Maxwell's theory of electromagnetism is regarded as one of the most important works in mathematical physics. His later work on the vortex theory of molecules provides a theoretical framework for the biological sciences as well. With Einstein's insightful look back into his work, the unifying theory of relativity with electromagnetism came to be known as the "theory of everything."

In this article, we reflect on an extension of Maxwell's theory of electromagnetism from the perspective of quantum information theory. Complex system dynamics have been studied based on coupled wave information propagation in scale-space, elucidating the nature of genotype information processing in 5-dimensional scale-spaces. In this theory, 4-dimensional space-time is considered a derived property of evolving pattern synergism.

Many other theories, methods, and results have additionally influenced our work that we present within the theory of stochastic resonance synergies. In our view, it offers a new perspective on neuroscience and physics.

#### Coordinate transformations and synergistic information binding in 5D

The dynamics of multidimensional information decomposition in quantum information carriers are based on orthogonal operators, rotors, and divergence. We utilize scale-space wave information propagation and tunnelling across the scales of a complex system's information flow.

We have analysed the evolving dynamics of various complex systems in physics and neuroscience, revealing topological patterns of expression in different dimensions and scales, along with properties and degrees of synergism.

#### Stochastic resonance and the polarity of matter and energy

Scale resonance of up- and down-scale waves conserves information in a bipolar data distribution within a 5-dimensional quadrupole, the information carrier. Exploration of a configuration space applies the principle of least action, with an expression of the underlying Lagrangian dynamics given by its path integral.

Topological maps of coupled regions bind partitioned information synergistically in a hierarchy of scales, projecting data partitions along the space of two principal components dynamically via coordinate transformations. A Green function has been derived, encoding transition symmetries in the quantum field of synergistically coupled oscillators, in terms of knot theory, unknotting entangled information in coupled oscillators across the scales.

A turbulent flow of convective clouds has been computationally analyzed using this dynamics, with fusion patterns shown in the IR images, indicating a rain process.

#### When or where does polarity matter?

In the light of Perelman's proof of Poincaré's conjecture in 4D, the short answer is: always and everywhere. The scale-space wave function preserves information about the distribution of prime numbers. From the perspective of algebraic number and group theory, a nucleon of information is described with a minimal descriptor from the finite set of triplet codes.

The mathematical structure of the set of triplet codes forms a basis for the periodic arrangement of atomic elements in limiting cases. Besides proving Riemann's hypothesis, it sheds new light on the significance of atomic numbers in describing the physical and chemical composition of atomic elements.

Asymptotic freedom of motion and the so-called 'fine structure constant' have been described in theory. This relationship follows from the polynomial complexity of motion in an information flow in limits.

We have studied triplet synergisms in human perception and movements, presenting a cross-modal analysis of colour constancy, intensity-independent auditory distance perception, and the equilibrium positions in the synergistic control of reaching movements.

#### Conclusion

Two synergistically coupled clusters of information extend Maxwell's theory of electromagnetism along 5D manifolds, exchanging information with scale-space waves and quantum tunnelling, regardless of the polarity of energy or matter.

A triplet synergism defines a nucleon of information with a minimal code from the finite set of descriptors. In our view, the evolving dynamics of triplet codes describe pattern formation in animate and inanimate systems at different levels of complexity and expression across the scales of the universe.

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