—
—
This comment is dedicated to
the conversion of quantities from the value space (positive area) to the value
space (positive area). It contains examples of solving psychology problems,
principles of point position projection and conducting excitation from the
incoming to the outgoing space.
—
Assume, that we control the
condition (width) of the pupil through the temperature difference. For
conducting excitation in the value space, we must create a mathematical point.
Assume, that the resting temperature will be 10 degrees Celsius (ds
= 10°C), and the pupil diameter at rest will be 1 millimeter (ws =
1mm). Assume, that one degree Celsius (ld = 1°C) corresponds to a
tenth of a millimeter (lw = 0.1mm). Point has the function of
converting the definition into the quantity of irritation (y = x^2 / 20).
Assume, that the mathematical point is dumb and insensitive (r = 101, e =
1.01). And the intervals between definition calls are 0.6 seconds (lc
= 0.6s). We have obtained a living being with a temperature norm of 10 degrees
Celsius, which at rest (in the absence of an irritant) has a pupil width of 1mm
and calls 100 definitions per minute.
Assume, that there is some irritant with a
temperature of 24 degrees Celsius (dx = 24°C), that our being
interacts with. Since the creature determines the temperature difference
between the norm of temperature (ds) and the temperature of the
irritant (dx), the difference of values (temperatures) in degrees
will have a magnitude of 14 degrees Celsius.
x (+) = dx – ds = 24°C –
10°C = 14°C
The difference of values (y) is given by a
function of the difference of values (x) and the proportionality of the spaces.
With a proportionality of 1 degree Celsius corresponds to 0.1 millimeters (1°C
>> 0.1mm) and a difference of 14 degrees Celsius at the input, at the
output will be obtained a difference of 0.98 millimeters.
y (+) = (x^2 / 20) * lw / ld
= (14°C^2 / 20) * 0.1mm / 1°C = 0.98mm
The magnitude of 0.98 millimeters is a
reaction to irritation (x) relative to the resting norm (ws), a
deviation from the norm. Since a positive temperature difference of 14 degrees
Celsius corresponds to a positive diameter difference of 0.98 millimeters (x
(+) >> y (+)), we add the difference of values (y) to the magnitude of
the resting condition (ws), the pupil of our creature should have a
diameter of 1.98 millimeters.
wy = ws + y = 1mm + 0.98mm
= 1.98mm
The magnitude of 1.98 millimeters is a
reaction to irritation (x) relative to absolute zero (point (O (w)) — the
property is not expressed). The magnitude of the deviation from the resting
norm (y) is given by the magnitude of the deviation from the resting norm (x),
the function (y = f (x)) and the proportionality of spaces (lw
>> ld). Assume, that the irritant has a temperature of 12
degrees Celsius (dx = 12°C). In this case, with the same resting
norm, the deviation from the norm at the input will be only 2 degrees Celsius.
x (+) = dx – ds = 12°C –
10°C = 2°C
In this case, the pupil's width should deviate
from the norm at the output by only 0.02 millimeters.
y (+) = (x^2 / 20) * lw / ld
= (2°C^2 / 20) * 0.1mm / 1°C = 0.02mm
If change the function to (y = x^2 +2x + 1),
then even with a slight irritation of 2 degrees Celsius, the reaction to
irritation will be 1.7 millimeters.
y (+) = (x^2 + x * 2 + 1) * lw / ld
= (2°C^2 + 2°C * 2 + 1) * 0.1mm / 1°C = 1.7mm
If change the proportionality of the spaces,
for example, one degree Celsius corresponds to 0.06 millimeters (1°C >>
0.06mm), then with the same function and input value difference, the output
value difference will be 1.02 millimeters.
y (+) = (x^2 + x * 2 + 1) * lw / ld
= (2°C^2 + 2°C * 2 + 1) * 0.06mm / 1°C = 1.02mm
Etc.
—
Suppose, that the stimulus has set a response
value of 0.98 millimeters (wy = 1.98mm). Assume, that at the moment
of interaction, the pupil width was 1.21 millimeters (wn = 1.21mm). Psychological
work to change this condition will be 0.77 millimeters.
dAw = wy – wn
= 1.98mm – 1.21mm = 0.77mm
Assume, that at the moment of interaction, the
pupil width was 2.44 millimeters (wn = 2.44mm). Psychological work
in this case will be minus 0.46 millimeters.
dAw = wy – wn
= 1.98mm – 2.44mm = – 0.46mm
The pupil should narrow by 0.46 millimeters
from the actual 2.44 millimeters to the 1.98 millimeters, set by the
irritation. The calculations of accumulated excitation (QA (c)) and
the current condition of the pupil (wn (c)) will also be different.
