Mathematizing The Lord Of The Rings

Fundamental entities

Set of parameters: P(θ) = {θ₁, θ₂, ..., θ_n} = P^θ

Set of constants: C(φ) = {φ₁, φ₂, ..., φ_n} = C^φ

Constitutional entities

Problem space: I_P(x, y, z, t) = I_{P(x, y, z, t)}(P_i^θ, C_k^φ)

Solution space: I_S(x, y, z, t) = I_{S(x, y, z, t)}(P_j^θ, C_l^φ)

Active entities

F(θ, φ): I_P(x, y, z, t) --> I_S(x, y, z, t)

E(x, y, z, t) = Ē

Game definition

Players

P^F: Frodo Baggins / P^S: Samwise Gamgee / P^P: Peregrin Took / P^M: Meriadoc Brandybuck / P^G: Gandalf / P^A: Aragorn / P^L: Legolas / P^I: Gimli / P^B: Boromir / P^R: Faramir / P^D: Denethor / P^S: Saruman / P^Z: Sauron / P^H: Gollum

Fixtures

C^S: Shire / C^B: Bree / C^W: Weathertop / C^R: Rivendell / C^C: Caras Galadhon (Lothlorien) / C^M: Moria / C^O: Rohan / C^H: Helm’s Deep / C^G: Gondor / C^L: Morgul Vale / C^Z: Mordor / C^U: Orodruin / C^I: Isengard

Problem function

I_P, _Ē = I_P(x, y, z, t, u)[({P^F, P^S}, {P^R, P^H}), ({P^P, P^M, P^G, P^A, P^L, P^I, P^B, P^D}, {P^S, P^Z})]

Solution function

I_{S, Ē} = I_P(x, y, z, t, u)(P^F, C^U)

As simple as that.

[caption id="" align="alignleft" width="240" caption="Making sense of Middle Earth"][/caption]