1. History
    Geometrization movement of the mid-20th century  Geometrization of the brain and tensor network theory 

2. Example
    Vestibulo-ocular reflex 

3. Applications
    Neural Networks and Artificial Intelligence 

4. References

5. External links

Tensor network theory is a theory of brain function (particularly that of the cerebellum) that provides a mathematical model of the transformation of sensory space-time coordinates into motor coordinates and vice versa by cerebellar neuronal networks. The theory was developed by Andras Pellionisz and Rodolfo Llinas in the 1980s as a geometrization of brain function (especially of the central nervous system) using tensors.

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History

Geometrization movement of the mid-20th century

The mid-20th century saw a concerted movement to quantify and provide geometric models for various fields of science, including biology and physics.^[3][4][5] The geometrization of biology began in the 1950s in an effort to reduce concepts and principles of biology down into concepts of geometry similar to what was done in physics in the decades before.^[3] In fact, much of the geometrization that took place in the field of biology took its cues from the geometrization of contemporary physics.^[6] One major achievement in general relativity was the geometrization of gravitation.^[6] This allowed the trajectories of objects to be modeled as geodesic curves (or optimal paths) in a Riemannian space manifold.^[6] During the 1980s, the field of theoretical physics also witnessed an outburst of geometrization activity in parallel with the development of the Unified Field Theory, the Theory of Everything, and the similar Grand Unified Theory, all of which attempted to explain connections between known physical phenomena.^[7]

The geometrization of biology in parallel with the geometrization of physics covered a multitude of fields, including populations, disease outbreaks, and evolution, and continues to be an active field of research even today.^[8][9] By developing geometric models of populations and disease outbreaks, it is possible to predict the extent of the epidemic and allow public health officials and medical professionals to control disease outbreaks and better prepare for future epidemics.^[8] Likewise, there is work being done to develop geometric models for the evolutionary process of species in order to study the process of evolution, the space of morphological properties, the diversity of forms and spontaneous changes and mutations.^[9]

Geometrization of the brain and tensor network theory

Around the same time as all of the developments in the geometrization of biology and physics, some headway was made in the geometrization of neuroscience. At the time, it became more and more necessary for brain functions to be quantified in order to study them more rigorously. Much of the progress can be attributed to the work of Pellionisz and Llinas and their associates who developed the tensor network theory in order to give researchers a means to quantify and model central nervous system activities.^[1]