easily falsified. Our best analog model is Relativity and to this date none of its predictions has been falsified although there are a few issues with general relativity that need to be investigated more.

Thank you for your comments.



James Putnam replied on Feb. 15, 2011 @ 04:14 GMT
Dear Efthimios Harokopos,

Thank you for replying. I see now that I left my point unclear:

Me: "I assume that you mean that uncertainty frees us from a digital universe."

Your response: "As a matter of fact I state the opposite that uncertainty is a feature of the digital world and determinism of the analog."

My point is this: A digital world lacks connection. Since it functions in a cooperative manner, there must be some form of continuity. I presumed that you considered uncertainty to fill in gaps and, in effect, smear a digital nature so that it might connect enough to mimic continuity.

Your analysis of this would be greatly appreciated. Please be as direct as necessary to make your point. Directness helps me to understand. Thank you.

James

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Author Efthimios Harokopos replied on Feb. 22, 2011 @ 15:23 GMT
Hello James,

I apologize for the delay in responding.

You are raising important points. In my paper, I framed no hypothesis about the specific structure of reality, whether analog or granular. As Newton said, "hypotheses that are not deduced from the phenomena, whether mechanical or occult, have no place in science, especially in experimental physics"

My essay was not about the ontology of spacetime. It was an effort to find a way of falsifying or corroborating the virtual reality conjecture. A virtual reality is generated by definition by a higher reality. I am not interested at all in specific proposals about possible ontologies. I began thinking this way long ago and soon I realized that unless those ontologies generate unique falsifiable prediction they are nothing more than metaphysical hypotheses.

The problem with these hypotheses, as I said before, is that they hardly produce any new predictions on top of relativity and QM. They remain in the realms of metaphysics, at least for now. Thus, I avoid them. I concentrated in providing a short - due to space limitations - account to justify the virtual reality hypothesis and a possible experiment. As a scientist, I cannot go that far. I cannot speak about things I do not understand, things that are not deduced from the phenomena. I hope you will understand.

However, I do not want to appear as if I am not escaping here. There are many possibilities I have thought of about this in the past. I think one that is plausible in the case that our reality is indeed generated by a higher reality is that the granular structure is part of a supersolid medium. The continuity part arises from the supersolid medium which allows for faster than light speeds in coordinating local operations in the virtual reality, in which the maximum speed is the speed of light in vacuum. The uncertainty arises from specific operations that I describe in another paper I am working on – actually a book – and I hope you will allow me to refrain from giving details here.

Thank you.

E. Harokopos




Bubba wrote on Feb. 12, 2011 @ 18:24 GMT
Very interesting article Mr Harkopos.

I was under the assumption that Zeno's paradoix was implicitly resolved with the advent of differential calculus and the idea of limits.

i.e. the sum of an infinite series may converge to a finite value, which in turn represents the limit of the series. The infinitesimal sum of dx(1/dx/dt) approaches a finite value over any abritrary interval on R, prodived dx/dt is continuos, smooth, and exists on the interval.

The erroneous assumption implicit in Zeno's paradox is that the sum of an infinite sries is always infinite.

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Author Efthimios Harokopos replied on Feb. 13, 2011 @ 10:05 GMT
Hi Bubba,

Thanks for an interesting comment. There is no erroneous assumption in Zeno's paradox. If you get the reference I mentioned (Barnes) you will see that the fundamental premise of Zeno is that "nothing can perform infinite many tasks". Calculus does not resolve this issue. Calculus provides asymptotic convergence conditions for mathematics only. The limit of the series as you say, it is only reached asymptotically. In mathematics we call that convergence. But what convergence means in the case of physical motion in infinitely divisible space? I don't know. If you know, I would be interested to find out, namely, when does the body in motion exactly reach its end point.

Barnes explains the whole issue well and also the argument of Aristotle which was the first and last viable argument against Zeno. Zeno's argument can be transformed to:

1.Motion is a supertask, because the completion of motion over any set distance involves an infinite number of steps

2.Supertasks are impossible

3.Therefore motion is impossible

There is huge literature on this subject and the concept of infinite supertask machines.

