Thus, the only logical possibilities are to accept non-Euclidean geometry as physically real, or to reject the entire notion of physical tests of the axioms of geometry, which can then be imagined as a formal system without any intrinsic real-world meaning.

This was then used to define the " quantity of motion " ( today called momentum ), and the principle of inertia in which mass replaces the previous Cartesian notion of intrinsic force.

* Theorema Egregium − The " remarkable theorem " discovered by Gauss which showed there is an intrinsic notion of curvature for surfaces.

This is used by Riemann to generalize the ( intrinsic ) notion of curvature to higher dimensional spaces.

Bernhard Riemann extended Gauss's theory to higher dimensional spaces called manifolds in a way that also allows distances and angles to be measured and the notion of curvature to be defined, again in a way that was intrinsic to the manifold and not dependent upon its embedding in higher-dimensional spaces.

The relation between merit and reward furnishes the intrinsic reason why in the matter of service and its remuneration, the guiding norm can be only the virtue of justice, and not disinterested kindness or pure mercy ; for it would destroy the very notion of reward to conceive of it as a free gift of bounty ( cf.

Because the concept of humility addresses intrinsic self-worth, it is emphasized in the realm of religious practice and ethics where the notion is often made more precise.

At the core of these theories is the notion that however one identifies, gender, sex, and sexuality are not intrinsic, but are socially constructed.

Fundamental analysis may be replaced or augmented by market criteria – what the market will pay for the stock, without any necessary notion of intrinsic value.

On one hand, the notion of intrinsic dimension refers to the fact that any low-dimensional data space can trivially be turned into a higher dimensional space by adding redundant ( e. g. duplicate ) or randomized dimensions, and in turn many high-dimensional data sets can be reduced to lower dimensional data without significant information loss.

He thereby derives the term ' General Systemantics ' in deference to the notion of a sweeping theory of system failure, but attributed to an intrinsic feature based on laws of system behavior.

In a number of cases, in certain highly multiethnic regions, such as North Caucasus, the notion of titular nation introduced intrinsic inequality between titular and non-titular nations, especially since the introduction of the " korenizatsiya " politics, according to which representatives of a titular nation were promoted to management position.

The works of physicists such as James Clerk Maxwell, and mathematicians Gregorio Ricci-Curbastro and Tullio Levi-Civita led to the development of tensor analysis and the notion of covariance, which identifies an intrinsic geometric property as one that is invariant with respect to coordinate transformations.

An imprecise notion of " exact solvability " as meaning: " The solutions can be expressed explicitly in terms of some previously known functions " is also sometimes used, as though this were an intrinsic property of the system itself, rather than the purely calculational feature that we happen to have some " known " functions available, in terms of which the solutions may be expressed.

This notion has no intrinsic meaning, since what is meant by " known " functions very often is defined precisely by the fact that they satisfy certain given equations, and the list of such " known functions " is constantly growing.

In mathematics, the dimension of an object is an intrinsic property independent of the space in which the object is embedded.

In algebraic geometry, in contrast, there is an intrinsic definition of tangent space at a point P of a variety V, that gives a vector space of dimension at least that of V. The points P at which the dimension is exactly that of V are called the non-singular points ; the others are singular points.

Women deserve the instrumental effects of gender equality in education and the intrinsic dimension of female education ; which in essence derives from the role of education in enhancing a woman ’ s set of capabilities.

Conversely, if he gives a heavy rating to his own reading, and finds more accurate facts in it than in the others, a point is chalked up for the intrinsic, objective meaningfulness of this type of mediumistic material.

The validity of this argument is subjective, depending on whether intrinsic rewards qualify as ' benefits '.

The American Sociology Association ( ASA ) acknowledges Public sociology saying, " The intrinsic scientific, policy, and public relevance of this field of investigation in helping to construct ' good societies ' is unquestionable " (" Altruism, Morality, and Social Solidarity ".

Absolute magnitude ( also known as absolute visual magnitude when measured in the standard V photometric band ) is the measure of a celestial object's intrinsic brightness.

The process of apoptosis is controlled by a diverse range of cell signals, which may originate either extracellularly ( extrinsic inducers ) or intracellularly ( intrinsic inducers ).

This type of interaction shows that apoptosis is activated via an intrinsic pathway.

Angular momenta of a classical object .< p > Left: intrinsic " spin " angular momentum S is really orbital angular momentum of the object at every point ,</ p >< p > right: extrinsic orbital angular momentum L about an axis ,</ p >< p > top: the moment of inertia tensor | moment of inertia tensor I and angular velocity ω ( L is not always parallel to ω )</ p >< p > bottom: momentum p and it's radial position r from the axis .</ p > The total angular momentum ( spin + orbital ) is J.

Spin is often depicted as a particle literally spinning around an axis, but this is a misleading and inaccurate picture: Spin is an intrinsic property of a particle, fundamentally different from orbital angular momentum.

A major habitat type, however, is a compromise, as it has an intrinsic inhomogeneity.

The intrinsic property is that it reflects radiation ( including light ) in a certain way.

Another method is to measure the brightness of an object and assume an intrinsic luminosity, from which the distance may be determined using the inverse square law.

These usually are not high-value coins, but the interest is in collecting a large volume of them either for the sake of the challenge, as a store of value, or in the hope that the intrinsic metal value will increase.

According to the Stanford Encyclopedia of Philosophy, Mohist consequentialism, dating back to the 5th century BCE, is the " world's earliest form of consequentialism, a remarkably sophisticated version based on a plurality of intrinsic goods taken as constitutive of human welfare.

