Robson Barry
Group for Advanced Methods in Epidemiology and Statistics, St. Matthew's University School of Medicine, Grand Cayman, UK.
Stud Health Technol Inform. 2009;149:236-48.
Quantum mechanics (QM) provides a variety of ideas that can assist in developing Artificial Intelligence for healthcare, and opens the possibility of developing a unified system of Best Practice for inference that will embrace both QM and classical inference. Of particular interest is inference in the hyperbolic-complex plane, the counterpart of the normal i-complex plane of basic QM. There are two reasons. First, QM appears to rotate from i-complex Hilbert space to hyperbolic-complex descriptions when observations are made on wave functions as particles, yielding classical results, and classical laws of probability manipulation (e.g. the law of composition of probabilities) then hold, whereas in the i-complex plane they do not. Second, i-complex Hilbert space is not the whole story in physics. Hyperbolic complex planes arise in extension from the Dirac-Clifford calculus to particle physics, in relativistic correction thereby, and in regard to spinors and twisters. Generalization of these forms resemble grammatical constructions and promote the idea that probability-weighted algebraic elements can be used to hold dimensions of syntactic and semantic meaning. It is also starting to look as though when a solution is reached by an inference system in the hyperbolic-complex, the hyperbolic-imaginary values disappear, while conversely hyperbolic-imaginary values are associated with the un-queried state of a system and goal seeking behavior.
量子力学（QM）提供了多种理念，有助于开发用于医疗保健的人工智能，并开启了开发一个统一的最佳实践推理系统的可能性，该系统将涵盖量子力学和经典推理。特别值得关注的是双曲复平面中的推理，它是基本量子力学中正常i复平面的对应物。原因有两个。首先，当对作为粒子的波函数进行观测时，量子力学似乎从i复希尔伯特空间旋转到双曲复描述，从而产生经典结果，此时经典的概率运算定律（例如概率合成定律）成立，而在i复平面中它们并不成立。其次，i复希尔伯特空间并非物理学的全部内容。双曲复平面出现在从狄拉克 - 克利福德演算到粒子物理学的扩展中，在相对论修正中，以及在旋量和扭曲子方面。这些形式的推广类似于语法结构，并促进了这样一种观点，即概率加权代数元素可用于容纳句法和语义意义的维度。看起来当一个推理系统在双曲复平面中得出解决方案时，双曲虚数值会消失，而相反，双曲虚数值与系统的未查询状态和目标寻求行为相关联。
