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Undecidability, Uncomputability, and Unpredictability Essay Contest
December 24, 2019 - April 24, 2020
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What Is “Fundamental”
October 28, 2017 to January 22, 2018
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Wandering Towards a Goal
How can mindless mathematical laws give rise to aims and intention?
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Trick or Truth: The Mysterious Connection Between Physics and Mathematics
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How Should Humanity Steer the Future?
January 9, 2014 - August 31, 2014
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It From Bit or Bit From It
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Questioning the Foundations
Which of Our Basic Physical Assumptions Are Wrong?
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Is Reality Digital or Analog?
November 2010 - February 2011
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What's Ultimately Possible in Physics?
May - October 2009
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The Nature of Time
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Vesselin Petkov: on 6/9/11 at 1:51am UTC, wrote Thank you, Vladimir. With my best wishes, Vesselin Petkov

Vladimir Tamari: on 6/6/11 at 8:46am UTC, wrote Congratulations for your win!

Michael Jeub: on 4/21/11 at 22:23pm UTC, wrote Thanks for the explanation. You are correct I should have done some...

Alan Lowey: on 3/19/11 at 11:03am UTC, wrote Dear Vesselin, Congratulations on your dedication to the competition and...

Honda Shing: on 3/17/11 at 7:28am UTC, wrote Dear Vesselin, Someone suggested me to read your essay a few weeks ago. I...

Eckard Blumschein: on 3/15/11 at 8:59am UTC, wrote Dear Vesselin, You excellently reminded of Feynman's mysticism and tried...

Lawrence Crowell: on 3/13/11 at 22:50pm UTC, wrote Your paper is interesting. I wrote a paper ...

Janko Kokosar: on 3/13/11 at 11:29am UTC, wrote Dear Mr Petkov You write very clearly. Reading your essay, I also obtain...


Steve Dufourny: "Hi Jim, yes it is in the present, the present is important, we exist in..." in The Quantum Clock-Maker...

Jim Snowdon: "Hi Steve, When light leaves the Sun, it does so in the present. ..." in The Quantum Clock-Maker...

Stefan Weckbach: "Unfortunately there is not much participation here on this site. So it..." in The Present State of...

Georgina Woodward: "Marcel, John, what do you think of the arguments I have presented?" in The Nature of Time

Lorraine Ford: "P.S. No matter what mathematicians do (and no matter what complexity..." in The Present State of...

Steve Dufourny: "Hello Daniele Oriti, I liked your approach for this quantum gravitation...." in The universe as a quantum...

Lorraine Ford: "David and Kelvin, But what IS consciousness? I would say that the..." in Consciousness and the...

Lorraine Ford: "Markus, I think you are over complexifying everything. I can only repeat..." in The Room in the Elephant:...

click titles to read articles

The Quantum Engineer: Q&A with Alexia Auffèves
Experiments seek to use quantum observations as fuel to power mini motors.

The Quantum Clock-Maker Investigating COVID-19, Causality, and the Trouble with AI
Sally Shrapnel, a quantum physicist and medical practitioner, on her experiments into cause-and-effect that could help us understand time’s arrow—and build better healthcare algorithms.

Connect the Quantum Dots for a New Kind of Fuel
'Artificial atoms' allow physicists to manipulate individual electrons—and could help to reduce energy wastage in electronic devices.

Can Choices Curve Spacetime?
Two teams are developing ways to detect quantum-gravitational effects in the lab.

The Quantum Engine That Simultaneously Heats and Cools
Tiny device could help boost quantum electronics.

September 24, 2021

CATEGORY: Is Reality Digital or Analog? Essay Contest (2010-2011) [back]
TOPIC: Continuous and Discrete Aspects of Nature by Vesselin Petkov [refresh]
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Author Vesselin Petkov wrote on Feb. 15, 2011 @ 12:34 GMT
Essay Abstract

The aim of this essay is to try to provide an open-minded look at some of the problems in fundamental physics which resulted from the idea of quantization. The sole reason for this attempt is to examine whether those problems might have been caused by an implicit exclusion of the correct, but radical and counter-intuitive research directions. Three topics will be discussed -- (i) the nature of the quantum object, (ii) quantum gravity, and (iii) whether or not the Planck scale implies discreteness of spacetime itself.

