The language of thought hypothesis (LOTH), sometimes known as thought ordered mental expression (TOME), is a view in linguistics, philosophy of mind and cognitive science, forwarded by American philosopher Jerry Fodor. It describes the nature of thought as possessing "language-like" or compositional structure (sometimes known as mentalese). On this view, simple concepts combine in systematic ways (akin to the rules of grammar in language) to build thoughts. In its most basic form, the theory states that thought, like language, has syntax.

Using empirical evidence drawn from linguistics and cognitive science to describe mental representation from a philosophical vantage-point, the hypothesis states that thinking takes place in a language of thought (LOT): cognition and cognitive processes are only 'remotely plausible' when expressed as a system of representations that is "tokened" by a linguistic or semantic structure and operated upon by means of a combinatorial syntax. Linguistic tokens used in mental language describe elementary concepts which are operated upon by logical rules establishing causal connections to allow for complex thought. Syntax as well as semantics have a causal effect on the properties of this system of mental representations.

These mental representations are not present in the brain in the same way as symbols are present on paper; rather, the LOT is supposed to exist at the cognitive level, the level of thoughts and concepts. The LOTH has wide-ranging significance for a number of domains in cognitive science. It relies on a version of functionalist materialism, which holds that mental representations are actualized and modified by the individual holding the propositional attitude, and it challenges eliminative materialism and connectionism. It implies a strongly rationalist model of cognition in which many of the fundamentals of cognition are innate.__See Wikipedia__.

Using empirical evidence drawn from linguistics and cognitive science to describe mental representation from a philosophical vantage-point, the hypothesis states that thinking takes place in a language of thought (LOT): cognition and cognitive processes are only 'remotely plausible' when expressed as a system of representations that is "tokened" by a linguistic or semantic structure and operated upon by means of a combinatorial syntax. Linguistic tokens used in mental language describe elementary concepts which are operated upon by logical rules establishing causal connections to allow for complex thought. Syntax as well as semantics have a causal effect on the properties of this system of mental representations.

These mental representations are not present in the brain in the same way as symbols are present on paper; rather, the LOT is supposed to exist at the cognitive level, the level of thoughts and concepts. The LOTH has wide-ranging significance for a number of domains in cognitive science. It relies on a version of functionalist materialism, which holds that mental representations are actualized and modified by the individual holding the propositional attitude, and it challenges eliminative materialism and connectionism. It implies a strongly rationalist model of cognition in which many of the fundamentals of cognition are innate.

Not just a mathematical process that allows transforming an input stream of data into an output stream with a different structure. In the terms of information theory and TAPe, calculation is a way/method/process/structure/hierarchy for obtaining new knowledge from input data.

in __abstract algebra__, **group theory** studies the __algebraic structures____ __known as __groups__. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as __rings____, ____fields__, and __vector spaces__, can all be seen as groups endowed with additional __operations__ and __axioms__. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. __Linear algebraic groups__ and __Lie groups__ are two branches of group theory that have experienced advances and have become subject areas in their own right

Mn __mathematics__, the __mathematician____ ____Sophus Lie__ (__/liː/____ ____LEE__) initiated lines of study involving integration of __differential equations____, ____transformation groups__, and __contact__ of __spheres__ that have come to be called.

The foundation of Lie theory is the __exponential map__ relating __Lie algebras__ to __Lie groups__ which is called the __Lie group-Lie algebra correspondence__. The subject is part of __differential geometry__ since Lie groups are __differentiable manifolds__. Lie groups evolve out of the identity (1) and the __tangent vectors__ to __one-parameter subgroups__ generate the Lie algebra. The structure of a Lie group is implicit in its algebra, and the structure of the Lie algebra is expressed by __root systems__ and __root data__.

Many authors use the term *intransitivity* to mean *antitransitivity. *In __mathematics__, intransitivity (sometimes called nontransitivity) is a property of __binary relations__ that are not __transitive__ __relations__. This may include any relation that is not transitive, or the __stronger property__ of antitransitivity, which describes a relation that is never transitive.

Here is a way of obtaining new knowledge from input data characterized by signs of both mathematical and linguistic transformations combined into a common system. It is a tool/method of Language of Though

Here is the doctrine of relations between objects with unknown characteristics (except for certain properties describing them), such as those which form the basis of the Theory of Active Perception as axioms.

According to TAPe, hierarchy is the non-cyclic position of parts or elements of something ordered from one class to another and organization of those elements or parts into a tree-type structure with the possibility of building various connections depending on the task. While the hierarchical nature of the system is reflected in the relations of dominance and subordination, then the heterarchical nature manifests itself in the links of coordination.

Theory of Active Perception uses a finite number of elements combined into groups of different levels according to certain laws. We call these elements filters-operators. A filter is a conditional mathematical value, endowed with other values, including absolute. Thus, a filter can be evaluated using the mass of the image which has gone through that filter.

Operators, however, have nothing to do with mathematics. An operator occurs (takes a value) with respect to filters. In fact, it is the same element as the filter — labeled in the same way, but no longer representing mathematical values. Rather, those are letters that are meaningful per se.

With these elements, TAPe describes the very shift from mathematics to language and back again — exactly what we call languagemathics that the human brain operates on.

Operators, however, have nothing to do with mathematics. An operator occurs (takes a value) with respect to filters. In fact, it is the same element as the filter — labeled in the same way, but no longer representing mathematical values. Rather, those are letters that are meaningful per se.

With these elements, TAPe describes the very shift from mathematics to language and back again — exactly what we call languagemathics that the human brain operates on.

T-bit is a description utilizing a subset of maximally informative connected data elements. In TAPe, a unit of data accounts for far more meaningful information than in modern computers that use arrays of structurally disconnected figures (zeros and ones).