Technical Analysis as to why the eye goes "down".

Dear "Repeating Rifle", (Bill)


Below is a statement of objective fact concerning
the behavior of the eye.

The paper that follows explains why (in mathematical
format) the eye MUST change with the applied minus lens.

How much clear can the experimental data become?

For thoughtful analysis.

If you kids are wearing a plus for prevention -- keep
them at it.

Enjoy!

Otis

********




Frank Schaeffel, Adrian Glasser and
Howard C. Howland,

"Accommodation, Refractive Error and
Eye Growth in Chickens",

VISION RES., Vol 28,
No. 5 pp 639-657, 1988. Pergamon Press.

RESULTS:

All eyes treated with positive lenses became consistently
more positive (hyperopic).

Negative lenses produced more negative (myopic) refractions
(focal states) in all eyes.

In a test of plus/minus lenses on left/right eyes, the eye with the
plus lens moved in a positive direction. The eye with a minus lens
moved in a minus direction.

The control group did not change significantly in any direction.


________________________________




Paper 29

THE RESPONSE OF A DYNAMIC EYE TO FOCAL PERTURBATIONS

By Otis Brown



Physical concepts are free creations of the human mind, and
are not, however it may seem -- uniquely determined by the
external world. In our endeavor to understand reality we are
somewhat like a man trying to understand the mechanism of a closed
watch. He sees the face and the moving hands, even hears it
ticking, but he has no way of opening the case.

If he is ingenious he may form some picture of the mechanism
which could be responsible for all the things he observes, but he
may never be quite sure his picture is the only one which could
explain his observations.

He will never be able to compare his picture the real
mechanism and he cannot even imagine the possibility of the
meaning of such a comparison.

Albert Einstein



THE CHARACTERISTIC RESPONSE OF THE EYE TO UNIT-STEP
DISPLACEMENTS

In the previous chapter we developed a very accurate equation
that duplicates the eye's behavior. The eye needs a very high
level of tracking accuracy; using very basic data, we can estimate
that the eye tracks its environment with a probable-error of
better than 0.57 diopters.

Detailed measurements made by Dr. Francis Young show major
changes in the optical components of the growing human and primate
eye. Paradoxically, the eye maintains an over-all focal accuracy
of better than one percent of its total power. The eye maintains
this accuracy (relative to its visual environment) even though
individual optical components are changing in an unpredictable
manner.

Dr. Lawrence Stark's work has demonstrated high level
accuracy for the accommodation (lens/retina) neurological system.
This chapter extends his work by developing a perturbation
(growth) control equation that accurately predicts the eye's
response to step-change disturbances.


LENS POWER CHANGE AS A FUNCTION OF TIME

The lens of the human eye undergoes a focal power change of
about 20 percent over a period of ten years. Without reference to
feedback control concepts, a systems engineer will be hard-pressed
to explain focal accuracies of one percent for the normal eye,
while major optical components are changing by 20 percent.

A graph of this focal change, and other optical parameter
changes have been published by Dr. Francis Young and Dr. George
A. Leary. (1) (See Figure 1)


A FOCAL BEHAVIOR EQUATION

As previously developed, the transfer function for the
long-term growth of the eye is: (2)

1/ (TAU s + 1)

Where: TAU = 100 Days. (The eye's time-constant)

When a step-function is applied to this transfer function,
the resulting equation is:

System's Response = [ Step Input / s ] * [ 1 / (TAU s + 1 ) ]

The time response of this function is: (3)

Focus = Offset + Accommodation + Step Input * [1 - EXP ( - t / TAU)]

If a perturbation occurs within the control loop, it will
cause not only a step-input to the system, but an immediate
perturbation in the focal setting of the eye:

System's Response = [ Perturbation ] * [ 1 / ( TAU s + 1 ) ]

The standard response for an impulse perturbation is:

Focus = Offset + Accommodation - Perturbation * EXP ( - t / TAU )

INITIAL VALUES FOR THE STANDARD CASE

Let's examine the equation as applied to wild monkey's eyes.

