SUBJECT: A proposed scientific study for myopia prevention.
Click here for a revised copy of the book on prevention.
otis_v4, How to Avoid Nearsightedness
“How to Avoid Nearsightedness”, describes why this preventive approach can be effective – with the people who have the motivation to make their professional goals and personal efforts successful – during four years in college.
ERRATUM PAGE FOR STATISTICS, Chapter VI
The “N” value for number of measurements is 22, not 23. The calculated value for the correlation coefficient is r = 0.99, not, r = 0.97. This is far more accurate that previously calculated. The “p” value is 1 E^-19, that far exceeds the required, “Highly Significant” value of 0.01.
These calculations are included on the “Sum of Squares”, Spread Sheet.
Science of the eye’s response to long-term near. A correlation of, r = 0.99, is virtually perfect.
Calculation of the “p” value for this study.
THE STANDARD ERROR OF THE ESTIMATE:
P Value Calculated
The “Sum of Squares” is included to verify the r = 0.99 for Dr. Young’s data on six primate eyes.
====================================
ERRATUM PAGES FOR, “How to Avoid Nearsightedness”
Figure 1.
The side-by-side diode circuit intended to create an open-loop at less-than 0.6 volts. The diodes acted as resistors – and the circuit did not work correctly. This circuit must be replaced by a dead-band circuit, consisting of an operational amplifier, and thee resistors, as shown.
Figure 2
Chapter IV, Figure 4: This circuit is re-drawn from the book. It show how the eye, “latches” or blocks its own recovery from the myopic state.
When the normal eye has a negative state, the image, “lifts off”, the retina, producing a non-linear control system and a blurred image. The diode in this analog computer simulates the clamping effect on the input signal under this condition. This is the major reason that it is so difficult to get the normal eye to move in a positive direction after it has a severe negative focal state.
Figure 3
The Analog Computer, used to predict the eye’s focal status under experimental conditions. Change the error detector resistors to 10k and 10k, and 50k, and 50k. This is to make the gain = 1, for both accommodation and the long-term control of the natural eye’s refractive state.
Transfer Function for the Actuator (Page 69)
Actuator:
Kv / s (Open Loop)
In this case, the “Kv”, is an Integrator. (See Op-Amp wired as an Integrator.)
This can be written, 1 / Tau-Integrator s
Or
K-Integrator / s, Where K = 1/ Tau.
Common practice is to use K, for Bode Plots.
Operational Equations:
Summation:
Eo = – [ Ein1 (Rf / Rin1) + Ein2 (Rf / Rin2) + Ein3 (Rf / Rin3) …. ]
None-Inverting (+) Input:
Eo = Ein ( 1 + Rf / Rin )
Inverting (-) Input:
E0 = Ein ( -Rf / Rin )
In the Analog Computer, the error detector must be configured for Gain = 1, in all cases.
The resistors for the Long-term system S/B all 10 k.
The resistors for the Accommodation system S/B all 50 k.
Myopiafree 
SUBJECT: The Definition of Words and Index for the Book.
How to obtain a Copy of: “How to Avoid Nearsightedness”.
This book is FREE on the Internet. You can find a copy on this site:
http://www.i-see.org/otis_brown/
Myopia Prevention For Pilots – By Don Rehm: This engineer has been promoting prevention for many years. His book, “How to Avoid Nearsightedness” can be read online.
GLOSSARY
The ill and unfit choice of words wonderfully obstructs the understanding.
– Francis Bacon
Errors, like straws, upon the surface flow; He who would search for pearls must dive below.
– John Dryden
HOW TO AVOID NEARSIGHTEDNESS
Accommodation
A blur controlled system that continuously monitors and changes the internal lens of the eye — too provide the sharpest focus possible. The retina controls this lens-system.
Accommodation, Average Value
The value of accommodation that is averaged over a 16 hour day.
Analog Computer
Generally, a simulation of a physical or physiological system, by using electronic operational amplifiers. The computer is an analogy of the physical system being tested. This type of computer is used when direct mathematical analysis is too cumbersome or complicated to use.
