Visual acuity

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https://en.wikipedia.org/wiki/Visual_acuity

 

Visual acuity
A typical Snellen chart that is frequently used for visual far acuity testing.
MeSH	D014792
MedlinePlus	003396
LOINC	28631-0

LogMAR – ETDRS Chart

Visual acuity (VA) commonly refers to the clarity of vision, but technically rates a person's ability to recognize small details with precision. Visual acuity depends on optical and neural factors. Optical factors of the eye influence the sharpness of an image on its retina. Neural factors include the health and functioning of the retina, of the neural pathways to the brain, and of the interpretative faculty of the brain.

The most commonly referred-to visual acuity is distance acuity or far acuity (e.g., "20/20 vision"), which describes someone's ability to recognize small details at a far distance. This ability is compromised in people with myopia, also known as short-sightedness or near-sightedness. Another visual acuity is near acuity, which describes someone's ability to recognize small details at a near distance. This ability is compromised in people with hyperopia, also known as long-sightedness or far-sightedness.

A common optical cause of low visual acuity is refractive error (ametropia): errors in how the light is refracted in the eyeball. Causes of refractive errors include aberrations in the shape of the eyeball or the cornea, and reduced ability of the lens to focus light. When the combined refractive power of the cornea and lens is too high for the length of the eyeball, the retinal image will be in focus in front of the retina and out of focus on the retina, yielding myopia. A similar poorly focussed retinal image happens when the combined refractive power of the cornea and lens is too low for the length of the eyeball except that the focused image is behind the retina, yielding hyperopia. Normal refractive power is referred to as emmetropia. Other optical causes of low visual acuity include astigmatism, in which contours of a particular orientation are blurred, and more complex corneal irregularities.

Refractive errors can mostly be corrected by optical means (such as eyeglasses, contact lenses, and refractive surgery). For example, in the case of myopia, the correction is to reduce the power of the eye's refraction by a so-called minus lens.

Neural factors that limit acuity are located in the retina, in the pathways to the brain, or in the brain. Examples of conditions affecting the retina include detached retina and macular degeneration. Examples of conditions affecting the brain include amblyopia (caused by the visual brain not having developed properly in early childhood) and by brain damage, such as from traumatic brain injury or stroke. When optical factors are corrected for, acuity can be considered a measure of neural functioning.

Visual acuity is typically measured while fixating, i.e. as a measure of central (or foveal) vision, for the reason that it is highest in the very center). However, acuity in peripheral vision can be of equal importance in everyday life. Acuity declines towards the periphery first steeply and then more gradually, in an inverse-linear fashion (i.e. the decline follows approximately a hyperbola). The decline is according to E₂/(E₂+E), where E is eccentricity in degrees visual angle, and E₂ is a constant of approximately 2 deg. At 2 deg eccentricity, for example, acuity is half the foveal value.

Visual acuity is a measure of how well small details are resolved in the very center of the visual field; it therefore does not indicate how larger patterns are recognized. Visual acuity alone thus cannot determine the overall quality of visual function.

Definition

Eye examination for visual acuity

Visual acuity is a measure of the spatial resolution of the visual processing system. VA, as it is sometimes referred to by optical professionals, is tested by requiring the person whose vision is being tested to identify so-called optotypes – stylized letters, Landolt rings, pediatric symbols, symbols for the illiterate, standardized Cyrillic letters in the Golovin–Sivtsev table, or other patterns – on a printed chart (or some other means) from a set viewing distance. Optotypes are represented as black symbols against a white background (i.e. at maximum contrast). The distance between the person's eyes and the testing chart is set so as to approximate "optical infinity" in the way the lens attempts to focus (far acuity), or at a defined reading distance (near acuity).

A reference value above which visual acuity is considered normal is called 6/6 vision, the USC equivalent of which is 20/20 vision: At 6 metres or 20 feet, a human eye with that performance is able to separate contours that are approximately 1.75 mm apart. Vision of 6/12 corresponds to lower performance, while vision of 6/3 to better performance. Normal individuals have an acuity of 6/4 or better (depending on age and other factors).

In the expression 6/x vision, the numerator (6) is the distance in metres between the subject and the chart and the denominator (x) the distance at which a person with 6/6 acuity would discern the same optotype. Thus, 6/12 means that a person with 6/6 vision would discern the same optotype from 12 metres away (i.e. at twice the distance). This is equivalent to saying that with 6/12 vision, the person possesses half the spatial resolution and needs twice the size to discern the optotype.

A simple and efficient way to state acuity is by converting the fraction to a decimal: 6/6 then corresponds to an acuity (or a Visus) of 1.0 (see Expression below), while 6/3 corresponds to 2.0, which is often attained by well-corrected healthy young subjects with binocular vision. Stating acuity as a decimal number is the standard in European countries, as required by the European norm (EN ISO 8596, previously DIN 58220).

The precise distance at which acuity is measured is not important as long as it is sufficiently far away and the size of the optotype on the retina is the same. That size is specified as a visual angle, which is the angle, at the eye, under which the optotype appears. For 6/6 = 1.0 acuity, the size of a letter on the Snellen chart or Landolt C chart is a visual angle of 5 arc minutes (1 arc min = 1/60 of a degree). By the design of a typical optotype (like a Snellen E or a Landolt C), the critical gap that needs to be resolved is 1/5 this value, i.e., 1 arc min. The latter is the value used in the international definition of visual acuity:

acuity = 1/gap size [arc min].

Acuity is a measure of visual performance and does not relate to the eyeglass prescription required to correct vision. Instead, an eye exam seeks to find the prescription that will provide the best corrected visual performance achievable. The resulting acuity may be greater or less than 6/6 = 1.0. Indeed, a subject diagnosed as having 6/6 vision will often actually have higher visual acuity because, once this standard is attained, the subject is considered to have normal (in the sense of undisturbed) vision and smaller optotypes are not tested. Subjects with 6/6 vision or "better" (20/15, 20/10, etc.) may still benefit from an eyeglass correction for other problems related to the visual system, such as hyperopia, ocular injuries, or presbyopia.

Measurement

Manual hand eye test in Ghana (2018).

Visual acuity is measured by a psychophysical procedure and as such relates the physical characteristics of a stimulus to a subject's percept and their resulting responses. Measurement can be by using an eye chart invented by Ferdinand Monoyer, by optical instruments, or by computerized tests like the FrACT.

Care must be taken that viewing conditions correspond to the standard, such as correct illumination of the room and the eye chart, correct viewing distance, enough time for responding, error allowance, and so forth. In European countries, these conditions are standardized by the European norm (EN ISO 8596, previously DIN 58220).

History

Year	Event
1843	Vision test types are invented in 1843 by the German ophthalmologist Heinrich Kuechler (1811–1873), in Darmstadt, Germany. He argues for need to standardize vision tests and produces three reading charts to avoid memorization.
1854	Eduard Jäger von Jaxtthal, a Vienna oculist, makes improvements to eye chart test types that were developed by Heinrich Kuechler. He publishes, in German, French, English and other languages, a set of reading samples to document functional vision. He uses fonts that were available in the State Printing House in Vienna in 1854 and labels them with the numbers from that printing house catalogue, currently known as Jaeger numbers.
1862	Herman Snellen, a Dutch ophthalmologist, publishes in Utrecht his "Optotypi ad visum determinandum" ("Probebuchstaben zur Bestimmung der Sehschärfe"), the first visual chart based on "Optotypes", advocating the need for standardized vision tests. Snellen's Optotypes are not identical to the test letters used today. They were printed in an "Egyptian Paragon" font (i.e. using serifs).
1888	Edmund Landolt introduces the broken ring, now known as the Landolt ring, which later becomes an international standard.
1894	Theodor Wertheim in Berlin presents detailed measurements of acuity in peripheral vision.
1978	Hugh Taylor uses these design principles for a "Tumbling E Chart" for illiterates, later used to study the visual acuity of Australian Aboriginals.
1982	Rick Ferris et al. of the National Eye Institute chooses the LogMAR chart layout, implemented with Sloan letters, to establish a standardized method of visual acuity measurement for the Early Treatment of Diabetic Retinopathy Study (ETDRS). These charts are used in all subsequent clinical studies, and did much to familiarize the profession with the new layout and progression. Data from the ETDRS were used to select letter combinations that give each line the same average difficulty, without using all letters on each line.
1984	The International Council of Ophthalmology approves a new "Visual Acuity Measurement Standard", also incorporating the above features.
1988	Antonio Medina and Bradford Howland of the Massachusetts Institute of Technology develop a novel eye testing chart using letters that become invisible with decreasing acuity, rather than blurred as in standard charts. They demonstrate the arbitrary nature of the Snellen fraction and warn about the accuracy of visual acuity determined by using charts of different letter types, calibrated by Snellen's system.

