Essay Abstract
While solving the mathematical problem of continuum, the author of the paper has come to a conclusion of the necessity to introduce into the numeral mathematics the continuity principle (continuum) which is defined in philosophy.
Author Bio
I am an independent theoretical physicist. My interest is the study of the foundations of theoretical physics. I have published in the Internet more than 20 scientific articles.
Murat
The issue is resolving how diiference occurs when there is discrete. And the answer is sequence. Continuous is the same state permanently. But if you have an unbelievably high speed and vanishingly small alteration it can appear continuous. Like a movie, which ultimately comprises frames.
Paul
Interesting ideas but are you just saying that physics requires continuous quantities rather than discrete, or are you saying that the continuum hypotheses is important for physics?
There is a concept of substance and phenomenon in philosophy. The continuity is substance, and vanishingly small alteration at an unbelievably high speed is the phenomenon, since it only seems that the process is continuous. To seem to be continuous and to be continuous in fact are different things. Unfortunately physicists in most cases can not distinguish between the phenomenon and the substance. The conclusion of my work is: firstly, the actual infinity cannot be represented, thus the use of actual infinity concept in mathematical theories is illegal; secondly, Cantor's set theory is wrong, because it is based on the concept of actual infinity. All the evidence in this theory are based on a potential infinity. Cantor's set theory creates many paradoxes, so this theory is incorrect and its use for mathematics should not be accepted.
The solution of continuum hypotheses represents great importance for physics. For instance, the basics of quantum mechanics are in contradiction with Aristotle's principle of continuity. According to quantum mechanics an electron in the atom at the emission of a photon makes an instant quantum leap from one orbital to another one. As the result physicists' consideration loses process-event of the photon and electron neutrinos creation at the transition of an electron from one orbital to another. The postulates of quantum mechanics, in principle, do not give the chances to understand the nature of the photon and electron neutrinos in the future.
Murat
I am not bothered about philosophy, which is a waste of time.
We know there is an existence and we know it involves difference. I am not interested in possible alternatives to what we can potentially know, since that is determined by an identifiable physical process, whilst alternatives are just belief.
Thus is order to resolve this apparent conundrum, the physical existence we can know must be an existential sequence of discrete, definitive, physically existent states. The problem is that we do not realise this. Generally we get as far as, 'it has changed'. Which is a contradiction in terms. If it has changed then it I something else.
Paul
The continuity problem in mathematics was solved by Dedekind 300 years ago. He is the author of the best definition of continuity (continuity principle); your essay adds nothing to the continuity theory or continuum.
Firstly, if the continuum problem had solved by Dedekind, so Gilbert in 1900 wouldn't put this problem as first on the list of unsolved problems of mathematics. Secondly, you need to know difference between a "continuum set" and a "continuum". They aren't similar definitions. So Dedekind worked in the concept of a continuum set. By the principle of continuity of Aristotle, I'm asserting that line of numbers, in principle is impossible to imagine like the actual infinite set. And thirdly, from my solution of continuum problem follows that the actual infinite number set unimaginable and therefore the theory of Cantor's set is wrong. In physics the foundations of quantum mechanics are in conflict with the principle of continuity of Aristotle, so the theory of quantum mechanics is wrong too, which was to be proved in my essay "Physical nature of rotation figures of atom's electron shells configurations formations (atom's electron shells configurations). Magnetic poles physical nature. Exchange energy physical nature". This essay participated in the previous contest.
My world view is based on the philosophy.
critic,
Stetigkeit und Irrationale Zahlen, Vieweg 1872, is not yet 300 years old. Moreover, Dedekind admitted in it that he hopes to persuade the reader because there is no evidence available for his cut.
murat Asgatovich gaisin,
Hilbert, not Gilbert referred to Cantor's cardinality when he spoke of the continuity problem. You are right in so far that Cantor's infinitum creatum sive transfinitum is logically untenable split thinking. Fraenkel who was perhaps the most important defender of Cantor's set theory admitted in 1923 that Cantor's definition of a set is untenable. Yes, Aristotle understood: "There is no actual infinity". Nonetheless, you can geometrically imagine the sum 1/2 1/4 1/8 ... as an entity of size 1 without knowing all single components.
If you read Fraenkel critically, you will even find in what Cantor's second diagonal argument was wrong. He assumed all of actually infinitely many numbers as fixed.
I will look for your previous essay. You might read and comment on the last two of mine.