Perturbation = 0 diopters Offset = +1.5 diopters

Time = 300 days TAU = 100 Days

Accommodation (Average) = - 0.9 diopters

Focus = Offset + Accommodation - Perturbation * EXP ( - t / TAU )

Focus = 1.5 + ( -0.9 ) - ( 0 ) * EXP ( -300/100 )

Focus = + 0.6 Diopters

This result corresponds to +0.577 diopters mean value,
obtained from measurements of a large number of wild (open-pen)
monkey's normal eyes.


A NEGATIVE IMPULSE

Now, consider the eye's response to a - 0.5 diopters change
in the focal power of the cornea. (This change could be induced
by use of a - 0.5 diopter contact lens) Prior to the perturbation,
the focal status was + 0.6 diopters. Immediately after the
perturbation: (At t = 0 )



Focus = Offset + Accommodation - Perturbation * EXP ( - t / TAU )

Focus = 1.5 + (-.9) - (-.5) * EXP ( - 0 / 100 )

Focus = +1.1 diopters

After 300 days, the focal status will be:

Focus = 1.5 + (-.9) - (-.5) * EXP ( - 300 / 100 )

Focus = + 0.625 or approximately + 0.6 diopters

The eye's focal control system has returned the eye to the
focal status that existed before the -0.5 diopter perturbation
occurred.

A POSITIVE IMPULSE

In a similar vein, we can predict the eye's response to a +
0.5 diopter perturbation. (Simulated by use of a +0.5 diopter
contact lens.)

Focus = 1.5 + (-.9) - ( +.5) * EXP ( - 300 / 100 )

Focus = + 0.575 or approximately + 0.6 diopter

(If the +0.5 contact lens is now removed, the eye's focal
status will be +1.0 diopters.)

Obviously, the human eye is not subject to only a single
perturbation. We can, nevertheless, deduce the control action of
the normal eye by studying the response of the eye to such
idealized disturbances.


THE EYE'S FOCAL RESPONSE TO NOISE

In actual fact, the eye is subject to continuous
perturbations (noise) while growing. This noise tends to
randomize the eyes' focal status. The control action of the
normal eye works to overcome this randomness, exercising control
over the appropriate optical components (corneal radius, length)
to ensure accurate focus. A study of monkeys' eyes demonstrates
that, with a steady state visual environment, their normal eyes
maintain a focal accuracy of better than 1.0 percent.


A STATISTICAL PROFILE OF WILD MONKEYS' EYES

The graph on the following page presents two
computer-generated statistical distributions for wild, or "open
pen" monkeys' eyes. The focal status histogram was obtained from
measurements made by Dr. Young on 375 monkeys. The accommodation
histogram is the estimated average value of accommodation for all
the monkeys. Some monkeys will spend more time looking at close
objects, and will have an average value of accommodation of
perhaps - 1.2 diopters (and corresponding focal state of + 0.3
diopters), while other monkeys will spend more time looking at
distant objects and will have an average value of accommodation of
perhaps - 0.6 diopters (and a corresponding focal state of + 1.1
diopters). The preliminary mean value for the 375 monkeys is -0.9
diopters (producing an over-all focal status of +0.6 diopters.)
(See Figure 2)


CONCLUSIONS

If the normal primate eye is to achieve a high level of focal
accuracy in the presence of continuous perturbations, the author
has concluded that the eye must employ dynamic control to set its
focus. This chapter presents a high performance model that
provides a focal control mechanism that is, as far as we can
determine, consistent with all the physical evidence pertaining to
the normal eye's behavior.

The model evolved as a result of a long investigation in
which many preliminary approaches were discarded because they led
to inconsistencies. It is clear that the number of approaches
that can satisfy the evidence is limited. An electrical engineer,
when faced with similar engineering requirements for focal
precision, will develop this type of design to meet the accuracy
requirements of the eye.

The philosophy of this chapter has been to study the focal
control process of the normal eye by treating it as a design
problem. The procedure followed is to develop a system model with
the focal performance capability comparable to the normal primate
eye.

