Foundations of mathematicsFoundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics. In this latter sense, the distinction between foundations of mathematics and philosophy of mathematics turns out to be vague. Foundations of mathematics can be conceived as the study of the basic mathematical concepts (set, function, geometrical figure, number, etc.
Least-upper-bound propertyIn mathematics, the least-upper-bound property (sometimes called completeness or supremum property or l.u.b. property) is a fundamental property of the real numbers. More generally, a partially ordered set X has the least-upper-bound property if every non-empty subset of X with an upper bound has a least upper bound (supremum) in X. Not every (partially) ordered set has the least upper bound property. For example, the set of all rational numbers with its natural order does not have the least upper bound property.
Holonomic brain theoryHolonomic brain theory is a branch of neuroscience investigating the idea that human consciousness is formed by quantum effects in or between brain cells. Holonomic refers to representations in a Hilbert phase space defined by both spectral and space-time coordinates. Holonomic brain theory is opposed by traditional neuroscience, which investigates the brain's behavior by looking at patterns of neurons and the surrounding chemistry.
Undefined (mathematics)In mathematics, the term undefined is often used to refer to an expression which is not assigned an interpretation or a value (such as an indeterminate form, which has the possibility of assuming different values). The term can take on several different meanings depending on the context. For example: In various branches of mathematics, certain concepts are introduced as primitive notions (e.g., the terms "point", "line" and "plane" in geometry). As these terms are not defined in terms of other concepts, they may be referred to as "undefined terms".
Maximum sustainable yieldIn population ecology and economics, maximum sustainable yield (MSY) is theoretically, the largest yield (or catch) that can be taken from a species' stock over an indefinite period. Fundamental to the notion of sustainable harvest, the concept of MSY aims to maintain the population size at the point of maximum growth rate by harvesting the individuals that would normally be added to the population, allowing the population to continue to be productive indefinitely.
Spontaneous orderSpontaneous order, also named self-organization in the hard sciences, is the spontaneous emergence of order out of seeming chaos. The term "self-organization" is more often used for physical changes and biological processes, while "spontaneous order" is typically used to describe the emergence of various kinds of social orders in human social networks from the behavior of a combination of self-interested individuals who are not intentionally trying to create order through planning.
