* Cartesian anxiety

* Cartesian anxiety

* Cartesian anxiety

* Cartesian anxiety

The adjective Cartesian refers to the French mathematician and philosopher René Descartes ( who used the name Cartesius in Latin ).

In mathematics, abscissa ( plural abscissae or abscissæ ) refers to that element of an ordered pair which is plotted on the horizontal axis of a two-dimensional Cartesian coordinate system, as opposed to the ordinate.

In mathematics, ordinate refers to that element of an ordered pair which is plotted on the vertical axis of a two-dimensional Cartesian coordinate system, as opposed to the abscissa.

Often, " the " unit square refers specifically to the square in the Cartesian plane with corners at ( 0, 0 ), ( 1, 0 ), ( 0, 1 ), and ( 1, 1 ).

In this expression, the mean squared displacement refers to just once Cartesian component

By analogy, the term " hyperrectangle " or " box " refers to Cartesian products of orthogonal intervals of other kinds, such as ranges of keys in database theory or ranges of integers, rather than real numbers.

A forerunner of the modern ideas of cyberspace is the Cartesian notion that people might be deceived by an evil demon that feeds them a false reality.

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.

Berlin saw Hamann as having recognised as the rationalist's Cartesian fallacy the notion that there are " clear and distinct " ideas " which can be contemplated by a kind of inner eye ", without the use of language – a recognition greatly sharpened in the 20th century by Wittgenstein's private language argument.

The term " Cartesian dualism " is also often associated with this more specific notion of causal interaction through the pineal gland.

The language of fibre bundles allows this notion of a section to be generalized to the case when E is not necessarily a Cartesian product.

This can easily be expressed in terms of a commutative diagram, and thus leads to the notion of a medial magma object in a category with a Cartesian product.

In phenomenology, the Cartesian problem evolves into a notion first espoused by Edmund Husserl of phenomenological epoché.

Hyperbolas arise in practice in many ways: as the curve representing the function in the Cartesian plane, as the appearance of a circle viewed from within it, as the path followed by the shadow of the tip of a sundial, as the shape of an open orbit ( as distinct from a closed and hence elliptical orbit ), such as the orbit of a spacecraft during a gravity assisted swing-by of a planet or more generally any spacecraft exceeding the escape velocity of the nearest planet, as the path of a single-apparition comet ( one travelling too fast to ever return to the solar system ), as the scattering trajectory of a subatomic particle ( acted on by repulsive instead of attractive forces but the principle is the same ), and so on.

Others have heeded, at least as a starting point, the indications given by Robbe-Grillet in the introduction to his screenplay: " Two attitudes are then possible: either the spectator will try to reconstitute some ' Cartesian ' scheme-the most linear, the most rational he can devise-and this spectator will certainly find the film difficult if not incomprehensible ; or else the spectator will let himself be carried along by the extraordinary images in front of him [...] and to this spectator, the film will seem the easiest he has ever seen: a film addressed exclusively to his sensibility, to his faculties of sight, hearing, feeling.

Social scientist and physician Nicholas A. Christakis explains that " for the last few centuries, the Cartesian project in science has been to break matter down into ever smaller bits, in the pursuit of understanding.

Hermite-Gaussian modes are particularly common, since many laser systems have Cartesian reflection symmetry in the plane perpendicular to the beam's propagation direction.

and thus the Cartesian product is a set since

This crucial distinction would be left unresolved and lead to what is known as the mind-body problem, since the two substances in the Cartesian system are independent of each other and irreducible.

Note that one formulation of AC is that the Cartesian product of a family of nonempty sets is nonempty ; but since the empty set is most certainly compact, the proof cannot proceed along such straightforward lines.

However, virtually all modern philosophers have noted that not only is Cartesian Dualism untenable since the interactionism problem breaks the causal closure of the physical, but the cogito itself is logically fallacious.

The Lamm equation also has extra terms, since it pertains to sector-shaped cells, whereas the Mason – Weaver equation pertains to box-shaped cells ( i. e., cells whose walls are aligned with the three Cartesian axes ).

Baars argues that this is distinct from the concept of the Cartesian theater, since it is not based on the implicit dualistic assumption of " someone " viewing the theater, and is not located in a single place in the mind ( in Blackmore, 2005 ).

Initially defending coherentism in his anti-foundationalist critique The Structure of Empirical Knowledge, BonJour has since moved to defend Cartesian foundationalism in such works as Epistemology and In Defense of Pure Reason.

Leibniz fought against the Cartesian dualist system in his Monadology and tried to surpass it through a metaphysical system considered at the same time monist ( since only the unextended is substantial ) and pluralist ( as far as substances are disseminated in the world in an infinite number ).

Cartesian means of or relating to the French philosopher and mathematician René Descartes — from his name — Rene Des-Cartes.

* Cartesian dualism, the philosophy of the distinction between mind and body developed by René Descartes

The invention of Cartesian coordinates in the 17th century by René Descartes ( Latinized name: Cartesius ) revolutionized mathematics by providing the first systematic link between Euclidean geometry and algebra.

Amidst this turmoil, René Descartes sought answers to philosophical questions through the use of logic and reason and formulated what would be called Cartesian Dualism in 1641.

René Descartes (; Latinized form: Renatus Cartesius ; adjectival form: " Cartesian "; 31 March 1596 – 11 February 1650 ) was a French philosopher, mathematician, and writer who spent most of his adult life in the Dutch Republic.

With regard to René Descartes, he is popularly said to have recorded the three dreams leading up to the Cartesian Cogito.

A Cartesian diver or Cartesian devil is a classic science experiment, named for René Descartes, which demonstrates the principle of buoyancy ( Archimedes ’ principle ) and the ideal gas law.

* René Descartes introduces the Cartesian coordinate system in his work La Géométrie and promotes intellectual rigour in Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences ( published in Leiden ).

This drastic distinction between inner world and outer world was most popularized by René Descartes when he solidified his principle of Cartesian dualism.

He was one of the followers of René Descartes who tried to work out more detailed versions of a generally Cartesian philosophy.

After finishing his military service, during which he began to read René Descartes, he studied for his licence ( bachelor's degree ), focusing on the influence of scholasticism on Cartesian thought.

Res extensa ( often translated " corporeal substance " by Descartes ) is one of the three substances described by René Descartes in his Cartesian ontology, alongside res cogitans and God.

The Cartesian coordinate system developed by René Descartes explicitly assumes this axiom by blending the distinct concepts of real number system with the geometric line or plane into a conceptual metaphor.

The Cartesian circle is a potential mistake in reasoning attributed to René Descartes.