Astigmatism
There is a “normal range” for astigmatism. It is between zero and two diopters. The FAA requires that you have 20/20 and less than two diopters of astigmatism. If you have 20/20 there is no point to wearing glasses for astigmatism.
Black Box Testing
A type of testing where it is necessary to establish a fundamental parameter of a previously untested system. In general, you control one parameter, while monitoring the effect on the second parameter.
Scientific Confirmation
Scientific testing in several different locations by different scientists where the same result is always obtained. When the results are consistent (as are tests conducted to determine the fundamental behavior characteristic of the normal eye) the result is considered to be an established fact.
Control System
A system, generally using power amplification, designed to keep one parameter (i.e. the eye’s desired focal state) within tight limits with respect to another parameter (i.e. average value of accommodation).
Corrective Lens
A term growing out of the Helmholtz-passive concept of the eye. It means that if a normal eye has a focal state of + 1.0 diopter then the “corrective” lens for the normal eye should be + 1.0 diopters. In a similar vein, if a normal eye has a focal state of -1.0 diopters, the “corrective” lens should be -1.0 diopters.
Cybernetics
The study of control systems in electronic and physiological systems. The analysis and comparison of feedback systems in man and machine.
Diopter
A unit of optical power. A focal length of one meter (approximately on yard, or 39.4 inches). The reciprocal of distance. A focal length of 1/2 meter represents a focal power of 2 diopters.
Emmetropia
A focal state of exactly zero for the eye. (Under the Helmholtz-passive concept, the only “normal” focal state of the eye.)
Experiment
The explicit steps you must take to determine a fact. (In the case of the eye, the explicit steps you must take to determine the fundamental behavior characteristic of all normal eyes.)
Eye Acuity Testing
The type of testing whereby you are required to read the standard Snellen eye chart at 20 feet. (The letters are 3/8 inch tall, and your successful reading of the chart indicates 20/20 vision.)
Eye
A dynamic system (similar to a camera) that controls light rays so that they will form an image on the retina.
Facts
Explicit measurement results that can be repeated as many times as desired. The entity to be tested, must be explicitly identified (i.e. the normal eye) to get consistent results. (You cannot run a test on the defective eye and reach a conclusion about the normal eye’s behavior.)
Farsightedness (Hyperopia)
A positive focal state of the natural eye.
Feedback Control
A method of linking (desired) output to (controlling) input.
First Class Medical
A Federal Aeronautics Administration (FAA) examination required of you to be fully qualified as a professional pilot. The chief visual requirement is the ability to read the 20/20 line on the eye chart. This represents a focal state of from 0 to +1.5 diopters. There is a visually less stringent (20/50) 3rd class medical certificate issued by the FAA.
Focal Length
The point at which an image will form after light rays pass through a lens, provided the object is located at a considerable distance from the lens.
Focal Measurement
The process of determining the focal length of a lens, or the focal status of the eye.
Focal Power
The ability of a lens to focus light rays. The shorter the focal length, the greater the focal power.
Heuristic
Serving to discover or to stimulate investigation. Assisting in the development of methods of demonstration which tend to lead a person to investigate further by himself.
Hyperopia
A positive focal state of the normal eye. (Sometimes called “Farsightedness”. This is not a defect of the eye.”
Infinity
For optical eye-testing purposes, a distance greater than 20 feet. Rays of light are considered to be parallel when the object is located at infinity.
Magnifying Glass
A positive lens
Mathematical Model
A conceptual scheme developed to represent physical reality. Mathematical models are essential to science, and are valued for their practical technical accuracy and the elegance and simplicity of their premise.
Model
A mechanical or electronic analogy of physical reality or a physical system.
Myopia
See nearsightedness
Nearsightedness
A negative focal state of the normal eye. (As defined and established in this book.)
Negative Lens
A lens that optically moves all objects closer to the eye. Also called a diverging lens. A lens with a negative (or virtual) focal length.
Noise
Unwanted or undesired perturbations in a system. Usually defined as having a broad bandwidth.