Confucius never stated whether man was born good or evil, noting that ' By nature men are similar ; by practice men are wide apart ' — implying that whether good or bad, Confucius must have perceived all men to be born with intrinsic similarities, but that man is conditioned and influenced by study and practise.

Modern calculations in quantum chemistry usually start from ( but ultimately go far beyond ) a molecular orbital rather than a valence bond approach, not because of any intrinsic superiority in the former but rather because the MO approach is more readily adapted to numerical computations.

This coordinate system sometimes is referred to as intrinsic or path coordinates or nt-coordinates, for normal-tangential, referring to these unit vectors.

In the field of parapsychology, claircognizance from late 17th century French clair ( clear ) and cognizance (< Middle English | ME cognisaunce < Old French | OFr conoissance, knowledge ) is a form of extra-sensory perception wherein a person acquires psychic knowledge primarily by means of intrinsic knowledge.

However, to the best of our knowledge, the electron's magnetic moment is not due to a current loop, but is instead an intrinsic property of the electron.

No one will deny that such broad developments and transitions are of great intrinsic interest and the study of ideas in literature would be woefully incomplete without frequent reference to them.

Like Structuralism, it places particular focus on the determination of identities, values and economies in relation to one another, rather than assuming intrinsic properties or essences of signs or components as starting points.

More precisely, matrices are tensors of type ( 1, 1 ), having one row index and one column index, also called covariant order 1 and contravariant order 1 ; see Tensor ( intrinsic definition ) for details.

When discussing non-moral goods, one may make a useful distinction between inherently serviced and material goods in the marketplace ( or its exchange value ), versus perceived intrinsic and experiential goods to the buyer.

Determining a precise distance to the LMC, as with any other galaxy, was challenging due to the use of standard candles for calculating distances, with the primary problem being that many of the standard candles are not as ' standard ' as one would like ; in many cases, the age and / or metallicity of the standard candle plays a role in determining the intrinsic luminosity of the object.

The wide intrinsic region makes the PIN diode an inferior rectifier ( one typical function of a diode ), but it makes the PIN diode suitable for attenuators, fast switches, photodetectors, and high voltage power electronics applications.

For example, whereas one of the benefits of the gold standard is that the intrinsic limitations to the growth of the money supply by the use of gold or silver would prevent inflation, if the growth of population or increase in trade outpaces the money supply, there would be no way to counteract deflation and reduced liquidity ( and any attendant recession ) except for the mining of more gold or silver under a gold or silver standard.

Also one intrinsic attribute of HTS is that it can withstand much higher magnetic fields than LTS, so HTS at liquid helium temperatures are being explored for very high-field inserts inside LTS magnets.

* All intrinsic and extrinsic muscles of the tongue are supplied by the hypoglossal nerve ( CN XII ), except for one of the extrinsic muscles, palatoglossus, which is innervated by CN X of the pharyngeal plexus.

* one who believes existence has no objective meaning, purpose, or intrinsic value, see nihilism

An intrinsic definition of the Gaussian curvature at a point P is the following: imagine an ant which is tied to P with a short thread of length r. She runs around P while the thread is completely stretched and measures the length C ( r ) of one complete trip around P. If the surface were flat, she would find C ( r ) = 2πr.

Here the action is undertaken for what one might call reasons intrinsic to the actor: some ethical, aesthetic, religious or other motive, independent of whether it will lead to success.

In particular one could define Riemannian manifold as a metric space which is isometric to a smooth submanifold of R < sup > n </ sup > with the induced intrinsic metric, where isometry here is meant in the sense of preserving the length of curves.

Many languages allow the speaker to specify whether one is talking about a male or female, whereas other languages do not require the speaker to make that choice as an intrinsic part of the language.

For two-tailed PC lipids, this ratio is nearly one so the intrinsic curvature is nearly zero.

The study of collective action shows that public goods are still produced when one individual benefits more from the public good than it costs him to produce it ; examples include benefits from individual use, intrinsic motivation to produce, and business models based on selling complement goods.

For someone born and raised in one of the poorest Neapolitan neighbourhoods this must have been quite an achievement, but in claiming the titles ( at the time they had become meaningless ) the comedian also mocked them for their intrinsic worthlessness.

This is the basis of his analogy between prudential actions and moral actions: in cases of altruistic action for another person's good that person's reasons quite literally become reasons for one if they are timeless and intrinsic reasons.

In The Possibility of Altruism, if one's reasons really are about intrinsic and timeless values then, qua subjective reason, one can only take them to be the guise of the reasons that there really are -- the objective ones.

The Catholic Encyclopedia states that " many of the recent critical students of the document, Donation of Constantine locate its composition at Rome and attribute the forgery to an ecclesiastic, their chief argument being an intrinsic one: this false document was composed in favour of the popes and of the Roman Church, therefore Rome itself must have had the chief interest in a forgery executed for a purpose so clearly expressed ".

Frederick Herzberg's two-factor theory, a. k. a. intrinsic / extrinsic motivation, concludes that certain factors in the workplace result in job satisfaction, but if absent, they don't lead to dissatisfaction but no satisfaction. The factors that motivate people can change over their lifetime, but " respect for me as a person " is one of the top motivating factors at any stage of life.

If one examines the textual paradigm of consensus, one is faced with a choice: either the " postdigital " society has intrinsic meaning, or it is contextualised into a paradigm of consensus that includes art as a totality.