The No Barber Principle: Towards Formalised Selection in the Inaccessible Game

Neil D. Lawrence

doi:10.48550/arXiv.2604.21945

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The No Barber Principle: Towards Formalised Selection in the Inaccessible Game

Neil D. Lawrence

, 2026.

Abstract

The inaccessible game is an information-theoretic dynamical system governed by three information loss axioms, a marginal entropy conservation constraint and maximum entropy dynamics. In this paper we look at selection in the game. Our aim is to develop a selection policy for the game rules based on a minimal set of assumptions. We seek necessary consistency constraints for self-determining dynamical systems. Specifically, we suggest that rules that quantify over distinctions they cannot internally represent risk impredicative-style circularity. Our criterion is motivated by an analogy with Russell’s paradox. We formulate a no-barber principle which prohibits dynamics that appeal to external adjudicators or structure lying outside the system. Through the no-barber principle we argue that the classical category FinProb is structurally incompatible with the no-copying instantiation studied here, while the noncommutative category NCFinProb, in which von Neumann entropy is characterised, is a more natural candidate for the game’s internal language.

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BibTeX


@Misc{publications/the-no-barber-principle-towards-formalised-selection-in-the-inaccessible-game,
  title = 	 {The No Barber Principle: Towards Formalised Selection in the Inaccessible Game},
  author = 	 {Lawrence, Neil D.},
  year = 	 {2026},
  doi = 	 {10.48550/arXiv.2604.21945},
  url = 	 {/publications/the-no-barber-principle-towards-formalised-selection-in-the-inaccessible-game.html},
  abstract = 	 {The inaccessible game is an information-theoretic dynamical system governed by
three information loss axioms, a marginal entropy conservation constraint and
maximum entropy dynamics. In this paper we look at selection in the game. Our
aim is to develop a selection policy for the game rules based on a minimal set
of assumptions. We seek necessary consistency constraints for self-determining
dynamical systems. Specifically, we suggest that rules that quantify over
distinctions they cannot internally represent risk impredicative-style
circularity. Our criterion is motivated by an analogy with Russell's paradox.
We formulate a no-barber principle which prohibits dynamics that appeal to
external adjudicators or structure lying outside the system. Through the
no-barber principle we argue that the classical category FinProb is
structurally incompatible with the no-copying instantiation studied here,
while the noncommutative category NCFinProb, in which von Neumann entropy is
characterised, is a more natural candidate for the game's internal language.
}
}

Endnote

%0 Generic
%T The No Barber Principle: Towards Formalised Selection in the Inaccessible Game
%A Neil D. Lawrence
%D 2026	
%F publications/the-no-barber-principle-towards-formalised-selection-in-the-inaccessible-game
%R 10.48550/arXiv.2604.21945
%U /publications/the-no-barber-principle-towards-formalised-selection-in-the-inaccessible-game.html
%X The inaccessible game is an information-theoretic dynamical system governed by
three information loss axioms, a marginal entropy conservation constraint and
maximum entropy dynamics. In this paper we look at selection in the game. Our
aim is to develop a selection policy for the game rules based on a minimal set
of assumptions. We seek necessary consistency constraints for self-determining
dynamical systems. Specifically, we suggest that rules that quantify over
distinctions they cannot internally represent risk impredicative-style
circularity. Our criterion is motivated by an analogy with Russell's paradox.
We formulate a no-barber principle which prohibits dynamics that appeal to
external adjudicators or structure lying outside the system. Through the
no-barber principle we argue that the classical category FinProb is
structurally incompatible with the no-copying instantiation studied here,
while the noncommutative category NCFinProb, in which von Neumann entropy is
characterised, is a more natural candidate for the game's internal language.

RIS


TY  - GEN
TI  - The No Barber Principle: Towards Formalised Selection in the Inaccessible Game
AU  - Neil D. Lawrence
DA  - 2026/04/21	
ID  - publications/the-no-barber-principle-towards-formalised-selection-in-the-inaccessible-game
DO  - 10.48550/arXiv.2604.21945
UR  - /publications/the-no-barber-principle-towards-formalised-selection-in-the-inaccessible-game.html
AB  - The inaccessible game is an information-theoretic dynamical system governed by
three information loss axioms, a marginal entropy conservation constraint and
maximum entropy dynamics. In this paper we look at selection in the game. Our
aim is to develop a selection policy for the game rules based on a minimal set
of assumptions. We seek necessary consistency constraints for self-determining
dynamical systems. Specifically, we suggest that rules that quantify over
distinctions they cannot internally represent risk impredicative-style
circularity. Our criterion is motivated by an analogy with Russell's paradox.
We formulate a no-barber principle which prohibits dynamics that appeal to
external adjudicators or structure lying outside the system. Through the
no-barber principle we argue that the classical category FinProb is
structurally incompatible with the no-copying instantiation studied here,
while the noncommutative category NCFinProb, in which von Neumann entropy is
characterised, is a more natural candidate for the game's internal language.

ER  -

APA


Lawrence, N.D.. (2026). The No Barber Principle: Towards Formalised Selection in the Inaccessible Game.  doi:10.48550/arXiv.2604.21945 Available from /publications/the-no-barber-principle-towards-formalised-selection-in-the-inaccessible-game.html.

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