Operational Amplifier
An amplifier specifically designed to perform some mathematical operation: (e.g., integration, differentiation, multiplication, division, addition, and subtraction.)
Ophthalmologist
A medical doctor specializing in diseases of the eye. He is required to have four years of college, four years of medical school, two years as an intern, and board certification as an ophthalmologist.
Optometrist
A professional who has completed five years of specialized college and is licensed to prescribe lenses for refractive errors of the eye.
Paradigm
A conceptual scheme that has received broad acceptance by scientists.
Perturbation
An unexpected and abrupt change to a system in a random direction with random magnitude.
Physiological Optics
The application of optical analysis, using Snell’s law. The analysis of image formation in the eye and the representation of the normal eye as a purely optical device.
Positioning Control System
A system, usually employing power amplification, designed for the sole purpose of maintaining very accurate relative position.
Positive Lens
A lens that optically moves all objects away from the eye. A magnifying lens. A converging lens.
Presbyopia
A situation resulting from the stiffness of the internal lens of the eye associated with old age. Sometimes (inaccurately) called farsightedness.
Reading Glass
A magnifying glass, or positive lens.
Retina
The light sensitive surface on the back of the eye.
Science
The systematic assessment of facts. The theoretical and experimental effort required to determine factual truth.
Servo System
A system, either mechanical or physiological, that “slaves” the output to the input. (The normal eye continually adjusts both its corneal power and relative length to maintain accurate focus. The focal state of the normal eye is “slaved” to its average visual environment.)
Statistical Testing
A mathematical method of organizing experimental data to rapidly come to a reasonable conclusion about experimental (factual) reality.
Testing
A systematic approach to confirming a physical fact concerning some defined entity. (The normal eye is a defined entity.)
Theory
A concept developed over the years for explaining an underlying physical reality.
Thought Experiment
A type of experiment that is designed to expose an old theory to existing knowledge in a way that isolates the root of the problem with a clarity that is unattainable in the laboratory.
Tonic Accommodation
A normal (and usually negative) neurological focal state for the eye. It occurs any time the retina is unable to perceive blur (which the accommodation system needs to focus properly) in its field of vision. This is also referred to as blank-field, or dark-focus accommodation.
Transfer Function
A mathematical function that relates the transformation of the output response to the input signal. In the case of the eye, “input” is the accommodation signal, and the “output” is the measured focal status of the eye.
Verification Process
A method of repeated testing to determine factual (experimental) truth.
Visual Acuity
In the normal human eye, visual acuity is given as 1 minute of angle, or the ability to read 3/8 inch letters clearly at 20 feet. Also referred to as 20/20 vision. At night, the resolving power (i.e. separation of stars) is about 3 to 5 minutes of arc. Some system refer 6 meters as the measurement distance. Thus 20/20 is 6/6. A newer system uses this fraction as the standard, thus 6/6 is 1.0, and 6/12 (20/40) is 0.5.
The U. S. Army discovered (ca. 1914) that the 1 minute of angle was an excessive requirement. A great many soldiers could pass the 20/40 line — but not the 20/20 line.
The Army did not wish to have a great mass of soldiers wearing glasses so they set the standard at 20/40 — and would not prescribe minus lenses if the soldier could read better-than that line. This level of vision has become standard throughout the world as the DMV-Snellen standard. You must always pass this line if you wish to avoid wearing minus-lens glasses.
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BOOK INDEX
BOOK INDEX FOR: HOW TO AVOID NEARSIGHTEDNESS I post this to give you an idea about the scientific subjects covered in this book.
