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Solving Problems in Robotics and Sensor Networks with Algebraic Topology

posted by n1 on Tuesday July 07 2015, @05:55AM   Printer-friendly
from the a-taurus-is-not-a-torus-but-it-can-make-donuts-in-a-car-park dept.

hellcat writes:

Topology isn't for everyone, but knowing the difference between your coffee cup and a doughnut is an essential workplace skill.

However, algebraic topology may be closer to us than you think. Drones, self-driving cars, and semi-autonomous AI are going to need it. And if you code, you're going to have to understand it. A little.

Unconventional mathematician Robert Ghrist rejects his field's "hippie aesthetic" in favor of suits and ties, loves medieval literature, reversed the usual way of teaching calculus in his popular MOOC, and is using one of mathematics' most abstract disciplines—algebraic topology—to solve real-world problems in robotics and sensor networks.

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  • (Score: 2, Informative) by khallow on Tuesday July 07 2015, @07:07PM

    by khallow (3766) Subscriber Badge on Tuesday July 07 2015, @07:07PM (#206196) Journal

    Neither the coffee cup nor the doughnut is a surface. Both are solid bodies with a non-empty interior.

    This is an important point. There are topologically distinct objects with the boundary of a torus (for example, the doughnut and a nontrivial knot bulked up with a little third dimension).

    Although I'm not sure whether they are open or closed sets.

    Depends precisely on whether you completely exclude the boundary or completely include it.

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  • (Score: 2, Interesting) by khallow on Tuesday July 07 2015, @07:13PM

    by khallow (3766) Subscriber Badge on Tuesday July 07 2015, @07:13PM (#206197) Journal
    For your edification, the knotted doughnut [thrillist.com] and the knotted coffee cup [etsy.com]. Now we have the knotting technology to safely distinguish between a coffee cup and a doughnut.