Topology Is Finally on Top
December 21, 2015
Topology’s time has finally come, according to “The Unreasonable Usefulness of Imagining You Live in a Rubbery World,” shared by 3 Quarks Daily. The engaging article reminds us that the field of topology emphasizes connections over geometric factors like distance and direction. Think of a subway map as compared to a street map; or, as writer Jonathan Kujawa describes:
“Topologists ask a question which at first sounds ridiculous: ‘What can you say about the shape of an object if you have no concern for lengths, angles, areas, or volumes?’ They imagine a world where everything is made of silly putty. You can bend, stretch, and distort objects as much as you like. What is forbidden is cutting and gluing. Otherwise pretty much anything goes.”
Since the beginning, this perspective has been dismissed by many as purely academic. However, today’s era of networks and big data has boosted the field’s usefulness. The article observes:
“A remarkable new application of topology has emerged in the last few years. Gunnar Carlsson is a mathematician at Stanford who uses topology to extract meaningful information from large data sets. He and others invented a new field of mathematics called Topological data analysis. They use the tools of topology to wrangle huge data sets. In addition to the networks mentioned above, Big Data has given us Brobdinagian sized data sets in which, for example, we would like to be able to identify clusters. We might be able to visually identify clusters if the data points depend on only one or two variables so that they can be drawn in two or three dimensions.”
Kujawa goes on to note that one century-old tool of topology, homology, is being used to analyze real-world data, like the ways diabetes patients have responded to a specific medication. See the well-illustrated article for further discussion.
Cynthia Murrell, December 21, 2015