Essay Abstract

In this essay, I aim to create perspective on set theory. The first section takes a look at set theory, how it has been defined and its applications. The second section tries to introduce volumes on set theory.

Author Bio

Independent researcher, passionate by insights.

Download Essay PDF File

Hi Christophe Tournayre,

Is there really any application of naive or other set theory (ZFC, NGB, etc.)?

I admire your excellently designed pictures. On my first glance I read "Hasenbrater, Pfeffer und Salz". On the second one I didn't see anything.

You concluded:

I tried to highlight how set theory is fundamental to us.

The core speculation is that energy degradation is applicable to all components of our universe, including physical laws and logic.

I think that there is value in trying to see the same things from a different angle.

I agree with your first sentence and with your last one.

Eckard Blumschein

Hi Christophe,

you have written "As 0 and 1 are the same thing, logic as pure information, cannot exist". Which follows on from your earlier statement "0 and 1 are equals. They are both a defined set." Rather than being the same 0 and 1 are representing non existence and existence, or (no current) off and (current) on, and maybe other contradictions. I would say the symbols are comparable in some ways such as they are both numerical symbols for example or both represent quantity, (if we allow that no quantity still is a kind of quantity). But they 0 and 1 are not just different but opposites. Existence can not be non existence and off can not be on. So the mathematical equals symbol doesn't work. I feel certain about that. I found this paper When is one thing equal to some other thing? Barry Mazur (2007) www.math.harvard.edu/~mazur/preprints/when_is_one.pdf But it is more complicated than I thought and I'm too tired to search it for corroboration of my decision.

You say a set can not be independent of its environment but you include information and logic. I think maybe you are confusing the pure information or logic with its carrier, current/s, nerve impulse/s or writing that is hosted by something brain computer, paper.The information itself or the logic itself doesn't posses energy to loose. They aren't material things but states and ideas.

I do agree with your "I think that there is value in trying to see the same things from a different angle."This competition is very helpful with that. I think you have chosen an interesting topic to focus on.

Kind regards Georgina

    Christophe,

    1тЙа 0 may be read as "I am not nothing". It is a necessary declaration of existence by opposition ot non-existence. Most of maths is about computing existence in that form. "1" and multiples of it while preserving its integrity... without ever making it turn to "0"; the no magic rule.

    Because my essay deals with a bottom-up approach, I use the rule of non-contradiction to define what may exist in the universe and how this existence is affected by context (motion etc.)

    Could you look if the set theory, as you understand it, supports the operation of logical substitution in substance as described in my essay, i.e. the NOT function does not specifically say which one replaces the other..Is it because the background is a larger set OR because the complex form came after the background.???

    Marcel,

    Dear Christophe Tournayre,

    In qualifying the aim of the 'What is Fundamental?' essay contest, Dr. Brendan Foster, the FQXi.org Science Projects Consultant wrote: "We invite interesting and compelling explorations, from detailed worked examples through thoughtful rumination, of the different levels at which nature can be described, and the relations between them.

    Real Nature has never had any abstract finite levels.

    I have concluded from my deep research that Nature must have devised the only permanent real structure of the Universe obtainable for the real Universe existed for millions of years before man and his finite complex informational systems ever appeared on earth. The real physical Universe consists only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

    Joe Fisher, ORCID ID 0000-0003-3988-8687. Unaffiliated

    Hi Christophe,

    I think I understand what you meant by environment now. Not the physical environment but the analytical environment; I would say context. That is to say, the set is not only its members but the boundary of the set that marks what is and isn't included, and the 'space/environment' is the context. So a description can be given like; 'this is the set of caged birds exhibited at the show', or 'this is the set of caged birds that will be included in the encyclopedia'. Which could be same birds but different contexts. The birds set members alone are not supplying enough information to understand the representation.

    Hi georgina,

    Thank you for your comments. Yes, I am talking about the analytical environment, not physical. In my view, talking about a static analytical environment compared to a dynamic physical environment is misleading. In a chess board, dynamics are taking place and there is nothing physical.

    Hi Georgina,

    I will two examples to highlight the relationship:

    - When we draw the movement of an object (physical environment) on a graph (analytical environment). The fixed frame is represented by the graph. There is nothing analytical about object. The graph is only acting as a point of reference.