INDEX
A
Accommodation, 28, 34, 39, 43, 45-50, 52-56, 59, 60, 62-68, 70-77, 81, 84, 89, 91-98, 101-102, 132, 137 Accuracy (equation predictive), 39, 46- 48 Analog, 29, 34, 84, 87, 89, 102, 132 Analysis of eye behavior, 25, 34, 43, 46, 50, 63, 70, 99, 115, 132, 133 Aperture, Iris, 82 Assumptions, 101, 105, 111
B
Black-box, 65, 132 Block diagram, 68, 84, 89 Bode, 102
C
Camera, 28-29, 65, 81, 82, 133 Cats (focal comparison), 41 Chart, Eye, 11-16, 57, 114, 116-118, 133, 134 Closed loop, 34, 39, 103 Colgate, Stirling, 2, 5, 6 Computer, 25, 29, 30, 32, 33, 36, 46, 80, 76, 79, 82, 85, 87, 97, 100, 101, 104, 114 Control Theory, 27, 28, 34-37, 43 Control System, 24, 33, 37, 39-41, 46, 57, 59, 64, 75, 79, 82, 84-87, 95, 107, 112, 114 Cornea, 14, 25, 27, 39, 94, 96 Correlation Coefficient, 34, 57, 59-60, 62 Cybernetic, 39, 63, 133
D
Dead-band, 81, 84, 86, 87 Delta (step-input to system), 28, 48, 52, 54, 67 Differential focal status, 106, 107, 109, 110 Diode, for simulation, 36, 86, 89 Diopter, Lens power, 10-13, 27
E
Electrical Engineer, 37, 97 Ergodic, (Time-Series, Ensemble), 105-107 Eskimos, 73-124 Experiment:
Constants, 52 Correlation, 34, 47, 62 Future, 63, 131 Predictions, 46, 48, 50, 51, 54, 56, 62, 63, 68, 70, 81, 116 Result, 62, 65 Thought, 43, 50, 137 Young’s, 51, 89
Eye, Accuracy, 39, 46, 48, 51, 63, 66, 72, 91, 101, 105-106, 110-111, 135
F
FAA (Medical), 12-16, 114, 116, 134 Feedback, 29, 49-50, 54, 63, 72, 84, 89, 92, 111, 133 Frequency (response, spectrum), 86- 87, 102, 123
G
Glasses, 3-6, 10-11, 19-23, 40, 114, 117, 120-121, 127 Group, Test and Control, 47-49, 54-56, 71, 121 Growth, Eye, 32-34, 37, 41, 43-45, 54, 56, 91, 93
H
Helmholtz, 33, 37, 39, 41, 43, 46-48, 50, 60-63 Historical Opinion, 19, 118 Hyperopia, 57, 134
I
Idealization of eye’s behavior, 68, 79, 96 Impulse disturbance, 37, 56, 67, 70, 94-95 Index of Refraction, 23, 25 Infinity, 47, 71, 74, 135 Iterative (equation), 68
L
Lens: Defined, 9-10 Contact, 3-4, 14, 94-96, 114 Effect of Negative, 8, 19-20, 51-54 Internal, eye, 26 Power, 10, 25-27, 39 Use, 1, 4, 5, 8, 10-11, 19 Used to Measure Eye, 57
M
Magnitude of experimental result for confirmation, 43, 50, 77, 101-102, 136 Mathematical (model), 17, 33-34, 46, 50, 62-63, 65, 79, 99, 132, 135, 137 Monkeys, 47, 50, 52-53, 57, 59, 67, 77, 96-97
N
Naval Academy, 13, 57, 64, 75 Negative Lens, 4-5, 7-8, 13, 16-19, 23, 29, 37-40 Noise, 63, 65, 67, 70, 81, 86-87, 96, 102, 105-110, 135
O
Offset (environment to focal state), 28, 36, 45, 48, 52, 56, 59, 67-68, 70- 71, 73, 93-95, 98, 101-102, 105 Ophthalmologist, 3, 13, 15, 21, 117, 121, 128, 135 Opinion, 19 Optical, 9, 19, 23, 33, 51, 81, 86-87, 89, 91-92, 96, 99, 101, 110-111, 127, 130, 133, 135-136 Optics, 5, 32-33, 66, 130, 136 Optometrist, 3, 6, 15, 19, 21, 121, 125, 127-128, 136
P
