Degrees of freedom problemIn neuroscience and motor control , the degrees of freedom problem or motor equivalence problem states that there are multiple ways for humans or animals to perform a movement in order to achieve the same goal. In other words, under normal circumstances, no simple one-to-one correspondence exists between a motor problem (or task) and a motor solution to the problem.
Graded vector spaceIn mathematics, a graded vector space is a vector space that has the extra structure of a grading or gradation, which is a decomposition of the vector space into a direct sum of vector subspaces, generally indexed by the integers. For "pure" vector spaces, the concept has been introduced in homological algebra, and it is widely used for graded algebras, which are graded vector spaces with additional structures. Let be the set of non-negative integers.
Phenomenology (philosophy)Phenomenology is the philosophical study of objectivity – and reality more generally – as subjectively lived and experienced. It seeks to investigate the universal features of consciousness while avoiding assumptions about the external world, aiming to describe phenomena as they appear to the subject, and to explore the meaning and significance of the lived experiences.
Graded ringIn mathematics, in particular abstract algebra, a graded ring is a ring such that the underlying additive group is a direct sum of abelian groups such that . The index set is usually the set of nonnegative integers or the set of integers, but can be any monoid. The direct sum decomposition is usually referred to as gradation or grading. A graded module is defined similarly (see below for the precise definition). It generalizes graded vector spaces. A graded module that is also a graded ring is called a graded algebra.
Phenomenology (psychology)Phenomenology or phenomenological psychology, a sub-discipline of psychology, is the scientific study of subjective experiences. It is an approach to psychological subject matter that attempts to explain experiences from the point of view of the subject via the analysis of their written or spoken word. The approach has its roots in the phenomenological philosophical work of Edmund Husserl. Early phenomenologists such as Husserl, Jean-Paul Sartre, and Maurice Merleau-Ponty conducted philosophical investigations of consciousness in the early 20th century.
Consciousness ExplainedConsciousness Explained is a 1991 book by the American philosopher Daniel Dennett, in which the author offers an account of how consciousness arises from interaction of physical and cognitive processes in the brain. Dennett describes consciousness as an account of the various calculations occurring in the brain at close to the same time. He compares consciousness to an academic paper that is being developed or edited in the hands of multiple people at one time, the "multiple drafts" theory of consciousness.
Phenomenology of PerceptionPhenomenology of Perception (Phénoménologie de la perception) is a 1945 book about perception by the French philosopher Maurice Merleau-Ponty, in which the author expounds his thesis of "the primacy of perception". The work established Merleau-Ponty as the pre-eminent philosopher of the body, and is considered a major statement of French existentialism. Merleau-Ponty attempts to define phenomenology, which according to him has not yet received a proper definition.
Graded (mathematics)In mathematics, the term "graded" has a number of meanings, mostly related: In abstract algebra, it refers to a family of concepts: An algebraic structure is said to be -graded for an index set if it has a gradation or grading, i.e. a decomposition into a direct sum of structures; the elements of are said to be "homogeneous of degree i ". The index set is most commonly or , and may be required to have extra structure depending on the type of . Grading by (i.e. ) is also important; see e.g. signed set (the -graded sets).
Multiple drafts modelDaniel Dennett's multiple drafts model of consciousness is a physicalist theory of consciousness based upon cognitivism, which views the mind in terms of information processing. The theory is described in depth in his book, Consciousness Explained, published in 1991. As the title states, the book proposes a high-level explanation of consciousness which is consistent with support for the possibility of strong AI. Dennett describes the theory as first-person operationalism.
Associated graded ringIn mathematics, the associated graded ring of a ring R with respect to a proper ideal I is the graded ring: Similarly, if M is a left R-module, then the associated graded module is the graded module over : For a ring R and ideal I, multiplication in is defined as follows: First, consider homogeneous elements and and suppose is a representative of a and is a representative of b. Then define to be the equivalence class of in . Note that this is well-defined modulo . Multiplication of inhomogeneous elements is defined by using the distributive property.