Social media, e-commerce, streaming video, e-mail, cloud documents, web pages, traffic flows, and network packets fill vast digital lakes, rivers, and oceans that we each navigate daily. This digital hyperspace is an amorphous flow of data supported by continuous streams that stretch standard concepts of type and dimension. The unstructured data of digital hyperspace can be elegantly represented, traversed, and transformed via the mathematics of hypergraphs, hypersparse matrices, and associative array algebra. This paper explores a novel mathematical concept, the semilink, that combines pairs of semirings to provide the essential operations for graph analytics, database operations, and machine learning. The GraphBLAS standard currently supports hypergraphs, hypersparse matrices, the mathematics required for semilinks, and seamlessly performs graph, network, and matrix operations. With the addition of key based indices (such as pointers to strings) and semilinks, GraphBLAS can become a richer associative array algebra and be a plug-in replacement for spreadsheets, database tables, and data centric operating systems, enhancing the navigation of unstructured data found in digital hyperspace.

中文翻译：

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数字超空间数学

社交媒体，电子商务，流视频，电子邮件，云文档，网页，流量和网络数据包充满了我们每天都在浏览的广阔的数字湖泊，河流和海洋。数字超空间是由连续流支持的无定形数据流，这些流扩展了类型和尺寸的标准概念。数字超空间的非结构化数据可以通过超图，超稀疏矩阵和关联数组代数的数学方法优雅地表示，遍历和转换。本文探讨了一种新颖的数学概念，即半链接，该半链接结合了成对的半环，以提供用于图形分析，数据库操作和机器学习的基本操作。GraphBLAS标准目前支持超图，超稀疏矩阵，半链接所需的数学模型，并无缝执行图，网络和矩阵运算。通过添加基于键的索引（例如指向字符串的指针）和半链接，GraphBLAS可以成为更丰富的关联数组代数，并可以替代电子表格，数据库表和以数据为中心的操作系统，从而增强了非结构化数据的导航在数字超空间中找到。