In the first case, with an excitability of (e = 1.1), after six seconds (c =
10), the condition of the pupil should change by 0.47 millimeters (dilation).
QA (c) = dAw – dAw
/ e^c = 0.77mm – (0.77mm / 1.1^10) = 0.47mm
The pupil diameter will be 1.68 millimeters.
wn (c) = wn + QA
(c) = 1.21mm + 0.47mm = 1.68mm
In this case, we add the magnitude of
accumulated excitation (QA (c)) to the actual coordinate (wn),
since the difference of values (dAw) is positive (wn <
wy). In the second case, the pupil's condition should change by
minus 0.28 millimeters (narrowing).
QA (c) = dAw – dAw
/ e^c = – 0.46mm – (– 0.46mm / 1.1^10) = – 0.28mm
The pupil diameter should be 2.16 millimeters.
wn (c) = wn + QA
(c) = 2.44mm + (– 0.28mm) = 2.16mm
In this case, we subtract the magnitude of
accumulated excitation (QA (c)) from the actual coordinate (wn),
since the difference of values (dAw) is negative (wn >
wy).
Etc.
—
Without the value (QImin), the
pupil will dilate or narrow an infinite number of calls, causing muscle and
nerve tension, because the accumulated excitation (QA (c)) cannot
mathematically equal the required psychological work (dAw). After
each call, there will be a residual irritation (QI (c)), that is not
equal to zero, which means, that the completed psychological work will always
be less, than the prescribed work (QA (c) < dAw). The
value (QImin) is a compromise and an acceptable error. Assume, that
the minimum portion of the irritation residue is 0.01 millimeters (QImin
= 0.01mm). In this case, with an actual excitation of 1.21 millimeters (wn
= 1.21mm) and a psychological work of 0.77 millimeters (dAw =
0.77mm), it will take almost 437 calls for a full reaction.
c = log (e) (dAw / QImin)
= log (1.01) (0.77mm / 0.01mm) = 437
With a call duration of 0.6 seconds, this is
almost four and a half minutes for fully excitation of pupil.
t = c * lc = 437 * 0.6s = 262.2s
The accumulated excitation will be 0.76
millimeters.
QA (c) = (dAw – dAw
/ e^c) = (0.77mm – 0.77mm / 1.01^437) = 0.76mm
Which is added to the initial coordinate,
because the value (dAw) is positive (wn < wy).
wn (c) = wn + QA
(c) = 1.21mm + 0.76mm = 1.97mm
With an actual excitation of 2.44 millimeters
(wn = 2.44mm) and a psychological work of minus 0.46 millimeters (dAw
= – 0.46mm), it will take 385 calls for a full reaction. The psychological work
value is taken without a minus sign, because we are interested in the quantity
of calls.
c = log (e) (dAw / QImin)
= log (1.01) (0.46mm / 0.01mm) = 385
With a call duration of 0.6 seconds, this is
almost four minutes for fully excitation of pupil.
t = c * lc = 385 * 0.6s = 231s
The accumulated excitation will be minus 0.45
millimeters.
QA (с) = (dAw – dAw / e^c) =
(– 0.46mm – (– 0.46mm / 1.01^385)) = – 0.45mm
Which is subtracted from the initial
coordinate, because the value (dAw) is negative (wn >
wy).
wn
(c)
= wn
+ QA
(с) = 2.44mm
+ (– 0.45mm)
= 1.99mm
Etc.
—
The quantity of time, required for full
excitation, is set by the values of the response to stimulation (dAw),
excitability (e), minimum portion of irritation (QImin), and
duration of time between calls (lc). If the psychological work is
increased to 1.7 millimeters (dAw = 1.7mm), for example, 516 calls
will be required.
c = log (e) (dAw / QImin)
= log (1.01) (1.7mm / 0.01mm) = 516
With a call duration of 0.6 seconds, this is
more than five minutes for full excitation.
t = c * lc = 516 * 0.6s = 309.6s
If increase the excitability, for example, to
1.21 (e = 1.21), will need only 27 calls.
