Part 1: The world

The world

The world $W$ contains observers who can make point-in-time observations $O_t$^[1] of $W$.

Ideas

An idea $I$ is a function that given input observations at time $t_1$ can generate expected observations at time ${t_1}+{t_\Delta}$.

Thinkers

A thinker^[2] $T$ can store ideas $I$ in $T$.

Skillsets

A skillset $S$ is the set of $\set{I_i, \mathellipsis, I_n}$ embedded in $T$.

Idea Creation

A thinker can generate a new idea $I_{new}$ from its current skillset $S$ and new observations $O$ in time $t$.

Value

An idea $I$ can be valued by a function $V$ which measures the accuracy of all of the predictions produced by the idea $O_{{t_1}+{t_2}}$ against the actual observations of the world $W$ at time ${}_{{t_1}+{t_2}}$. Idea $I_i$ is more valuable than idea $I_j$ if it produces more accurate observations holding the size of $|I|$ constant.

Fictions

A fiction^[3] $F$ is an $I$ that does not accurately model $W$.

Messages

Thinkers can communicate $I$ to other thinkers by encoding $I$ into messages $M_I$.

Signal

The Signal $\Omega$ of a message is the value of its ideas divided by the size of the message.

Fashions

A fashion $Z_{M_I}$ is a different encoding of the same idea $I$.

Teachers

A teacher is a $T$ who communicates messages $M$ to other $T$. A thinker $T$ has access to a supply of teachers $\tau$ within geographic radius $r$ so that $\tau = \set{T|T < r}$.

Learning

The learning function $L$ applies $M_I$ to $T$ to produce $T^\prime$ containing some memorization of the message $M_I$ and some learning of the idea $I$.

Objectives

A thinker $T$ has a set of objectives $B_T$ that they can maximize using their skillset $S_T$.

Technologies

$T$ can use their skillset $S$ to modify the world to contain technologies $X$.

Technology Creation

Technology creation is a function that takes a set of thinkers and a set of existing technologies as input to produce a new technology $X_{new}$.

Artifacts

With $X$ $M_I$ can be encoded to a kind of $X$ called an artifact $A$.

Creators

A creator $\chi$ is a $T$ who produces $A$.

Outliers

An outlier $\sigma$ is a $\chi$ who produces exceptionally high quality $A$.

Copies

A copy $K_A$ is an artifact that contains the same $M$ as $A$.

Derivatives

A derivative $A^{\prime}$ is an artifact updated by a $\chi$ to better serve the objectives $B$ of $\chi$.

Libraries

A library $J$ is a collection of $A$.

Attention

Thinkers $T$ have a finite amount of attention $N$ to process messages $M$.

Distribution

Distribution is a function that takes artifact $A$ at location $o$ and moves it to the thinker's location $T_o$.

Publishers

A publisher is a set of $T$ specializing in production of $A$.

Censors

A censor is a function that wraps the distribution function and may prevent an $A$ from being distributed.

Part 2: Adding copyright to the model

Masters

A master $\Psi$ is now legally assigned to each artifact for duration $d$ so $A$ becomes $A^{\Psi}$.

Royalties

A royalty $R$ is a payment from $T$ to $\Psi$ for a permission on $A^\Psi$.

Permission Function

For every $A^\Psi$ used in $\Pi$ a permission function $P$ must be called and resolve to $>-1$ and royalties of $\sum{R_{A^\Psi}}$ must be paid. If any call to $P$ returns $-1$ the creation function $\Pi$ fails. If a $P$ has not resolved for $A^{\Psi}$ in time $d$ it resolves to 0.^[4] $P$ always resolves with an amount of uncertainty $\theta$ that the $\Psi$ is actually the legally correct $A^\Psi$.

Classes

The Royal Class $T_{R+}$ is the set of $T$ who receive more $R$ than they spend. Each member of the Non-Royal Class $T_{R-}$ pays more in $R$ than they receive.

Public Domain

A public domain artifact $A^0$ is an artifact claimed to have no $\Psi$ or an expired $d$. The $P$ function still must be applied to all $A^0$ and the uncertainty term $\theta$ still exists for all $A^0$.