Physiology

Daylight vision (i.e. photopic vision) is subserved by cone receptor cells which have high spatial density (in the central fovea) and allow high acuity of 6/6 or better. In low light (i.e., scotopic vision), cones do not have sufficient sensitivity and vision is subserved by rods. Spatial resolution is then much lower. This is due to spatial summation of rods, i.e. a number of rods merge into a bipolar cell, in turn connecting to a ganglion cell, and the resulting unit for resolution is large, and acuity small. There are no rods in the very center of the visual field (the foveola), and highest performance in low light is achieved in near peripheral vision.

The maximum angular resolution of the human eye is 28 arc seconds or 0.47 arc minutes, this gives an angular resolution of 0.008 degrees, and at a distance of 1 km corresponds to 136 mm. This is equal to 0.94 arc minutes per line pair (one white and one black line), or 0.016 degrees. For a pixel pair (one white and one black pixel) this gives a pixel density of 128 pixels per degree (PPD).

6/6 vision is defined as the ability to resolve two points of light separated by a visual angle of one minute of arc, corresponding to 60 PPD, or about 290–350 pixels per inch for a display on a device held 250 to 300 mm from the eye.

Thus, visual acuity, or resolving power (in daylight, central vision), is the property of cones. To resolve detail, the eye's optical system has to project a focused image on the fovea, a region inside the macula having the highest density of cone photoreceptor cells (the only kind of photoreceptors existing in the fovea's very center of 300 μm diameter), thus having the highest resolution and best color vision. Acuity and color vision, despite being mediated by the same cells, are different physiologic functions that do not interrelate except by position. Acuity and color vision can be affected independently.

The diagram shows the relative acuity of the human eye on the horizontal meridian. The blind spot is at about 15.5° in the outside direction (e.g. in the left visual field for the left eye).

The grain of a photographic mosaic has just as limited resolving power as the "grain" of the retinal mosaic. To see detail, two sets of receptors must be intervened by a middle set. The maximum resolution is that 30 seconds of arc, corresponding to the foveal cone diameter or the angle subtended at the nodal point of the eye. To get reception from each cone, as it would be if vision was on a mosaic basis, the "local sign" must be obtained from a single cone via a chain of one bipolar, ganglion, and lateral geniculate cell each. A key factor of obtaining detailed vision, however, is inhibition. This is mediated by neurons such as the amacrine and horizontal cells, which functionally render the spread or convergence of signals inactive. This tendency to one-to-one shuttle of signals is powered by brightening of the center and its surroundings, which triggers the inhibition leading to a one-to-one wiring. This scenario, however, is rare, as cones may connect to both midget and flat (diffuse) bipolars, and amacrine and horizontal cells can merge messages just as easily as inhibit them.

Light travels from the fixation object to the fovea through an imaginary path called the visual axis. The eye's tissues and structures that are in the visual axis (and also the tissues adjacent to it) affect the quality of the image. These structures are: tear film, cornea, anterior chamber, pupil, lens, vitreous, and finally the retina. The posterior part of the retina, called the retinal pigment epithelium (RPE) is responsible for, among many other things, absorbing light that crosses the retina so it cannot bounce to other parts of the retina. In many vertebrates, such as cats, where high visual acuity is not a priority, there is a reflecting tapetum layer that gives the photoreceptors a "second chance" to absorb the light, thus improving the ability to see in the dark. This is what causes an animal's eyes to seemingly glow in the dark when a light is shone on them. The RPE also has a vital function of recycling the chemicals used by the rods and cones in photon detection. If the RPE is damaged and does not clean up this "shed" blindness can result.

As in a photographic lens, visual acuity is affected by the size of the pupil. Optical aberrations of the eye that decrease visual acuity are at a maximum when the pupil is largest (about 8 mm), which occurs in low-light conditions. When the pupil is small (1–2 mm), image sharpness may be limited by diffraction of light by the pupil (see diffraction limit). Between these extremes is the pupil diameter that is generally best for visual acuity in normal, healthy eyes; this tends to be around 3 or 4 mm.

If the optics of the eye were otherwise perfect, theoretically, acuity would be limited by pupil diffraction, which would be a diffraction-limited acuity of 0.4 minutes of arc (minarc) or 6/2.6 acuity. The smallest cone cells in the fovea have sizes corresponding to 0.4 minarc of the visual field, which also places a lower limit on acuity. The optimal acuity of 0.4 minarc or 6/2.6 can be demonstrated using a laser interferometer that bypasses any defects in the eye's optics and projects a pattern of dark and light bands directly on the retina. Laser interferometers are now used routinely in patients with optical problems, such as cataracts, to assess the health of the retina before subjecting them to surgery.

The visual cortex is the part of the cerebral cortex in the posterior part of the brain responsible for processing visual stimuli, called the occipital lobe. The central 10° of field (approximately the extension of the macula) is represented by at least 60% of the visual cortex. Many of these neurons are believed to be involved directly in visual acuity processing.

Proper development of normal visual acuity depends on a human or an animal having normal visual input when it is very young. Any visual deprivation, that is, anything interfering with such input over a prolonged period of time, such as a cataract, severe eye turn or strabismus, anisometropia (unequal refractive error between the two eyes), or covering or patching the eye during medical treatment, will usually result in a severe and permanent decrease in visual acuity and pattern recognition in the affected eye if not treated early in life, a condition known as amblyopia. The decreased acuity is reflected in various abnormalities in cell properties in the visual cortex. These changes include a marked decrease in the number of cells connected to the affected eye as well as cells connected to both eyes in cortical area V1, resulting in a loss of stereopsis, i.e. depth perception by binocular vision (colloquially: "3D vision"). The period of time over which an animal is highly sensitive to such visual deprivation is referred to as the critical period.

The eye is connected to the visual cortex by the optic nerve coming out of the back of the eye. The two optic nerves come together behind the eyes at the optic chiasm, where about half of the fibers from each eye cross over to the opposite side and join fibers from the other eye representing the corresponding visual field, the combined nerve fibers from both eyes forming the optic tract. This ultimately forms the physiological basis of binocular vision. The tracts project to a relay station in the midbrain called the lateral geniculate nucleus, part of the thalamus, and then to the visual cortex along a collection of nerve fibers called the optic radiation.

Any pathological process in the visual system, even in older humans beyond the critical period, will often cause decreases in visual acuity. Thus measuring visual acuity is a simple test in accessing the health of the eyes, the visual brain, or pathway to the brain. Any relatively sudden decrease in visual acuity is always a cause for concern. Common causes of decreases in visual acuity are cataracts and scarred corneas, which affect the optical path, diseases that affect the retina, such as macular degeneration and diabetes, diseases affecting the optic pathway to the brain such as tumors and multiple sclerosis, and diseases affecting the visual cortex such as tumors and strokes.

Though the resolving power depends on the size and packing density of the photoreceptors, the neural system must interpret the receptors' information. As determined from single-cell experiments on the cat and primate, different ganglion cells in the retina are tuned to different spatial frequencies, so some ganglion cells at each location have better acuity than others. Ultimately, however, it appears that the size of a patch of cortical tissue in visual area V1 that processes a given location in the visual field (a concept known as cortical magnification) is equally important in determining visual acuity. In particular, that size is largest in the fovea's center, and decreases with increasing distance from there.

