Lie great number of lies, depending on how the political wind blows." The question of whether lies can reliably be detected through nonverbal means is a subject of some controversy. Polygraph "lie detector" machines measure the physiological stress a subject endures in a number of measures while he/she gives statements or answers questions. Spikes in stress are purported to indicate lying. The accuracy of this method is widely disputed, and in several well-known cases it was proven to have been deceived. Nonetheless, it remains in use in many areas, primarily as a method for eliciting confessions or employment screening. Polygraph results
Lie group symmetries include rotation about an axis. What must be understood is the nature of 'small' transformations, for example, rotations through tiny angles, that link nearby transformations. The mathematical object capturing this structure is called a Lie algebra (Lie himself called them "infinitesimal groups"). It can be defined because Lie groups are smooth manifolds, so have tangent spaces at each point. The Lie algebra of any compact Lie group (very roughly: one for which the symmetries form a bounded set) can be decomposed as a direct sum of an abelian Lie algebra and some number of simple ones. The structure of