Chronobiology: the biology of time, has had a difficult
path to becoming a legitimate, important and widely understood portion
of algorithmic, scientific theory, research, development, application
and even philosophy. This difficulty is largely due to our widespread
impression that we all understand time intuitively, and only need to have
our intuitive impressions quantitated with readily available physics and
engineering mathematics and technology. It is closely related to our false
confidence in the old adage "Seeing is Believing" where we now know how
much of our visual "Perception Screen of Reality" is faked and filled
in with our preconceived impression of what is "out there" tied in at
a relatively few sample points to our saccadic or tracking retinal images,
which are themselves systematically preprocessed before being allowed
to become visual reality. Scientifically we are at fault for continuing
to use the term "Time" ambiguously to describe the well ordered sequence
of macro and micro events in slow (compared with the velocity of light
C) Newtonian physical frames of reference, and the very different and
most untimely and confidently perceived conscious and subconscious biological
passage of "time".

Years
ago I introduced the term "Happening" as a makeshift term for this biological
entity in developing the "H" transform as a biomimetic entity, and shall
use it until a better term arises. The "H" transform revolves about the
idea that is firmly established in our intuitive consciousness that biological
time or "happening" is an irreversible sequence of events, paced by an
autonomous, internal "zeitgeber" that meticulously beats out the moment
by moment progression of biological time that we have innocently assumed
to be in step with clock time, and which we tend to expect to be in pace
with another person's time beat. Decades ago we learned that many biological
processes are time dependent in an orderly way, relating to a logarithmic
scale proportional to the reciprocal of absolute temperature, yielding
a characteristic and a thermodynamic activation energy that might be biochemically
significant. While biological time processes do in many cases follow this
rule, some are nearly temperature independent, either by compensation
or basic independence.

We
know very well, however, that biological time does not depend merely on
temperature or, indeed, other environmental features. The quota of biological
time (or happening) that is fed regularly into the conscious and subconscious
perceptorium can find itself invested in temporal or spatial on goings
in the conscious mental processes or in the subconscious or autonomic
systems or even in the dream domain, and these "happening" sequences need
not be phase coherent, one with the other. The H transform is a simple
algorithmic manipulable tool to approximate the biological time process.
We start with a simplistic four dimensional biological time world of three
orthogonal spatial dimensions of matching scale to incorporate the common
X, Y, Z spatial dimensions and a fourth T dimension, scaled in an Einstein
honoring fashion with C to incorporate the speed of light correction.
We now move the T term to the left side of the equation leaving dx2+dy2+dz2+c2dT2=dH2.
Action in the X,Y,Z spatial domain must be paid for by a decrease in T,
the clock time component, to remain within the budget of increasing Happening.
This relationship works well for understanding how "time flies" when one
is busy or enjoying current action, but hangs heavy on one's hands when
bored or pursuing tiresome or unattractive work. The H transform was only
a small start, however, toward realizing the power of the Three Quadrature
Transform compaction algorithms. If we take only the derivative term and
treat it as a finite difference variable X/ T we come up with a remarkably
useful compaction form. In recording biological and other time series
data for subsequent or real time analysis, we are frequently frustrated
by the enormous amount of data that must be recorded noting the value
of the function at each very short increment of time.

If
we are recording bioelectric data, for example, as I have frequently had
to do, one may very well need to record, with a precision of 10 micro
volts or better, a signal with a span of at least 10 millivolts or 1000
values of the ordinate, with a time resolution of at worst 1 millisecond.
This accumulates data at a rate 1000 x 1000 or 1 million states per second.
One minute of this, not to mention a day long recording, can be overwhelming.
By inverting this series in a distant relative of the Fourier transform,
one can declare a JND, Just Noticeable Difference, as for example the
10 pvolts and 1 millisecond increment as mentioned, and now never record
the value of the variable at all, except for a given starting point, and
record only an increment of 1 JND with a sign bit to imply that it "happened"
up or down, and a time record of how many JNDs it was since something
happened before without loss of precision or accuracy. During long periods
of inaction, nothing at all gets recorded, and during frantic changes
one simply records ups and downs at the limiting slew rate as a useful
approximation to a step function that will not lose track by saturation.
This device has been used to good purpose in recording of animal activities
such as birds in nests and rodents in burrows where there are long periods
of absence or sleep. It's done well even for the electro cardiogram and
vector cardiogram where the QRS must be detailed while the T and U systems
may be compacted. We have found that another biomimetic nonlinear compaction
algorithm utilizing the shape of the trigonometric arc tangent function
is nearly ideal.