Optical aspects

Besides the neural connections of the receptors, the optical system is an equally key player in retinal resolution. In the ideal eye, the image of a diffraction grating can subtend 0.5 micrometre on the retina. This is certainly not the case, however, and furthermore the pupil can cause diffraction of the light. Thus, black lines on a grating will be mixed with the intervening white lines to make a gray appearance. Defective optical issues (such as uncorrected myopia) can render it worse, but suitable lenses can help. Images (such as gratings) can be sharpened by lateral inhibition, i.e., more highly excited cells inhibiting the less excited cells. A similar reaction is in the case of chromatic aberrations, in which the color fringes around black-and-white objects are inhibited similarly.

Expression

Visual acuity scales

20 ft	10 ft	6 m	3 m	Decimal	MAR	LogMAR
20/1000	10/500	6/300	3/150	0.02	50	1.70
20/800	10/400	6/240	3/120	0.025	40	1.60
20/600	10/300	6/180	3/90	0.033	30	1.48
20/500	10/250	6/150	3/75	0.04	25	1.40
20/400	10/200	6/120	3/60	0.05	20	1.30
20/300	10/150	6/90	3/45	0.067	15	1.18
20/250	10/125	6/75	3/37	0.08	12.5	1.10
20/200	10/100	6/60	3/30	0.10	10	1.00
20/160	10/80	6/48	3/24	0.125	8	0.90
20/125	10/62	6/38	3/19	0.16	6.25	0.80
20/100	10/50	6/30	3/15	0.20	5	0.70
20/80	10/40	6/24	3/12	0.25	4	0.60
20/60	10/30	6/18	3/9	0.33	3	0.48
20/50	10/25	6/15	3/7.5	0.40	2.5	0.40
20/40	10/20	6/12	3/6	0.50	2	0.30
20/30	10/15	6/9	3/4.5	0.67	1.5	0.18
20/25	10/12	6/7.5	3/4	0.80	1.25	0.10
20/20	10/10	6/6	3/3	1.00	1	0.00
20/16	10/8	6/4.8	3/2.4	1.25	0.8	−0.10
20/12.5	10/6	6/3.8	3/2	1.60	0.625	−0.20
20/10	10/5	6/3	3/1.5	2.00	0.5	−0.30
20/8	10/4	6/2.4	3/1.2	2.50	0.4	−0.40
20/6.6	10/3.3	6/2	3/1	3.00	0.333	−0.48

Visual acuity is often measured according to the size of letters viewed on a Snellen chart or the size of other symbols, such as Landolt Cs or the E Chart.

In some countries, acuity is expressed as a vulgar fraction, and in some as a decimal number. Using the metre as a unit of measurement, (fractional) visual acuity is expressed relative to 6/6. Otherwise, using the foot, visual acuity is expressed relative to 20/20. For all practical purposes, 20/20 vision is equivalent to 6/6. In the decimal system, acuity is defined as the reciprocal value of the size of the gap (measured in arc minutes) of the smallest Landolt C, the orientation of which can be reliably identified. A value of 1.0 is equal to 6/6.

LogMAR is another commonly used scale, expressed as the (decadic) logarithm of the minimum angle of resolution (MAR), which is the reciprocal of the acuity number. The LogMAR scale converts the geometric sequence of a traditional chart to a linear scale. It measures visual acuity loss: positive values indicate vision loss, while negative values denote normal or better visual acuity. This scale is commonly used clinically and in research because the lines are of equal length and so it forms a continuous scale with equally spaced intervals between points, unlike Snellen charts, which have different numbers of letters on each line.

A visual acuity of 6/6 is frequently described as meaning that a person can see detail from 6 metres (20 ft) away the same as a person with "normal" eyesight would see from 6 metres. If a person has a visual acuity of 6/12, he is said to see detail from 6 metres (20 ft) away the same as a person with "normal" eyesight would see it from 12 metres (39 ft) away.

The definition of 6/6 is somewhat arbitrary, since human eyes typically have higher acuity, as Tscherning writes, "We have found also that the best eyes have a visual acuity which approaches 2, and we can be almost certain that if, with a good illumination, the acuity is only equal to 1, the eye presents defects sufficiently pronounced to be easily established." Most observers may have a binocular acuity superior to 6/6; the limit of acuity in the unaided human eye is around 6/3–6/2.4 (20/10–20/8), although 6/3 was the highest score recorded in a study of some US professional athletes. Some birds of prey, such as hawks, are believed to have an acuity of around 20/2; in this respect, their vision is much better than human eyesight.

When visual acuity is below the largest optotype on the chart, the reading distance is reduced until the patient can read it. Once the patient is able to read the chart, the letter size and test distance are noted. If the patient is unable to read the chart at any distance, they are tested as follows:

Name	Abbreviation	Definition
Counting Fingers	CF	Ability to count fingers at a given distance. This test method is only used after it has been determined that the patient is not able to make out any of the letters, rings, or images on the acuity chart. The letters CF, and the testing distance, would represent the patient's acuity. For example, the recording CF 5' would mean the patient was able to count the examiner's fingers from a maximum distance of 5 feet directly in front of the examiner. (The results of this test, on the same patient, may vary from examiner to examiner. This is due more so to the size differences of the various examiner's hands and fingers, than fluctuating vision.)
Hand Motion	HM	Ability to distinguish whether or not there is movement of the examiner's hand directly in front of the patient's eyes. This test method is only used after a patient shows little or no success with the Counting Fingers test. The letters HM, and the testing distance, would represent the patient's acuity. For example, the recording HM 2' would mean that the patient was able to distinguish movement of the examiner's hand from a maximum distance of 2 feet directly in front of the examiner. (The results of the Hand Motion test are often recorded without the testing distance. This is due to the fact that this test is performed after the patient cannot "pass" the Counting Fingers test. At this point, the examiner is usually directly in front of the patient, and it is assumed that the Hand Motion test is performed at a testing distance of 1 foot or less.)
Light Perception	LP	Ability to perceive any light. This test method is used only after a patient shows little or no success with the Hand Motion test. In this test, an examiner shines a pen light at the patient's pupil and asks the patient to either, point to the light source, or, describe the direction that the light is coming from (up, out, straight ahead, down and out, etc.). If the patient is able to perceive light, the letters LP are recorded to represent the patient's acuity. If the patient is unable to perceive any light, the letters NLP (No Light Perception) are recorded. A patient with no light perception in one eye is considered blind in the respective eye. If NLP is recorded in both eyes, the patient is described as having total blindness.

Legal definitions

Various countries have defined statutory limits for poor visual acuity that qualifies as a disability. For example, in Australia, the Social Security Act defines blindness as:

A person meets the criteria for permanent blindness under section 95 of the Social Security Act if the corrected visual acuity is less than 6/60 on the Snellen Scale in both eyes or there is a combination of visual defects resulting in the same degree of permanent visual loss.

In the US, the relevant federal statute defines blindness as follows:

[T]he term "blindness" means central visual acuity of 20/200 or less in the better eye with the use of a correcting lens. An eye that is accompanied by a limitation in the fields of vision such that the widest diameter of the visual field subtends an angle no greater than 20 degrees shall be considered for purposes in this paragraph as having a central visual acuity of 20/200 or less.

A person's visual acuity is registered documenting the following: whether the test was for distant or near vision, the eye(s) evaluated and whether corrective lenses (i.e. glasses or contact lenses) were used:

• Distance from the chart
  • D (distant) for the evaluation done at 20 feet (6 m).
  • N (near) for the evaluation done at 15.7 inches (400 mm).
• Eye evaluated
  • OD (Latin oculus dexter) for the right eye.
  • OS (Latin oculus sinister) for the left eye.
  • OU (Latin oculi uterque) for both eyes.
• Usage of spectacles during the test
  • cc (Latin cum correctore) with correctors.
  • sc: (Latin sine correctore) without correctors.
• Pinhole occluder
  • The abbreviation PH is followed by the visual acuity as measured with a pinhole occluder, which temporarily corrects for refractive errors such as myopia or astigmatism.
  • PHNI means No Improvement of visual acuity using a pinhole occluder.