Actually, Zeno's task can be modeled by a Grandi series, which converges to infinity:

http://en.wikipedia.org/wiki/Thomson's_lamp

http://e
n.wikipedia.org/wiki/Supertask#Zeno

In order to resolve the paradox many assume that motion is possible and then declare the argument of Zeno unsound using modus tollens.

However, it is the very possibility of motion that Zeno challenged.

Note that solution that claim that as soon as motion starts it concluded because each subsequent motion takes less time, so that the time intervals converge to a finite value according to calculus, are naive because according to Zeno, motion cannot even start. Zeno's philosophy was that there is no such thing called motion. Everything is immovable, at rest, and what we see is an illusion. I think what we see may be virtual reality. In a virtual reality, motion is possible because it is pixelized. But again, what I think is not important. It is what experiments will show that is important. Talk is cheap in physics, almost.

Thanks and regards.




Bubba wrote on Feb. 12, 2011 @ 19:23 GMT
Also, all of the variations of Zeno's Paradox also lack any self-consistency and self-referential integrity.

For example, the argument put forth that in order to travel an interval AD one must first travel half that interval AB, and so on, leads to obvious problems.

The lack of consistency arises when one states that once one reaches the first half-interval AB, another half-interval awaits and this progression continues indefinitely. One must therefore complete an infinite amount of actions and can never arrive at the end of the interval. The obvious problem here is, you managed to travel the first half-interval AB in a finite amount of actions without encountering infinity.That interval AB itself is arbitrary and contains an infinite number of half-intervals. Since the original intent is to show one can never reach the original interval AD in a finite umber of steps and actions, how is it you came to traverse the sub-interval AB? Based on the assumptions, an infinite number of actions would also have been required for that interval.

This should immediately tell one that the something is amiss with the idea of actions on intervals as they relate to the infinite.

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Author Efthimios Harokopos replied on Feb. 13, 2011 @ 10:06 GMT
Please see my response above.




Author Efthimios Harokopos wrote on Feb. 13, 2011 @ 10:39 GMT
Hello Bubba,

I apologize for an error in my post. I wanted to say that the Grandi series converges to 1/2 at infinity. However, at the same time, depending on solution, the series has no sum. Thus, the series diverges.

So, instead of using the typical calculus approach which sets infinitesimal values to zero, the Grandi series approach should convince you that this is not a trivial problem.

To illustrate this further, consider S = at^2/2, the known equation. Now, consider that the body moves ds in time dt. The equation becomes:

s+ds = a(t+dt)^2/2 which with some algebra becomes:

2s+2ds = at^2 +2atdt+a(dt)^2

But as^2 = 2s, so we get: 2s+ds = 2s+2atdt+a(dt)^2, which reduces to:

2ds = 2atdt +a(dt)^2 or ds/dt = at +dt/2

But calculus tells us that ds/dt = at. How can that be?

The mathematician response is that in the limit dt goes to zero. But is it exactly zero? If it is exactly zero, then S+ds will be forever equal to s and motion cannot take place. If it is not zero, then s = at+dt/2 and these sums of dt/2 diverge. Of course, mathematicians can always add a few more axioms and get anything they want.

By this response, triggered by your well put argument, I want to show that calculus wants its cake and eat it too when it comes to justifying motion (although it describes the phenomenon correctly). Things are not that simple. There is a lot of work to be done to transform our naive views of reality to something more advance that can help us to progress.

All the best.

Efthimios



T H Ray replied on Feb. 13, 2011 @ 12:33 GMT
As Einstein recognized, the calculus of continuous functions requires specifying boundary conditions. Because "From the standpoint of epistemology it is more satisfying to have the mechanical properties of space completely determined by matter ..." Einstein's finite but unbounded, quasi-Euclidean model of relative matter rest states came mathematically complete, with the origin of inertia assumed at the boundary of a singularity, and otherwise unexplained. (The foregoing is picked up from the technical note in my essay "Can we see reality from here?")

