A student refuses to answer Dr. Steadman's quiz. How to react.

Dr. Scott Steadman


Dear Scott,


Subject: Turn-about is fair play. What if a student in your
course flatly refuses to answer your basic quiz questions?


Re: I see no reason to crunch through your single decaying
exponential model when you provide no human data to assert
its validity. Scott


[Scott -- let me point out that a sophisticated control system
must show a time-constant response to a step-input.
Further, you must work up to the human-primate model by
first verifying the model on the adolescent monkey-primate eye.
In fact it is VERY IMPORTANT that the equation (transfer
function) be verified by direct-measurement on the
a population of adolescent-primate eyes. OSB]


DISCUSSION

Let us supposed you are teaching a course on analog modeling of
a control system.

Further, let us suppose that you wish to determine the
general background of your class, as well as their ability to
solve basic exponetial equations.

You pass out the test and 8 out of the 9 turn in the answers.

The 9th student turns in the test with no answers, but
informs you that the questions are "insulting" to him -- and he is
refusing to answer them. Or that he sees no reason to "crunch"
through the numbers to produce the correct answers you required of
him.


QUESTION -- IN ALL HONESTY!

Tell my how you would deal with that student?

Would you give him a "A+" because he said he was listed in
who's who or for any other reason he might provide?

Or would you give him an "F" for failure to answer the
questions?

Would you suggest he resign from your course on mathematical
modeling -- and pursue a course in some other field?

I do not see how a student with that attitude could continue
in your course.

Do you? And if so, please explain why and how?

Best,

Otis


***********


THE FOUR PROBLEM GROUPS


A test, or "questions" can often serve to clear-the-air, and
achieve a "clear mind" on a specific issue. The following
questions are designed to clarify the issues we have been
discussing.

I would expect that engineers and scientists will take the
following test and provide the correct questions.

Please answer the following multiple-choice questions.



PROBLEM 1

One hundred children (14 years of age) have been maintained
in a distant visual environment of -0.8 diopters for one year.

We find their initial refractive status (for the entire
group) is +0.7 diopters

At this point, half the children begin wearing a -1.0 diopter
lens. The other half wear no lens. Both groups continue to live
in the same visual environment, but obviously "environment" is
-1.0 diopters "closer". Thus, the accommodation system will be
"adjusted" for this change.

Use the following equation to answer the following questions.

Long-
Term = Offset + Accommodation + Delta * [ 1 - Exp( -Time/Tau ) ]
Focus


The "Delta" in this case equals the applied lens; which is
-1.0 diopters. The accommodation system will be -1 diopter
"closer" for 16 hours a day, 7 days a week.

1. What is the status of the test group after 1 day?

(a) .69 Diopters
(b) -1.50 Diopters
(c) .70 Diopters
(d) Since heredity controls the focal setting of the eye, both
groups will continue to have the same focal status. In all
cases, the refractive status of the control group will be
identical to the test group.

2. What is the focal status of the test group after 30 days?

(a) -0.781 Diopters
(b) 0.441 Diopters
(c) 1.700 Diopters
(d) 0.700 Diopters

3. What is the focal status of the test group after 200 days?

(a) -.200 Diopters
(b) .172 Diopters
(c) -.165 Diopters
(d) .700 Diopters

4. What is the focal status of the test group after 360 days?

(a) +3.250 Diopters
(b) -3.000 Diopters
(c) -0.273 Diopters
(d) 0.700 Diopters


PROBLEM 2

The adolescent human eye is in the process of growing. As it
grows the optical components of the eye continually change in
value. Let us assume that there is a sudden optical shift of +1.0
diopters. (This would constitute noise in the system.) This
change in total power of the eye produces a new refractive status
of =0.2 Diopters. For purposes of this these, the average value
of accommodation remains constant at -0.7 Diopters for both eyes.

The original focal status was +.8 diopters. Immediately
after the one-diopter focal perturbation the focal status is -.2
diopters.

This situation could be induced by the application of a +1.0
diopter contact lens. Please use the equation:

Focus = Offset + Accommodation - Perturbation * Exp(-t/Tau)

Focus = 1.5 D - 0.7 D - ( +1.0 D ) * Exp ( -Time / 100 )

1. What is the focal status of this eye after 1 day?

(a) -.190 Diopters
(b) 4.20 Diopters
(c) -.200 Diopters
(d) Since genetic information controls the optical components,
the eye will not recover from focal perturbations. The
focal status will remain at -.200 diopters. In all cases,
the refractive status of the control group will be
identical to the test group.