So, distant visual acuity of 6/10 and 6/8 with pinhole in the right eye will be: DscOD 6/10 PH 6/8. Distant visual acuity of count fingers and 6/17 with pinhole in the left eye will be: DscOS CF PH 6/17. Near visual acuity of 6/8 with pinhole remaining at 6/8 in both eyes with spectacles will be: NccOU 6/8 PH 6/8.

"Dynamic visual acuity" defines the ability of the eye to visually discern fine detail in a moving object.

Measurement considerations

Visual acuity measurement involves more than being able to see the optotypes. The patient should be cooperative, understand the optotypes, be able to communicate with the physician, and many more factors. If any of these factors is missing, then the measurement will not represent the patient's real visual acuity.

Visual acuity is a subjective test meaning that if the patient is unwilling or unable to cooperate, the test cannot be done. A patient who is sleepy, intoxicated, or has any disease that can alter their consciousness or mental status, may not achieve their maximum possible acuity.

Patients who are illiterate in the language whose letters and/or numbers appear on the chart will be registered as having very low visual acuity if this is not known. Some patients will not tell the examiner that they do not know the optotypes, unless asked directly about it. Brain damage can result in a patient not being able to recognize printed letters, or being unable to spell them.

A motor inability can make a person respond incorrectly to the optotype shown and negatively affect the visual acuity measurement.

Variables such as pupil size, background adaptation luminance, duration of presentation, type of optotype used, interaction effects from adjacent visual contours (or "crowding") can all affect visual acuity measurement.

Testing in children

Main article: Infant vision

The newborn's visual acuity is approximately 6/133, developing to 6/6 well after the age of six months in most children, according to a study published in 2009.

The measurement of visual acuity in infants, pre-verbal children and special populations (for instance, disabled individuals) is not always possible with a letter chart. For these populations, specialised testing is necessary. As a basic examination step, one must check whether visual stimuli can be fixated, centered and followed.

More formal testing using preferential looking techniques use Teller acuity cards (presented by a technician from behind a window in the wall) to check whether the child is more visually attentive to a random presentation of vertical or horizontal gratings on one side compared with a blank page on the other side – the bars become progressively finer or closer together, and the endpoint is noted when the child in its adult carer's lap equally prefers the two sides.

Another popular technique is electro-physiologic testing using visual evoked (cortical) potentials (VEPs or VECPs), which can be used to estimate visual acuity in doubtful cases and expected severe vision loss cases like Leber's congenital amaurosis.

VEP testing of acuity is somewhat similar to preferential looking in using a series of black and white stripes (sine wave gratings) or checkerboard patterns (which produce larger responses than stripes). Behavioral responses are not required and brain waves created by the presentation of the patterns are recorded instead. The patterns become finer and finer until the evoked brain wave just disappears, which is considered to be the endpoint measure of visual acuity. In adults and older, verbal children capable of paying attention and following instructions, the endpoint provided by the VEP corresponds very well to the psychophysical measure in the standard measurement (i.e. the perceptual endpoint determined by asking the subject when they can no longer see the pattern). There is an assumption that this correspondence also applies to much younger children and infants, though this does not necessarily have to be the case. Studies do show the evoked brain waves, as well as derived acuities, are very adult-like by one year of age.

For reasons not totally understood, until a child is several years old, visual acuities from behavioral preferential looking techniques typically lag behind those determined using the VEP, a direct physiological measure of early visual processing in the brain. Possibly it takes longer for more complex behavioral and attentional responses, involving brain areas not directly involved in processing vision, to mature. Thus the visual brain may detect the presence of a finer pattern (reflected in the evoked brain wave), but the "behavioral brain" of a small child may not find it salient enough to pay special attention to.

A simple but less-used technique is checking oculomotor responses with an optokinetic nystagmus drum, where the subject is placed inside the drum and surrounded by rotating black and white stripes. This creates involuntary abrupt eye movements (nystagmus) as the brain attempts to track the moving stripes. There is a good correspondence between the optokinetic and usual eye-chart acuities in adults. A potentially serious problem with this technique is that the process is reflexive and mediated in the low-level brain stem, not in the visual cortex. Thus someone can have a normal optokinetic response and yet be cortically blind with no conscious visual sensation.

"Normal" visual acuity

Visual acuity depends upon how accurately light is focused on the retina, the integrity of the eye's neural elements, and the interpretative faculty of the brain. "Normal" visual acuity (in central, i.e. foveal vision) is frequently considered to be what was defined by Herman Snellen as the ability to recognize an optotype when it subtended 5 minutes of arc, that is Snellen's chart 6/6-metre, 20/20 feet, 1.00 decimal or 0.0 logMAR. In young humans, the average visual acuity of a healthy, emmetropic eye (or ametropic eye with correction) is approximately 6/5 to 6/4, so it is inaccurate to refer to 6/6 visual acuity as "perfect" vision. On the contrary, Tscherning writes, "We have found also that the best eyes have a visual acuity which approaches 2, and we can be almost certain that if, with a good illumination, the acuity is only equal to 1, the eye presents defects sufficiently pronounced to be easily established."

6/6 is the visual acuity needed to discriminate two contours separated by 1 arc minute – 1.75 mm at 6 metres. This is because a 6/6 letter, E for example, has three limbs and two spaces in between them, giving 5 different detailed areas. The ability to resolve this therefore requires 1/5 of the letter's total size, which in this case would be 1 minute of arc (visual angle). The significance of the 6/6 standard can best be thought of as the lower limit of normal, or as a screening cutoff. When used as a screening test, subjects that reach this level need no further investigation, even though the average visual acuity with a healthy visual system is typically better.

Some people may have other visual problems, such as severe visual field defects, color blindness, reduced contrast, mild amblyopia, cerebral visual impairments, inability to track fast-moving objects, or one of many other visual impairments and still have "normal" visual acuity. Thus, "normal" visual acuity by no means implies normal vision. The reason visual acuity is very widely used is that it is easily measured, its reduction (after correction) often indicates some disturbance, and that it often corresponds with the normal daily activities a person can handle, and evaluates their impairment to do them (even though there is heavy debate over that relationship).

Other measures

Normally, visual acuity refers to the ability to resolve two separated points or lines, but there are other measures of the ability of the visual system to discern spatial differences.

Vernier acuity measures the ability to align two line segments. Humans can do this with remarkable accuracy. This success is regarded as hyperacuity. Under optimal conditions of good illumination, high contrast, and long line segments, the limit to vernier acuity is about 8 arc seconds or 0.13 arc minutes, compared to about 0.6 arc minutes (6/4) for normal visual acuity or the 0.4 arc minute diameter of a foveal cone. Because the limit of vernier acuity is well below that imposed on regular visual acuity by the "retinal grain" or size of the foveal cones, it is thought to be a process of the visual cortex rather than the retina. Supporting this idea, vernier acuity seems to correspond very closely (and may have the same underlying mechanism) enabling one to discern very slight differences in the orientations of two lines, where orientation is known to be processed in the visual cortex.

The smallest detectable visual angle produced by a single fine dark line against a uniformly illuminated background is also much less than foveal cone size or regular visual acuity. In this case, under optimal conditions, the limit is about 0.5 arc seconds or only about 2% of the diameter of a foveal cone. This produces a contrast of about 1% with the illumination of surrounding cones. The mechanism of detection is the ability to detect such small differences in contrast or illumination, and does not depend on the angular width of the bar, which cannot be discerned. Thus as the line gets finer, it appears to get fainter but not thinner.

Stereoscopic acuity is the ability to detect differences in depth with the two eyes. For more complex targets, stereoacuity is similar to normal monocular visual acuity, or around 0.6–1.0 arc minutes, but for much simpler targets, such as vertical rods, may be as low as only 2 arc seconds. Although stereoacuity normally corresponds very well with monocular acuity, it may be very poor, or absent, even in subjects with normal monocular acuities. Such individuals typically have abnormal visual development when they are very young, such as an alternating strabismus, or eye turn, where both eyes rarely, or never, point in the same direction and therefore do not function together.