    - In the chess game, it is the opposite. There is a dynamic information movement (analytical environment) on a board (physical environment). The fixed frame is represented by the board. There is nothing physical about chess. The board is only acting as a point of reference.

    In my view, in these two examples, we are dealing with the opposite end of the same curve. Both environments are linked and interdependent.

    Dear Christophe,

    I think FQXi.org might be trying to find out if there could be a Natural fundamental. I am surprised that so many of the contest's entrants do not appear to know what am fundamental to science, or mathematics, or quantum histrionics.

    Joe Fisher, Realist

    Hi Christophe,

    I like the opposites you have explained. The board is like a coordinate grid that can be taken away. Though there must remain knowledge of the scale of the move components and limitations of movement (that the board illustrates),as well as the rules of the game. It can be played without a board by experts with trained memory but most would find that too difficult. I can only imagine a few moves ahead with the board to 'remember' all of the places of the pieces in play at the same time. An opposite of the chess is the objects in the World and coordinate grids we impose to make sense of where things are in relation to each other(mappings).

    Whereas the board is physical the coordinate grid is analytical. The coordinates can be dispensed with but there must still be that which is controlling, permitting and constraining movement. In the chess game the rules and scale and boundaries can be within the memory of a brain and functioning of a mind or the memory and functioning of a computer program. Which, if the hosting of that information is ignored, is just information. Whereas the control of the physical objects, it seems to me must be physical. Direct physical interactions between objects. Or forces acting on, and between objects, because of the surrounding existent base medium having been affected by what the matter is and is doing. The set of objects or information and the analytical environment is not enough. Kind regards Georgina

    Hi Georgina,

    You can say that the chess board is a make-up of the mind. But the convergence function you see on the chess board between a larger set on a smaller set is not a make-up of the mind. Do you agree with me?

    Hi Christophe,

    It would be exception circumstances though. Two players such as chess Grand masters could play by using spoken coordinates to communicate their moves and their exceptional memories to keep track of all of pieces, I assume. A board could then be used for an audience so that they can see and understand what the Grand masters are doing. Then your first statement could be true. I'm not certain how you are using the word 'make-up'. I think you mean 'make-believe', as it is for the players. I'm sorry I don't know what'convergence function' means. I also do not know what the larger and smaller set, are referring to. There are more chess pieces in play at the start of the game than later on. So if it is a set of pieces in play it must be getting smaller-not just the pieces moving.The set of pieces in play diminishing in membership and the set of 'out' pieces growing. I haven't thought about sets being dynamic and changing in number of members. I have thought of sets as the static representations I was taught about in Secondary school. So these are interesting ideas to me. If you are talking about just the set of 'in play' pieces,'with members diminishing, why isn't that also 'make -believe' as the pieces like the board are being imagined? Is it because the players are not thinking about the complete set of pieces in the game and how that is changing. Only the moves, and the rules and the current and imaginary future positions.Making the analysis of the set something extra? Could you clarify your second sentence in plain English if possible?

    Hi Georgina,

    I will explain it with two examples:

    Set size

    To quantify set size, it is best to forget about players and imagine two computers playing one against each other. The game is chess but it can be replaced by another game. The same game rules are given to each computer.

    A computer with 10ko of memory (running with a frequency of 10 Mhz) will be better at chess than a computer with 1ko of memory (running with a frequency of 1Mhz). A computer with 100ko of memory will be better than a computer with 10ko of memory. A computer with 1Mo of memory will be better than a computer of 100Ko. A computer with 10Mo of memory will be better than a computer of 1Mo.

    In this example, the computer memory/frequency size is the deciding factor on which computer is winning the game. The larger the computer set size (memory/frequency), the stronger is the computer. Given the same set of rules, a computer with a larger set size will be winning over a computer of smaller set size.

    Chess game

    To visualise a chess game, it is best to forget about pieces. I will explain chess with differentials. A Game is starting with equal position on the board and same number of pieces for each player. There is no differential between players.

