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FQXi FORUM
May 25, 2012
CATEGORY:
FQXi Essay Contest - Is Reality Digital or Analog?
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TOPIC: Could Infinity Solve the Analog-Digital Dilemma? by Antonio Leon [refresh]
TOPIC: Could Infinity Solve the Analog-Digital Dilemma? by Antonio Leon [refresh]
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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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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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.
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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.
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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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.
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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
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I am not sure about these constructions in physics honestly.
Cheers LC
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Sub: Possibility of manipulation in judging criteria – suggestions for improvement.
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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.
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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...
view entire post
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