Author Bio

Vesselin Petkov received a graduate degree in physics from Sofia University, a doctorate in philosophy from the Institute for Philosophical Research of the Bulgarian Academy of Sciences, and a doctorate in physics from Concordia University. He taught at Sofia University and is currently teaching at Concordia University. He wrote the book "Relativity and the Nature of Spacetime" (2ed, Springer 2009) and edited the books "Relativity and the Dimensionality of the World" (Springer 2007), "Minkowski Spacetime: A Hundred Years Later" (Springer, 2010), and "Space, Time, and Spacetime: Physical and Philosophical Implications of Minkowski's Unification of Space and Time" (Springer, 2010).

Download Essay PDF File

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John Benavides wrote on Feb. 18, 2011 @ 09:25 GMT
Dear Vesselin

I enjoyed very much your essay. I agree with many of your objections about widespread notions but I think you are missing a fundamental point that it will close all your reasonings and I think it can enrich your ideas. I invite you to read my essay to understand what I think you are missing and I would like to hear your opinions.


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Author Vesselin Petkov replied on Feb. 20, 2011 @ 03:27 GMT
Dear John,

Thank you for both your comments and your invitation to read your essay. I will certainly do it.

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Chris Kennedy wrote on Feb. 19, 2011 @ 19:52 GMT
Very well written. Many thought provoking questions. Feynman would be proud.

With regard to your double slit explanation: if the electron is in different times as opposed to spaces, how is it (assuming random nature) that it always takes a path in time that produces an interference pattern? Why wouldn't the electron sometimes land in a spot permitted by single slit and not double?

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Author Vesselin Petkov replied on Feb. 20, 2011 @ 03:30 GMT
Thank you for your comments, Chris.

Regarding your question, let me first say that I would not call what I described an "explanation"; I simply wanted to demonstrate that it is not unthinkable to imagine a quantum object that is both always registered as a localized entity and is going through both slits. That idea needs to be tested and further developed; the initial proposal (back in the eighties) described the constituents of an electron as appearing where the maxima of a somewhat real de Broglie wave are. So you asked the most relevant and essential (but still open) question, which follows from the discussed idea.

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re castel wrote on Feb. 25, 2011 @ 10:38 GMT

I find your concern regarding "the nature of the quantum object" very interesting. You have a very thought-provoking essay that touches on the ideas that I have proponed in my own essay.

Therefore, I am also giving you my vote.

I hope you will also read my essay and also give me your vote.


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Author Vesselin Petkov replied on Feb. 26, 2011 @ 04:27 GMT
Thank you for your comments, Rafael. I have freed my weekend to continue reading the essays here and will certainly read yours.

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Don Limuti ( wrote on Feb. 26, 2011 @ 20:31 GMT

1. A well written essay (perhaps another prize) good work.

2. I agree with you about particles and how they manifest discontinuously.

You are obviously sticking your neck out and you have my admiration.

3. My work is more into the speculative realm (maybe much more) but you may find things of interest there that may aid your work. If you have the time take a look at:

a. this essay contest: Making Waves

b. last essay contest: Gravity from the Ground UP

c. My web site:

Wishing you the best,

Don Limuti

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Author Vesselin Petkov replied on Feb. 27, 2011 @ 19:54 GMT
Thanks a lot Don.

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Peter Jackson wrote on Mar. 3, 2011 @ 11:20 GMT

I've only just read your essay and wish I had sooner. A very clear and well written analysis with pertinent questions, worth a good score. But I also see it as a precursor to mine, which reports on a model seeming to answer the most key questions, and falsifiably! - effectively a quantisation of both space-time and gravity. I initially assumed it incorrect, but have failed to prove that, and no-one else has yet been able to help.

Your own view would be much appreciated if you have time. But you can't get the value from just 'scanning' it. Be prepared for a 'coal face' logical reality approach, and to stretch your dynamic visualisation skills beyond previous limits.

Best of luck in the contest.


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Robert Spoljaric wrote on Mar. 4, 2011 @ 12:35 GMT
Dear Dr. Petkov,

Beautiful essay. In it you tell us: "(t)he assumption that electrons (and quantum objects in general) do not exist continuously in time appears to provide unexpected but reasonable conceptual answers to probably all

quantum puzzles."