    As game starts, differentials are being created. First player (the white) has the advantage of creating the first differential on the chess board. At first, it is only moving pieces position. But as the game moves on, a player is winning a pawn against the other player. Here, an easy to quantify differential (piece advantage) has been created. As the game moves on, a player is starting to win more pieces than the other, differentials are being larger. It goes till a player is checkmate, here the differential is infinite. There is no coming back from a checkmate.

    The game goes from a situation where there is no order (no differential), to a situation of irreversible order (checkmate).

    The game rules can be simplified or made more complexes.

    * If no player has the right to take any pieces of the other player, and pieces have the right to move backwards, the game moves on infinitely. In this scenario, no differential can be created.

    * If rules are very simple and few pieces and a small board, the game will go to a tie because no differential is being created.

    When two computers play against each others, the computer set size is deciding the outcome of the game.

    That is why I am saying there is convergence function on the chess board between a larger set on a smaller set. Basically, a computer with a larger set will set the order on a computer with a smaller set. It is the set size which decides the outcome of the game.

    Please let me know if it is not clear, it is good to talk about these subjects. I should have inserted more details in my essay.

    Hi Christophe, thanks. It isn't completely clear, I still don't now what "convergence function of ...on" means but I understand the examples. They are illustrating something completely different from what I thought you were saying. Yes I see that the better memory wins. As it would be also for a good chess player able to imagine and remember planned moves ahead in the game as well as positions of all the other pieces, rather than someone playing by responding to current moves and positions relevant to them, retaining only some parts of the game-play, as it is progressing, in mind. The one with the larger set is likely to dominate and win the game. I don't want to say bigger will always be better, even though in this bit of set theory it seems that it is. Especially not if the idea is taken to a different context than chess.

    The larger memory might be un-reliable in some way. A person might, for example, be prone to distraction from concentration, or have ill health allowing errors to be made. A smaller reliable memory could then be better than the bigger unreliable one. For the machine it seems the more information and connections the more vulnerability to corruption. I'm not saying that from any kind of expertise but personal experience of computers and how things stop working when data gets corrupted. The difference is, it seems to me, similar to that between a very reliable car that can be fixed with basic tools and a very high tech. one that has more to go wrong and needs expertise and specialist equipment to fix.

    I think my misunderstanding of your point was illustrating something about conservation. Even the imaginary chess pieces that are out have not disappeared. As, for the serious chess players, they have values and of course queens can be brought back into play. They are in another 'holding'set. For the material pieces they have to be somewhere when no longer part of the set of pieces in play. Even if discarded or broken the matter is still somewhere -so in another set.

    Actually any piece could be chosen to come back into play by a player who's pawn gets to the opposite side of the board. It has just always been my experience that it is a queen that is chosen.

    Hi Georgina, I will make the distinction between two points of your comment.

    On rules:

    You highlighted rules can be different for each piece, for example a queen can be brought back into the game. In my opinion, a rule can be compared to a function. So yes, pieces are another "holding set". In standard chess, a rule is to allow the queen to be bought back into the game. When it happens, it creates a large differential on the game set. The queen rule is local, I mean that we can play chess without this rule. I took "Chess" as an example, but I could have taken "Draughts".

    In the "Draughts" game, differentials between pieces are lower and rules are simpler. We could say that in "Draughts", functions are weaker than in "Chess". Still the convergence function (described in my previous comment) between a larger set on a smaller set still applies. You can make two computers playing against each other in "Draughts" and you will get the same results as in "Chess". I think as humans, we are not well equipped to see the curve of the convergence function, information looks flat to us.

    On pieces:

    You indicate that pieces still exist in another set, they only have been taken out of the chess game, they can be discarded or broken. I agree with your statement but cautiously.

    I will take the moving objects to show my way of thinking this subject. In the moving object example (described in previous comment), the object movement is draw on a graph (analytical environment). We take off the graph and our scale, the object will be still moving. The earth is moving around the sun, whether we are here or not. The object is moving against something we might not be aware of, but it is moving against "something else".

    In chess, it is less obvious that piece differentials exist outside the chess board. When you play on a computer, pieces out of the board is nowhere to be found. Still the differential potential of the lost pieces exist as long as the game is on.