c = log (e) (dAw / QImin)
= log (1.21) (1.7mm / 0.01mm) = 27
With a call duration of 0.6 seconds, this is
only 16.2 seconds for full excitation.
t = c * lc = 27 * 0.6s = 16.2s
If increase the accuracy from hundredths (QImin
= 0.01mm) to thousandths (QImin = 0.001mm), the quantity of calls
will increase to 39 calls.
c = log (e) (dAw / QImin)
= log (1.21) (1.7mm / 0.001mm) = 39
With a call duration of 0.6 seconds, this is
23.4 seconds for pupil dilation.
t = c * lc = 39 * 0.6s = 23.4s
If increase the time interval between calls to
1.3 seconds (lc = 1.3s), the total time for pupil dilation will
increase to 50.7 seconds.
t = c * lc = 39 * 1.3s = 50.7s
Etc.
—
We live in a physical world, where the
difference of temperature and pupil diameter cannot be infinite. Therefore, the
correspondence of spaces (ld >> lw) can be set
through maxima. Assume, that the maximum temperature difference for our
creature is 35 degrees Celsius (dmax = 35°C). If the temperature of
the irritant is above 45 degrees Celsius, there is no sense in determining the
temperature difference, because our creature will burn, die, and become charred
at such a temperature difference. Assume, that the maximum difference in our
creature's pupil diameter is 7 millimeters (wmax = 7mm), i.e. at a
norm of 1 millimeter, the pupil does not dilate beyond 8 millimeters. In this
case, the correspondence of spaces will be the correspondence of their
maximums. In our example, one degree Celsius will correspond to 0.2 millimeters
(1°C >> 0.2mm)
lw = ld * wmax
/ dmax = 1°C * 7mm / 35°C = 0.2mm
The ratio of the maxima sets only the proportionality
of the spaces. In a linear relationship (y = x), a difference of 10 degrees
Celsius will correspond to a difference of 2 millimeters, a difference of 20
degrees Celsius will correspond to a difference of 4 millimeters, etc. With a
difference of 40 degrees Celsius and above, nothing will happen to the pupil,
because the creature will die. However, if we change the function to (y = 2 *
x), then with a difference of 20 degrees Celsius or more, the pupil should be
at its maximum condition of 8 millimeters. Therefore, the maximum difference in
input values should be equivalent to the maximum difference in output values. For
example, with a non–linear function (y = x^2 / 35), the maximum difference in
output values will be 7 millimeters, which is consistent with the maximum
possible value of 7 millimeters (wmax = 7mm). In this case, a
difference of 10 degrees Celsius will correspond to a difference of 0.57
millimeters.
y (+) = (x^2 / 35) * lw / ld
= (10°C^2 / 35) * 0.2mm / 1°C = 0.57mm
The pupil width should be 1.57 millimeters,
almost minimal.
wy = ws + y = 1mm + 0.57mm
= 1.57mm
A value difference of 20 degrees Celsius will
correspond to a value difference of 2.29 millimeters.
y (+) = (x^2 / 35) * lw / ld
= (20°C^2 / 35) * 0.2mm / 1°C = 2.29mm
A value difference of 30 degrees Celsius will
correspond to a value difference of 5.14 millimeters.
y (+) = (x^2 / 35) * lw / ld
= (20°C^2 / 35) * 0.2mm / 1°C = 5.14mm
Etc. The relationship will no longer be
linear, although it will remain directly proportional, the higher the
temperature difference, the larger the pupil diameter should be. As a
consequence, the creature should react more strongly to a stronger stimulus,
than to a weaker one, but should still react weakly to an average stimulus.
This eliminates weak and average irritant, that do not yet require additional
tension from the creature. If change the function to (y = dmax – x^2
/ 35), the relationship becomes inversely proportional, the higher the
temperature difference, the smaller the pupil diameter. A value difference of
10 degrees Celsius will correspond to a value difference of 6.43 millimeters.
y (+) = (dmax – x^2 / 35) * lw
/ ld = (35°C – 10°C^2 / 35) * 0.2mm / * 1°C = 6.43mm
The pupil width should be 7.43 millimeters,
almost maximum.
wy = ws + y = 1mm + 6.43mm
= 7.43mm
A value difference of 20 degrees Celsius will
correspond to a value difference of 4.71 millimeters.
y (+) = (dmax – x^2 / 35) * lw
/ ld = (35°C – 20°C^2 / 35) * 0.2mm / * 1°C = 4.71mm
A value difference of 30 degrees Celsius will
correspond to a value difference of 1.86 millimeters.
y (+) = (dmax – x^2 / 35) * lw
/ ld = (35°C – 30°C^2 / 35) * 0.2mm / * 1°C = 1.86mm
Etc. The inverse proportion is also found in
psychology, for example, the higher the magnitude of danger, the quieter need
to behave. In the case of maximum danger, the effect of stupor is obtained,
when with a maximum difference of values, the value of the reaction is
practically zero.
