Essay Abstract

No significant aspect of reality seems to be infinitely divisible, except perhaps space and time. Two entities usually considered as continuums modeled by the densely ordered set of the real numbers. The formal consistency of the analog model of spacetime depends, therefore, on the consistency of the densely ordered sets, which in turn depends on the consistency of the actual infinity hypothesis. Under the assumption that reality is itself consistent, that dependence makes it possible to test the consistency of the analog model: to prove the inconsistency of the actual infinity. This paper presents five short arguments suggesting that notion could be, in fact, inconsistent. In consonance with that possibility, the paper introduces a new way of discussing on some elementary aspects of spacetime and of relativity in cell-automaton like models. It also suggests an experimental way to test a simplified digital model of spacetime.

Author Bio

The author is a geologist (Univ. Granada, Spain) with regular studies in Mathematics (UNED, Madrid, Spain) and Logic and Philosophy of Science (UNED, Madrid, Spain). Research and publications in physical aspects of organic evolution, a field that he abandoned to devote all of his time to examine the hypothesis of the actual infinity from the critical perspective of a non-platonic field naturalist. After eighteen years of research and discussions, he is now evaluating the consequences of this and other presocratic ideas on the foundations and development of experimental sciences.

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  • [deleted]

Hello dear Antonio Leon,

Your work was a pleasure to read.The infinity is so difficult to explain. Generality, still that generality infusing us rationalities. It is so essential. Infinity and its interpretation is so correlated to the evolution of our space-time. As the sisters of our walls of perception. Physicality seems under purely finite systems, they could involve infinite perception in their analysis, yet they are finished, coded and precise in their pure evolution.Can we see? no! is it infinite? no! just finite but far of us, can we see the Planck scale, no, can we imagine it, yes but with rationality.All has its specific system in fact.And its number!

The infni, the -, 0 are human inventions, the infinite is a perception of our walls,for example, we have a finite number of stars in our Universe,can we calculate it, no, can we appraoch it , yes with the evolution of course.

Best Regards and good luck for this contest.

    • [deleted]

    Hello Antonio,

    You are one more fighter against the actual infinity. If you read German, I recommend to you the booklet "Mathematik des Unendlichen" by Prof. W. Mueckenheim, a dean in Augsburg.

    In my essay I take a slightly different position: If we deviate from Cantor and return to infinity as a fiction that can neither be enlarged nor exhausted, then we may consider two mutually complementing aspects of it: Seen from inside the rational numbers, there is just a potential infinity that cannot be reached, seen from outside we may consider the actually infinite entity of all elements that belong to a converging series. I see G. Cantor a tragic figure who got insane. Read Ebbinghaus as to conclude that the current mainstream mathematics performs some sort of self-deception. The question is how do they interpret the real numbers. I tend to see Peirce correct when he spoke of a pseudo-continuum (of Q). I am suggesting to consider the real numbers as a true (Peirce) continuum outside the realm of numbers that are subject to trichotomy.

    Regards,

    Eckard

    • [deleted]

    We can multiplicate the numbers but that doesn't mean that the finite system changes....I can multiplicate the number of stars and the number of moons for example, that doesn't mean that this number of cosmological spheres exist.an add is more logic.

    We can thus confound the walls, the infinity, and the finite systems, evidently if the rationality about the pure number is not inserted.

    All is a question of general point of vue in fact...

    Congratulations and good luck.

    Best Regards

    Steve

    10 days later
    • [deleted]

    Mr. Sanchez,

    Hi. I thought your essay was very good. I also discuss actual and potential infinites in my essay (Reality is digital but its perception as digital or analog depends on the perspective of the observer). The main issue I have with measuring the size of an infinite subset relative to the size of the set from which it was extracted relates to my background in biochemistry and is as follows. Mathematicians say that if you start with a single, initial set of all the positive integers and then pull out the subset of even integers and pair off the evens in the subset one-to-one with all the integers in the initial set, then you can see that because of the one-to-one correspondence, the number of elements in the subset is the same as in the original set. This is a thought experiment, but it is still an experiment and should use proper experimental technique. However, the pairing off method uses very bad experimental technique, in my opinion. That is, the system to be studied is the single original set of all the positive integers. The experimental processing is pulling out the subset and pairing it off with the elements in the original set. The results from this experimental processing on two separate sets (equal set sizes) are then assumed to be the same as in the original single set. This is similar to studying the interactions of a cell nucleus with the rest of the cell (ie, the cytoplasm) by pulling out the nucleus, putting it in a separate test tube from the rest of the cell, studying it there and assuming the results of the processed, separate nucleus-cytoplasm systems are the same as in the single, whole cell. They're usually not, and this assumption would be totally incorrect and not tolerated in biochemistry because the processing creates the possibility of experimental artifacts (errors introduced by processing). This bad experimental technique shouldn't be acceptable in mathematics either. Even if you say that mathematics is in its own abstract realm, it's also still used in the physical realm of physics. Its use of bad experimental method makes the use of infinities in physics problematic, IMHO