Motion acuity

The eye has acuity limits for detecting motion. Forward motion is limited by the subtended angular velocity detection threshold (SAVT), and horizontal and vertical motion acuity are limited by lateral motion thresholds. The lateral motion limit is generally below the looming motion limit, and for an object of a given size, lateral motion becomes the more insightful of the two, once the observer moves sufficiently far away from the path of travel. Below these thresholds subjective constancy is experienced in accordance with the Stevens' power law and Weber–Fechner law.

Subtended angular velocity detection threshold (SAVT)

There is a specific acuity limit in detecting an approaching object's looming motion. This is regarded as the subtended angular velocity detection threshold (SAVT) limit of visual acuity. It has a practical value of 0.0275 rad/s. For a person with SAVT limit of ${\displaystyle {\dot{\theta }}_t}$, the looming motion of a directly approaching object of size S, moving at velocity v, is not detectable until its distance D is

${\displaystyle D⪅\sqrt{\frac{S\cdot v}{\dot{{\theta }_t}}-\frac{S^2}{4}},}$

where the S²/4 term is omitted for small objects relative to great distances by small-angle approximation.

To exceed the SAVT, an object of size S moving as velocity v must be closer than D; beyond that distance, subjective constancy is experienced. The SAVT ${\displaystyle {\dot{\theta }}_t}$ can be measured from the distance at which a looming object is first detected:

${\displaystyle {\dot{\theta }}_t\approx \frac{4S\cdot v}{S^2+4D^2},}$

where the S² term is omitted for small objects relative to great distances by small-angle approximation.

The SAVT has the same kind of importance to driving safety and sports as the static limit. The formula is derived from taking the derivative of the visual angle with respect to distance, and then multiplying by velocity to obtain the time rate of visual expansion (dθ/dt = dθ/dx · dx/dt).

Lateral motion

There are acuity limits (${\displaystyle {\dot{\theta }}_t}$) of horizontal and vertical motion as well. They can be measured and defined by the threshold detection of movement of an object traveling at distance D and velocity v orthogonal to the direction of view, from a set-back distance B with the formula

${\displaystyle {\dot{\theta }}_t\approx \frac{B\cdot v}{B^2+D^2}.}$

Because the tangent of the subtended angle is the ratio of the orthogonal distance to the set-back distance, the angular time rate (rad/s) of lateral motion is simply the derivative of the inverse tangent multiplied by the velocity (dθ/dt = dθ/dx · dx/dt). In application this means that an orthogonally traveling object will not be discernible as moving until it has reached the distance

${\displaystyle D⪅\sqrt{\frac{B\cdot v}{{\dot{\theta }}_t}-B^2},}$

where ${\displaystyle {\dot{\theta }}_t}$ for lateral motion is generally ≥ 0.0087 rad/s with probable dependence on deviation from the fovia and movement orientation, velocity is in terms of the distance units, and zero distance is straight ahead. Far object distances, close set-backs, and low velocities generally lower the salience of lateral motion. Detection with close or null set-back can be accomplished through the pure scale changes of looming motion.

Radial motion

The motion acuity limit affects radial motion in accordance to its definition, hence the ratio of the velocity v to the radius R must exceed ${\displaystyle {\dot{\theta }}_t}$:

${\displaystyle {\dot{\theta }}_t⪅\frac{v}{R}.}$

Radial motion is encountered in clinical and research environments, in dome theaters, and in virtual-reality headsets.

Angular resolution

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https://en.wikipedia.org/wiki/Angular_resolution

 

A series of images representing the magnification of M87* with an angular size of some microarcseconds, comparable to viewing a tennis ball on the Moon (magnification from top left corner counter−clockwise to the top right corner).

Angular resolution describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object, thereby making it a major determinant of image resolution. It is used in optics applied to light waves, in antenna theory applied to radio waves, and in acoustics applied to sound waves. The colloquial use of the term "resolution" sometimes causes confusion; when an optical system is said to have a high resolution or high angular resolution, it means that the perceived distance, or actual angular distance, between resolved neighboring objects is small. The value that quantifies this property, θ, which is given by the Rayleigh criterion, is low for a system with a high resolution. The closely related term spatial resolution refers to the precision of a measurement with respect to space, which is directly connected to angular resolution in imaging instruments. The Rayleigh criterion shows that the minimum angular spread that can be resolved by an image forming system is limited by diffraction to the ratio of the wavelength of the waves to the aperture width. For this reason, high resolution imaging systems such as astronomical telescopes, long distance telephoto camera lenses and radio telescopes have large apertures.

Definition of terms

Resolving power is the ability of an imaging device to separate (i.e., to see as distinct) points of an object that are located at a small angular distance or it is the power of an optical instrument to separate far away objects, that are close together, into individual images. The term resolution or minimum resolvable distance is the minimum distance between distinguishable objects in an image, although the term is loosely used by many users of microscopes and telescopes to describe resolving power. As explained below, diffraction-limited resolution is defined by the Rayleigh criterion as the angular separation of two point sources when the maximum of each source lies in the first minimum of the diffraction pattern (Airy disk) of the other. In scientific analysis, in general, the term "resolution" is used to describe the precision with which any instrument measures and records (in an image or spectrum) any variable in the specimen or sample under study.

The Rayleigh criterion

"Rayleigh criterion" redirects here. Not to be confused with Rayleigh roughness criterion.

 

Airy diffraction patterns generated by light from two point sources passing through a circular aperture, such as the pupil of the eye. Points far apart (top) or meeting the Rayleigh criterion (middle) can be distinguished. Points closer than the Rayleigh criterion (bottom) are difficult to distinguish.

The imaging system's resolution can be limited either by aberration or by diffraction causing blurring of the image. These two phenomena have different origins and are unrelated. Aberrations can be explained by geometrical optics and can in principle be solved by increasing the optical quality of the system. On the other hand, diffraction comes from the wave nature of light and is determined by the finite aperture of the optical elements. The lens' circular aperture is analogous to a two-dimensional version of the single-slit experiment. Light passing through the lens interferes with itself creating a ring-shape diffraction pattern, known as the Airy pattern, if the wavefront of the transmitted light is taken to be spherical or plane over the exit aperture.

The interplay between diffraction and aberration can be characterised by the point spread function (PSF). The narrower the aperture of a lens the more likely the PSF is dominated by diffraction. In that case, the angular resolution of an optical system can be estimated (from the diameter of the aperture and the wavelength of the light) by the Rayleigh criterion defined by Lord Rayleigh: two point sources are regarded as just resolved when the principal diffraction maximum (center) of the Airy disk of one image coincides with the first minimum of the Airy disk of the other, as shown in the accompanying photos. (In the bottom photo on the right that shows the Rayleigh criterion limit, the central maximum of one point source might look as though it lies outside the first minimum of the other, but examination with a ruler verifies that the two do intersect.) If the distance is greater, the two points are well resolved and if it is smaller, they are regarded as not resolved. Rayleigh defended this criterion on sources of equal strength.

Considering diffraction through a circular aperture, this translates into:

${\displaystyle \theta \approx 1.22\frac{\lambda }{D}(\text{considering that}\sin \theta \approx \theta )}$

where θ is the angular resolution (radians), λ is the wavelength of light, and D is the diameter of the lens' aperture. The factor 1.22 is derived from a calculation of the position of the first dark circular ring surrounding the central Airy disc of the diffraction pattern. This number is more precisely 1.21966989... (OEIS: A245461), the first zero of the order-one Bessel function of the first kind ${\displaystyle J_1(x)}$ divided by π.

The formal Rayleigh criterion is close to the empirical resolution limit found earlier by the English astronomer W. R. Dawes, who tested human observers on close binary stars of equal brightness. The result, θ = 4.56/D, with D in inches and θ in arcseconds, is slightly narrower than calculated with the Rayleigh criterion. A calculation using Airy discs as point spread function shows that at Dawes' limit there is a 5% dip between the two maxima, whereas at Rayleigh's criterion there is a 26.3% dip. Modern image processing techniques including deconvolution of the point spread function allow resolution of binaries with even less angular separation.