Measurements on individual optical components of the eye are
exacting, and it is difficult to say which optical component
causes a specific problem. The researcher can be aided by an
engineering approach to this complex system, since the eye is an
intricate data-processing system. The primary neurological
process is controlling a dynamic (100 day time-constant) focal
system on a microscopic level.

It should be remembered that there are several major optical
components of focus, any of which can dramatically affect the
focal state of the normal human eye. While the eye is growing,
these components are continually changing in value.


Figure 2

Histograms for the Average Accommodation Status and the Focal
Status of the Normal Eye


DIOP FOCAL ACCOM
TERS STATUS MODATE ESTIMATED ACCOMMODATION STATUS -- PERCENT
.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0
....................................................
-1.5 .0 .2 .
-1.4 .0 .9 . A
-1.3 .1 2.7 . A
-1.2 .1 6.5 . A <---------------<< Accommodation
-1.1 .2 12.1 .F A
-1.0 .3 17.6 .F A
-.9 .4 20.0 . F A<---
-.8 .6 17.6 . F A V
-.7 .8 12.1 . F A V
-.6 1.1 6.5 . F A |
-.5 1.4 2.7 . F |
-.4 1.8 .9 . A F |
-.3 2.3 .2 . F Offset 1.5 Diopters >>-->|
-.2 2.9 .0 . F |
-.1 3.4 .0 . F |
.0 4.0 .0 . F |
.1 4.6 .0 . F |
.2 5.1 .0 . F |
.3 5.6 .0 . F |
.4 6.0 .0 . F |
.5 6.2 .0 . F v
.6 6.3 .0 . F<-------------------
.7 6.2 .0 . F
.8 6.0 .0 . F
.9 5.6 .0 . F
1.0 5.1 .0 . F
1.1 4.6 .0 . F
1.2 4.0 .0 . F
1.3 3.4 .0 . F<----------------<< Focal Status
1.4 2.9 .0 . F
1.5 2.3 .0 . F
1.6 1.8 .0 . F
1.7 1.4 .0 . F
1.8 1.1 .0 . F
1.9 .8 .0 . F
2.0 .6 .0 . F
...................................................
.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0
MEASURED FOCAL STATUS -- PERCENT

When a physiologist experiments on this complicated data
processing operation, he is in the same position as a technician
who is presented with a computer system that determines rocket
guidance. He is then told to make measurements on the individual
components of the device until he determines which component
establishes the tracking accuracy of the system. Actually, the
physiologist is in a more difficult position because so much of
the data processing of the eye is at the molecular level, almost
beyond the reach of his instruments.

The mathematical systems concepts used in automatic control
evolved out of necessity, as it became apparent that modern servo
systems could not be understood by studying the characteristics of
their individual components. This truth applies just as strongly
to complex processes encountered in biological-optical systems.
The electronics engineer can establish a solid mathematical
foundation for an analysis that will accurately predict the normal
eye's focal control response.

The same equation that precisely anticipates the normal eye's
perturbation control also predicts that nearsightedness can be
avoided. In addition, the equation can give conceptual and
practical guidance to a successful nearsightedness avoidance
effort.

There are other more sophisticated means of determining the
eye's tracking accuracy, and these techniques will be developed in
the next chapter.


APPENDIX

Focal
Accuracy: The eye is about 2.4 cm in length. The eye must have a
focal power of 57 diopters to focus light on the retina.
The focal status histogram for normal eyes has a
standard deviation of .843 diopters, and a probable
error of .843 X .674 = .568 diopters. We may,
therefore, specify that the eye has a tracking probable
error of .568/57 or approximately one percent of its
total focal power. This is the worst-case value. For a
number of reasons, we should expect that the tracking
accuracy of the normal eye will be considerably better
than one percent. In the next chapter we will provide
an analysis that demonstrates that the actual tracking
probable-error is on the order of 1/10 diopters.


