An algebraic theory to discriminate qualia in the brain

The mind-brain problem is to bridge relations between in higher mental events and in lower neural events. To address this, some mathematical models have been proposed to explain how the brain can represent the discriminative structure of qualia, but they remain unresolved due to a lack of validation methods. To understand the qualia discrimination mechanism, we need to ask how the brain autonomously develops such a mathematical structure using the constructive approach. Here we show that a brain model that learns to satisfy an algebraic independence between neural networks separates metric spaces corresponding to qualia types. We formulate the algebraic independence to link it to the other-qualia-type invariant transformation, a familiar formulation of the permanence of perception. The learning of algebraic independence proposed here explains downward causation, i.e. the macro-level relationship has the causal power over its components, because algebra is the macro-level relationship that is irreducible to a law of neurons, and a self-evaluation of algebra is used to control neurons. The downward causation is required to explain a causal role of mental events on neural events, suggesting that learning algebraic structure between neural networks can contribute to the further development of a mathematical theory of consciousness.