Using a small-angle approximation, the angular resolution may be converted into a spatial resolution, Δℓ, by multiplication of the angle (in radians) with the distance to the object. For a microscope, that distance is close to the focal length f of the objective. For this case, the Rayleigh criterion reads:

${\displaystyle \mathrm{\Delta }\ell \approx 1.22\frac{f\lambda }{D}}$.

This is the radius, in the imaging plane, of the smallest spot to which a collimated beam of light can be focused, which also corresponds to the size of smallest object that the lens can resolve. The size is proportional to wavelength, λ, and thus, for example, blue light can be focused to a smaller spot than red light. If the lens is focusing a beam of light with a finite extent (e.g., a laser beam), the value of D corresponds to the diameter of the light beam, not the lens Since the spatial resolution is inversely proportional to D, this leads to the slightly surprising result that a wide beam of light may be focused to a smaller spot than a narrow one. This result is related to the Fourier properties of a lens.

A similar result holds for a small sensor imaging a subject at infinity: The angular resolution can be converted to a spatial resolution on the sensor by using f as the distance to the image sensor; this relates the spatial resolution of the image to the f-number, f/#:

${\displaystyle \mathrm{\Delta }\ell \approx 1.22\frac{f\lambda }{D}=1.22\lambda \cdot (f/\mathrm{\#})}$.

Since this is the radius of the Airy disk, the resolution is better estimated by the diameter, ${\displaystyle 2.44\lambda \cdot (f/\mathrm{\#})}$

Specific cases

Log-log plot of aperture diameter vs angular resolution at the diffraction limit for various light wavelengths compared with various astronomical instruments. For example, the blue star shows that the Hubble Space Telescope is almost diffraction-limited in the visible spectrum at 0.1 arcsecs, whereas the red circle shows that the human eye should have a resolving power of 20 arcsecs in theory, though normally only 60 arcsecs.

Single telescope

Point-like sources separated by an angle smaller than the angular resolution cannot be resolved. A single optical telescope may have an angular resolution less than one arcsecond, but astronomical seeing and other atmospheric effects make attaining this very hard.

The angular resolution R of a telescope can usually be approximated by

${\displaystyle R=\frac{\lambda }{D}}$

where λ is the wavelength of the observed radiation, and D is the diameter of the telescope's objective. The resulting R is in radians. For example, in the case of yellow light with a wavelength of 580 nm, for a resolution of 0.1 arc second, we need D=1.2 m. Sources larger than the angular resolution are called extended sources or diffuse sources, and smaller sources are called point sources.

This formula, for light with a wavelength of about 562 nm, is also called the Dawes' limit.

Telescope array

The highest angular resolutions for telescopes can be achieved by arrays of telescopes called astronomical interferometers: These instruments can achieve angular resolutions of 0.001 arcsecond at optical wavelengths, and much higher resolutions at x-ray wavelengths. In order to perform aperture synthesis imaging, a large number of telescopes are required laid out in a 2-dimensional arrangement with a dimensional precision better than a fraction (0.25x) of the required image resolution.

The angular resolution R of an interferometer array can usually be approximated by

${\displaystyle R=\frac{\lambda }{B}}$

where λ is the wavelength of the observed radiation, and B is the length of the maximum physical separation of the telescopes in the array, called the baseline. The resulting R is in radians. Sources larger than the angular resolution are called extended sources or diffuse sources, and smaller sources are called point sources.

For example, in order to form an image in yellow light with a wavelength of 580 nm, for a resolution of 1 milli-arcsecond, we need telescopes laid out in an array that is 120 m × 120 m with a dimensional precision better than 145 nm.

Microscope

The resolution R (here measured as a distance, not to be confused with the angular resolution of a previous subsection) depends on the angular aperture ${\displaystyle \alpha }$:

${\displaystyle R=\frac{1.22\lambda }{{\mathrm{N}\mathrm{A}}_{\text{condenser}}+{\mathrm{N}\mathrm{A}}_{\text{objective}}}}$ where ${\displaystyle \mathrm{N}\mathrm{A}=n\sin \theta }$.

Here NA is the numerical aperture, ${\displaystyle \theta }$ is half the included angle ${\displaystyle \alpha }$ of the lens, which depends on the diameter of the lens and its focal length, ${\displaystyle n}$ is the refractive index of the medium between the lens and the specimen, and ${\displaystyle \lambda }$ is the wavelength of light illuminating or emanating from (in the case of fluorescence microscopy) the sample.

It follows that the NAs of both the objective and the condenser should be as high as possible for maximum resolution. In the case that both NAs are the same, the equation may be reduced to:

${\displaystyle R=\frac{0.61\lambda }{\mathrm{N}\mathrm{A}}\approx \frac{\lambda }{2\mathrm{N}\mathrm{A}}}$

The practical limit for ${\displaystyle \theta }$ is about 70°. In a dry objective or condenser, this gives a maximum NA of 0.95. In a high-resolution oil immersion lens, the maximum NA is typically 1.45, when using immersion oil with a refractive index of 1.52. Due to these limitations, the resolution limit of a light microscope using visible light is about 200 nm. Given that the shortest wavelength of visible light is violet (${\displaystyle \lambda \approx 400\mathrm{n}\mathrm{m}}$),

${\displaystyle R=\frac{1.22\times 400\text{nm}}{1.45+0.95}=203\text{nm}}$

which is near 200 nm.

Oil immersion objectives can have practical difficulties due to their shallow depth of field and extremely short working distance, which calls for the use of very thin (0.17 mm) cover slips, or, in an inverted microscope, thin glass-bottomed Petri dishes.

However, resolution below this theoretical limit can be achieved using super-resolution microscopy. These include optical near-fields (Near-field scanning optical microscope) or a diffraction technique called 4Pi STED microscopy. Objects as small as 30 nm have been resolved with both techniques. In addition to this Photoactivated localization microscopy can resolve structures of that size, but is also able to give information in z-direction (3D).

Present

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Present

 

When the time the photo is taken is the present, the train's past location is on the left and its future location is on the right.

The present (or here and now) is the time that is associated with the events perceived directly and in the first time, not as a recollection (perceived more than once) or a speculation (predicted, hypothesis, uncertain). It is a period of time between the past and the future, and can vary in meaning from being an instant to a day or longer.

It is sometimes represented as a hyperplane in space-time, typically called "now", although modern physics demonstrates that such a hyperplane cannot be defined uniquely for observers in relative motion. The present may also be viewed as a duration (see specious present).

Historiography

Contemporary history describes the historical timeframe immediately relevant to the present time and is a certain perspective of modern history.

Philosophy and religion

Quotations You shouldn't chase after the past or place expectations on the future. What is past is left behind. The future is as yet unreached. Whatever quality is present you clearly see right there, right there. — Buddha, Bhaddekaratta Sutta What we perceive as present is the vivid fringe of memory tinged with anticipation. — Alfred North Whitehead, The Concept of Nature

Philosophy of time

Main article: Philosophy of time

"The present" raises the question: "How is it that all sentient beings experience now at the same time?" There is no logical reason why this should be the case and no easy answer to the question.

In Buddhism

Buddhism and many of its associated paradigms emphasize the importance of living in the present moment — being fully aware of what is happening, and not dwelling on the past or worrying about the future. This does not mean that they encourage hedonism, but merely that constant focus on one's current position in space and time (rather than future considerations, or past reminiscence) will aid one in relieving suffering. They teach that those who live in the present moment are the happiest. A number of meditative techniques aim to help the practiser live in the present moment.

See also: Mindfulness (Buddhism) § Examples from contemplative and daily life

Christianity and eternity

Christianity views God as being outside of time and, from the divine perspective past, present and future are actualized in the now of eternity. This trans-temporal conception of God has been proposed as a solution to the problem of divine foreknowledge (i.e. how can God know what we will do in the future without us being determined to do it) since at least Boethius. Thomas Aquinas offers the metaphor of a watchman, representing God, standing on a height looking down on a valley to a road where past present and future, represented by the individuals and their actions strung out along its length, are all visible simultaneously to God. Therefore, God's knowledge is not tied to any particular date.