REFERENCES

1. Young, F., Leary, G. VISUAL CHARACTERISTICS OF APES AND
PERSONS (207-225) Progress in Ape Research (1977)

2. Brown, O., Berger, R. A NEARSIGHTEDNESS COMPUTER (343-346)
Proceedings of the 7th New England Bioengineering
Conference (1979)

3. Brown, O., Young, F. PHYSIOLOGICAL MODELING: THE LONG-TERM
GROWTH OF THE EYE Proceedings of the 8th New England
Bioengineering Conference (1980)

 

BIG SNIP.................................................


Not based on proven data concerning HUMAN eyes Otis.
Your usual data of apes and chickens mixed with some humans in the blender.
The outcome?
A soup or should I say your usual soap?
The usual blabla instead of proof by Otis.

Also writing "by Otis Brown" followed immediately by a text written by
Albert Einstein is realy weird.

Jan (normally Dutch spoken)

 

Dear Jan,

In the original text, each chapter had an italized quote.

Since this is a basic "text" editor, that was "lost".

Einsteins statment was to the effect that there is
no "perfect" representatin of experimental "reality",
and the the concept of the "pure" eye as exclusively
a rigid box might be an "idealization" that has
lost is believeablity.

What we are arguing about is whether the NATURAL EYE
changes its REFRACTIVE STATUS as the VISUAL ENVIRONMENT
IS MOVED NEGATIVE.

This is NOT A DEFECTIVE PROCESS. If you take an
eye with a refractive status of +1.5 diopter (population
of this status), and place a minus lens of -1.5 diopter,
the refractive status will move in a negative direction
by about 1.0 diopter.

At the end of this test, this young eye will have
a refractive status of +0.5 diopters -- AND WILL NOT
HAVE "failed" anything.

The point is that this eye behaves "dynamically",
and you insist that it does not.

This is indeed a pure-scientific argument, and some
people with a more "open" intellect will begun
to understand this type of technical analysis.

I regret it if you do not.

Best,

Otis

Engineer


***********

 

Dear Jan,

OK, I get it.

The chicken eye goes "down" when you place a minus lens
on it -- because it is a sophisticated control system.

1. {Going "down" proves that the natural eye is dynamic.
I said NOTHING about ANY DEFECT. Only the OBJECTIVE,
repeatable scientific truth.) Isn't the "repeatable
experiment the "exemplar" of fundamental science?

2. Ok, so you agree with me that all chicken eyes
are dynamic in the above sense -- and do not
challenge the statement.

3. Then we study two speciese of primate eye.
(We must make drastic changes to the "population"
to see the underlying "control" effect.)
As per Dr. Francis Young's work to determine
if the primate eye was "dynamic", i.e., changes
its REFRACTIVE STATUS as the enviroment had
an imposted "step change", you again agree
that the adolescent primate (monkey) eye is
dyanamic, since Dr. Young was a VERY CAREFUL
experimeter -- and his experiment can be repeated
as many times as you like.

4. But they we come to the human-primate eye, and
you tell me, that the human eye IS A BOX CAMERA
that does not change its refractive status
as the visual environment is changed.

5. So human eyes are "box-cameras", and all
other eyes are "dynamic" by direct test.

Interesting theory you have there, Jan.


Best,

Otis
Engineer

******

 

<further snip>
Are you proposing that if you put a minus lens on a hyperopic eye, that it
will become less hyperopic? I've heard you advocating "plus" for those who
are myopic, are you also advocating "minus" for those who are hyperopic? And
if you don't, please explain in the context of your theories why it works
one way and not the other.

 

The below shows you do not.
You are trying to lay words in to my mouth I never spoke.
As asked before, when you quote, quote correct Otis.
One big request, do not try to think for me or pretend you can.
You have a hard time to think even for yourself Otis.
And proof your idea works on human eyes Otis.

 

snip

Of course, Schaeffel was using high power lenses to simulate congenital
refractive error in chicks with no refractive error. He was studying how
chick eyes recover from congenital error.

Here is a study that used minus lenses of the correct power to correct
myopia. In this study, myopia did not increase in response to the use of a
minus lens.