—
The excitability value can be set by angles
from zero degrees (full non–excitability) to 90 degrees (instantaneous
excitability in one call of consciousness). Suppose, that there is a certain
angle of irritation of 11.5 degrees (fI = 11.5°). In this case, with
an actual excitation of 1.21 millimeters (wn = 1.21mm) and a
psychological work of 0.77 millimeters (dAw = 0.77mm), 215 calls
will be required to dilate the pupil.
c = log (Cos (fI)) (QImin
/ dAw) = log (0.98) (0.01mm / 0.77mm) = 215
Or 129 seconds.
t = c * lc = 215 * 0.6s = 129s
At an irritation angle of 81.5 degrees (fI
= 81.5°), the creature will demonstrate an instant reaction in 2.3 calls.
c = log (Cos (fI)) (QImin
/ dAw) = log (0.148) (0.01mm / 0.77mm) = 2.3
Or 1.4 seconds.
t = c * lc = 2.3 * 0.6s = 1.4s
With the same angle of 11.5 degrees (fI
= 11.5°), an actual excitation of 2.44 millimeters (wn = 2.44mm) and
psychological work of minus 0.46 millimeters (dAw = – 0.46mm), 189.5
calls will be required for a full reaction. The minus sign is skipped, because
we are interested in the quantity of calls.
c = log (Cos (fI)) (QImin
/ dAw) = log (0.98) (0.01mm / 0.46mm) = 189.5
In seconds, this is 113.7 seconds.
t = c * lc = 189.5 * 0.6s = 113.7s
Etc.
—
The magnitude of the excitability can also be
a derivative of the magnitude of the definition. Suppose, that the maximum
temperature difference for our creature is 35 degrees Celsius (dmax
= 35°C), and the maximum irritation angle is 90 degrees (fmax = 90°),
then one degree Celsius corresponds to 2.57 degrees of irritation angle.
lf = ld * fmax
/ dmax = 1°C * 90° / 35°C = 2.57°
With a function (y = x^2 / 35) and a
difference of 13 degrees Celsius (x = 13°C), the pupil should change its
condition to 0.97 millimeters relative to the normal condition.
y (+) = (x^2 / 35) * lw / ld
= (13°C^2 / 35) * 0.2mm / 1°C = 0.97mm
Or up to 1.97 millimeters in total.
wy = ws + y = 1mm + 0.97mm
= 1.97mm
With an initial excitation of 1.21 millimeters
(wn = 1.21mm), the psychological work will be 0.76 millimeters.
dAw = wy – wn
= 1.97mm – 1.21mm = 0.76mm
A temperature difference of 13 degrees Celsius
corresponds to an angle of 33.41 degrees.
fI = x * lf / ld
= 13°C * 2.57° / 1°C = 33.41°
The pupil will be excited by 0.75 millimeters
in 24 calls.
c = log (Cos (fI)) (QImin
/ dAw) = log (0.835) (0.01mm / 0.76mm) = 24
Or in 14.4 seconds.
t = c * lc = 24.1 * 0.6s = 14.4s
If the difference of values increases to 32
degrees Celsius (x = 32°C), then the pupil should change its condition to 5.85
millimeters.
y (+) = (x^2 / 35) * lw / ld
= (32°C^2 / 35) * 0.2mm / 1°C = 5.85mm
Or up to 6.85 millimeters in total.
wy = ws + y = 1mm + 5.85mm
= 6.85mm
With an initial excitation of 1.21 millimeters
(wn = 1.21mm), the psychological work will be 5.64 millimeters.
dAw = wy – wn
= 6.85mm – 1.21mm = 5.64mm
A temperature difference of 32 degrees Celsius
corresponds to an angle of 82.24 degrees.
fI = x * lf / ld
= 32°C * 2.57° / 1°C = 82.24°
The pupil will be excited by 5.63 millimeters
in just 3.2 calls.
c = log (Cos (fI)) (QImin
/ dAw) = log (0.135) (0.01mm / 5.64mm) = 3.2
Or in 6.06 seconds.
t = c * lc = 10.1 * 0.6s = 6.06s
Etc. As a result, a creature is more and
faster excited by a stronger stimulus, than by a weaker one. In our case,
excitation by 0.75 millimeters occurred in 14.4 seconds, but excitation by 5.63
millimeters occurred in 6.06 seconds, almost twice as fast with seven times
more psychological work. This technique is often used for the creature's self–preservation,
where seconds decide all.
