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

Discussion in 'Optometry Archives' started by Otis Brown, Sep 26, 2004.

  1. Otis Brown

    Otis Brown Guest

    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
     
    Otis Brown, Sep 26, 2004
    #1
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