Figure 2.

Intrinsicality. (a) Activation functions without bias ($\eta =0$) and different levels of constraint ($\tau =0$, $\tau =1$ and $\tau =10$). (b) System S analyzed in this figure. The remaining panels show on top the causal graph of the mechanism $M=\left\{A\right\}$ at state $m=\left\{1\right\}$ constraining different output purviews and on the bottom the probability distributions of the purviews (effect repertoires). The black bars show the probabilities when the mechanism is constraining the purview, and the white bars show the unconstrained probabilities after the complete partition ${\psi }^0$. The “*” indicates the state selected by the maximum operation in the intrinsic difference (ID) function. (c) The mechanism fully constrains the unit B in the purview $Z=\left\{B\right\}$ (${\tau }_B=0$), resulting in state $z=\{\uparrow \}$ defining the amount of intrinsic information in the mechanism as $\phi (m,Z,{\psi }^0)=ID({\pi }_e\left(B\right|M=\uparrow )\mid {\pi }_e^{{\psi }^0}\left(B\right|M=\uparrow \left)\right)={\pi }_e(B=\uparrow |A=\uparrow )·|log({\pi }_e(B=\uparrow |A=\uparrow )/{\pi }_e^{{\psi }^0}(B=\uparrow |M=\uparrow \left)\right)|=1·0.69=0.69$. (d) After adding a slightly undetermined unit (${\tau }_C=1$) to the purview ($Z=\{B,C\}$), the intrinsic information increases to $1.11$. The new maximum state ($z=\{\uparrow ,\uparrow \}$) has now much higher informativeness ($|log({\pi }_e(BC=\uparrow \uparrow |A=\uparrow )/{\pi }_e^{{\psi }^0}(BC=\uparrow \uparrow |A=\uparrow \left)\right)|=1.26$) but only slightly lower selectivity ($\pi (BC=\uparrow \uparrow |A=\uparrow )=0.89$), resulting in expansion. (e) When instead of C, we add the very undetermined unit D to the purview (${\tau }_D=10$), the new purview ($Z=\{B,D\}$) has a new maximum state ($z=\{\uparrow ,\uparrow \}$) with marginally higher informativeness ($|log({\pi }_e(BC=\uparrow \uparrow |A=\uparrow )/{\pi }_e^{{\psi }^0}(BC=\uparrow \uparrow |A=\uparrow \left)\right)|=0.79$) and very low selectivity (${\pi }_e(BC=\uparrow \uparrow |A=\uparrow )=0.55$), resulting in dilution.