Optical correction of form deprivation myopia inhibits refractive recovery
in chick eyes with intact or sectioned optic nerves.
Wildsoet CF, Schmid KL.
School of Optometry, University of California, 94720-2020, Berkeley, CA,
USA.

Chicks eyes with experimentally induced myopia will change back to
emmetropia when the myopia inducing treatment was removed. In this
experiment, experimentally induced myopia was fully corrected or
undercorrected with minus lenses. Chick eyes stabilized their myopia at a
level consistent with the correcting lens power used, myopia did not
progress with use of correcting lens.

Dr Judy

 

Dear Ry,

I am not proposing that we place a -1.5 diopter lens
on the natural eye with normal refractive states.

To prove the point I would place a -1.5 diopter
on a selected population of normal primate
eyes, where they were selected to have
a refractive staus of between +1.0 and +2.0 diopters.

The normal primate eye, in the wild, or in an
"open pen" environment have refractive status
from zero to +2.0 diopters.

Thus the theory of Jan it:

Refractive status = Heredity

Which means there must be no change in
refractive status between the +1.5 diopter
primates. If the predictions of his theory is
correct then

Test Group (-1.5 diopters = Control Group (no change in
visual environment

I predict that the test group will change according
by about -1.0 diopters in about three months.

Since an eye with a positive refractive status is
normal under these circumstances, and both
groups (if human) would have 20/20, it follows
that we are only comparing the predictions
of two scientific theories.

I hope this clarifies the issue.

Best,

Otis
Engineer

*****

 

Dear Jan,

Why don't you make a clear and clean statement about
the effect of the minus lens on the refractive
status of the natural eye.

Is you theory that:

Refractive status = Heredity

Or do you agree with me that the
refractive status OF THE NATURAL PRIMATE EYE
will change (as per the e ^ (-t /Tau) equation.

Understand that the strictly natural primate eye
must behave one way or the other.

Or are you again going ot change the subject
and evade the quesiton?

[I am certain you are not going to answer -- because
if you do, you will get many questions about even
the "safety" of the minus lens -- which is what
is in doubt in this discussion.]

Best,

Otis

Engineer

 

Thanks for the response, but no, it doesn't answer my question. I'm not
particularly interested in your arguement with Jan at the moment. Let me
restate my question:

1) Do you believe that placing a "minus 1.5" lens on a eye with a
"refractive status" of +2.0 will after three months (citing your answer
below) will move to a "refractive status" of +1.0?

 

Dear "Ry",

Some further clarifications:

I believe that a negative refractive state of the
eye can be prevented. If a pilot, or highly motivated
person "catches" the situation, by checking his
vision at 20/40, I believe he can clear it at
that point by use of a strong plus lens.

This is what Dr. Stirling Colgate did
for himself, and you can read what
he said (for free) on my site:

www.myopiafree.com

I acknowledge that this type of "motivation" is
very difficult to inspire in a person and
most people will "turn off" if you would suggest
that this type of work is necessary at the
20/40 level. That truth does not make prevention
"impossible" but it does make it very difficult indeed.

Once a person decides to use a minus lens, then I have
nothing further to say on the subject. I agree that
you can not get out of it if you choose to even
"start" with the minus lens.

To further respond to your questions:




Otis> > This is NOT A DEFECTIVE PROCESS. If you take an
Otis> > At the end of this test, this young eye will have

I would not use the word "hyperopic" because the requirement
for perfect vision at the Naval Academy describes the
eye as having 20/20 and refractive states from between
zero to +1.5 dipoters.


I've heard you advocating "plus" for those who

Otis> Not the case. I advocate that a person
learn to use the plus BEFORE he fails the 20/40 line
on the eye chart. As such, the person is not the
threshold. It depends on whether you call 20/40 vision
"myopic" or not. Clearly I believe that a highly
motivated person can clear his vision from
-1/2 diopter (20/40) to 20/20 (> 0.0 diopters)
in about 6 months of hard, consistent use of
a +2.5 diopter lens -- for all close work.


are you also advocating "minus" for those who are hyperopic?