Parallel light rays, 47, 74 Perspective (of eye concepts), 66 Perturbation, 56, 63-70, 73, 80-81, 86- 87, 91, 93-97, 99-102, 105-112, 135, 136 Physiological, 32-33, 37, 41, 43, 45, 63, 72, 79, 87-89, 100, 111, 130, 133, 136, 137 Physiologist, 99 Piecewise equation (for focal state), 68-70 Pilots, 18, 113-115, 126, 131 Poison (optical), 19 Positive Lens, 5-6, 9-10, 15, 17, 19, 40, 57, 66, 117, 134, 136 Prentice, Charles, 20, 31 Primate, 36, 51-52, 62-64, 72-73, 90- 91, 97, 99, 101, 110, 121 Probable Error (system tracking), 66, 91, 100, 110 Prolonged confined environment, 73, 74 Program (noise predictive), 107
Q
Qualitative theories (comparison), 39, 51, 56, 72 Quantitative theories (comparison), 28, 34, 37, 39, 46, 51-52, 56, 63, 72, 77
R
Ramp (increasingly confined environment), 37, 73-75 Refraction, 19-20, 23-25, 37 Retina, 26-27, 39, 43, 71, 81-82, 84, 89, 91, 100, 110, 122-123, 133, 136-137 Rigid (optical) system, 28, 51 RMS (Root Mean Square), 105-110
S
Science, 2, 31, 33, 39, 43, 36, 65, 113, 126, 135-136 Servo, 54, 62, 63, 66-68, 71-73, 77-78, 84, 86-87, 99, 102, 110, 137 Servomechanism, 62, 112 Servo-Myopia, 73 Simulation, 37, 83-87, 112, 132 Stark, Lawrence, 34, 41, 91, 112 Stability of focus, 34, 63 Statistical tests (distribution), 62, 86-87, 97, 105-107, 137 Step-input (delta), 46, 93 Stop (optical), 79, 86-89, 116 Student, 8, 13, 20, 57, 74-75, 113, 118, 131 Students “t” (statistical test), 59 Synthesis of dynamic behavior, 62-63
T
Testing, 9, 12, 23, 37, 48, 65, 125, 128, 132, 133, 135, 137-138 Thought experiment, 43, 50, 137 Time-constant (dynamic focal behavior), 36, 45-46, 51-52, 54, 63, 66, 67, 70, 77, 86, 94, 99, 102 Tonic accommodation, 81, 89-90, 137 Tracking (environment), 66, 70, 91, 99- 100, 102, 105-106, 110-111 Transfer Function (for eye’s behavior), 34, 45, 47, 56, 67-68, 70, 75, 86, 93, 102, 137 Twenty-Twenty (20/20), 1, 5-6, 11-16, 22, 57, 73, 75, 113, 115-117, 131, 133-134, 138
V
Verification, 9, 23, 70, 77, 110, 137
Y
Young, Francis, 34, 41, 53, 73, 77, 89, 91, 92, 97, 131
END OF INDEX FOR BOOK
Papers in, “How to Avoid Nearsightedness”.
Paper 7: Prevention of Myopia at the U. S. Naval Academy (Not in book)
Paper 9: Analysis of accommodation. (Not in Book).
=========================
Chapter IV = Paper 1
Chapter V = Paper 2
Chapter VI = Paper 4
Chapter VII = Paper 6
Chapter VIII = Paper 8
Chapter IX = Paper 3
Chapter X = Paper 5
The chapters were placed in order to make
the representation of the eye’s proven behavior consistent.
((((((((((((((((((((((
Conversion of Chapter back to Paper on the natural eye’s dynamic behavior.
Paper 1 = Chapter IV
Paper 2 = Chap V
Paper 3 = Chap IX
Paper 4 = Chap VI
Paper 5 = Chap X
Paper 6 = Chap VII
Paper 7 = No chapter (about Proposed Naval Academy Study )
Paper 8 = Chap VIII
Paper 9 = Not in book, 1996
Page 10 = Summary
General Checking.
Plus arm of Op-Amp. Definition, max gain of 2
Gain = 2 * ( Rf / (Rf + Rin) ) = Gain with voltage divider.
Gain – voltage to + terminal:
Eout = Ein * (Rin + Rf ) * Rin