—
Assume, that we convert a valid definition
(temperature difference) into an abstract definition (danger). In this case,
our creature will perceive the temperature difference not as warm–hot, but as
dangerous. Suppose, that 1 degree Celsius (ld = 1°C) corresponds to
0.4 units of danger (ld' = 0.4Ir). The conversion function will have
the form (x' = x^2 – 2 * x). This function has a special feature, when (x) is
less than or equal to two, the function returns a negative or zero value, i.e.
a difference of two degrees Celsius or less can be considered not dangerous for
our creature. But the higher the temperature difference, the more dangerous it
is. At an irritant temperature of 26 degrees Celsius (dx = 26°C),
the temperature difference will be 16 degrees Celsius.
x (+) = dx – ds = 26°C –
10°C = 16°C
The actual definition is indicated as
positive. The abstract definition is always positive and does not need to be
indicated. The danger value will be 112 units of irritation.
x' = (x^2 – 2x) * ld' / ld
= (16°C^2 – 2 * 16°C) * 0.5Ir / 1°C = 112Ir
Suppose, that the function of converting the
magnitude of danger into the magnitude of the pupil diameter is linear (y =
x'), and one unit of danger (ld' = 1Ir) corresponds to 0.005
millimeters (lw = 0.005mm). Then the pupil's condition should
deviate by 0.56 millimeters from the norm.
y (+) = x' * lw / ld' =
112Ir * 0.005mm / 1Ir = 0.56mm
Etc.
—
We live in a physical world, where the
difference of values is constantly changing, which is why every living creature
has consciousness. Consciousness is the definition of the difference of values
with some frequency (lc). Next, the value of the definition (x) is
converted into the value of the reaction (y), the value of the psychological
work (dAw) is calculated, and a portion of this work (QE)
is performed. Then, the definition is called again. This process continues indefinitely
to respond to changes in the actual reality until the living being dies. If the
definition value is a constant value in each call, then the creature is
recursively excited over a certain quantity of calls (c) to a value (QA
(c) = dAw – QImin). If, during the excitation, the
difference of values in the definition (x) changes, then the magnitude of the
difference of values in the work performed (y) will also change. Suppose, that the stimulus increases the temperature
linearly at a rate of 4 degrees Celsius per second from 12 degrees Celsius. With 0.6 seconds between calls — that's 2.4 degrees
Celsius per call. At the beginning of the first consciousness iteration lasting
0.6 seconds, the difference of values (temperatures) in degrees will be defined
as 2 degrees Celsius.
x (+) = dx – ds = 12°C –
10°C = 2°C
A temperature difference of 2 degrees Celsius
at the input corresponds to a diameter difference of 0.02 millimeters at the
output.
y (+) = (x^2 / 20) * lw / ld
= (2°C^2 / 20) * 0.1mm / 1°C = 0.02mm
This is an instruction to change the pupil's
condition from its current value to 1.02 millimeters.
wy = ws + y = 1mm + 0.02mm
= 1.02mm
Suppose, that the actual condition of the
pupil is an excitation of 1.08 millimeters (wn = 1.08mm), then the
response to stimulation should be a pupil constriction of 0.06 millimeters.
dAw = wy – wn
= 1.02mm – 1.08mm = – 0.06mm
With an excitability of 1.4 (e = 1.4, r =
3.5), the portion of pupil excitation in the first call will be minus 0.017
millimeters.