Eckard
Eskard,
The sum of an infinite geometric series 1/2 1/4 1/8 ... is not equal to 1, even in the geometrically imagine, because it is based on a potentially endless process of fragmentation. But the limit of the sum of an infinite geometric series is equal to 1. Nuance, but it is very important for a proper understanding of the nature of infinity.
Dear Asgatovich
I agree with the idea in your conclusion, but perhaps we need a solution is specific and more detailed.
http://fqxi.org/community/forum/topic/1802
Hello, Murat!
I enjoyed reading your essay and your all articles on http://www.sciteclibrary.ru/rus/avtors/g.htm
l pleasantly surprised by the breadth and depth of your views and ideas. In September, the Moscow State University hosts a conference on the philosophy of mathematics. Will you participate?
I wish you success! Vladimir
Dear Murat,
Your essay is really interesting,but I need have time to check your references in details also. Please check my essay, you will find some different approach to fundamental problems of physics, but I hope you will welcome it as an independently thinking men. I am appreciated your work as a ,,good,,
Best wishes,
George
Dear Murat,
I think I understand where you are coming from with regard to continuum problem. Do you mean that it is at odds with Quantum Mechanics? If so then I think geometry can solve this, because it can be both discrete and continuous. Sorry if I've misunderstood this.
Also did you conclude Bit from It or It from Bit?
Best wishes,
Antony
Murat,
If given the time and the wits to evaluate over 120 more entries, I have a month to try. My seemingly whimsical title, "It's good to be the king," is serious about our subject.
Jim
Murat,
I see from the comments that sadly few have understood or seen the value of your proposition. I certainly do and commend you, as you'll see from my own essay which develops the theme by testing the power of continuous helical curves. I refer to Bayesian inverse distributions (quantum iPAD's) between cardinals as 'fuzzy subsets'.
Have you explored the parallel with Godel's 'n-valued'/fuzzy logic?
You also beautifully point out the issues with infinities, transcendental and irrational numbers, and the limitations of symbols, as I do with both. I loved your reference to "mathematical objects which can be calculated with arbitrary exactness." I suggest a position for a 'Dirac line' between and defining metaphysical math/derivatives, as separate from real physical nature as entities and interactions.
I'm pleased to have taken something more from your essay, including learning of Aristotle's great wisdom, and a greater confidence to reject the cardinalisation I too discuss and constrain. As an astronomer I have also found compelling argument for the essential dark energy condensate and foundation of nature as a continuum.
I believe your essay needs to be more widely read, and I'm pleased to be able to score it well. You may also be familiar with or wish to read that of Vladimir Rogozhin, but I greatly look forward to your views and comments on mine, particularly my suggestion regarding the foundations of the poor logic and mathematics.
Both our essays may perhaps be summed up as examining the; "existence of the intermediate cardinal between cardinal number and cardinal of continuum."
Very best of luck in the competition.
Peter
Dear Murat,
We are at the end of this essay contest.
In conclusion, at the question to know if Information is more fundamental than Matter, there is a good reason to answer that Matter is made of an amazing mixture of eInfo and eEnergy, at the same time.
Matter is thus eInfo made with eEnergy rather than answer it is made with eEnergy and eInfo ; because eInfo is eEnergy, and the one does not go without the other one.
eEnergy and eInfo are the two basic Principles of the eUniverse. Nothing can exist if it is not eEnergy, and any object is eInfo, and therefore eEnergy.
And consequently our eReality is eInfo made with eEnergy. And the final verdict is : eReality is virtual, and virtuality is our fundamental eReality.
Good luck to the winners,
And see you soon, with good news on this topic, and the Theory of Everything.
Amazigh H.
I rated your essay.
Please visit My essay.
I am not sure I understand it, but I gave you a in to help out.
Hope you like mine:
http://www.fqxi.org/community/forum/topic/1616
Dear Murat,
I have now finished reviewing all 180 essays for the contest and appreciate your contribution to this competition.
I have been thoroughly impressed at the breadth, depth and quality of the ideas represented in this contest. In true academic spirit, if you have not yet reviewed my essay, I invite you to do so and leave your comments.
You can find the latest version of my essay here:
http://fqxi.org/data/forum-attachments/Borrill-TimeOne-V1.1a.pdf
(sorry if the fqxi web site splits this url up, I haven't figured out a way to not make it do that).
May the best essays win!
Kind regards,
Paul Borrill
paul at borrill dot com
