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?
Creating perspective on set theory by Christophe Tournayre
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
Hi Christophe Tournayre
you said "I answered your comment in https://fqxi.org/community/forum/topic/3029"..........But I could not find your answer.
You said...."When I read your essay and if the universe behave as you described, the question that comes to my mind is: Before modern physics was discovered, where do ancient people thinking and actions fit into your theory?".................
I will give one example about a temple of God Shiva in Telagana State, Near Hyderabad. It shows the shadow of God shiva linga, any time of day in a year. It is "Chaya Someswara Swamy temple, built around 1000 years back, uses interference of light 600 years before its invention by Newton.... Hope you will spend some time with wiki and Utube links below...
https://en.wikipedia.org/wiki/Chaya_Someswara_Swamy_temple
https://www.youtube.com/watch?v=Nd0dditL5HY
Best Regards
=snp
18 days later
Thank you for your feedback.
5 days later
Dear Christophe
If you are looking for another essay to read and rate in the final days of the contest, will you consider mine please?
A couple of days in and semblance of my essay taking form, however the house bound inactivity was wearing me. I had just the remedy, so took off for a solo sail across the bay. In the lea of cove, I had underestimated the open water wind strengths. My sail area overpowered. Ordinarily I would have reduced sail, but this day I felt differently. My contemplations were on the forces of nature, and I was ventured seaward increasingly amongst them. As the wind and the waves rose, my boat came under strain, but I was exhilarated. All the while I considered, how might I communicate the role of natural forces in understanding of the world around us. For they are surely it's central theme.
Beyond my essay's introduction, I place a microscope on the subjects of universal complexity and natural forces. I do so within context that clock operation is driven by Quantum Mechanical forces (atomic and photonic), while clocks also serve measure of General Relativity's effects (spacetime, time dilation). In this respect clocks can be said to possess a split personality, giving them the distinction that they are simultaneously a study in QM, while GR is a study of clocks. The situation stands whereby we have two fundamental theories of the world, but just one world. And we have a singular device which serves study of both those fundamental theories. Two fundamental theories, but one device? Please join me in questioning this circumstance?
My essay goes on to identify natural forces in their universal roles, how they motivate the building of and maintaining complex universal structures and processes. When we look at how star fusion processes sit within a "narrow range of sensitivity" that stars are neither led to explode nor collapse under gravity. We think how lucky we are that the universe is just so. We can also count our lucky stars that the fusion process that marks the birth of a star, also leads to an eruption of photons from its surface. for if they didn't then nebula gas accumulation wouldn't be halted and the star would again be led to collapse.
Could a natural organisation principle have been responsible for fine tuning universal systems? Faced with how lucky we appear to have been, shouldn't we consider this possibility?
For our luck surely didnt run out there, for these photons stream down on earth, liquifying oceans which drive geochemical processes that we "life" are reliant upon. The Earth is made up of elements that possess the chemical potentials that life is entirely dependent upon. Those chemical potentials are not expressed in the absence of water solvency. So again, how amazingly fortunate we are that these chemical potentials exist in the first instance, and additionally within an environment of abundant water solvency such as Earth, able to express these potentials.
My essay is an attempt at something audacious. It questions the fundamental nature of the interaction between space and matter Guv = Tuv, and hypothesizes the equality between space curvature and atomic forces is due to common process. Space gives up an energy potential in exchange for atomic forces in a conversion process, which drives atomic activity. And furthermore, that Baryons only exist because this energy potential of space exists, and is available for exploitation. Baryon characteristics and behaviours, complexity of structure and process might then be explained in terms of being evolved and optimised for this purpose and existence. Removing need for so many layers of extraordinary luck to eventuate our own existence. It attempts an interpretation of the above mentioned stellar processes within these terms, but also extends much further. It shines a light on molecular structure that binds matter together, as potentially being an evolved agency that enhances rigidity and therefor persistence of universal system. We then turn a questioning mind towards Earths unlikely geochemical processes, (for which we living things owe so much) and look at its central theme and propensity for molecular rock forming processes. The existence of chemical potentials and their diverse range of molecular bond forming activities? The abundance of water solvent on Earth, for which many geochemical rock forming processes could not be expressed without? The question of a watery Earth? is then implicated as being part of an evolved system that arose for purpose and reason, alongside the same reason and purpose that molecular bonds and chemical process arose.
By identifying process whereby atomic forces draw a potential from space, we have identified means for their perpetual action, and their ability to deliver perpetual work. Forces drive clocks and clock activity is shown by GR to dilate. My essay details the principle of force dilation and applies it to a universal mystery. My essay raises the possibility, that nature in possession of a natural energy potential, will spontaneously generate a circumstance of Darwinian emergence. It did so on Earth, and perhaps it did so within a wider scope. We learnt how biology generates intricate structure and complexity, and now we learn how it might apply for intricate structure and complexity within universal physical systems.
To steal a phrase from my essay "A world product of evolved optimization".
Best of luck for the conclusion of the contest
Kind regards
Steven Andresen
Darwinian Universal Fundamental Origin