Prof Carlsson's (http://math.stanford.edu/~gunnar/ http://math.stanford.edu/~gunnar/) "Topology and Data" paper provides a good overview: http://www.ams.org/jou

Prof Carlsson's (http://math.stanford.edu/~gunnar/ http://math.stanford.edu/~gunnar/) "Topology and Data" paper provides a good overview: http://www.ams.org/journals/bull/2009-46-02/S0273-0979-09-01249-X/S0273-0979-09-01249-X.pdf http://www.ams.org/journals/bull/2009-46-02/S0273-0979-09-01... My recent dive into the literature has enlightened my thinking in terms of database and systems design. It has led me to think more in terms of properties, invariants, intervals, constraints, and dynamic fluidity -- "there are no things" (only actions and properties): https://edge.org/response-detail/11514 https://edge.org/response-detail/11514 Maybe the antiquated abstractions we have been using for database systems is what limits us. Maybe we need to stop thinking in terms of things -- objects, partitions, and static state -- and start thinking in terms of millions of fluid dynamic processes. Maybe Jim Starkey is on the right track: http://www.nuodb.com/about-us/jim-starkey http://www.nuodb.com/about-us/jim-starkey. Sussman seems to be converging there too -- see his talk "We Really Don't Know How to Compute" (http://www.infoq.com/presentations/We-Really-Dont-Know-How-To-Compute http://www.infoq.com/presentations/We-Really-Dont-Know-How-T...) and his work on the Propagator (https://github.com/ProjectMAC/propagators https://github.com/ProjectMAC/propagators). The rapid flow of data id stressing our system designs is making this more apparent, and we're starting to see stream processing systems emerge like Google Dataflow and Apache Flink. Ideas from functional programming and immutable state are looking more prescient. Now our database management systems need to evolve. "At no period in human culture have men understood the psychic mechanisms involved in invention and technology. Today it is the instant speed of electric information that, for the first time, permits easy recognition of the patterns and the formal contours of change and development. The entire world, past and present, now reveals itself to us like a growing plant in an enormously accelerated movie. Electric speed is synonymous with light and with the understanding of causes." — Marshal McLuhan, Understanding Media: The Extensions of Man (1964) 'okram's recent paper provides a new graph-based model for stateless functional flows that could be applied in other systems: See "Quantum Walks with Gremlin" (http://arxiv.org/pdf/1511.06278v1.pdf http://arxiv.org/pdf/1511.06278v1.pdf) And Vladimir Kornyak touches on some of these ideas in these papers: 1. On Compatibility of Discrete Relations (2005) http://arxiv.org/pdf/math-ph/0504048.pdf http://arxiv.org/pdf/math-ph/0504048.pdf 2. Structural and Symmetry Analysis of Discrete Dynamical Systems (2010) http://arxiv.org/pdf/1006.1754.pdf http://arxiv.org/pdf/1006.1754.pdf 3. Discrete Dynamical Models: Combinatorics, Statistics and Continuum Approximations (2015) http://mmg.tversu.ru/images/publications/2015-vol3-n1/Kornyak-2015-01-05.pdf http://mmg.tversu.ru/images/publications/2015-vol3-n1/Kornya...