If motion is primary, as Mach believed, the origin of inertia needs no explanation. We know that this cannot be true, however, because also as Einstein recognized, because of the problem describing continuous function physics without singularities. So cosmology, once subbed as mere philosophy, has taken--if not the leading, at least an important supporting--role in physics.

Tom

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Anonymous replied on Feb. 13, 2011 @ 18:11 GMT
Hi Efthimios,

.

btw, I found your article to offer a lot of food for thought and hope you score high on the final ballot. Best of luck.

Anyway, regarding this issue, I don't think the problem here is one of infinity, it is the way we think about infinity.

First of all, I think we need to keep in mind that mathematics simply represents a model for reality. You...

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Bubba replied on Feb. 13, 2011 @ 18:12 GMT
sorry, forgot to attach my handle to last post. This is Bubba.

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Author Efthimios Harokopos wrote on Feb. 13, 2011 @ 19:29 GMT
Thanks for your detailed response. I agree with you about calculus but I disagree - for whatever it worth - with your statement that "Basically then, in the context of this discussion, motion is possible and exists because we observe it to exist." This is not the point of Zeno’s paradoxes.

I will refer to a story that is reported by some ancient Greek philosophers. Zeno, most do not know, was an advisor to Pericles, the man who established Democracy. One day he was giving a speech in the central Agora of Athens, trying to convince people that motion is impossible. When he stated his arguments, the philosopher Antiphon - a real person by the way - got up from his marble sit and started walking up and down in front of Zeno in a silent protest. Everyone laughed. However, by the end of his talk, it was reported that Zeno had convinced everybody in the audience that motion is impossible.

The point is, we observe something we call motion but is this motion in 3-dimensional infinitely divisible space? This is the issue. Sure, we got motion; it is all over the place. But maybe it is not what people think it is. Maybe it is not motion in 3-D space but something like recreation of 3-D space from a higher dimensionality space, a sort of virtual reality.

This is the issue. I think it is a misunderstanding that Zeno said motion is impossible. He specifically limited his argument to infinitely divisible 3-D space with absolute time. In Relativity for example, motion is possible because everything is in eternal motion in a 4-D spacetime, as I attempt to describe in the paper.

Thanks again.

Efthimios



T H Ray replied on Feb. 15, 2011 @ 12:53 GMT
Efthimios,

I appreciate enormously your clarification of Zeno's point, because I am reminded of sitting through a conference presentation a few years ago, in which the presenter claimed to have solved Zeno's paradoxes (specifically, tortoise and hare; and arrow paradox) through some assumptions about time and space he had manipulated.

At the Q & A following, I asked (innocently, in fact), "Well, is motion possible?"

The reaction was as if I had two heads. Hadn't I just heard the presentation? The presenter and others went through all the main points of discussion about time and space. I asked again, "Then if the paradox is resolved, what's the answer: Is motion possible?" The time-space explanation took off again, with the added suggestion that perhaps I wasn't asking a proper question.

I replied, "It's the question that Zeno asked."

And I think that had never even crossed the presenter's mind, as he presented a solution to a problem that had never actually been posed.

Zeno's question is equivalent to the origin of inertia. We still don't know.

Tom

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Anonymous replied on Feb. 15, 2011 @ 15:42 GMT
There is an interesting story in one of Richard Ferynmans popular lectures on science. A student oncer asked him if, when he was viewing an object, if he was really 'seeing' the object or the light that is reflected from the object.

He just replied by telling the story of a philophers who slowly starved to death because every time he was presented with a meal, he spent all his time contemplating whether or not the food was really just reflections of light.

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Anonymous wrote on Feb. 19, 2011 @ 02:40 GMT
Dear Efthimios

I read the response to Lieu's paper you cited above. Again the assumption is that quantum foam is a reality. This idea is speculative and is based on Born's probability interpretation. In my Beautiful Universe paper on which my present fqxi paper is based I have suggested that on the contrary nature may be precisely local, causal and deterministic at the minutest scale - and...