Emmetropia is a refractive state of 0.0 diopters. As such,
essentially eyes with 20/20 are almost all "hyperopic",
as described by the Naval Academy acceptance criteria.
I reject the work "hyperopia" to describe the absoluty
natural and normal eye. It gives a very false idea
about the natural eye.


And

In order to do that it would be necessary to go into detail concerning
a mathematical model of accommodation. I could do this,
but it would take some time.

Just say that, the accommodation system can "track"
a negative "delta" in accommodation in a "linear" manner,
and therfore it is easier to demonstrate a forced negative
change, rather than a "positive change".

But positive change (from 20/40 to 20/20) is possible - given
that the person has great personal resolve to "work" the
issue properly.

I have proposed a study of that type -- but the issue
remains to be resolved.

Best,

Otis
Engineer

 

Why don't you show proof Otis, your idea about the plus lens works?
Further, do not speak on my behalve, quote correct and if you can't, do not
try to show text I never wrote (examples again below).
Several times people have shown your idea about preventing myopia is, in
general, useless.
You are, untill now, not capable to prove your idea of preventing myopia
works in human eyes.
Untill you prove I would say you are the loser.

An example of your bad habit in not correct quoting, not a text I wrote.

Nice try Otis, I want to speak about human eyes, you stick to the eyes of
apes and chickens.

Understand that YOU must prove it does in human eyes.

Untill now you are the one who is avoiding giving answers or proof.
Lots of explainations are already send in your direction but your receiver
must be out of order.

You are the one in doubts, I have none in prescribing when necessary.
IMHO we are not having a discussion, I simple asked for proof your idea
about preventing myopia works.
You NEVER show such Otis.

Free to Marcus Porcius Cato: "censeo Carthagnem esse delendam''

I declare that Otis idea about preventing myopia in humans must be proved by
Otis himself or destroyed.

Jan (normally Dutch spoken)

 

Good question Ry.

Otis however, gives no direct answers on direct questions.

Jan (normally Dutch spoken)

 

Otis,

Please provide a link supporting your statement to the above AS DESCRIBED
by the Naval Acadamey ACCEPTENCE CRITERIA?????

Bet you can't!

Allen

 

Otis> Assuming an adolescent eye, then yes, I would expect
that will be the result.

Otis> I do suggest using a "test group" and a "control group"
for this test, consisting of at least 10 individuals in
each group.

Jan judges that I do not provide "direct answers", so you
decide. I would place a wager on the outcome of that
type of experiment. I wonder if Jon would?

Best,

Otis

 

Perfect Otis, the frase ''I would expect''.
No proof to show Otis?

Suggest the experiment to your advisor's childs Otis.
I have no doubts about the type of answering of this OD.

Free to Marcus Porcius Cato: "censeo Carthagnem esse delendam''

I declare that Otis idea about preventing myopia in humans must be proved by
Otis himself or destroyed.

Jan (normally Dutch spoken)

 

My comments are below.

As long as the parameters of the person's eyesight remain within your
limits, couldn't they use your methods?

True enough, that's a small amount of hyperopia. Can this same methodology
be used on a eye with a "refractive status" of +2.5? +3.5?

Call it whatever you want. If the "refractive status" of an eye is -x, it is
generally called myopic. If the "refractive status" is +x, it is generally
called hyperopic.

As I would define someone at -0.5 as myopic, I take the answer to be "yes I
advocate plus, for the very mildly myopic." And could this method be used
for someone at -1.0?

The term "hyperopia" is just that, a term. Call it a "positive refractive
status" if you like. The point is, there are some individuals with a
"positive refractive status" that makes them 20/40 on a Snellen chart. Let's
say that is +2.25 for the sake of discussion. Would you advocate putting a
"minus" lens on their eye so they could move their "refractive status" to
+1.25 and thus pass the Snellen?

I understand what you're saying, but it seems a convient out. If someone
fails, they lacked sufficient "resolve".