Near the origin or base value the arc tan is nearly equal to the function
itself in basic radian measure but the function flattens to an asymptote
for infinity so it can never saturate but only lose detailed resolution.
Returning now to the features that lead to the very powerful general biological
three quadrature transform and its extension into Hierarchical Biological
Control and Regulation, let us follow one strand that leads to early technical
utilization of the three quadrature algorithm. When we first started to
record quantitatively the time course of the nerve axon potential and
its components, we were working near the limits of photographic recording
speed with newly available sealed off cathode ray tubes operating with
300-400 volts of electron acceleration and the fastest camera lenses and
film available, sometimes resorting to pre-exposure sensitization of the
film by vapor treatment. We were exasperated by the dimming of the beam
record during rapidly changing phases of the action potential because
exposure time was decreased by as much as 20 fold. Devising the R-C electronic
differentiation circuitry, and making it scalar rather than vector by
diodes, allowed us to brighten the cathode ray beam in proportion to the
derivative of trace speed, to give something near constant brightness
pictures, even though the up and down stroke sharpness suffered a bit.
It was only a small technical step to devise the inverse function integrator
circuit to implement the first major use of the three quadrature principle
to construct a device'irStich deliberately synthesized three quadrature
components.

This
device, applied to an intrinsically very sensitive galvanometer constructed
for me by A. C. Downing, allowed us to knob-adjust plus or minus, the
personality of the galvanometer used to record millisecond details of
the thermal response of nerve and muscle to electrical stimuli, resolving
the response to micro degree level. Separate knobs adjusting individually
the terms of the second order differential equation to which the galvanometer
corresponded closely, allowed one to adjust the suspension spring constant
0 terms, the viscosity and electric damping 0 terms and the 0 moment of
inertia term, plus or minus to any desired level. Actually one could introduce
negative moment of inertia or damping with hilarious results, and one
could easily reach near infinite sensitivity with accompanying appearance
of Brownian motion and environmental residual noise. This fundamentally
new and widely applicable class of control was published with full documentation
in the Journal of Scientific Instruments, Vol. 15, No. 7, July 1938. In
April of this year the IEEE journal Spectrum published an article written
by one of its associate editors, Glenn Zorpette, hailing the discovery
of this principle by a David B. Parkinson, as applied to the design of
a gun director. I could not resist sending him a copy of the published
reprint anticipating this "discovery" by some two years. I have never
received a reply from him, but an edited version of my letter was published
in the letters-to-the-editor column.

The
Three Quadrature Transform has now become required learning in modern
control engineering where it goes by the PID acronym for Proportional,
Integral, Derivative principle. , but the Biomimetic aspect still has
far to go. This is perhaps the time to introduce into Biomimetic Chronobiology,
in a very simplified way, the first whisper of the grandiose Brain-Mind-Spirit
and even Soul domain into which it slowly intrudes. While utilizing in
its function form the notions of Chronodifferentiatian and Integration
electronically, it became evident that the R-C model was adequate on an
engineering approximation basis where the current in the circuit was determined
by E, the voltage divided by R according to Ohm's law. The little voltage
across the capacitor could be neglected with an error of only a few percent.
Likewise in the differentiator the current in the sample resistor was
primarily determined by the capacitor with small admittance compared with
the resistor. Here was a fine place to apply for a first time the feed-forward
principle, that lagged far behind the acceptance and application of feedback
theory, primarily negative but increasingly utilizing the positive. By
utilizing our knowledge that the error term would be just that caused
by potential drop across the sample resistor R, we can dynamically sample
that voltage and feed forward into the integrator or differentiator signal,
an addetidum just equal to the error, and in a compensating sense so as
to have exact differentiation and integration. This principle and its
implementation was published jointly with my student, D. R. Dubbert, in
Review of Scientific Instruments, Vol. 20, No. 3, page 170, March 1940.