    Anyways, nice essay and thanks for listening to my comment.

    Roger

    12 days later

    Antonio,

    A fine essay. A part of my essay also touches on the relevance of the mathematical infinite to the topic of discrete vs. continuous.

    I have one observation for you: The distinction between finite and infinite, which is the focus of your essay, is different than the distinction between digital and analog (or discrete and continuous). The countable infinite, in particular, is not a continuum but is discrete. Dispensing with the infinite thus would restrict us to not merely a discrete theory, but a finite discrete theory.

    Regards,

    Tom

    10 days later
    • [deleted]

    I like your essay because it points out, or at least eludes to, the inherent problem associated with anything that has infinity as a limit condition. I view the problem in applying such limit conditions in science as being a result of the fact that such limits are also an inherent problem in mathematics. I view infinity as an imaginary limit and any "counting" or segmentation less than infinity is also imaginary. I personnaly believe everything is finite in the real universe, and things like time and space are "potentially" infinite, but we have no way to determine if that is true because we have no degree of freedom relative to time to observe.

    If you get a chance check out my essay at http://fqxi.org/community/forum/topic/893

    It looks at this question from an artistic perspective and describes the universe as a purely imaginary construct.

    • [deleted]

    Your argument on page 5 has a problem. The ordinal number ω is the least infinite ordinal identified with the cardinal number אּ0. This is then an identificaiton of a set, for infinity is not a number in the proper sense. It is a set. So your construction concerning the predecessor to a transfinite ordinal is not a proper definition. It is like trying to call an element of a set the predecessor of the set itself.

    I am not sure about these constructions in physics honestly.

    Cheers LC

    18 days later
    • [deleted]

    Sub: Possibility of manipulation in judging criteria - suggestions for improvement.

    Sir,

    We had filed a complaint to FQXi and Scienticfic American regarding Possibility of manipulation in judging criteria and giving some suggestions for improvement. Acopy of our letter is enclosed for your kind information.

    "We are a non-professional and non-academic entrant to the Essay contest "Is Reality Digital or Analog". Our Essay under the same name was published on 29-12-2010. We were associated with Academic Administration as a part of our profession before retirement. From our experience, we were concerned about the problems and directions of current science. One example is the extended run and up-gradation given to LHC, (which was set up to finally prove that Standard Model and SUSY were wrong), even when Tevatron is closing down. Thus, after retirement, we were more focused on foundational works addressing, in one of its many facets, our understanding of the deep or "ultimate" nature of reality.

    Specifically we were concerned about the blind acceptance of the so-called "established theories" due to the rush for immediate and easy recognition even on the face of contradictions raising questions on the very theories. One example is the questions being raised on the current theories of gravitation after the discovery of Pioneer anomaly. While most students know about MOND, they are not aware of the Pioneer anomaly. Most of the finalists of this contest have either not addressed or insufficiently addressed this question. We hold that gravity is a composite force that stabilizes. This way we can not only explain the Pioneer anomaly and the deflection of the Voyager space-craft, but also the Fly-by anomalies.

    Similarly, we were concerned about the blind acceptance of some concepts, such as inertial mass increase, gravitational waves, Higg's boson, strings, extra-dimensions, etc. Some of these are either non-existent or wrongly explained. For example, we have given a different explanation for ten spatial dimensions. Similarly, we have explained the charge interactions differently from the Coulomb's law. We have defined time, space, number and infinity etc., differently and derived all out formulae from fundamental principles. There are much more, which we had discussed under various threads under different Essays. We are the only entrant who defined "reality" and all other technical terms precisely and strictly used this definition throughout our discussion.

    Though our essay was on foundational concepts and we derived everything from fundamental principles, it was basically alternative physics. Moreover, we are not known in scientific circles because we did not publish our work earlier. Hence it is surprising that even we got a community rating of 3.0 and (12 ratings) and Public Rating of 2.5 (2 ratings). We have no complaints in this regard. However, we have serious reservations about the manner in which the finalists were chosen.