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Constantinos Ragazas wrote on Mar. 7, 2011 @ 22:43 GMT
Yiassou Efthimie,

To the question, “is reality analog or digital” you answer “reality is fundamentally digital”. To the same question, I respond that “we cannot know 'what is' but can only know what our 'measurements' of 'what is' are”. In my paper “The Interaction of Measurement” I present a mathematical argument that shows we cannot know a quantity E(t) (as a function of time) directly through our measurements of E(t) – if these measurements involve an absorption of E in making the measurement.

Although I have not included a discussion of this result in my essay, I thought you may be interested in considering it – especially as you are interested in the philosophy of science. But what I do include in my essay you will find very significant.

The key result in my essay is to mathematically derive Planck's Law of blackbody radiation without using 'energy quanta' or statistics. This result shows that Planck's Law is an exact mathematical tautology that describes the interaction of measurement. This clearly explains why the blackbody spectrum obtained experimentally is so indistinguishable from the theoretical curve.

I hope you can support my efforts to put this iconoclastic result in front of the 'panel of experts' for 'peer review'.

Yia hara,

Constantinos

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Vladimir F. Tamari wrote on Mar. 8, 2011 @ 09:42 GMT
Dear Efthimios,

Following my suggestion to possibly use moire effects to design an experiment to discover the granularity of the Universe: I just read a recent Nature journal article Vol 469 pp. 39-41 and pp 72-75 has an article by M. O'Sullivan et al entitled "Vernier templating..." that might prove interesting. The Vernier effect relies on two scales one slightly smaller than the other to measure extremely small distances, using a geometry identical to the moire effect. The paper studies a spherical configuration, and may provide some food for thought.

Best wishes, Vladimir

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Alan Lowey wrote on Mar. 19, 2011 @ 11:19 GMT
Dear Efthimios,

Congratulations on your dedication to the competition and your much deserved top 35 placing. I have a bugging question for you, which I've also posed to all the potential prize winners btw:

Q: Coulomb's Law of electrostatics was modelled by Maxwell by mechanical means after his mathematical deductions as an added verification (thanks for that bit of info Edwin), which I highly admire. To me, this gives his equation some substance. I have a problem with the laws of gravity though, especially the mathematical representation that "every object attracts every other object equally in all directions." The 'fabric' of spacetime model of gravity doesn't lend itself to explain the law of electrostatics. Coulomb's law denotes two types of matter, one 'charged' positive and the opposite type 'charged' negative. An Archimedes screw model for the graviton can explain -both- the gravity law and the electrostatic law, whilst the 'fabric' of spacetime can't. Doesn't this by definition make the helical screw model better than than anything else that has been suggested for the mechanism of the gravity force?? Otherwise the unification of all the forces is an impossiblity imo. Do you have an opinion on my analysis at all?

Best wishes,

Alan

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Author Efthimios Harokopos replied on Mar. 21, 2011 @ 22:02 GMT
Dear Alan,

Thank you very much for your kind words.

Newton's law of universal gravitation, to which you referred, is a mathematical expression that has no physical meaning, according to his inventor, Newton himself. This is the well-known "hypotheses non fingo" phrase of Newton:

http://en.wikipedia.org/wiki/Hypotheses_non_fingo

The expression "fabric of spacetime", if I am not mistaken, is used for the 4-dimensional geometry of the spacetime of general relativity. There, gravity is not a force but only motion that results from the geometry of spacetime.

I'm not sure we can talk about the mechanism of gravity when we do not know what gravity is in the first place. Regardless, as far as I know, any mechanism that has been proposed using some kind of "material influence", like graviton flux, for example, should create some type of drag on celestial bodies that has not been observed. It can also create heat that has not been observed.

Gravity is a mysterious force. I believe, for whatever it worth, that what we call gravity is an "outside force" that makes our reality "functional", the term I use in my paper. The best mathematical model we have of this phenomenon today of that of general relativity on a macroscale.