QE (c) = dAw / r * (e ^
(с – 1)) = – 0.06mm / 3.5 * (1.4 ^ (1 – 1)) = – 0.017mm
The actual pupil diameter at the end of the
first iteration of consciousness will be 1.063 millimeters.
wn
(с) = wn
+ QE
(c)
= 1.08mm
– 0.017mm
= 1.063mm
If, at the beginning of the second iteration
of consciousness, the creature would determine the same temperature difference
of 2 degrees Celsius, then it would continue to calculate, as we did earlier. The
magnitude of the definition of 2 degrees Celsius would correspond to the same
difference in diameters of 0.02 millimeters or pupil width of 1.02 millimeters,
only the magnitude of work performed would change, because in 0.6 seconds would
change the magnitude of actual pupil excitation from the initial width of 1.08
millimeters to the current (in this iteration of consciousness) pupil width of
1.063 millimeters. Therefore, the quantity of psychological work in the second
iteration of consciousness would decrease to minus 0.043 millimeters.
dAw = wy – wn
= 1.02mm – 1.063mm = – 0.043mm
The second portion of pupil excitation in the
second call would be minus 0.012 millimeters.
QE (c) = dAw / r * (e ^
(с – 1)) = – 0.043mm / 3.5 * (1.4 ^ (1 – 1)) = – 0.012mm
The actual pupil diameter at the end of the
second iteration of consciousness would be 1.051 millimeters.
wn
(с) = wn
+ QE
(c)
= 1.063mm
+ (– 0.012mm)
= 1.051mm
Etc., until the pupil width would have
narrowed to a value of about 1.02 millimeters, set by a temperature difference
of 2 degrees Celsius. But the definition is not a constant, so after 0.6
seconds, at the beginning of the second iteration of consciousness, the
creature will determine a new difference of 4.4 degrees Celsius, because during
this time, the stimulus for some reason warmed up by 2.4 degrees Celsius.
x (+) = dx – ds = 14.4°C
– 10°C = 4.4°C
The temperature difference of 4.4 degrees
Celsius at the input now corresponds to a diameter difference of 0.097
millimeters at the output.
y (+) = (x^2 / 20) * lw / ld
= (4.4°C^2 / 20) * 0.1mm / 1°C = 0.097mm
Now, this is a command to change the condition
of the pupil from the current value (which has changed to 1.063 millimeters
after the first iteration of consciousness) to 1.097 millimeters, because the
difference of values in the definition has increased.
wy = ws + y = 1mm +
0.097mm = 1.097mm
The creature hurried to constrict the pupil
0.6 seconds ago, because now it needs to dilate by 0.034 millimeters.
dAw = wy – wn
= 1.097mm – 1.063mm = 0.034mm
After 0.6 seconds, the pupil will dilate by
0.01 millimeters.
QE (c) = dAw / r * (e ^
(с – 1)) = 0.034mm / 3.5 * (1.4 ^ (1 – 1)) = 0.01mm
And the actual pupil diameter at the end of
the second iteration will be 1.073 millimeters.
wn
(с) = wn
+ QE
(c)
= 1.063mm
+ 0.01mm
= 1.073mm
Etc. The pupil's width changes according to
the actual reality in each iteration of consciousness, first 1.08 millimeters,
after 0.6 seconds 1.063 millimeters, after another 0.6 seconds 1.073
millimeters, etc.
—
Assume, that the creature's pupil is already
in a condition of excitation, measuring 1.21 millimeters (wn =
1.21mm). In the absence of an irritant, this condition becomes redundant, but
only the irritant (dx) can return the creature to a condition of
rest (or set any other condition). In the absence of an irritant and provided,
that the value of the actual condition is greater, than the resting norm (wn
> ws), the actual condition of the creature is perceived as an
irritant (dx = wn) in each iteration of consciousness,
the norm of rest is perceived as the condition of rest of the creature (ds =
ws), and the incoming and outgoing spaces are self–referential (recursive). In
this case, their dimensions should correspond one–to–one (1mm >> 1mm). In
the first iteration of consciousness, the creature will determine the deviation
from the norm of 0.21 millimeters.
x (+) = dx – ds = 1.21mm
– 1mm = 0.21mm
Assume, that the conversion function has the
form (y = x / 5). In this case, the magnitude of deviation from the resting
norm (y) will be equivalent to the residual irritation (QI (c)), in
the first iteration of consciousness it will be 0.042 millimeters.
y (+) = (х / 5) * lw
/ ld
= (0.21mm
/ 5) * 1mm
/ 1mm
= 0.042mm
The pupil diameter in this case should be
1.042 millimeters.
wy = ws + y = 1mm + 0.042mm
= 1.042mm
The quantity of psychological work will be
minus 0.168 millimeters.
dAw = wy – wn
= 1.042mm – 1.21mm = – 0.168mm
This value will be equivalent to the quantity
of excitation (QE (c)). However, the actual magnitude of excitation
will depend on the magnitude of excitability. With an excitability of 3.5 (e =
3.5, r = 1.4) in 0.6 seconds (one iteration of consciousness) the portion of
excitation will only be a fraction of the magnitude of psychological work. The
pupil will constrict by minus 0.12 millimeters.