2. What is the focal status of this eye 30 days after the
optical change has occurred?

(a) .270 Diopters
(b) -.0592 Diopters
(c) 1.400 Diopters
(d) -.200 Diopters

3. What is the focal status after 100 days?

(a) +.200 Diopters
(b) +.397 Diopters
(c) +0.432 Diopters
(d) -0.200 Diopters

4. What is the focal status after 360 days?

(a) +.617 Diopters
(b) +.200 Diopters
(c) +0.772 Diopters
(d) -0.200 Diopters


PROBLEM 3

Eighteen monkeys are living in a caged environment. they
have an average visual environment of -1.8 diopters. at the start
of the test half of the monkeys are placed in a hooded (-2.6
diopter) visual environment. As a result, the environment "delta"
is -0.8 diopters.

The refractive status of both groups (average) at the start
of the test is -0.300 diopters. Using the following equation,
calculate the refractive status of the test group for the
following days after the start of the test.

Focus = Offset + Accommodation + Delta * [ 1 - Exp(-t/Tau) ]

1. What is the focal status of the test monkeys after 1 day?

(a) -.308 Diopters
(b) +1.300 Diopters
(c) -0.300 Diopters
(d) Since the eye's focal status is genetically determined,
the focal status of the test group will be identical to the
focal status of the control group.

2. What is the focal status of the test monkeys after 30 days?

(a) -.445 Diopters
(b) -.507 Diopters
(c) +.200 Diopters
(d) -.300 Diopters

3. What is their focal status after 60 days.

(a) -1.433 Diopters
(b) -6.661 Diopters
(c) -0.661 Diopters
(d) -0.300 Diopters

4. What is their focal status after 360 days.

(a) +1.078 Diopters
(b) -0.782 Diopters
(c) -1.080 Diopters
(d) -0.300 Diopters


PROBLEM 4

CHANGE IN REFRACTIVE STATE BETWEEN THE LEFT AND RIGHT EYES

The natural eye of primates have refractive states that are
very close to each other in terms of diopters. It is believed
that the eyes can maintain this accuracy because each eye controls
its refractive status to its accommodation system.

Since the environment of each eye is almost identical, it
should be possible to prove this thesis. The method is very
simple. Change the "environment" with an applied contact lens of
a reasonable negative value of say -2.0 diopters.

In this test the refractive state of both eyes is +0.8
diopters. The average visual environment has been maintained at
-0.7 diopters.

A contact lens of -2.0 diopters applied to the left eye will
change the refractive status of that eye to +2.8 diopters. The
"input" accommodation signal will change by -2.0 diopters.

Thus the "input" to the right eye is -0.7 diopters, and the
left eye is -2.8 diopters.

The right eye, with no "perturbation-lens" act as the
"control" eye.


The Challenge

Calculate the refractive status (with the contact lens in
place) for the following days after the "t = 0" perturbation is
applied.

The equation is:

Focus = Offset + Accommodation - Perturbation * Exp(-t/Tau)

Focus = +1.5 D - 0.7 D - ( -2.0 D ) * Exp ( -Time / 100 )

1. What is the focal status of the left eye after 1 day?

(a) +2.78 Diopters
(b) +2.80 Diopters
(c) +0.80 Diopters
(d) Since genetic information controls the optical
components of the eye -- the differential refractive
status of the eyes will remain at +2.0 diopters.

2. What is the focal status of the left eye 30 days
after the optical change has occurred?

(a) -3.50 Diopters
(b) +2.28 Diopters
(c) +1.40 Diopters
(d) +2.80 Diopters

3. What is the focal status of the left eye after 100 days?

(a) +0.80 Diopters
(b) -1.50 Diopters
(c) +1.53 Diopters
(d) +2.80 Diopters

4. What is the focal status of the left eye after 360 days?

(a) +0.80 Diopters
(b) -3.20 Diopters
(c) +0.85 Diopters
(d) +2.80 Diopters

 

I believe that in this case, Dr. Steadman is the professor and you are the
student.

DrG


(Otis Brown) wrote in

 

(Otis Brown) wrote in

Bingo!! Exactly why this particular model isn't teaching us anything about
mechanism.

Scott

 

Easy: Flunk'em!

Marks aren't for the student's enjoyment but are certification
to others that the student has mastered the material. If a
student doesn't want to learn, they should not enroll.