    A set of thirty-five finalists (the "Finalists") have been chosen based on the essays with the top Community ratings that have each received at least ten ratings. The FQXi Members and approved Contest entrants rate the essays as "Community evaluators". Since many of the FQXi Members are also approved Contest entrants, this effectively makes the contestant as the judge for selection of the finalists. This process not only goes against the foundational goals of the Contest, but also leaves itself open for manipulation.

    Most contestants are followers of what they call as "mainstream physics". Thus, they will not be open to encourage revolutionary new ideas because it goes against their personal beliefs either fully (like our essay) or partially (like many other essays that did not find place in the final list. One example is Ms Georgina Parry. There are many more.) The prime reason for such behavior is cultural bias and basic selfish instinct of human beings. Thus, truly foundational essays will be left out of the final list.

    In support of the above, we give a few examples. While there are some really deserving contestants like Mr. Julian Barbour, who really deserve placement in the final listing, the same cannot be said for many others. Mr. Daniele Oriti, who tops the list of finalists, says that whether reality is digital or analog "refers, at least implicitly, to the 'ultimate' nature of reality, the fundamental layer." He admits that "I do not know what this could mean, nor I am at ease with thinking in these terms." Then how could he discuss the issue scientifically? Science is not about beliefs or suppositions. His entire essay exhibits his beliefs and suppositions that are far from scientific descriptions. He admits it when he talks about "speculative scenario". Yet, his essay has been rated as number one by the Community.

    The correspondence between us and Mr. Efthimios Harokopos under his Essay and our comments under the various top ranking finalists show the same pattern. One example is Mr. Paul Halpern. We have raised some fundamental questions under the essay of Mr. Hector Zenil. If the answers to these questions are given, most of the finalists will be rejected. If the idea is to find out the answers to these questions, then also most of the finalists will be rejected.

    The public that read and rated the essays are not just laymen, but intelligent persons following the developments of science. Their views cannot be ignored lightly. Mr. Daniele Oriti, who tops the list of finalists as per community rating, occupies 35th place in public rating. Mr, Tejinder Singth, who is 7th among the list of finalists as per community rating, occupies 25th place in public rating. If public rating is so erroneous, it should be abolished.

    Secondly, the author and interested readers (including FQXi Members, other contest entrants, and the general public) are invited to discuss and comment on the essay. Here personal relationship and lobbying plays an important role. An analysis of the correspondence between various contestants will show that there was hectic lobbying for mutual rating. For example: Eckard Blumschein (Finalist Sl. No. 15) had written on Mar. 15, 2011 to Mr. Ian Durham (Finalist Sl. No. 3) "Since you did not yet answered my question you give me an excuse for not yet voting for you." There are many such examples of open lobbying. One of the first entrants visited most contestants and lobbied for reading his essay. Thus, not only he has received the highest number of posts under his Essay, but has emerged as one of top contenders.

    The above statement gets further strengthened if we look at the voting pattern. More than 100 essays were submitted between Feb.1-15. Of these 21 out of 35 are the finalists. Of these the essays of 14 contestants were published in 5 days between Feb. 14-18. Is it a mere coincidence? For some contestants, maximum rating took place on the last day. For example, on the last date alone, Mr. Paul Halpern rose from 14th place to 5th place, Mr. Donatello Dolce rose from 35th place to 14th place, and Mr. Christian Stoica came into the top 35. All these cannot be coincidental.

    Thirdly, no person is allowed to submit more than one essay to the Contest, regardless if he or she is entering individually or as part of a collaborative essay. Yet, we suspect that some have indulged in such activities. For example, we commented below the essay of one contestant on March 4. We got a reply from the next contestant the same day. The correspondence continued. The original contender has not replied to us. In fact he has only replied twice in 20 posts. This is surprising.

    In view of the above, we request you to kindly review your judging process and forward all essays to an independent screening committee (to which no contestant or their relatives will be empanelled), who will reject the essays that are not up to the mark and select the other essays without any strict restriction on numbers to the final judges panel. This will eliminate the problems and possibilities discussed by us. This will also have the benefit of a two tier independent evaluation.

    Our sole motive for writing this letter is to improve the quality of competition. Hence it should be viewed from the same light".

    Regards,

    Basudeba.

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