User:Thepigdog/book/chapter2-players-in-a-game
If I play a game of tennis, and the opposing player hits the ball over the net, and I hit it back then we are locked in a game. Our identities no longer matter, for the game to go on, but we have identity. We are player A and player B. Player A hits the ball, over the net, and player B hits it back.
The game is the same, no matter who plays it.
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[edit] However I count my dogs, the dogs are just the same
If I have five dogs and put them in with three more dogs, then I have eight dogs. Or if I have three dogs and put them in with five dogs we also have eight dogs.
We humans were made to generalise, and here is the game; if I have A dogs and put them in with B dogs then I have A plus B dogs. And if I have B dogs and put them in with A dogs then we have B + A dogs. And A plus B always equals B plus A, because the pack of dogs is always the same pack, no matter how the pack is formed. This rule is the game, and it does not matter who plays it.
- A plus B = B plus A
means
- 6 plus 7 = 7 plus 6
- 5 plus 9 = 9 plus 5
- 100 plus 1000 = 1000 plus 100
A and B are now not the identities of objects, but the identities of players in the rule. They are called variables. Identity associates an object with an identity. Whereas, a variables associates a player in a game with an identity.
A and B are still names, but are no longer associated with a single object. Each time we go out to play with our rule we select the identity of these names. The identity may be different when we go out to play next time. But today the identities of A and B are five and six and the rule,
- A plus B = B plus A
means,
- five plus six = six plus five
[edit] The King and his Court
A prince goes to the court of the King of a neighboring power. The King wines him and dines him before locking him in the tower.
The next year the brother of the prince things to himself, about the quality of accomodation at the Kings court, and thinks "Maybe the food, accomodation and women are hotter here. I care not to visit the King.".
For many years the new prince lives in his domain, but without nowing what the King is doing. Trade is down, there is a shortage of pork belly, and the prince is feeling a bit "out of the mix".
The new prince things to himself; "I myself cannot go but my youngest brother John is an upstart, and extremely expendable, maybe he should go as my representative". So the new princes younger brother goes in place of the prince.
The irksome younger brother is the representative of the prince. He is not the prince but stands in the princes place as his representative.
A name is a cheap representative of an object. An object is represented in my mind by all the data describing that object. This is an expensive thing to be carrying around, and not the sort of thing you want to send across the border to enjoy the Kings hospitality.
[edit] A symbol
A symbol is a character or word that has a meaning of itself. A symbol is like the irksome younger brother. It stands ready to take on representational duties.
When a symbol represents one object it becomes a name. When a symbol represents a player in a game it becomes a variable.
When we make a statement about a person we use a name to shorten the statement. Instead of saying.
- "Please invite the man with the long beard and the scraggy nose to join the feast."
we say,
- "Please invite John to join the feast."
We are representing,
- "the man with the long beard and the scraggy nose"
by the name symbol John. We can replace the name symbol John by its text to get back the original statement.
[edit] Many irksome younger brothers
A few years later, the second youngest brother of the prince has an unfortunate daliance with the sister of the princes intended, and so the prince feels similar levels of warmth and filial loyalty to second youngest brother as to the first. Now the prince has two representatives whose absence from the court for an extended period would not overtax the endurance of the prince. The prince thinks,
- The youngest brother Robert is irksome.
- The second youngest brother Bruce is also irksome.
Now, "send representative to visit the King" becomes "send irksome brother to visit the king". It doesnt matter to the prince which irksome brother will go. They both will do.
But one brother only must go as the reprentative. Now later the prince is hearing the exploits of the royal visit, and hears the news,
- The representative got drunk and ran around in his underware, chasing the milk maid,
- The representative spent 50 deniro on wine, food, and women at the local baudyhouse.
These reprehensible tales are about one and only one brother, as only one brother was selected as the representative. And because the prince chose Bruce to go these statements mean,
- Bruce got drunk and ran around in his underware, chasing the milk maid,
- Bruce spent 50 deniro on wine, food, and women at the local baudyhouse.
they could never mean,
- Robert got drunk and ran around in his underware, chasing the milk maid,
- Bruce spent 50 deniro on wine, food, and women at the local baudyhouse.
unless these events happened on separate trips, as the prince selected only one over frisky younger sibbling, to be the representative of the prince.
The princes position may be described as,
- Send irksome brother to visit the King.
to which these second level statements statements applied,
- Robert is irksome
- Bruce is irksome
These second level statemants transform,
- Send irksome brother to visit the King.
to one of,
- Send Robert to visit the King.
- Send Bruce to visit the King.
But once the journey is embarked on only one of these statements can be true.
