Table 1.

Terms used in the theory

Symbol	Meaning	Comments
$f\in {\mathbb{R}}_{\ge 0}$	Fitness	$f\left(t\right)$, varies in time
$w\in {\mathbb{R}}^K$	Relevant part of the world	$w\left(t\right)$, varies in time; $K$ is huge and varies in time
$F$	Fitness operator	$f=Fw$, $F$ transforms $w\left(t\right)$ to $f\left(t\right)$; $F$ is nonlinear and nonstationary
$f_i\in {\mathbb{R}}^{p_i}$	A component of the fitness $f$	$f_i\left(t\right)$, with $f\left(t\right)$ produced by transforming $\left\{f_i\left(t\right)\right\}$; $p_i$ and the number of components vary in time
$w_i\in {\mathbb{R}}^{q_i}$	A component of the world $w$	$w_i\left(t\right)$, with $w\left(t\right)$ produced by transforming $\left\{w_i\left(t\right)\right\}$; $q_i$ and the number of components vary in time
$F_i$	A componentwise fitness operator	$f_i=F_i{w}_i$, $F_i$ transforms $w_i\left(t\right)$ to $f_i\left(t\right)$; $F_i$ is nonlinear and nonstationary
$x\in {\mathbb{R}}_{\ge 0}$	Individual’s estimate of own fitness	$x\left(t\right)$, varies in time
$u\in {\mathbb{R}}^k$	Sensed part of the world	$u\left(t\right)$, varies in time; $k$ is large (yet $k\ll K$) and varies in time
$X$	Fitness estimator (i.e. estimation operator)	$x=Xu$, $X$ transforms $u\left(t\right)$ to $x\left(t\right)$; $X$ is nonlinear and nonstationary
$x_i\in {\mathbb{R}}^{n_i}$	A component of the fitness estimate $x$	$x_i\left(t\right)$, with $x\left(t\right)$ produced by transforming $\left\{x_i\left(t\right)\right\}$; $n_i$ and the number of components vary in time
$u_i\in {\mathbb{R}}^{m_i}$	A component of the sensed world $u$	$u_i\left(t\right)$, with $u\left(t\right)$ produced by transforming $\left\{u_i\left(t\right)\right\}$; $m_i$ and the number of components vary in time
$X_i$	A componentwise fitness estimator	$x_i=X_i{u}_i$, $X_i$ transforms $u_i\left(t\right)$ to $x_i\left(t\right)$; $X_i$ is nonlinear and nonstationary
${\overline{X}}_i$	Approximate inverse of fitness estimator $X_i$	${\overline{X}}_i\approx X_i^{-1}$
${\widehat{u}}_i\in {\mathbb{R}}^{m_i}$	Communicated report on $x_i$	${\widehat{u}}_i={\overline{X}}_i{x}_i$
$u_i^{\prime }\in {\mathbb{R}}^{m_i}$	Report as received	$u_i^{\prime }\approx {\widehat{u}}_i$
$X_i^{\prime }$	Receiver’s version of $X_i$	$X_i^{\prime }$ and $X_i$ are similar
$x_i^{\prime }\in {\mathbb{R}}^{n_i}$	Receiver’s estimate of sender’s fitness component estimate	$x_i^{\prime }=X_i^{\prime }{u}_i^{\prime }\approx x_i$
$G$	Gain operator	$G$ amplifies and transforms $\left(x_i-X_i{\widehat{u}}_i\right)$ to ${\widehat{u}}_i$
$f^{+}\in {\mathbb{R}}_{\ge 0}$	Fitness-to-be	The increased fitness that gradually results from modulated stochastic changes
$Q_{X_i}$	Quality of estimator $X_i$	Accuracy by which $x_i$ estimates $f_i$
$Q_{{\overline{X}}_i}$	Quality of inversion of $X_i$	Accuracy of ${\overline{X}}_i$ as an inverse of $X_i$