In my essay is a generalisation of the energy of a photon, which renders your assumption superfluous, but does raise the question of whether or not it will eventually answer all quantum puzzles. Being a physicist you may be able to answer that question.

All the best,


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Robert Spoljaric replied on Mar. 4, 2011 @ 23:31 GMT
Dear Dr. Petkov,

If I may, I would just like to add that it follows - from what I said above - that the 'Nature of the Quantum object' at the 'quantum' level is Light.

Once again thank you for your thoughts,


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T H Ray wrote on Mar. 4, 2011 @ 15:48 GMT

Your essay is an oasis in the desert of confusion. Thanks!

Hope you get a chance to read mine, too.


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Adolfo Leija wrote on Mar. 6, 2011 @ 13:02 GMT
Hi Vesselin,

these are some comments on three passages of you essay.


"I think everyone would agree that we will never gain deep understanding of the

world if legitimate physical questions – such as those of the nature of the entities living

at the quantum scale – are ignored by labeling them metaphysical or philosophical"

I go further in this regard. I think we will never gain a full deep understanding of the world (Reality), however we will keep asking questions and trying to understand how Reality works.

"We, as species, would not have survived if Dirac’s analysis and

conclusion were wrong because in such a case photons reflected by different objects

would interfere before hitting our eyes’ retina and we would be unable to see the world


This type of argument makes me think that Feynman was not joking when he said nobody understands Quantum Mechanics. The type of argument is " The results are correct because if they are different then I would not exist" In this type of arguments we disregard the possibility that the model is wrong or incomplete.

Still with Feynman. I also think he wasn't joking because knowing how a black box behaves does not mean we know or understand what it is inside. In this respect Quantum Mechanics it is just a model for what we think it is inside a black box and we are still trying to understand what is it inside.

"The Eleatics believed that being (what exists) is continuous

and that nothing can come into or go out of being because it would contradict a basic

postulate – being exists, non-being does not exist – which can be deduced from what

we perceive"

Existence and Non- Existence are not separable, because Non-Existence is a function of Existence. We always need an object to say that there is "nothing". I think of an empty box and say that there is nothing in there. Well, I can look closer and say there is air in there. On this sense we can keep looking for smaller scales and look closer as we can. In the same context, we define Existence for what we do perceive and Non Existence for what we do not perceive. In this way Reality could be Digital.

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James Lee Hoover wrote on Mar. 7, 2011 @ 19:23 GMT

You make clear the esoteric. My essay is clear but perhaps too fanciful.

Jim Hoover

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Peter Mastro wrote on Mar. 8, 2011 @ 12:14 GMT
Hello Vesselin,

I enjoyed your essay. One of the things I enjoyed about it most is that it obviates the difference between how a scientist views and interprets phenomena differently than an artist. If I take for example the Feynman experiment that perplexes science. The fundamental problem with a "science" view of light is that it views photons as things that area zipping through space. The analogy I always draw is that if you look at a body of water and observe the waves in it, the molecules in the water are not moving through the water. They move back and forth and up and down to maintain balance in relation to the forces that are acting upon them. The Feynman experiment supposes that space is nothing when it is not. Science should view space as a photonic energy field that is structured such that photon density increases in relation to its proximity to mass, and it should view mass as a point in space where time turns from 3D to 4D. The interference in the Feynman experiment is not the individual photon that is injected into the space, but rather the behavior of the "potential" photons that already exist in the space of the experiment that are "pushed" discretely.

As for quantizing gravity, in my mind the quantization of gravity is the same as the quantization of time. Time is the only singular force at work in the universe that all forces delineated by science stem from. The problem with using the Planck scale as a measure in all of space is that it will be observable because the observer observational model will create it. Unobserved the planck scale can only be used relationally. Time is the only constant, and the concept of distance or scale or mass or energy are all defined in relation to it.

If you get a chance I would be interested in what your view is of how I tend to view these scientific models. If you are interested in where I am coming from you can take a look at my essay here.

Thanks for your essay I enjoyed it and will be giving you high marks in the community rating.


