For Larry -- Time-constant calculation for a more negative visual-environment

Dear Larry,


"Science is the attempt to make the chaotic diversity of our
sense-experience correspond to a logically uniform system of thought."

Albert Einstein


Subject: Clarification of the servo-control concept and the
time-constant calculation for a negative (linear) input.

Re: Predicting the behavior of the natural eye to a
more negative accommodation signal.

Otis> Let me clarify my statement using a negative "step-change"
in the accommodation signal.

Otis> However, since you "explode" when I talk about the human
eye, I will use the primate (monkey) eye and the word
"refractive state" to avoid offending you.


Larry> You say you have proof that a -3d myope can become a -1D
myope by removing the spectacle correction for 100 days.

Otis > I ABSOLUTLY NEVER SAID ANYTHING LIKE THAT! Mike Tyner said
it. What I said was that the natural eye, when tested,
evinces a time-constant of 100 days, from a negative
"step-input" to the system. (See equation below.)

Otis> However, to clarify, this is exactly what I do say about the
dynamic behavior of the natural eye when OBJECTIVELY
tested.

Otis> Let me change this and say how we can change the refractive
state of a population of individuals (primates) with a
refractive state of -1.0 diopters, and we wish to change
their refractive state in a negative direction.

Otis> Please accept that the accommodation system takes on the
value of:

1. The visual environment.

2. The applied minus lens.

Otis> We then select a population of primates with a refractive
state of -1.0 diopters (let us say 100 primates).

Otis> We force 1/2 to wear a -2.0 diopter lens, the control group
remains in its previous visual environment.

Otis> The effect of the minus 2 diopter lens is to change the
average-value of accommodation by 2 diopters. That is the
ONLY difference between the test group and control group.

Otis> Your assumption is that: Refractive status = Heredity
Perhaps wrong -- but I accept that you believe this to be
true. Therefore, no difference in refractive status can
develop between the test group versus the control group.
i.e., there is not time-constant, and no change.


Otis> The concepts of dynamic eye states that

Focus of control group = -1.0 diopters

Focus of test group at start = -1.0 diopters

Proportional change:

Focus Change = Step Input * [1 - e^ (- t / TAU)]

Applying values:

Step change in control group = -2.0 diopters

Focus Change = ( -2.0 D) * [1 - e ^ (-100 days / Tau)]

Focus Change = -2.0 * 0.632

Focus Change = -1.26 diopters

Otis> So now we can predict the refractive status of the test
group relative to the control group.

Otis> Since the starting refractive status was -1.0 diopters, the
refractive status of the eyes wearing a -2.0 diopter lens
will be:

Focal status = -1.0 diopter -1.26 diopters

Focal Status = -2.26 diopters

Otis> Please notes that this is an average of the 50 eyes in the
test group.


Otis> Thus the change is not 2.0 diopters, as you intimated, but
by calculation the change is -1.26 diopters.


Otis> I hope this clarifies the behavior of the natural,
adolescent primate eye, and its response to step-input
changes it its average visual environment.

Otis> I understand your theory and assumption is that there must
not be, and can not be any refractive change, so your
theory insists that:

Refractive Status of Test Group = -1.0 diopters

Refractive Status of Control Group = -1.0 diopters

Otis> Obviously the predictive power of your theory leaves
something to be desired.


Best,

Otis

Engineer