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Neural Waves

Using wave packets to describe locally isolated bundles of energy waves is aesthetically pleasing because of its mathematical simplicity, and its ubiquitous existence in Nature.

The wave packet equation in a one-dimensional channel can be written as

We want to apply the wave packet equation to the progapation of a semantic sequence.

The basis coefficients a[k] are string sequences organized in a hierarchical binary tree structure. These string sequences are the embedded wave packets in the neural wave. The organization of this structure could also be recursive. We can express the wave packet as wavelet coefficients in the following function, phi.

Phi above describes the neural wave in a cluster layer.

Neuronal Cluster Layer

Using the wave packet Fourier integral approach to filtering doesn't involve using the classical feed forward model, but computer science methods of efficiently incorporating these algorithms in practical use is just beginning to be developed. It might be that the optimal neural network will consist primarily of template matching lookups aided by fast hashing algorithms to these Fourier lexicons. The wave model follows the way real brain waves propagate through specific neural channels or pathways.

Modelling neurons using the wave packets is the best way I know of to represent real brain waves propagating through specific neural channels or pathways. Using this wave model of neurons is an elegant methodology for adding properties of synchronization to oscillating neural circuits.

Neural waves of energy sweeps harmoniously across layers of brain cells or neurons repeatedly many times a second so that the brain can make decisions on sensory stimulation from outside the body and on biochemical signals inside the body. The neural waves signals neurons to fire or synapse in sequence in a chain reaction. Coherent information arises from the different sequences of neurons which synapse. Essentially, the power of the brain lies in its capacity to control which sequences of neurons synapse.

Dendritic Tree Layers

John Von Neumann's unfinished notes were published after his death in 1958 in a little book called The Computer and the Brain.

"It is noteworthy that the frequency in question is not directly equal to any intensity of stimulus, but rather that it is a monotone function of the later. This permits the introduction of all kinds of scale effects and expressions of precision in terms that are conveniently and favorably dependent on the scales that arise."

"In the above, the frequencies of certain periodic or nearly periodic pulse-trains carried the message, i.e. the information. These were distinctly statistical traits of the message."

"Clearly, other traits of the (statistical) message could also be used: indeed, the frequency referred to is a property of a single train of pulses whereas every one of the relevant nerves consists of a large number of fibers, each of which transmits numerous trains of pulses. It is, therefore, perfectly plausible that certain (statistical) relationships between such trains of pulses should also transmit information. In this connection it is natural to think of various correlation-coefficents, and the like."

John Von Neumann described the neuron incredibly well more than 50 years ago. His background in quantum mechanics which was based on wave theory helped him visualize the basic signal processing properties in the spike train. He mentioned that the oscillations in the neural network permits "all kind of scale effects." I interpret this to mean from resonance or harmonic vibrations in the neural circuits. The last line in his quote above, that "... it is natural to think of various correlation-coefficients, and the like.", is brilliant. He knew intuitively the method to unravel the neural code.

We know that thought processes are naturally wrapped or packaged in language. Language elements such as words, sentences, and the associations these language elements create in the minds exists because the brain's architecture is built to accomodate language intrinsically. Language seems to reflect the architecture of how the mind is built.

Spoken and written language enables us to associate or connect sequences of word elements together. Spoken language in particular places special meaning on the temporal sequence of words. Images are composed of picture elements which are meaningful to each other in terms of the spatial relationship they have to each other. Both verbal and visual language elements can be described by sequences of words or picture elements, and our brain processes this information by associating these elements together in a sequence.

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