Interactive Mathematical Visualization

这是一项为期两年的持续资助的第一年。这项研究的一个长期目标是开发和利用技术，使科学家能够研究和解决数学和物理中没有自动化辅助就无法进行的问题。另一个长期目标是推导出关于人类能力的性质以及在精神上参与抽象数据空间的限制的一般原则。将智能约束交互(基于规则)方法与半自动优化技术相结合，开发出一种领域无关的约束交互系统。这个系统将被设计成允许操纵作为不可观测对象的变换的对象，这些对象在概念上是难以理解的数学特性。将不可观测对象转换为可操作可观测对象的模拟对于开发人类学习过程来掌握抽象问题是有用的。抽象的概念包括相对大小和速度估计、不熟悉的维度、物理中的混沌过程以及多体问题中的相互作用。对表示的依赖于域的约束被用来形成所需的一类空间配置的模型。这导致了一种合理的自动化方法。还将研究对对象的直接、上下文无关的操纵，而不是对对象的操纵，而不是对相应的代理“控制”对象的操纵。这一努力试图为理解人类通过抽象概念的视觉表征进行心理参与的能力奠定基础。这将作为后续视觉心理物理理论实验的基础。//

This is the first year of a two year continuing grant. One long-term goal of this research is to develop and exploit techniques to make it possible for scientists to study and solve problems in mathematics and physics that could not be undertaken without automated assistance. Another long term goal is to deduce general principles about the nature of human capabilities and limitations in mental engagement with abstract data spaces. intelligent constraint-based interaction (rule-based) methods will be combined with semi-automated optimization techniques develop a domain-independent interactive system of constraints. This system will be designed to allow manipulation of objects that are transforms of non-observables which are conceptually difficult mathematical properties. Simulations that transform non-observables into manipulatable observables are useful to exploit human learning processes to master abstract problems. The abstract concepts range from issues of relative size and speed estimation, unfamiliar dimensions, and chaotic processes in physics and interactions in many-body problems. Domain-dependent constraints on representations are used to form a model of a desired class of spatial configurations. This leads to a rational automation methodology. Direct, context-free manipulation of objects, rather than manipulation of objects, rather than manipulation of corresponding surrogate "control" objects, will also be examined. This effort seek to lay a foundation for understanding human capacity for mental engagement with visual representations of abstract concepts. This will be useful as a basis for subsequent experiments on psychophysical theories of visualization.//