Advertising

Advertising is a function $\varLambda$ that takes an $A$ and combines it with an orthogonal artifact $A_j^\Psi$ that serves $B_\Psi$.

Part 3: Predicted effects of copyright

Effect on Z

We should expect the ratio of Fashions $Z$ to Ideas $I$ to significantly increase since there are countless $M$ that can encode $I$ and each unique $M$ can be encoded into an $A^\Psi$ that can generate $R$ for $\Psi$.

Effect on F

We should expect the number of Fictions $F$ to increase since $R$ are required regardless if the $M$ encoded by $A$ accurately predicts the world or not. $\Psi$ are incentivized to create $A$ encoding $F$ that convince $T$ to overvalue $A^\Psi$.

Effect on $\varLambda$

We should expect a significant increase in the amount of advertising $\varLambda$ as $\chi$ are prevented from generating $A^{\prime}$ with ads removed.

Effect on $|M|$

We should expected the average message size $|M|$ to increase because doing so increases $R$ by decreasing $\theta$ and increasing $A^\Psi$.

Effect on $\Omega$

We should expect the average signal $\overline{\Omega}$ of messages to decrease.

Effect on K

We should expect the ratio of number of copies $K$ to new ideas $I_{new}$ to increase since the cost of creating a new idea $α$ is greater than the cost of creating a copy $K$ and royalties are earned from $A$ not $I$.

Effect on $\Pi$

We should expect the speed of new artifact creation to slow because of the introduction of Permission Functions $P$.

Effect on J

We should expect libraries to contain an increasing amount of fashions $Z$, fictions $F$, and copies $K$ relative to distinct ideas $I$.

Effect on S

We should expect a decrease in the average thinker's skillset $\overline{S}$ as more of a thinker's $N$ is used up by $Z, F, K$ and less goes to learning distinct $I$.

Effect on $I^\prime$

We should expect the rate of increase in new ideas to be lower due to the decrease in $\overline{S}$.

Effect on Classes

We should expect the Royal Class $T_{R+}$ to receive an increasing share of all royalties $R$ as surplus $R$ is used to obtain more $R$ streams.

Effect on $\sigma$

We should expect a small number of outlier creators to move from $T_{R-}$ to $T_{R+}$.

Effect on $A^0$

We should expect a decrease in the amount of $A^0$ relative to $A^\Psi$ as $T_{R+}$ will be incentivized to eradicate $A^0$ that serve as substitutes for $A^\Psi$. In addition, the cost to $T$ of using any $A^0$ goes up relative to before because of the uncertainty term $\theta$.

Effect on $A^{\prime}$

We should expect the number of $A^{\prime}$ to fall sharply due to the addition of the Permission Functions $P$.

Effect on B

We should expect $A$ to increasingly serve the objective functions of $\Psi$ over the objective functions $B_T$.

Effect on Q

We should expect the number of Publishers $Q$ to decrease due to the increasing costs of the permission functions and economies of scale to the winners.

Effect on U

We should expect censorship to go up to enforce copyright laws.

Effect on $A_©$

We should expect the number of $A$ promoting © to increase to train $T$ to support a © system.

Effect on $T_{R-}$

We should expect the Non-Royal Class $T_{R-}$ to pay an increasing amount of $R$, deal with an increasing amount of noise from ${Z + F + K}$, and have increasingly lower skillsets $\overline{S}$.

Conclusions

Notes

[1] The terms in this model could be vectors, matrices, tensors, graphs, or trees without changing the analysis.

[2] We will exclude thinkers who cannot communicate from this analysis.

[3] The use of "fictions" here is in the sense of "lies" rather than stories. Fictional stories can sometimes contain true $I$, and sometimes that may be the only way when dealing with censors ("artists use lies to tell the truth").

[4] If copyright duration is 100 years then that is the max time it may take $P$ to resolve. Also worth noting is that even a duration of 1 year introduces the permission function which significantly complicates the creation function $\Pi$.