Understanding Nature's Choice of Genetic Languages

Robert Rosén

Trent Slade

Binary logic and qubit-based formalisms have dominated scientific modeling due to their success in deterministic physics and digital computation. However, many natural systems—ecological networks, genetic coding, social dynamics, language, and evolutionary optimization—are fundamentally non-binary, exhibiting cyclic dominance, neutrality, ambiguity, and triadic closure. This work proposes a unified ternary formalism for wild complexity, grounded in the mathematics of the qutrit and the Lie group SU(3), as a native descriptive language for these systems. By extending state spaces from H2 to H3 and dynamics from Pauli to Gell-Mann operators, the framework captures cyclic flow, constructive symmetry, and trialitic coupling that binary models structurally exclude. The analysis demonstrates how antisymmetric f_abc generators encode ecological Rock–Paper–Scissors dynamics and trophic cycles, while symmetric d_abc generators model coalition stability, genetic degeneracy, and social buffering via neutrality. Ternary error correction is shown to underlie the genetic code’s wobble structure and aligns with optimal bounds set by the Ternary Golay Code. In language and artificial intelligence, qutrit-based semantic models and three-valued logic naturally represent ambiguity, polysemy, and epistemic uncertainty, providing a principled route to mitigating hallucination. In evolutionary computation, qutrit genetic algorithms demonstrate superior exploration via rotation and disaster operators unavailable to binary search. Finally, these results are situated within deeper triality principles from Spin(8), Cartan geometry, and teleodynamics, arguing that triadic structure is not incidental but a fundamental organizational law of living, social, and cognitive systems.

Apoorva D. Patel

The execution of Grover's quantum search algorithm needs rather limited resources without much fine tuning. Consequently, the algorithm can be implemented in a variety of physical set-ups, which involve wave dynamics but may not need other quantum features. Several of these set-ups are described, pointing out that some of them occur quite naturally. In particular, it is entirely possible that the algorithm played a key role in the selection of the universal structure of genetic languages.

Robert Rosén

Apoorva Patel

V. G. Deı̆buk, Andrij V. Biloshytskyi

Methods of quantum/reversible logic synthesis are based on the use of the binary nature of quantum computing. However, multiple-valued logic is a promising choice for future quantum computer technology due to a number of advantages over binary circuits. In this paper we have developed a synthesis of ternary reversible circuits based on Muthukrishnan-Stroud gates using a genetic algorithm. The method of coding chromosome is presented, and well-grounded choice of algorithm parameters allowed obtaining better circuit schemes of one- and n-qutrit ternary comparators compared with other methods. These parameters are quantum cost of received reversible devices, delay time and number of constant input (ancilla) lines. Proposed implementation of the genetic algorithm has led to reducing of the device delay time and the number of ancilla qutrits to 1 and 2n-1 for one- and n-qutrits full comparators, respectively. For designing of n-qutrit comparator we have introduced a complementary device which compares output functions of 1-qutrit comparators.