The
principle is widely employed by biological organisms in applying stored
experience corrections to bodily movements and future plans, and employs
the three quadrature principle freely, even to the point of almost robotic
actions without conscious thought in many of our most sophisticated skilled
actions. The three quadrature compaction strategy is so basic and widely
applied biologically that we are essentially unaware of its power, and
actually give it a complicated dissected up character in standard sensory
physiology. If we examine any of the numerous sensory transducers that
keep us in touch with the external world and the internal world as well,
we find that without fail, they report on the current value of their variable
such as light intensity, sound pressure, strength of smell or taste. With
rare special exceptions, they all accommodate, acclimate, and in doing
so reduce the intensity of their signal. Given a small increment, they
report this with extra generous signal, and even extend this confusion
spatially or in frequency domain, giving us, when biologically unified,
one of the very smart parts of biological pattern recognition. What does
all this add up to? The biotransducer has discovered that by making a
scaled, properly dimensioned mix of the function of time, the derivative
of the time function, and the scaled time integral of the function, be
it sound, heat, light, motion or force, it yields a mathematically or
biologically deconvolutable value of very concentrated information. Only
a sample starting point (constant of integration) is needed to allow running
three quadrature interpretation and feedback, feedforward, and as we shall
see later, feed-up and feed-down. A mathematically trained physicist or
engineer will often spend quite a while convincing himself or herself
of the legitimacy of this compaction principle, as it is not commonly
taught in these circles as an axiomatic concept.

We now approach the consolidation of the Three Quadrature Compaction algorithms,
the Hierarchical intrinsic structure of all biology, the Recapitulation
Principles as they impact the now widely studied Circadian Chronobiology,
and continue into Biomimetic episodal Chronobiology. Biological processes
are, to a very large extent, systematically repetitive; organisms reproduce
themselves, cells reproduce cells, families reproduce families and communities
replace their members in a repetitious but not really periodic fashion.
We know that many human processes repeat at about 24 hour intervals; or
at integral or at sub integral multiples of 24 hours. They are circadian.
Free running they may operate on perhaps 23 or 27 hour cycles, pulled
into near sync by environmental influences such as light, sound, temperature,
hunger, etc. The idea of periodic cyclicity is so dominant that the biologically
better matching episodality has been neglected. Biological sequences repeat
themselves time and time again in rhythmic, nearly repetitious style but
never quite periodic. Just as vibrato and syncopation give life to a musical
presentation, but go on to discord when overdone, so does episodal modulation
permit adjustment, feature matching and nuances to repetitive processes
and other coupled sequences, but goes on to pathology when overdone. If
we adopt the "episode" as the biological time unit, then the patterns
that can be computer averaged to discover the intrinsic pattern must be
phase modulatable. We can do well to replace the cyclic phase in our thinking
by the characteristic "template" phase that need not be assembled from
low sinusoidal "harmonics". It may have sharp peaks or deep valleys and
interesting intermediates. These templates may be important, for example,
in determining drug timing.

