Quaternity & Physics
Excerpts taken from "The Entangled Mind: The Green Knight, Black Holes and Quaternity" by Jamroz, Wes
Arrangement of the pieces after 30 rounds(i.e. after 120 piles)
During most of the game, the number of variants per round fluctuates between 2.8 and 4.7 million. It is only in the final stage of the game that the number of possible variants drops. On average, there are about 3 million possible variants per round. Usually, it takes 200-280 piles to finish a game. This corresponds to 50-70 rounds.
This means that the number of available variants in a 50-round game is in the range of (3 x 10⁶)⁵⁰. If you enter this formula into a scientific calculator- you will get the answer: infinity! Of course a larger computer can give the numerical answer which is in the range of 10³⁰⁰. In practice, however, such an answer is meaningless. The bottom line is that the number of variants in the game of quaternity, i.e, the Q number, is more than googol times higher than the Planck number. This means that the number of possible variants in outside the physical realm.
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The complexity of quaternity, however, is not only related to the number of possible variants of the game. The other factor that contributes further to the game's complexity is that there are four players playing against each other.
When playing quaternity, one is playing against three opponents on the same board at the same time. So, there are six simultaneous games being played between the four players. In other words, each player must follow and respond to all these six elements of the game. This situation is equivalent to the n-body problem, which was described previously. In this context, one may look at traditional chess as an analogy of the two-body problem. Traditional chess is a deterministic interaction between two players. This is why it is possible to have a computer compete effectively with humans.
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Quaternity, on the other hand, may be looked at as a special case of the four-body system, i.e., each of the four players interacts with three other players. These mutual interactions are like extra dimensions that add further complexity to the game. Therefore, the game is outside of the rules of probability and calculations. It is impossible to have a binary computer capable of playing a perfect game of quaternity. Quaternity provides an entirely new medium for exercising those modes of operation of the mind that humans possess but which remain in their latent states. We can refer to these latent states as various degrees of perceptivity.
Playing quaternity is like experiencing a fairy tale. However, you are not only reading it. Instead, you are writing your own tale, and as you are writing, you are living it. And your tale has a unique structure, which provides a degree of flexibility but within certain boundaries. By experiencing these self-made tales, one may start to perceive a sequence of events from an entirely new perspective. Exposure to these sorts of experiences brings into action the right hemisphere and, at the same time, attenuates the left hemisphere. In other words, it stimulates the brain to switch from a single mode - into a simultaneous operation of sequential and holistic modes.
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Post-checkmate transformation of the green pieces
At this point, it is interesting to quote Richard Feynman, a great physicist who received the Nobel Prize in 1965 for the development of quantum electrodynamics. Feynman compared Nature and the way it operates to a sort of game of chess being played by God. And what physicists are trying to do, according to his analogy, is to figure out the rules of the game. They do not know the game - but are able to observe te movements of things, just like observing the movement of pieces on the board. Feynman alluded to the possibility of the next revolution in physics - which would take place when, one day, a new rule of the game is discovered. He suggested, as an example, a rule as a bishop changing its color. Interestingly enough, such a rule is part of quaternity. As shown in the above diagram, when one of the players is checkmated, all his pieces (not just a bishop) change their color. According to Feynman's prediction, such a new rule would mark a coming revolution in physics.
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So, what is this critical feature that is hidden behind the changing of a bishop's color that would mark a revolution in physics? What kind of a new property of matter does it imply?
In terms of quaternity, changing the bishop's color is the result of a checkmate. Is it then possible to find a quantum effect analogous to a check?
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In quantum measurements, an experimenter must consider or "measure" a particle. When captured, an electron or a photon is transformed from its wavy form into a particle. As a result, the particle ceases to be a wave. Technically, such capture is called a wave function's collapse. Because it is then that the probabilistic nature of the wave is transformed
into a particle-like form: a wave of probability is turned into a fact. The collapse is one of the mysterious aspects of the quantum measurement problem.
Let's illustrate the sequence leading to the previous checkmate by using the Q-diagram. The overall layout of the scheme of the checkmate is presented below. The green dot indicates the position of the green king. The arrowheads (red, grey, and black) and the green square indicate all the five "royal squares" surrounding the green king.
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