    Thank you for your comments and your curiosity. My essay is not clear, I will try to make it better next time.

    Christophe,

    thank you so much for your replies, I appreciate you taking the time. Your essay is actually very thought provoking and interesting, though at face value it seems rather simple. I like where the thoughts you expressed have led. I understand the idea of movement even without the analytical framework or physical co-ordinates and scale, such as the board. Best wishes Georgina

    Dear Christophe;

    Your essay is a tour through a labirinth without entrance and without way out.

    It is easy to get lost in simplicity. You did that to me.

    Thank you;

    Diogenes

      Hi Dr. Christophe Tournayre

      Wonderful analysis using and creating perspective on set theory Dr Christophe Tournayre.......... People should use its full potential.................. very nice idea.... I highly appreciate your essay and hope you may please spend some of the valuable time on Dynamic Universe Model also and give your some of the valuable & esteemed guidance

      Some of the Main foundational points of Dynamic Universe Model :

      -No Isotropy

      -No Homogeneity

      -No Space-time continuum

      -Non-uniform density of matter, universe is lumpy

      -No singularities

      -No collisions between bodies

      -No blackholes

      -No warm holes

      -No Bigbang

      -No repulsion between distant Galaxies

      -Non-empty Universe

      -No imaginary or negative time axis

      -No imaginary X, Y, Z axes

      -No differential and Integral Equations mathematically

      -No General Relativity and Model does not reduce to GR on any condition

      -No Creation of matter like Bigbang or steady-state models

      -No many mini Bigbangs

      -No Missing Mass / Dark matter

      -No Dark energy

      -No Bigbang generated CMB detected

      -No Multi-verses

      Here:

      -Accelerating Expanding universe with 33% Blue shifted Galaxies

      -Newton's Gravitation law works everywhere in the same way

      -All bodies dynamically moving

      -All bodies move in dynamic Equilibrium

      -Closed universe model no light or bodies will go away from universe

      -Single Universe no baby universes

      -Time is linear as observed on earth, moving forward only

      -Independent x,y,z coordinate axes and Time axis no interdependencies between axes..

      -UGF (Universal Gravitational Force) calculated on every point-mass

      -Tensors (Linear) used for giving UNIQUE solutions for each time step

      -Uses everyday physics as achievable by engineering

      -21000 linear equations are used in an Excel sheet

      -Computerized calculations uses 16 decimal digit accuracy

      -Data mining and data warehousing techniques are used for data extraction from large amounts of data.

      - Many predictions of Dynamic Universe Model came true....Have a look at

      http://vaksdynamicuniversemodel.blogspot.in/p/blog-page_15.html

      I request you to please have a look at my essay also, and give some of your esteemed criticism for your information........

      Dynamic Universe Model says that the energy in the form of electromagnetic radiation passing grazingly near any gravitating mass changes its in frequency and finally will convert into neutrinos (mass). We all know that there is no experiment or quest in this direction. Energy conversion happens from mass to energy with the famous E=mC2, the other side of this conversion was not thought off. This is a new fundamental prediction by Dynamic Universe Model, a foundational quest in the area of Astrophysics and Cosmology.

      In accordance with Dynamic Universe Model frequency shift happens on both the sides of spectrum when any electromagnetic radiation passes grazingly near gravitating mass. With this new verification, we will open a new frontier that will unlock a way for formation of the basis for continual Nucleosynthesis (continuous formation of elements) in our Universe. Amount of frequency shift will depend on relative velocity difference. All the papers of author can be downloaded from "http://vaksdynamicuniversemodel.blogspot.in/ "

      I request you to please post your reply in my essay also, so that I can get an intimation that you replied

      Best

      =snp

        Dear Fellow Essayists

        This will be my final plea for fair treatment.,

        FQXI is clearly seeking to find out if there is a fundamental REALITY.

        Reliable evidence exists that proves that the surface of the earth was formed millions of years before man and his utterly complex finite informational systems ever appeared on that surface. It logically follows that Nature must have permanently devised the only single physical construct of earth allowable.

        All objects, be they solid, liquid, or vaporous have always had a visible surface. This is because the real Universe must consist only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

        Only the truth can set you free.

        Joe Fisher, Realist