Physical science

Special relativity

A visualisation of the present (dark blue plane) and past and future light cones in 2D space.

The original intent of the diagram on the right was to portray a 3-dimensional object having access to the past, present, and future in the present moment (4th dimension).

It follows from Albert Einstein's Special Theory of Relativity that there is no such thing as absolute simultaneity. When care is taken to operationalise "the present", it follows that the events that can be labeled as "simultaneous" with a given event, can not be in direct cause-effect relationship. Such collections of events are perceived differently by different observers. Instead, when focusing on "now" as the events perceived directly, not as a recollection or a speculation, for a given observer "now" takes the form of the observer's past light cone. The light cone of a given event is objectively defined as the collection of events in causal relationship to that event, but each event has a different associated light cone. One has to conclude that in relativistic models of physics there is no place for "the present" as an absolute element of reality, and only refers to things that are close to us. Einstein phrased this as: "People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion".

Cosmology

Further information: Physical cosmology, Cosmic time, and Chronology of the universe

In physical cosmology, the present time in the chronology of the universe is estimated at 13.8 billion years after the singularity determining the arrow of time. In terms of the metric expansion of space, it is in the dark-energy-dominated era, after the universe's matter content has become diluted enough for metric expansion to be dominated by vacuum energy (dark energy). It is also in the universe's Stelliferous Era, after enough time for superclusters to have formed (at about 5 billion years), but before the accelerating expansion of the universe has removed the local supercluster beyond the cosmological horizon (at about 150 billion years).

Archaeology, geology, etc.

In radiocarbon dating, the "present" is defined as AD 1950.

Grammar

In English grammar, actions are classified according to one of the following twelve verb tenses: past (past, past continuous, past perfect, or past perfect continuous), present (present, present continuous, present perfect, or present perfect continuous), or future (future, future continuous, future perfect, or future perfect continuous). The present tense refers to things that are currently happening or are always the case. For example, in the sentence, "she walks home everyday," the verb "walks" is in the present tense because it refers to an action that is regularly occurring in the present circumstances.

Verbs in the present continuous tense indicate actions that are currently happening and will continue for a period of time. In the sentence, "she is walking home," the verb phrase "is walking" is in the present continuous tense because it refers to a current action that will continue until a certain endpoint (when "she" reaches home). Verbs in the present perfect tense indicate actions that started in the past and is completed at the time of speaking. For example, in the sentence, "She has walked home," the verb phrase "has walked" is in the present perfect tense because it describes an action that began in the past and is finished as of the current reference to the action. Finally, verbs in the present perfect continuous tense refer to actions that have been continuing up until the current time, thus combining the characteristics of both the continuous and perfect tenses. An example of a present perfect continuous verb phrase can be found in the sentence, "she has been walking this route for a week now," where "has been walking" indicates an action that was happening continuously in the past and continues to happen continuously in the present.

Law of noncontradiction

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Principle

In logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the same time, e. g. the two propositions "p is the case" and "p is not the case" are mutually exclusive. Formally this is expressed as the tautology ¬(p ∧ ¬p). The law is not to be confused with the law of excluded middle which states that at least one, "p is the case" or "p is not the case" holds.

One reason to have this law is the principle of explosion, which states that anything follows from a contradiction. The law is employed in a reductio ad absurdum proof.

To express the fact that the law is tenseless and to avoid equivocation, sometimes the law is amended to say "contradictory propositions cannot both be true 'at the same time and in the same sense'".

It is one of the so called three laws of thought, along with its complement, the law of excluded middle, and the law of identity. However, no system of logic is built on just these laws, and none of these laws provide inference rules, such as modus ponens or De Morgan's laws.

The law of non-contradiction and the law of excluded middle create a dichotomy in "logical space", wherein the two parts are "mutually exclusive" and "jointly exhaustive". The law of non-contradiction is merely an expression of the mutually exclusive aspect of that dichotomy, and the law of excluded middle, an expression of its jointly exhaustive aspect.

Interpretations

One difficulty in applying the law of non-contradiction is ambiguity in the propositions. For instance, if it is not explicitly specified as part of the propositions A and B, then A may be B at one time, and not at another. A and B may in some cases be made to sound mutually exclusive linguistically even though A may be partly B and partly not B at the same time. However, it is impossible to predicate of the same thing, at the same time, and in the same sense, the absence and the presence of the same fixed quality.

Heraclitus

According to both Plato and Aristotle, Heraclitus was said to have denied the law of non-contradiction. This is quite likely if, as Plato pointed out, the law of non-contradiction does not hold for changing things in the world. If a philosophy of Becoming is not possible without change, then (the potential of) what is to become must already exist in the present object. In "We step and do not step into the same rivers; we are and we are not", both Heraclitus's and Plato's object simultaneously must, in some sense, be both what it now is and have the potential (dynamic) of what it might become.

So little remains of Heraclitus' aphorisms that not much about his philosophy can be said with certainty. He seems to have held that strife of opposites is universal both within and without, therefore both opposite existents or qualities must simultaneously exist, although in some instances in different respects. "The road up and down are one and the same" implies either the road leads both ways, or there can be no road at all. This is the logical complement of the law of non-contradiction. According to Heraclitus, change, and the constant conflict of opposites is the universal logos of nature.

Protagoras

Personal subjective perceptions or judgments can only be said to be true at the same time in the same respect, in which case, the law of non-contradiction must be applicable to personal judgments. The most famous saying of Protagoras is: "Man is the measure of all things: of things which are, that they are, and of things which are not, that they are not". However, Protagoras was referring to things that are used by or in some way related to humans. This makes a great difference in the meaning of his aphorism. Properties, social entities, ideas, feelings, judgments, etc. originate in the human mind. However, Protagoras has never suggested that man must be the measure of stars or the motion of the stars.

Parmenides

Parmenides employed an ontological version of the law of non-contradiction to prove that being is and to deny the void, change, and motion. He also similarly disproved contrary propositions. In his poem On Nature, he said,

the only routes of inquiry there are for thinking:

the one that [it] is and that [it] cannot not be
is the path of Persuasion (for it attends upon truth)
the other, that [it] is not and that it is right that [it] not be,
this I point out to you is a path wholly inscrutable
for you could not know what is not (for it is not to be accomplished)

nor could you point it out... For the same thing is for thinking and for being

The nature of the 'is' or what-is in Parmenides is a highly contentious subject. Some have taken it to be whatever exists, some to be whatever is or can be the object of scientific inquiry.

Socrates

In Plato's early dialogues, Socrates uses the elenctic method to investigate the nature or definition of ethical concepts such as justice or virtue. Elenctic refutation depends on a dichotomous thesis, one that may be divided into exactly two mutually exclusive parts, only one of which may be true. Then Socrates goes on to demonstrate the contrary of the commonly accepted part using the law of non-contradiction. According to Gregory Vlastos, the method has the following steps:

1. Socrates' interlocutor asserts a thesis, for example, "Courage is endurance of the soul", which Socrates considers false and targets for refutation.
2. Socrates secures his interlocutor's agreement to further premises, for example, "Courage is a fine thing" and "Ignorant endurance is not a fine thing".
3. Socrates then argues, and the interlocutor agrees, that these further premises imply the contrary of the original thesis, in this case, it leads to: "courage is not endurance of the soul".
4. Socrates then claims that he has shown that his interlocutor's thesis is false and that its negation is true.

Plato's synthesis

Plato's version of the law of non-contradiction states that "The same thing clearly cannot act or be acted upon in the same part or in relation to the same thing at the same time, in contrary ways" (The Republic (436b)). In this, Plato carefully phrases three axiomatic restrictions on action or reaction: in the same part, in the same relation, at the same time. The effect is to momentarily create a frozen, timeless state, somewhat like figures frozen in action on the frieze of the Parthenon.

This way, he accomplishes two essential goals for his philosophy. First, he logically separates the Platonic world of constant change from the formally knowable world of momentarily fixed physical objects. Second, he provides the conditions for the dialectic method to be used in finding definitions, as for example in the Sophist. So Plato's law of non-contradiction is the empirically derived necessary starting point for all else he has to say.

