Lie detection One recent instrument using cognitive chronometry for this purpose is the timed antagonistic response alethiometer, or TARA. Brain-reading uses fMRI and the multiple voxels activated in the brain evoked by a stimulus to determine what the brain has detected, and so whether it is familiar. People often evaluate lies based on non-verbal behavior, but are quick to place too much merit in misleading indicators, such as: avoidance of eye contact, increased pauses between statements, and excessive movements originating from the hands or feet. Non-invasive lie detection using non-verbal behavior is performed by the Silent Talker Lie Detector. Silent Talker monitors
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