QE (c) = dAw / r * (e ^
(с – 1)) = – 0.168mm / 1.4 * (3.5 ^ (1 – 1)) = – 0.12mm
After 0.6 seconds, the pupil diameter will be
1.09 millimeters.
wn
(с) = wn
+ QE
(c)
= 1.21mm + (– 0.12mm) = 1.09mm
In the next iteration, after 0.6 seconds, the
creature will determine a new difference of values 0.09 millimeters, because
the pupil width (wn) has narrowed by the magnitude (QE (c))
to 1.09 millimeters. The new pupil width is again taken as the value of
irritant (dx = 1.09mm), because the magnitude of the current
condition is greater, than the norm of rest (wn > ws).
x (+) = dx – ds = 1.09mm
– 1mm = 0.09mm
The magnitude of deviation from the norm now
should be 0.09 millimeters.
y (+) = (х / 5) * lw
/ ld
= (0.09mm
/ 5) * 1mm
/ 1mm
= 0.018mm
The pupil diameter in this case should be
1.018 millimeters.
wy = ws + y = 1mm + 0.018mm
= 1.018mm
The magnitude of psychological work now is
minus 0.072 millimeters.
dAw = wy – wn
= 1.018mm – 1.09mm = – 0.072mm
The magnitude of the excitation will be minus
0.026 millimeters.
QE (c) = dAw / r * (e ^
(с – 1)) = – 0.072mm / 1.4 * (3.5 ^ (1 – 1)) = – 0.051mm
The pupil diameter will be 1.039 millimeters.
wn
(с) = wn
+ QE
(c)
= 1.09mm
+ (– 0.051mm)
= 1.039mm
Etc. This will be repeated until the magnitude
of the required psychological work (dAw) is less, than the
statistical error (QEmin), and the difference between the actual
pupil condition and the normal pupil condition is within the acceptable range
((wy – ws) < QImin).
—
If translate the result into a more familiar
linear (uniform) condition change, then the excitation portions (QE (c))
and the average rate of condition change (dv (c)) will be equal to each other
(QE (c) = dv (c)). For example, with 205 calls
(c = 205) and 4.99 millimeters of accumulated excitation (QA (c) =
4.99mm), the average rate of change in the pupil condition will be 0.24
millimeters per call.
QE
(c)
= dv (c)
= QA
(c)
/ с = 4.99mm
/ 205 = 0.024mm
In the more familiar seconds, this is 0.4
millimeters per second.
dv (t) = QE (c) / lc =
0.024mm / 0.6s = 0.04mm/s
Another way to determine the linear (average)
speed is to measure the pupil condition at the beginning of the interaction (wn),
at the end of the interaction (wn (t)), and the time (t), that has
elapsed since the beginning to the end of the interaction. In our case, 205
calls are 123 seconds.
dv (t) = (wn (t) – wn) /
t = 4.99mm / 123s = 0.04mm/s
Etc.
—
Assume, that the maximum rate of change of the
pupil condition is 0.02 millimeters per second (dvmax (t) =
0.02mm/s) or 0.012 millimeters per call (dvmax (c) = 0.012mm), this
is the limit of the speed of operation of the executive mechanism. Otherwise,
this is the maximum portion of excitation, that can conduct our creature. In
this case, the creature physically will not be able to get excited by 4.99
millimeters in just 205 calls. The creature at least will need 249.5 seconds or
415.8 calls for full excitation at the maximum rate of pupil condition change.
cmin = QA (c) / dvmax
(c) = 4.99mm / 0.012mm = 415.8
Assume, that the maximum difference of the
pupil diameters of our creature is 7 millimeters (wmax = 7mm), and
the margin of error is 0.001 millimeters (QImin = 0.001mm). In this case,
the minimum quantity of calls for full excitation at the maximum rate of change
in the pupil condition will be 583.25 calls (350 seconds). The pupil will not
be able to expand faster from the resting condition to the maximum.
cmin = (wmax – QImin)
/ dvmax (c) = (7mm – 0.001mm) / 0.012mm = 583.25
Etc.
—
Thanks to everyone, who read to the end..
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