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Concepts
We still do not know the specific mechanisms of brain or neural
computation. But the great studies of the past on brain physiology
has enabled us to form a simple and intuitive model of how the
brain generally works.
The Heart of the Matter
Measuring Information
The cornerstone of Kant's philosophy is based on the operational distinction
he made between information created from sensory perception and the
information that exists independently of the object of that perception.
As we study how we perceive things, we learn from modern physics that the
creation of information lies not only in our immediate sensory perception
of objects, but that the formation of information is actually embedded
in our mechanism of perception. Following this line of reasoning one
could conclude that there maybe no necessity for thinking that knowledge or
information creation could exist independently, "a-priori", of the
object. Knowledge has its basis in the physical world of direct experience.
Continuing further along this mode of thinking which is based on modern
experimental physics, one can infer that within a finite duration of
time there is always a limit to the amount of information that can be
created [1,2]. This is the fundamental basis upon which I've built this
model [3,4,5] of neural computation or consciousness.
Physical Measurement of Events in Time
From experimental physics, we know that we can only observe or measure
an event in time to an accuracy limited by the uncertainty principle, ie.,
dE * dt >= h,
where dE is the energy of a signal, dt is the time duration of
a signal and h is Planck's constant. A detector cannot measure an
event in time with accuracy greater than dt where
dt >= h/dE.
Note, that the limit of temporal resolution separating two time
dependent Gaussian pulses is the standard deviation (one-half the width
at the half-height of the pulse). The temporal resolution, dt, is
also related to the highest physical frequency component of the signal.
Nyquist's theorem says that in order to resolve a signal of frequency f
the "carrier" frequency needs to be 2f [6]. The temporal resolution
dt is equal to the carrier frequency of the signal 1/2f.
In a 2001 article,
Measuring Information as a Function of Time[2],
I stated that the smallest time interval measurable for neurons is
h/dE. An example of nature building a biological organ to the limitations
of a physical system is the human eyes. Human eyes have evolved to
resolve images up to the physical optical resolution limit. Similarily,
the lower temporal limit of pulses triggered by neurons exist only for
the duration limited by dt which is define by the uncertainty principle:
dt >= h/dE.
The uncertainly principle is not only true for microscopic quantum
systems, but true for macroscopic "pure" waves in general. The
uncertainty principle is true for all wave phenomena. You cannot
observe a wave's exact temporal duration or amount of total energy
simultaneously. You only can see or measure certain energetic aspects
of a wave set, a localize energy disturbance in matter, within a finite
time period. Heisenberg's principle is used to discuss the small world.
Nyquist's theorem is use to discuss the large universe. But the
uncertainty principle is true for all worlds.
Direct Experience
We know from personal experience that individual optical nerve cells
in our eyes require a few seconds to adjust to the level of brightness.
The cones and rods in our eyes require time to readjust their level of
firing threshold to ambient light. When the nerve cell fires it depolarizes
its electro-chemical potential, also called action potential.
It recovers after firing by repolarization of the action potential.
The same is true in our ears. Our sensitivity for hearing sound is
usually greater at night when the noise level decreases.
From experiments [7], we know that the visual nerve cell's (rods)
temporal resolution has been measured to be in order of 0.1 second
or using Nyquist's formula 5 hertz. We know from our own experience
that we see image frames at 8 to 16 hertz. These images are produced
by the synapses of nerve cells on the retina and by the synapses of
neurons in the neural circuits [8] of the visual cortex. Comparing the
temporal response time in the visual circuits to that of a single
rod nerve cell, we see that is at least twice as fast to get an
image from neurons working together as it is from a single neuron.
Furthermore, the each neuron needs to recharge after firing
depolarization which makes the neuron inactive.
Communication needs to occur between all of the neurons in the
cones and rods in the eyes, and the neural circuits in the cortex
to inhibit the firing of some of nerve cells while enabling others to
fire. The creation of images is optimized with the synchronization
of all the neurons communicating together from the retinal cells in
the eyes and to the circuits in the visual cortex.
Neurons of the auditory circuits in the cochlea try to synchronize
themselves with each other in feedback loops. Specialized neurons
excite and inhibit the timing of the signals to form a coincidence
circuit detector. The ear is an amazing achievement of Nature because
we can hear frequencies from 20 Hz to 20 kHz. I've read that the spike
trains density of individual neurons in the auditory circuits can only
get as high as 500 hertz. So the neurons in the ear achieve almost
a 3 orders of magnitude increase in sensitivity by working together.
Neural circuits might use design techniques such as "pipelining,"
a common computer optimization technique, to achive faster computing
response. In pipelining, arrays are cells used for parallel computation.
Examples from neural circuit experiments show that individual neurons
in the circuit play different roles in synchronizing when they synapse.
References
1. The Limits of Information,
Glenn Takanishi, Nov. 2010
2. Measuring Information as a Function
of Time, Glenn Takanishi, Nov. 2001.
3.
Waves, Pulses, and the Theory of Neural Masses
, Walter J. Freeman, 1972
4.
Linear Analysis of Neural Masses
, Walter J. Freeman, 1972
5.
A Personal Note
, Glenn Takanishi, Nov. 2010
6.
Theory of Communication, Dennis Gabor, 1946,
The Journal of the Institution Of Electrical Engineers, 93(3):429-457.
7.
Webvision, NCBI Bookshelf,
Michael Kalloniatis and Charles Luu, 2005
8.
Moshe Abeles, Corticonics; Neural Circuits of the Cerebral Cortex,
Cambridge University Press, 1991.
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