# Glossary of Notation

Money: A symbolic token of power that can be transferred between economic agents.

Price: A quantity of money needed to activate or inactivate an economic agent.  “Activate” could mean transfer ownership, or perform a service, while “inactivate” could mean retracting a threat of force.

Capital: A financial asset which is valued according to the discount formula (risk-adjusted expected future earnings discounted to a present value).

Priority Theory of Value: The social value of something is measurable by its centrality to the society.

Generator Paradox: The observation that a system of planning based on energy value can result in generators always being the only rational use of resources.

The following is old information with no plans of being updated:

Resource: $r = (identifier, quantum, dependencies, properties) \in R$ $\|R\| = n$ $parameter$ (abbreviation/alternate abbreviation): Description $identifier$ (id/id): A hashable and unique identifier to describe $r$. $quantum$ (q/q): The standard SI unit of this resource. When choosing this, keep in mind values will truncate below q. $dependencies$ (で/de): A set of resources that compose $r$. $superclasses$ (sup): The set of all resources which could be considered generalizations of this resource. $subclasses$ (sub): The set of all resources which could be considered specializations of this resource. $surveys$ (sv): The set of observations of this resource. $properties$ (ろ/ro): A set of properties defining $r$

Supply: $s \in S \subset \mathbb{S}$
Monoid: $s = kr, s_{id} = r_{id}$
Domain: $0 \le k < \infty, k \in \mathbb{Z}_+$
Sets: $S={s_i}: \left [ s_{i,properties} \ni (location \in \{ locations \rightarrow reachable \}) \right ] \forall i \le n$ $\mathbb{S} = \{ S_i \} \forall i \le n; \|\mathbb{S}\|=\left (\binom{n}{k} \right )$

Demand: $d \in D \subset \mathbb{D}$
Monoid: $d = \delta r, d_{id} = r_{id}$
Domain: $-\infty < \delta < \infty , \delta \in \mathbb{Z}$
Sets: $D={d_i}: \left [ d_{i,properties} \ni (location \in \{ locations \rightarrow reachable \}) \right ] \forall i \le n$ $\mathbb{D} = \{ D_i \} \forall i \le n; \|\mathbb{D}\|=\left (\binom{n}{\delta} \right )$

Exploitation: $e \in E \subset \mathbb{E}$
Monoid: $e = \epsilon r, e_{id} = r_{id}$
Domain: $0 \le \epsilon \le k, \epsilon \in \mathbb{Z}_+$
Sets: $E={e_i}: \left [ e_{i,properties} \ni (location \in \{ locations \rightarrow reachable \}) \right ] \forall i \le n$ $\mathbb{E} = \{ E_i \} \forall i \le n; \|\mathbb{E}\|=\left (\binom{n}{\epsilon} \right )$

Subsets of R: $R \supseteq \{ \mathbb{ M, C, P} \}$ $m \in \mathbb{M}$

The most basic subset of R, the basic and advanced materials. $\mathbb{M}_B$: Basic materials: $\{m \in \mathbb{M}\}: m_{de} = \{ \O\}$ $\mathbb{M}_A$: Advanced materials: $\{m \in \mathbb{M}\}: m_{de} \subseteq \mathbb{M}$
Economies are constrained between $\mathbb{M} = R\ and\ \mathbb{M} = \{\O\}$ $c \in \mathbb{C}$

The intermediate subset of R, the components.
Components have at least one material dependency: $c_{de} \subseteq \mathbb{M}$
Components are members of at least one set of product dependencies: $\exists p \in \mathbb{P}: p_{de} \ni c$
Components exist because of a process that acted on one or more materials: $\exists \varphi : f_p(M\subseteq\mathbb{M}, \varphi)\rightarrow c$ $p \in \mathbb{P}$

The highest-level subset of R, the products.
Products are not materials or components: $p \notin \{\mathbb{C,M}\}$
Products’ dependency sets are composed of components: $p_{de} \ni r:r\in\mathbb{C}$
Products exist because of a process that acted on one more components: $\exists\varphi:f_p(C\in\mathbb{C},\varphi)\rightarrow p$

Normal good: $\frac{dS_{x.de}}{dt} > 0 \rightarrow \frac{dD_x}{dt} > 0$

Ordinary good: $\frac{d(x.de)}{dt} < 0 \rightarrow \frac{dD_x}{dt} > 0$

Inferior good: $\frac{dS_{x.de}}{dt} > 0 \rightarrow \frac{dD_x}{dt} < 0$

Durable good:
x is a durable good iff: $f(I,O), x\in I \rightarrow x\in O$

Non-durable good:
x is a non-durable good iff: $f(I,O), x\in I \rightarrow x\notin O$

Agents:

An agent is an individual or organization that acts on or is served by the economy. $a=(id, mutex, history, requests)$ $id$: (id/id) Hashable and unique identifier $mutex$: (む/mu) The current mutex, if any, that a has locked. $history$: (ひ/hi) The allocation/deallocation and use history of a. $requests$: (れ/re) Catalog or feature requests from a.
Set: $A = \{a_i\}\forall i\le N; \|A\|=N$
Derivations:
The set D (all demand) is at least the set of all requests for all agents in A. $D \supseteq \{a_{re}\}\forall a\in A$
The set E (all exploitation) is at least the set of all allocations and uses of all agents in A. $E \supseteq \{a_{hi}\}\forall a\in A$