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Vladimir F. Tamari wrote on Mar. 8, 2011 @ 14:33 GMT
Dear Vesselin

I enjoyed your essay and learned some interesting things from it. Many years ago when proposing a scheme to cancel diffraction effects, I quoted Dirac's saying that a photon only interferes with itself; now thanks to you I see his reasoning for this conviction. Your essay presents with great expertise a number of fundamental questions that I have already answered in 2005, albeit with a great deal less expertise, relying for the most part on my physical and geometrical intuition and imagination as an inventor. I would greatly appreciate it if you can look at my ideas to reconstruct physics both in the fqxi essay, and in my earlier 2005 Beautiful Universe paper on which it is based.

With best wishes for your success, Vladimir

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Wilhelmus de Wilde wrote on Mar. 8, 2011 @ 15:48 GMT
Dear Vesselin,

Thank you for an essay that is really understandable, even for a non physicist like me, and moreover you are the first who is touching the problem of the Planck scale, scientists have thought about all possible kind of things happening after this scale , so the for example the points of the disintegrated world line of the electron that are ^robabelistic scattered over a spa

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wilhelmus de wilde replied on Mar. 8, 2011 @ 16:08 GMT
sorry Vesselin, I touched a wrong button, so I continue now my post :

(and could not read it twice in order to change the errors...)

probabelistically sctattered over all over space time " is a sentence I really like, because I place all that scattered points (not only from one electron but from all partcles in our universe and also of all possible paralel universes in a total simultanaeity (essay : realities out of total simultaneity (

I liked also your reasoning that because a falling object does not resist its fall means that it is not subjected to gravaitational force, but second thought gave me the idea that it does indeed not resist but as it falls towards a body with a great gravitational force the velocity increases, the subject itself may not be aware of that fact when it is in for exemple an elevator falling down, the subject is staying at the same velocity as the elevator ... (same with a space ship) See also the article by George Gamow Gravityin Scientific American march 4 1961 (now available as special Archive article (
ity), how do you see that ?

best regards and good luck


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Michael Jeub wrote on Mar. 9, 2011 @ 01:50 GMT
I read the "theory of heat radiation" by Plank and translated by Masius and the formulas and how Plank came up with the stuff you show it as though Plank used those formulas. My question is whether the "Theory of Heat Radiation" by Plank is the document in which he shows how he got quantization. Didn't Plank take Wien and Raleigh and Boltzmann and put them in his concept of black radiation. Is there another work of his that deals with the entropy of Einstein fields or G? Your formulas are correct and are expressions for Freedman universes or some kinds of universal entropy we recognize in our physics books. However, the roads to the Planck scale are different for Planck, but you imply that his was Adler's. I get your point but do not follow back from those formulas directly to Planck's work or what he "noticed" in his work. As an editor and writer would you make such a correction to reflect that we construct natural units and attribute them to Planck as Planck units based on his quantization hypothesis? It is important for me to know what a scientist notices and what is constructed afterwards. Please correct me if I am wrong, but I don't think Planck constructed those formulas. But if you have and more references for how that came to be characterized in 1899, I would like to know.

It was interesting to hear you explain how inertia of one object (a planet) is separate for the system of objects but that there is some greater generalization in terms of helicity or helix, but not dependent on the sun. The world tube is composite of geodesics? I have always assumed like Mach that inertia and spin etc. are all related, but wil we have the sensitivity yet to measure world tube differences? I always assumed that the vacuum encompasses all objects so that the true absolute free fall does not exist.

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Author Vesselin Petkov replied on Mar. 9, 2011 @ 04:52 GMT
"As an editor and writer would you make such a correction to reflect that we construct natural units and attribute them to Planck as Planck units based on his quantization hypothesis?"

Before making such a request I think it would have been nicer (and wiser) if you had first checked M. Planck's paper "Uber irreversible Strahlungsvorgange" (On irreversible radiation processes) to which I referred through Adler's article (ref. 14 in my essay). Please have a look at the last page of Planck's paper and you will see that it was indeed Planck himself who introduced those units and called them "natural units" (he defined four natural units - length, mass, time, temperature).

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Michael Jeub replied on Apr. 21, 2011 @ 22:23 GMT
Thanks for the explanation. You are correct I should have done some checking. Often it is the case that I do not have access to the things cited in an article. It is generally not nice or wise that physics make too many shortcuts with history, but I am getting used to it.


