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
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 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.