A student might have mastered the material anyways, but the
prof cannot certify it because he doesn't know it. My personal
observation is that mastery usually is too happy to show itself,
and is often extremely tolerant of beginners. I equate arrogance
with defensiveness likely indicating ignorance.

I don't see the turnabout.

What do you mean by time-constant? Response might be constant over
historic time for simple PID (proportional-integral-derivitive)
control systems, but not for QDMC (Quadratic Dynamic Matrix
Control), feed-forward or the predictive controls if _any_
of the inputs have changed.

-- Robert

 

(Otis Brown) wrote in

The student would not get credit for those quiz questions. If the student
happened to be enrolled in my class, that would mean something to a good
student. For a variety of reasons, I choose not to enroll in your class.

Scott

 

What if this 9th student who refuses to answer the insulting questions
decides to ask questions of the examiner. Should he be awarded an A+?

This is exactly what you did Otis. You refused to answer my question
on which patient will have a greater accomodative demand at say 33 cm
---a -10.00 diopter myope or a -1.00 diopter myope wearing his
spectacle lenses at 13mm from his corneal plane.

You asume that a greater accomodative demand at near is needed as
myopia progresses (wearing spectacles) and then use this assumption to
form the basis for your theory. What if this assumption does not hold
water. Should you not first use your calculator and discover for
yourself if this is fact or fiction. Why have you not done so?

Roland J. Izaac

 

Dear Scott,

It depends on what you are looking for.

If you wish to confirm or deny that the NATURAL EYE
is a sophisticated system, then you seek
to determine if it is "open-loop" or
"closed-loop".

If the natural eye is "closed-loop", then applying
a "step-input" to the accommodation SYSTEM, would
result in NO CHANGE in the refractive status of
the test group, relative to the control group.

If the sytem is "closed-loop", then you would
expect a response (damped sine, oscillation,
over-damped) response as part of a
mathematical model of strictly THE NATURAL
EYE'S BEHAVIOR.

Absolutly NO DEFECT OR FAULT will be determined
by this type of experimental work.

Only "system's identification" concerning
open-loop response or closed-loop response.

This is "taxonomy", or clasification as
to the true nature of the NATIVE OR NATURAL
eye.

It is a matter of simple "input" and "output"
(black-box) testing. Hard to miss the
point I would think.

Best,

Otis
Engineer

cc: Control-system engineers -- food for thought

 

Otis, here it is. A myope wearing a correctly prescribed pair of
spectacles needs to accomodate less then an emetrope. As his Rx
increases, the demand for accomodation decreases. Suprised!! So now
how do you explain "stair case myopia"? What exactly is the "step
input?"

Roland J. Izaac

 

Roland,

Otis beeing not familiar with the different feedback mechanism's in the
human body, why should he have knowledge about optics ?
I take it for granted he is not even familair with the near triad either
which is involved also in this matter.

Otis has one positive side, at least to me.
All his useless recommandations of using the pluslens make me eager to use
my brains in trying to find explainations for the ''why'' and "how" about
ametropia.
A discussion about this phenonomen in this newsgroup should be more than
wellcome and should be open for any one who is not afraid to speak out
his/her ideas and who also is not afraid to accept his ideas are show'n
wrong.
All with the idea you can't make an omelette whithout braking eggs even if
these eggs are your own thoughts.

Jan (normally Dutch spoken)

 

Contradicted? I saw speculation explaining a failed test of an improper
deduction from an unproved theory. The test succeeded in proving the
deduction was improper, though. I guess we'll just have to wait for further
studies.

Cathy

 

No contradiction Cathy.
Two different issues.

Mike is referring to the part under of the myopia instead of full
correction for long-distance
Roland is pointing to the less accommodation needed in fully for the
long-distance (with glasses) corrected myopes compared to emmetropes for the
same reading distance.

Jan (normally Dutch spoken)

 

No contradiction Cathy.
Two different issues.

Mike is referring to the part undercorrection of the myopia instead of full
correction for long-distance
Roland is pointing to the less accommodation needed in fully for the
long-distance (with glasses) corrected myopes compared to emmetropes for the
same reading distance.

Jan (normally Dutch spoken)

 

I think you're saying accommodation itself can't be the myopia trigger
because (1) emmetropes can bounce back from the accommodative demand while
(2) myopes, accommodating less than the emmetropes to see the same thing at
the same distance, can't bounce back.