I am not sure if I answered your question, probably not I guess, but I am inclined to think that we should not be looking for a mechanism of gravity in our world of phenomena because it does not belong there. If it did, we would have known it already.

Regards.



Alan Lowey replied on Mar. 23, 2011 @ 12:52 GMT
Dear Efthimios,

thanks for the link btw, I didn't know that one. I don't quite understand the "drag" aspect you talk of, other than the force of attraction. Why would a graviton create "heat"? okay through mechanical friction...ummm...I don't think we can say that this "hasn't been observed" due to no-one having entertained the idea in the first place.

I just thought last night that the original quandry w.r.t the orbit of Mercury can likely be explained by the 'inclination hypothesis' i.e. that gravity is stronger on the plane of rotation of a celestial body. It's too much to explain in one go but there's plenty of circumstancial evidence to support this claim. I'm working on it right now.

Best wishes,

Alan

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Vladimir F. Tamari wrote on Jun. 3, 2011 @ 02:30 GMT
Alan,

You mentioned an " 'inclination hypothesis' i.e. that gravity is stronger on the plane of rotation of a celestial body."

This sounds reasonable if you think of the GR concept of "frame dragging": At the equator the frame is dragged at a maximum rate, and it is null at the poles. This is also in accord with how matter affects the gravitational field around it in my Beautiful Universe theory: Any local effect is transferred from lattice node to its neighbors, so the dragging would indeed spread as the gravitational wave GR predicts, and as you observe, it is strongest at the equatorial plane because motion is fastest there.

Best wishes from Vladimir

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Michal Krajnansky wrote on Aug. 23, 2012 @ 17:21 GMT
Dear Mr. Efthimios,

I cannot possibly expect you to check this thread after a year but let's give it a shot.

I feel some unease with your approach, however I am not educated in physics, so please be patient.

To make it as clear as possible, as I understand it, your proposed experiment is essentially that of checking something what I would call the 'local computational capacity' of the universe, that would more precisely be 'time scale resolution computational capacity', as the proposed experiment concerns accelerated computation in a local preocupied space. Is that correct?

I have some doubts about the realizability of this experiment, or, its interpretational value. You predict the appearance of a noise of some kind in the output, if your hypothesis is correct. However, you do not propose any of its particular properties. When eventually found, it would feel temptating to ascribe it to the features of the suggested virtual functional reality.

But what would really be its nature? Probably it would be something of a stochastic process. Could it not be in the same manner related to the anyway profound question of nature of chance?

Relatedly, I have a problem with your use of the term 'true description of reality'. I do not believe any such property can be ascribed to any scientific theory. Anyway, they are just the models of the universe, which itself is as it is (in the spirit of scientific realism). In this sense, all of physical theories are just tools for making more or less accurate predictions of matters, of course. None can be favoured because of its metaphysical foundations.

I have no problem with the possibility of existence of fundamental limitations on the local (space- or time-bound) computational power of universe. However, your proposed idea indeed seems to me metaphysical in essence. I fail to see the signs of its testability.

Kind regards,

Michal Krajnansky

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Author Efthimios Harokopos replied on Nov. 14, 2014 @ 15:58 GMT
Michael,

I do not expect you to read this after two years. I do not approach experiments from an emotional viewpoint, like you said that you "feel some unease". People also felt unease to fly a plane or break the sound barrier last century. The only way to see what experiments produce is to do them. You say "However, your proposed idea indeed seems to me metaphysical in essence." But how can an experiment be metaphysical?

"When eventually found, it would feel temptating to ascribe it to the features of the suggested virtual functional reality."

No, this is not what the paper says. The paper says that "The objective of this experiment will be to falsify or corroborate the functional virtual reality model"

I am looking for falsification indication, of the particular idea. If I get constraints on local computation, that can only be a loose corroboration of the virtual reality hypothesis. More experiments will have to be made and on different grounds to get a full corroboration. I am looking at a first step. That is all.

Thank you.




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