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Peter wrote on Mar. 9, 2011 @ 12:59 GMT

Then, what is your answer to the question of the essay? I don't see any answers but only general and historic references going back to 20 centuries ago.

IMO, the objective of the essay contest is for providing a thesis against or for discrete or continuous and then try to support it. I don't think this essay contest deals with the philosophy and history of science.

I was really disappointed by this essay.

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Sreenath B N wrote on Mar. 10, 2011 @ 05:55 GMT
Dear Vesselin Petkov,

I went thro' your exhilerating essay with ease and enthusiasm but in the end was disappointed to know that you suggested no solution to quantize gravity.I urge you to go thro' my article and see how gravity is quantized.

best regards and good luck.

Sreenath B N.

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Jacek Safuta wrote on Mar. 11, 2011 @ 21:32 GMT
Dear Vesselin,

Thank you for your essay.

You write: …The physics behind the two descriptions is fundamentally different – as gravity is either a force or a manifestation of the curvature of spacetime…

Let us assume, as I propose in my essay, that all interactions are not forces but a manifestation of the (exotic) curvature of spacetime? All troubles with physics are gone. This is really simple approach however being only a concept at the moment. How do you think: is it worth to try?

Jacek Safuta

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Janko Kokosar wrote on Mar. 13, 2011 @ 11:29 GMT
Dear Mr Petkov

You write very clearly. Reading your essay, I also obtain one idea for my article. I will give there your reference: (I was late for this contest, so my ideas can be read here.)

Anyway, I claim that physics is quantized. But, I claim that elementary particles are statistical combinations of 0 and 1 Planck's mass (approximately said). Elementary particles are also nodes of space-time net. In my opinion space-time is emergent, similarly as a computer network is emergent.

But, I have not found anyone on this contest who cited Zeilinger-Brukner, whoose claim that information is very small volume is finite. Probably I have different taste for physical theories. :)

So there fails still your opinion whether information on a small piece of space is finite or infinite, although your space-time is infinite.



I have also an article, which is not speculative and it is a base for the above article: There are also additional claims about connections between matter and space-time. I need someone who will be the arxiv endorser for this article. So that I will get opportunity, that my theories will be discussed.

I have also essay on FQXI from one year ago:

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Lawrence B Crowell wrote on Mar. 13, 2011 @ 22:50 GMT
Your paper is interesting. I wrote a paper

which discusses the interrelationship between discrete and continuous structures. I am not sure if you will find this commensurate with yours.

The Planck scale does not in my opinion means space is discrete. I think it means this is the smallest region one can localize a quantum bit.

Cheers LC

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Eckard Blumschein wrote on Mar. 15, 2011 @ 08:59 GMT
Dear Vesselin,

You excellently reminded of Feynman's mysticism and tried to overcome it by a more cautious consideration. In the end I did not yet see serious consequences while your will perhaps not hurt anybody.

My essay in combination with what I today replied on desynchronization to Georgina Parry in my thread 833 causes a lot of opposition from virtually all mathematicians and physicists. I cannot expect immediate acceptance. You are invited to accept the challenge and refute my reasoning even after the contest has finished.



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Honda Shing wrote on Mar. 17, 2011 @ 07:28 GMT
Dear Vesselin,

Someone suggested me to read your essay a few weeks ago. I wish I had taken the advice and read it earlier. I like the way you reasoned the discreteness of a particle's existance in time based on experimental facts and logical deduction.

In my essay, "A Connectivity Theory of Space and Time", I proposed an explanation for the apparent discreteness of particle trajectories. Based on the postulates of the proposed theory, a world line becomes a collection of "world points". Since it closely resembles some of your conclusions, I think you may be interested to review the essay.


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Alan Lowey wrote on Mar. 19, 2011 @ 11:03 GMT
Dear Vesselin,

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,


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Vladimir F. Tamari wrote on Jun. 6, 2011 @ 08:46 GMT
Congratulations for your win!

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Author Vesselin Petkov replied on Jun. 9, 2011 @ 01:51 GMT
Thank you, Vladimir.

With my best wishes,

Vesselin Petkov

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