This is a very fruitful area of research to extend the prevailing "cosinor"
analysis. Biomimetic examination of chronobiological events inevitably
leads to examination of systematic and specific causality; what makes
this happen and why biophysically? This is the domain of control theory
and its varied models for which, in the earlier part of this discussion
we have just developed a rich resource and lexicon. For almost two centuries
we have been discovering regulatory and control principles and strategies
in the engineering and physics domains, only to rediscover the same concepts
later and in different terms in the biological world. Perhaps we should
reverse this sequence and lead engineering and physical science with new
major strategies based on long known, if poorly understood, biological
information. A simplistically correct concept can often delay seriously
the advance to next stages, and this is unusually appropriate in Chronobiologically
related control and regulation theory. The idea of "Set Point" regulation
hit engineering with James Watt's steam engine fly ball governor. One
set the balls for a desired speed, and then gravity and centrifugal force
competed to set the steam valve to the desired value. Perhaps the engine
did tend to "run away" or "hunt" if the regulator was made too sensitive,
and perhaps the engine slowed down a bit when load increased, but this
was a small price to pay for good utility regulation. Think of all the
thermostats, barostats and auto cruise controls that still share this
shortcoming. Early in the century, biology and/or medicine discovered
this big principle and Homeostasis, as epitomized by Walter Cannon in
his Wisdom of the Body, became the new ideal that would "explain" biological
stability from body temperature, blood pressure, to pH. In both the engineering
and the biological cases the homeostatic model falls short and must be
replaced by a homeodynamic model, also called a cyber physiological model,
that recognizes a moving target of ideality.

Engineering
is far along its way with this idea under the general title of servo regulation,
now learning about useful non-linearity, but biology is just learning
its benefits for incorporating feedback and feed-forward into robust stability.
If we wish to remain leaders in this Biomimetic mission to understand
biological supervision, we must be experimenting and seeking quantitative
understanding and expression for the next hierarchy of ideology beyond
homeodynamic-cyber physiological imagery. The key to this domain lies
in dynamic reprogrammability of the strategies and priorities of homeodynamic
approach, with introduction of heuristic line and staff command structures,
a region being vigorously pursued, with relatively poor biomimetic startup
information, by our neural-net computer architecture friends. We know
full well from the remarkable advances and some failures now being made
under the title of Psychoneuroimmunology, as well as mentally and spiritually
aided healing, that our mental control system has fantastic abilities
and hidden resources to which we need primarily the mental password to
advance and enhance ordinary physiology, pharmacology and surgical medical
treatment. By introducing new strategies in chronobiological and psychobiological
guidance, we can hope to make commonplace, Chronobiologically restructuring
procedures whereby the subconscious, the conscious and even the super-conscious
can be phase coordinated toward an optimum.

In
our own little world of VCRS (Voluntary Cardio Respiratory Synchronization),
where we take a procedure originally intended only to give a stationary
dynamic coherency between the cardiac and respiratory processes to yield
a precise "Epitome Vectorelectrocardiogram", which it did very well, we
now realize that we have a clinical tool that is an entering wedge into
voluntary autonomic reprogramming and possibly even further psychiatrically
applicable procedures. With a fast computer we can analyze the autonomic
"template" of vagus cardiac control as a projection of autonomic time
and respiratory condition. By demystifying the mathematically complex
procedure by computer-converting the personal template into a readily
understood "Song of the Heart", the patient can use this tool as a procedure
to alter favorably a faulty or less than optimal pattern. Arrhythmias
and control gain are first targets but only a start to gaining access
to the central control station. These modifications can be made without
deep understanding by simply "willing" the pattern of song to change in
a desirable direction (when we have learned enough to offer this advice).
Even beyond this intrinsically Biofeedback procedure, we can utilize the
biofeedforward strategy in which the song can lead rather than follow
the patient's own pattern. Most recently we have been designing and trying
to bring into operation, with very limited resources, a new version of
VCRS - the Baby VCRS and its companion, the Baby Teletransducer. These
devices, reduced to the size of a small "hang on the belt" pack, will
contain both the CPU and auxiliary processing electronics and a recording
unit, probably a stereo micro-tape recorder utilizing audio frequency
coding combined with vocal recording capability. How far this Biomimetic-Chronobiological
project will go and how fast is simply a challenge to our ingenuity, marketing
ability and tenacity.
