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1st order neuron/neuropil approximations (Private wiki).

We seek to answer three questions raised over a century ago by the Nobel laureate Santiago Ramón y Cajal. In his preface to the Spanish edition of "Histology of the Nervous System" he wrote: "Practitioners will only be able to claim that a valid explanation of a histological observation has been provided if three questions can be answered satisfactorily: what is the functional role of the arrangement in the animal; what mechanisms underlie this function; and what sequence of chemical and mechanical events during evolution and development gave rise to these mechanisms?"

From the effects of water structure on axonal pulse propagation to the use of matrices to analyze the topological propagation of pulses in neuropils, and the growth rules that cause the axon/dendrite arbors to take the shapes that they do, we have made significant advances in answering Cajal's three questions.

Author 1: JDL wiki page Jonathan D. Lettvin

Neuron and neuropil systems, and Axonal pulse propagation mechanisms

Author 2: CLS wiki page Campbell L. Searle

Electrochemistry of axonal-membrane dynamics

Author 3: JYL wiki page Jerome Y. Lettvin

Axonal pulse propagation mechanisms


We see a brain as a community of individual creatures. Each creature has simple rules for eating, growing, secreting, and excreting, and responding to influences. We believe the rules are probably easy to grasp, and so are community structures and functions. With this it should be possible to construct an artificial brain.

Since natural systems seem to produce similar solutions with different materials, we focus on solving paradoxes with effective system design, signal flow, and imitative approximation, rather than precise correlation with a specific animal. Our experiences creating emulations of neurons and neuropils have been successful.

Example Paradox: We discriminate two stars separated by a visual angle of less than 0.1 the diameter of a photoreceptor from the distorted and spectrally smeared diffraction pattern on the retina. Spatial frequency transforms fail to achieve this discrimination. This paradox has been fully solved using our methods.

We follow simple design rules:

  1. Designs must have no single point of failure;
  2. Faulty parts produce only slight degradation;
  3. Parts fit together naturally, and adapt quickly;
  4. Transforms self-assemble using simple rules;
  5. Energy consumption is low in equilibrium and activity;
  6. Ordinary/Priority signal transmission consumes no/little energy;
  7. Novices can understand why the parts resemble neurons;
  8. Novices can understand why communities resemble brain structures.

more rules will be published later

Author Details

Jonathan D. Lettvin

Automorphing systems of sensory transform inversions and motor actuation protocols consistent with neural topology and physiology. This includes a thorough review of Visual mathematics and Speculative neural modelling.

A Sampling of Developed Invariant Visual Transforms
Contrast Invariance10 Decade Photoreceptor TransductionModulating Excitation/Inhibition
Local ContrastColor ConstancyTransverse Chromatic Deaberration
HyperacuityLongitudinal Chromatic DeaberrationSpherical Deaberration
Asymmetry InversionTranslation/Rotation/Scale/Tilt InvarianceMultiple Viewpoint 3D Reconstruction
Scatter InversionTransducer Damage InvariancePupil Shape Inversion

Campbell L. Searle

Jerome Y. Lettvin



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