Mathematical object

A mathematical object is an abstract object arising in mathematics. The concept is studied in philosophy of mathematics.

In mathematical practice, an object is anything that has been (or could be) formally defined, and with which one may do deductive reasoning and mathematical proofs. Commonly encountered mathematical objects include numbers, permutations, partitions, matrices, sets, functions, and relations. Geometry as a branch of mathematics has such objects as hexagons, points, lines, triangles, circles, spheres, polyhedra, topological spaces and manifolds. Another branch—algebra—has groups, rings, fields, group-theoretic lattices, and order-theoretic lattices. Categories are simultaneously homes to mathematical objects and mathematical objects in their own right. In proof theory, proofs and theorems are also mathematical objects.

The ontological status of mathematical objects has been the subject of much investigation and debate by philosophers of mathematics.

Cantorian framework

Goal

A goal is a desired result that a person or a system envisions, plans and commits to achieve: a personal or organizational desired end-point in some sort of assumed development. Many people endeavor to reach goals within a finite time by setting deadlines.

It is roughly similar to purpose or aim, the anticipated result which guides reaction, or an end, which is an object, either a physical object or an abstract object, that has intrinsic value.

Goal setting

Goal setting may involve establishing specific, measurable, achievable, relevant, and time-bounded (SMART) objectives, but not all researchers agree that these SMART criteria are necessary.

Research on goal setting by Edwin A. Locke and his colleagues suggests that goal setting can serve as an effective tool for making progress when it ensures that group members have a clear awareness of what each person must do to achieve a shared objective. On a personal level, the process of setting goals allows individuals to specify and then work toward their own objectives (such as financial or career-based goals). Goal-setting comprises a major component of personal development and management.

Object (philosophy)

An object is a technical term in modern philosophy often used in contrast to the term subject. A subject is an observer and an object is a thing observed. For modern philosophers like Descartes, consciousness is a state of cognition that includes the subject—which can never be doubted as only it can be the one who doubts–—and some object(s) that may be considered as not having real or full existence or value independent of the subject who observes it. Metaphysical frameworks also differ in whether they consider objects exist independently of their properties and, if so, in what way.

The pragmatist Charles S. Peirce defines the broad notion of an object as anything that we can think or talk about. In a general sense it is any entity: the pyramids, Alpha Centauri, the number seven, a disbelief in predestination or the fear of cats. In a strict sense it refers to any definite being.

A related notion is objecthood. Objecthood is the state of being an object. One approach to defining it is in terms of objects' properties and relations. Descriptions of all bodies, minds, and persons must be in terms of their properties and relations. The philosophical question of the nature of objecthood concerns how objects are related to their properties and relations. For example, it seems that the only way to describe an apple is by describing its properties and how it is related to other things. Its properties may include its redness, its size and its composition, while its relations may include "on the table", "in the room" and "being bigger than other apples".

Nocturne

A nocturne (from the French which meant nocturnal, from Latin nocturnus) is usually a musical composition that is inspired by, or evocative of, the night. Historically, nocturne is a very old term applied to night Offices and, since the Middle Ages, to divisions in the canonical hour of Matins.

History

The name nocturne was first applied to pieces in the 18th century, when it indicated an ensemble piece in several movements, normally played for an evening party and then laid aside. Sometimes it carried the Italian equivalent, notturno, such as Wolfgang Amadeus Mozart's quadraphonic Notturno in D, K.286, written for four lightly echoing separated ensembles of paired horns with strings, and his Serenata Notturna, K. 239. At this time, the piece was not necessarily evocative of the night, but might merely be intended for performance at night, much like a serenade. The chief difference between the serenade and the notturno was the time of the evening at which they would typically be performed: the former around 9:00pm, the latter closer to 11:00 pm.

Nocturne (disambiguation)

A nocturne is a musical composition inspired by, or evocative of, night.

Nocturne may also refer to:

Art

Music

Nocturne (painting)

Nocturne painting is a term coined by James Abbott McNeill Whistler to describe a painting style that depicts scenes evocative of the night or subjects as they appear in a veil of light, in twilight, or in the absence of direct light. In a broader usage, the term has come to refer to any painting of a night scene, or night-piece, such as Rembrandt's The Night Watch.

Whistler used the term within the title of his works to represent paintings with a "dreamy, pensive mood" by applying a musical name. He also titled (and retitled) works using other terms associated with music, such as a "symphony", "harmony", "study" or "arrangement", to emphasize the tonal qualities and the composition and to de-emphasize the narrative content. The use of the term "nocturne" can be associated with the Tonalism movement of the American of the late 19th century and early 20th century which is "characterized by soft, diffused light, muted tones and hazy outlined objects, all of which imbue the works with a strong sense of mood." Along with winter scenes, nocturnes were a common Tonalist theme.Frederic Remington used the term as well for his nocturne scenes of the American Old West.