Traditionally, Euclidean geometry is treated by scientists as a priori and objective. However, when we take the position of an agent, the problem of selecting a best route should also factor in the abilities of the agent, its embodiment and particularly its cognitive effort. In this paper we consider geometry in terms of travel between states within a world by incorporating information processing costs with the appropriate spatial distances. This induces a geometry that increasingly differs from the original geometry of the given world as information costs become increasingly important. We visualise this "cognitive geometry" by projecting it onto 2- and 3-dimensional spaces showing distinct distortions reflecting the emergence of epistemic and information-saving strategies as well as pivot states. The analogies between traditional cost-based geometries and those induced by additional informational costs invite a generalisation of the notion of geodesics as cheapest routes towards the notion of infodesics. In this perspective, the concept of infodesics is inspired by the property of geodesics that, travelling from a given start location to a given goal location along a geodesic, not only the goal, but all points along the way are visited at optimal cost from the start.
翻译:传统上,欧几里德的几何学被科学家视为一种先验性和目标。然而,当我们选择一个代理人的位置时,选择一条最佳路线的问题也应该考虑到该代理人的能力、其外形和特别是其认知努力。在本文中,我们通过结合信息处理成本和适当的空间距离来考虑世界国家间旅行的几何学。这引出了一种随着信息成本变得日益重要而日益不同于特定世界原始几何学的几何学。我们通过投射到2和3维空间,显示明显扭曲,反映成象和信息节约战略的出现以及主轴状态。传统的基于成本的几何形学与因额外信息成本而引发的几何行之间的相似之处,使得对大地学概念的概括化成为通向科学学概念的最廉价的路径。 从这个角度看,信息学概念的灵感来自从一个特定起始地点到一个特定目标地点的地学特性,从一个最佳的目标开始,从一个最高的目标开始,而是从所有到一个最高的成本开始。