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

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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).

Queer heterosexuality

From Wikipedia, the free encyclopedia

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

Queer heterosexuality is heterosexual practice or identity that is also controversially called queer. "Queer heterosexuality" is argued to consist of heterosexual, cisgender, and allosexual persons who show nontraditional gender expressions, or who adopt gender roles that differ from the hegemonic masculinity and femininity of their particular culture.

The concept was first discussed in the mid-1990s, critically within radical feminism, and as a positive identification by Clyde Smith in a paper delivered at a conference in Amsterdam in 1997; in 2003, The Village Voice published an article called, "The Queer Heterosexual", which has since been cited by others using the term.

The idea that any heterosexual can be called "queer" is highly contested. Some in the LGBTQ+ community consider the use of the term "queer" by heterosexual people to be an offensive misappropriation, involving people not experiencing oppression for their sexual orientation or gender identity appropriating aspects of queer identities perceived as "fashionable" or attractive, and disregarding the concurrent oppression experienced by those they appropriate from.

Feminist criticism and queer theory

Kitzinger and Wilkinson argued that the rehabilitation of heterosexuality through "'queer' heterosexuality" as "a concept derived from postmodernist and queer theory" is seen as flawed from a radical feminist perspective. Acknowledging that 'queer heterosexuality' is rarely explored in detail, they explain that "the notion of the 'queer heterosexual' had become established in queer theory", gaining currency not because people are convinced it is possible or desirable, but "because queer heterosexuality is a necessary component of 'gender-fucking'" in Butlerian terms. 'Queer heterosexuality' becomes named in the project as destabilising all such categories, and moving towards a world where categories such as 'heterosexual' are rendered redundant. The queer theory was created to understand the concepts of gender, besides the binary, male, and female.

In a 2004 paper, Annette Schlichter describes the discourse on queer heterosexuality as aiming at "the de- and possible reconstruction of heterosexual subjectivity through the straight authors' aspiration to identify as queer". In the paper, a genealogy of queer heterosexuality is outlined, pointing out that "The queer critique of sexual normativity is both bound to the history of specific identities and committed to the destabilization of sexual identities—including those that have become hegemonic", while "Critics concerned about issues of lesbian visibility and difference occasionally raise the specter of the queer heterosexual ... as an indication of the queer project's perversion of social and political identities and their relations to power."

Putting to one side the question of whether the idea of homosexual contagion is necessarily homophobic, Guy Davidson uses the article from the Village Voice as an example of how the idea of queer subversion of heterosexuality can have "politically positive implications", specifically in relation to Tristan Taormino's writing on celebration of the LGBT movement's queering of heterosexual sex practices the production of the "queer heterosexual".

In Straight writ queer, the authors acknowledge that the queer heterosexual is only starting to emerge from the closet, seeking in the book to "identify and out the queer heterosexual" in historic and contemporary literature and to identify "inherently queer heterosexual practices" which critique heteronormativity and open up possibilities for the future. The examples in the book include anchorites, the Marquis de Sade and Algernon Charles Swinburne as examples of queer heterosexuals. "Male masochism disavows a masculinity predicated on phallic mastery, and hence becomes a strategic site for queer heterosexual resistance to heteronormativity".

In a 2018 paper, Heather Brook compares how the term 'same-sex marriage' is similarly oxymoronic to 'queer heterosexuality'. They both challenge and connect to essentialist understandings of heterosexuality. However, where 'same-sex marriage' aims to gain social capital from the normativeness of heterosexual marriage, 'queer heterosexuality' pulls on the fluidity of queerness. Brook describes how both terms incite fear of appropriation and the pejoration of a gendered understanding of societal institutions. Specifically, when straight people use 'queer', a term which was reclaimed by the community it now describes, to describe their heterosexuality, it straightens the word within the social consciousness. Brook posits that queer heterosexuality forces an exploration of how heteronormative institutions like marriage can be defined outside of binary oppositions like "hetero and homo; men and women; queer and straight".

Examination of masculinity

In 2005, Robert Heasley explored queer heterosexuality among a group of men that he identifies as "straight-queer males." According to Heasley, these men are self-identified heterosexuals who do not find social spaces dominated by traditionally masculine personalities to be comfortable. Heasley believes that a lack of understanding of masculinity can be addressed by creating a terminology to describe non-hegemonic masculine behavior. He lists seriously discussing homosexuality, being held or cuddled, hand-holding, dressing femininely, and expressing emotional openness among the behaviors displayed by straight-queer males.

Men who have been surveyed about their "mostly straight" behavior gave various reasons for this self-identification: some felt constrained by traditional models of gender and sexual orientation, others found men attractive. Some had a small amount of sexual interest in men but no desire for romantic same-sex relationships or intercourse, while others felt romantic but not sexual interest in other men.

Controversy

As 'queer' is generally defined either as a synonym for LGBT, or defined as "non-heterosexual", the term 'queer heterosexual' is considered controversial. Some LGBT people disapprove of the appropriation of 'queer' by cisgender heterosexual individuals, as the term has been used as a slur to oppress LGBT people. Straight celebrities self-identifying as queer have also faced backlash, with some arguing that their identities constitute "playing" with the "fashionable" parts of being LGBT, without having to suffer the resulting oppression of being LGBT, thus trivializing the struggles experienced by queer people.

For someone who is homosexual and queer, a straight person identifying as queer can feel like choosing to appropriate the good bits, the cultural and political cache [sic], the clothes and the sound of gay culture, without the laugh riot of gay-bashing, teen shame, adult shame, shame-shame, and the internalized homophobia of lived gay experience.

Critics of the term compare the use of 'queer heterosexual' to the appropriation engaged in by celebrities like Madonna, who used vogue dancing – a style and subculture originating amongst gay men, particularly African-American and Latino gay men – in her performances, profiting from the use of it while the style's originators did not. Daniel Harris, author of The Rise and Fall of Gay Culture, said that people who call themselves a 'queer heterosexual' "are under the impression they're doing something brave. [...] I'm a little sick that straight men would use those (terms)". Sky Gilbert referred to Calvin Thomas as "a little heterosexual male desperately wishing to be a card-carrying member of the gay community."

Gay reviewer Jameson Fitzpatrick said of James Franco's Straight James / Gay James: "I can't imagine the difficulty of being a straight, cis person who isn't fooled by the foundational fictions of hetero- and cisnormative power structures and doesn't wish to perpetuate them—except to say that I can't imagine that difficulty could possibly be greater than the various violences that many queer people still face today. This might be key to the problem that persists in Franco's claim to queerness, and what about it that rankles so many gay men: a lack of perspective." Fitzpatrick said he knew many people who might qualify as a queer heterosexual, but none who would use the label for themselves, and none who would "flaunt their privilege" as Fitzpatrick viewed Franco as doing in his book. A discussion of Franco and queer heterosexuality by Anthony Moll rejects the idea that Franco's art is queer: "From the concept of the interview between his straight self and his gay selves, to his ham-handed attempt to discuss queer heterosexuality, Franco comes across as a novice queer theorist who is talking through interesting, yet ultimately incomplete, ideas".