The comparison of degree doesn't rule out accommodation as the trigger for
the ones who can't bounce back, does it? It only rules out myopia as a
definite outcome of accommodation. Nor does it rule out accommodation as a
trigger for current emmetropes who may find it impossible in the future to
bounce back. To rule out accommodation, wouldn't you have to remain in an
environment where there'd be no stimulus closer than your farthest focal
distance?

Cathy

 

Dear Jan and Roland,

Provided we use the word,
Mythical "box camera", where
the only NORMAL eye is a refractive status
of EXACTLY 0.0 diopters -- then yes,
we can analyize the eye in that manner.

The problem. The natural eye
is a sophisticated optical control system,
and must FIRST be represented in that manner,
before any work even intimating "defect" is used.

This issue does depend on PROVING that the
completely natural eye is a "closed loop"
system (electrical engineering, not OD term)
or an open-loop system.

Since this testing has nothing to do
with optometry, but only "concept" objective
testing, I doubt that you will either understand
the intellectual issues, or understand the
consequence of the correct answers.

Anyone wishing to argue this issue should
first take and PASS my quiz -- so we
know we are talking the "right language".

Failure to do so indicates to me that
we can not proceed, in an engineering
sense.

Always, new ideas and concepts crash
against "accepted beliefs". In a
sense of honesty and fair play, we
should continue to argue these
issues in mathematically modeling
the fundamental behavior characteristic
of the natural eye.


Best,

Otis
Engineer

cc: Other scientists, engineers, and students
interested in this difficult problem.

 

Maybe you don't understand what "undercorrection of myopia" means. Half the
myopic children were using relative plus at all distances (undercorrected),
the other half were wearing their full myopic correction. The
undercorrected group became more myopic.

Dr Judy

 

The other big problem with the "accommodation causes myopia" idea is the
existence of hyperopes. In North America, about 75% of the adult population
is hyperopic, and only 25% are myopic. Hyperopes accommodate at all
distances, including infinity, at all times yet they never become myopic.
If accommodation caused myopia, then there should be no hyperopes at all.

Dr Judy

 

You have a way of saying things that adds definition to the picture I have
in my mind. Whether or not it's progress, I appreciate being brought back
on track. All the replies sure keep the discussion alive in my house. But
there is still some ruling out to do before I can consider this settled. If
I may ...

I am thinking hyperopes have this in common with emmetropes: they can bounce
back from accommodating, although, as you say, not to complete relaxation.
Unlike emmetropes, they can't accommodate enough to meet the demand for
near. For Roland's issue, hyperopes would be accommodating more than the
other two to see the same thing at the same distance, so hyperopes fit with
emmetropes for the distinction Roland made.

I'm not looking to prove accommodation causes myopia. Instead, how has
accommodation been scientifically eliminated as a catalyst? That emmetropes
and hyperopes don't succumb to the power of accommodation doesn't eliminate
it as the catalyst for those who do succumb, especially when there's nothing
else wrong with them. Studies that allow accommodation aren't eliminating it
even as they look for other causes.

An added benefit for y'all: it would muck up Otis' formula.

Cathy

 

Yes, I got that. It looked to me like the researchers panicked. The gap
did not grow the 2nd year. The graph did not show axial length, only extra
lens strength needed. All of a sudden 0.25 diopter is a big deal? It
hadn't been after 12 months. Do you change a prescription for 0.25D? Did
they? Do they now? The extra 0.25D was such a big deal to O'Leary that he
decided, a deduction from a speculation, and advises that no correction is
worse. Where's his data for this? 1938? But maybe I did rush to
judgement. Maybe Mike's contradiction is that the staircase is really a
slide.

Cathy

 

They can go back to non accommodation, so to say complete relaxation.
But not corrected they see unsharp at distance and nearby.

Not necessaraly so.
Remember an eye with an error in optical power of -0,25dpt is already called
an hypermetropic eye.

two to see the same thing at the same distance.

Only if he is wearing glasses.
When hypermetropics and myopics are wearing contactlenses all the three
(hypermetropic-emmetropic-myopic) have to accommodate in the same amount for
the same nearby point.

 

Well, now. This puts a twist on things. I figured the minus lens made up
for the shortfall in the myopic eye, like a subsidy. If all -opes
accommodate the same amount when corrected (glasses vs. contacts aside), the
smaller accommodation capability of the myope must be stretched out
(figuratively), like taffy, to match the emmetrope's. The same work from a
smaller provision? Ouch!

Cathy