In contrast, Aristotle reverses Plato's order of derivation. Rather than starting with experience, Aristotle begins a priori with the law of non-contradiction as the fundamental axiom of an analytic philosophical system. This axiom then necessitates the fixed, realist model. Now, he starts with much stronger logical foundations than Plato's non-contrariety of action in reaction to conflicting demands from the three parts of the soul.

Aristotle's contribution

The traditional source of the law of non-contradiction is Aristotle's Metaphysics where he gives three different versions.

• Ontological: "It is impossible that the same thing belong and not belong to the same thing at the same time and in the same respect." (1005b19-20)
• Psychological: "No one can believe that the same thing can (at the same time) be and not be." (1005b23–24)
• Logical (aka the medieval Lex Contradictoriarum): "The most certain of all basic principles is that contradictory propositions are not true simultaneously." (1011b13-14)

Aristotle attempts several proofs of this law. He first argues that every expression has a single meaning (otherwise we could not communicate with one another). This rules out the possibility that by "to be a man", "not to be a man" is meant. But "man" means "two-footed animal" (for example), and so if anything is a man, it is necessary (by virtue of the meaning of "man") that it must be a two-footed animal, and so it is impossible at the same time for it not to be a two-footed animal. Thus "it is not possible to say truly at the same time that the same thing is and is not a man" (Metaphysics 1006b 35). Another argument is that anyone who believes something cannot believe its contradiction (1008b).

Why does he not just get up first thing and walk into a well or, if he finds one, over a cliff? In fact, he seems rather careful about cliffs and wells.

Avicenna

Avicenna's commentary on the Metaphysics illustrates the common view that the law of non-contradiction "and their like are among the things that do not require our elaboration." Avicenna's words for "the obdurate" are quite facetious: "he must be subjected to the conflagration of fire, since 'fire' and 'not fire' are one. Pain must be inflicted on him through beating, since 'pain' and 'no pain' are one. And he must be denied food and drink, since eating and drinking and the abstention from both are one [and the same]."

Indian philosophy

The law of non-contradiction is found in ancient Indian logic as a meta-rule in the Shrauta Sutras, the grammar of Pāṇini, and the Brahma Sutras attributed to Vyasa. It was later elaborated on by medieval commentators such as Madhvacharya.

Leibniz and Kant

Leibniz and Kant both used the law of non contradiction to define the difference between analytic and synthetic propositions. For Leibniz, analytic statements follow from the law of non contradiction, and synthetic ones from the principle of sufficient reason.

Russell

The principle was stated as a theorem of propositional logic by Russell and Whitehead in Principia Mathematica as:

${\displaystyle \mathbf{\ast }\mathbf{3}\cdot \mathbf{24}.⊢.\sim (p.\sim p)}$

Dialetheism

Graham Priest advocates the view that under some conditions, some statements can be both true and false simultaneously, or may be true and false at different times. Dialetheism arises from formal logical paradoxes, such as the Liar's paradox and Russell's paradox.

Alleged impossibility of its proof or denial

The law of non-contradiction is alleged to be neither verifiable nor falsifiable, on the grounds that any proof or disproof must use the law itself prior to reaching the conclusion. In other words, in order to verify or falsify the laws of logic one must resort to logic as a weapon, an act which is argued to be self-defeating. Since the early 20th century, certain logicians have proposed logics that deny the validity of the law.

Logics known as "paraconsistent" are inconsistency-tolerant logics in that there, from P together with ¬P, it does not imply that any proposition follows. Nevertheless, not all paraconsistent logics deny the law of non-contradiction and some such logics even prove it.

Some, such as David Lewis, have objected to paraconsistent logic on the ground that it is simply impossible for a statement and its negation to be jointly true. A related objection is that "negation" in paraconsistent logic is not really negation; it is merely a subcontrary-forming operator.

In popular culture

The Fargo episode "The Law of Non-Contradiction", which takes its name from the law, was noted for its several elements relating to the law of non-contradiction, as the episode's main character faces several paradoxes. For example, she is still the acting chief of police while having been demoted from the position, and tries to investigate a man that both was and was not named Ennis Stussy, and who both was and was not her stepfather. It also features the story of a robot who, after having spent millions of years unable to help humanity, is told that he greatly helped mankind all along by observing history.

Principle

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Principle 

The concept of blind justice is a moral principle.

A principle is a fundamental truth or proposition that serves as the foundation for a system of beliefs or behavior or a chain of reasoning.That is a guide for behavior or evaluation. In law, it is a rule that has to be or usually is to be followed. It can be desirably followed, or it can be an inevitable consequence of something, such as the laws observed in nature or the way that a system is constructed. The principles of such a system are understood by its users as the essential characteristics of the system, or reflecting the system's designed purpose, and the effective operation or use of which would be impossible if any one of the principles was to be ignored. A system may be explicitly based on and implemented from a document of principles as was done in IBM's 360/370 Principles of Operation.

Examples of principles are, entropy in a number of fields, least action in physics, those in descriptive comprehensive and fundamental law: doctrines or assumptions forming normative rules of conduct, separation of church and state in statecraft, the central dogma of molecular biology, fairness in ethics, etc.

In common English, it is a substantive and collective term referring to rule governance, the absence of which, being "unprincipled", is considered a character defect. It may also be used to declare that a reality has diverged from some ideal or norm as when something is said to be true only "in principle" but not in fact.

As law

As moral law

Socrates preferred to face execution rather than betray his moral principles.

 

Main article: Ethics

A principle represents values that orient and rule the conduct of persons in a particular society. To "act on principle" is to act in accordance with one's moral ideals. Principles are absorbed in childhood through a process of socialization. There is a presumption of liberty of individuals that is restrained. Exemplary principles include First, do no harm, the golden rule and the doctrine of the mean.

As a juridic law

Main article: Principle of legality

It represents a set of values that inspire the written norms that organize the life of a society submitting to the powers of an authority, generally the State. The law establishes a legal obligation, in a coercive way; it therefore acts as principle conditioning of the action that limits the liberty of the individuals. See, for examples, the territorial principle, homestead principle, and precautionary principle.

As scientific law

Archimedes principle, relating buoyancy to the weight of displaced water, is an early example of a law in science. Another early one developed by Malthus is the population principle, now called the Malthusian principle. Freud also wrote on principles, especially the reality principle necessary to keep the id and pleasure principle in check. Biologists use the principle of priority and principle of Binomial nomenclature for precision in naming species. There are many principles observed in physics, notably in cosmology which observes the mediocrity principle, the anthropic principle, the principle of relativity and the cosmological principle. Other well-known principles include the uncertainty principle in quantum mechanics and the pigeonhole principle and superposition principle in mathematics.

As axiom or logical fundament

Principle of sufficient reason

Main article: Principle of sufficient reason

The principle states that every event has a rational explanation. The principle has a variety of expressions, all of which are perhaps best summarized by the following:

For every entity x, if x exists, then there is a sufficient explanation for why x exists.

For every event e, if e occurs, then there is a sufficient explanation for why e occurs.

For every proposition p, if p is true, then there is a sufficient explanation for why p is true.

However, one realizes that in every sentence there is a direct relation between the predicate and the subject. To say that "the Earth is round", corresponds to a direct relation between the subject and the predicate.

Principle of non-contradiction

Portrait bust of Aristotle; an Imperial Roman copy of a lost bronze sculpture made by Lysippos

 

Main article: Law of noncontradiction

According to Aristotle, “It is impossible for the same thing to belong and not to belong at the same time to the same thing and in the same respect.” For example, it is not possible that in exactly the same moment and place, it rains and does not rain.

Principle of excluded middle

Main article: Law of excluded middle

The principle of the excluding third or "principium tertium exclusum" is a principle of the traditional logic formulated canonically by Leibniz as: either A is B or A isn't B. It is read the following way: either P is true, or its denial ¬P is. It is also known as "tertium non datur" ('A third (thing) is not'). Classically it is considered to be one of the most important fundamental principles or laws of thought (along with the principles of identity, non-contradiction and sufficient reason).