## Friday, May 04, 2012

### Fair and Square

Fair and Square .
Andre Willers
4 May 2012
“The unspeakable in pursuit of the uneatable.” Oscar Wilde.
Synopsis :
A simple game that is smarter than the players .
Discussion :
What does the game teach ?
1.Manual dexterity
2.Short term memory
3.Pattern recognition.
4.Pattern creation
5.If-Then analysis
6.Social skills
7.Randomness
8.Colors
9.Negotiating skills

The Game:
A Rubik cube with the standard 3x3 x6 = 36 faces .
These faces are made up of the 9 non-zero digits , plus 26 letters of the alphabet , plus one wildcard . They are each colored differently .
Three or more related faces form a pattern . Every pattern scores points .
The player with the most points wins .
The Rules :
1.The House (ie parent) rules if a relation is Fair , but this is subject to appeal to dictionaries , mathematical formulae , sheer persuasion , etc. Relations is 3 or more things in a logical sequence . Even a random start will give some points , if the player is smart enough to see them . But non-obvious ones will need some persuasion . Hence the social skills bit.
2.The more faces in a relation , the more points: 3 faces , 1 point ; 4 faces,2 points , etc .
3.Numerical and alphabetical points are addititive . If the appeal rules include Text abbreviations , the same applies . The same for the wild card .(ie some sub-patterns could be double counted)
4. The cost to play : half a point for a click . Wipeout is set by agreement by players or house. A player can pass .
5.If the game freezes (ie everyone passes three times) , every player (including the house) forfeits 2/3 of their points (including negative points-think it through) . The cube is randomized and play resumes . But the House rotates to the next player with the second-highest score . (Just to set the cat amongst the pigeons !) . Negative score players cannot resume play in the same game .
6.Cashing out: Positive points get paid out .
Negative points get nothing. So , they get to play for nothing . That’s life . Live with it .
7. Players may collude .
8.Keeping track of points : use chips (sweets , etc)

Why is the game smarter than the players ?
The Rules of Appeal and Reset , combined with Human Nature (a Beth(3.x) system) , always results in a new set of rules (This is because A+~A is less than the Universum) . The system bootstraps .
See Appendix I and Appendix II , where I have done some preliminary analyses of a similar system .
As you can see , games like Tarot are too smart (ie they have little redundancy) . Humans require the assurance of cross-checking (redundancy) .
“Fair and Square” includes the players , so only a Beth(4) player could beat it .
Try .
Andre

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Appendix I
Tarot .
Andre Willers
7 May 2010

Synopsis:
Tarot is a finite representation of complexity to up Beth(4) level .

Discussion:
1.Can infinite manipulations be represented by finite rules?
Yes . Done all the time with the finite rules of differentiation and integration in mathematics.
2.Archetypes:
Postulate an infinity of delineated entities interacting . Two varieties of interactions can be found : Euler (ie infinitesimal with e as basis . Newtonian or Einsteinian systems)
or Fibonacci , (a finite change interaction . Also known as Quantum systems).
Both self-generate finite rules for infinite processes .
These finite rules are known as archetypes .
And there are a finite number of them . And we can enumerate them .
Why?
Also known as the Power Law . Infinite feedback systems of delineated entities self-combine to form hierarchical systems below Beth(4) levels .
See http://andreswhy.blogspot.com "AI"
Quantum systems , by definition , can only be enumerated in qubits .
An Image to illustrate this :
Imagine a hologram of n dimensions sliced by a plane . The plane is a computer screen or your 2-dimensional mental screen .
Past Beth(4) , the mind is acting in it's native mode , which is quantum mode .
The n-tuple entendre is standard for information transfer .
Information bleed-through from quantum systems leads to a finite number of rules .
Sigh . I cannot make it simpler than this .
Why there are 40+16=56 minor cards I have discussed before . It is intimately tied to ArithI and prime numbers .
Why there are only 22 major arcana cards to handle the rest of the infinite feedback systems up to Beth(4) levels I will have to think about . At the moment , I simply do not know why there are so few . But there it is .
See http://andreswhy.blogspot.com "Betablockers and Trauma memory"
Tarot cards represent a finite (less than 100) images's and procedures of infinite processes below native quantum processing .
Happy hunting!
Andre

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Appendix II
Tarot II
Andre Willers
10 May 2010

See http://andreswhy.blogspot.com "The inside of Zero"
You need 26 dimensions to describe a non-rotating ArithI system .
See http://andreswhy.blogspot.com "NewTools-Reserves" for the argument that any reserve should be 1/3 .

Tarot =26*3=78 . The minimum sufficient necessary . The alphabet .

Subsets:
With rotations you need minimum sufficient 2x26=52 .

The rotations at minimum necessary should be through 4 dimensions . 3 Space and one time at a minimum necessary sufficient . These are the ArithII dimensions , and are completely specified by the rotations .Notice that they are subsumed by the 26*3 dimensions above .

This gives 52+4=56 , the number of minor arcana .

We know we only need 78 . So the remainder must be 22 .

So we have
26+26 = 52 (min necessary suff through dim rotations for ArithI systems)
4= dimensions needed for rotation (see 4colour theorem)
78 = 26x3 The minimum necessary sufficient for any set of dimensions .
The remainder is 78 – (52+4) = 22 dimensions for infinite feedback . Quite remarkable .

Note that 52/78 = 0.66666 . The reserve (remainder 1/3) is then the indeterminate element .

The major Arcana .is then Major . Not what I expected . 1/3 of the data in the system is in the Major Arcana . Make of it what you will .

A bit further on , you will be a really good poker player .

Andre

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