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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) by MichaelDavidCrawford on Tuesday July 07 2015, @06:43AM

    by MichaelDavidCrawford (2339) Subscriber Badge <mdcrawford@gmail.com> on Tuesday July 07 2015, @06:43AM (#206006) Homepage Journal

    His Calculus course is quite difficult as he teaches integration first as that was how it developed historically.

    Or rather, he teaches integration first because he enjoys the sight of students passing out in class every friday morning when problem sets were due.

    It is not hard at all to derive newton's law of gravity from kepler's law of planetary motion. It seems reasonable that a spherical planet will have the same gravity as a point paricle of the same mass but newton required twenty years to actually prove it.

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  • (Score: 0) by Anonymous Coward on Tuesday July 07 2015, @07:04AM

    by Anonymous Coward on Tuesday July 07 2015, @07:04AM (#206009)

    But what does the milk from a spherical cow taste like?

    • (Score: 2) by cafebabe on Saturday July 18 2015, @02:44PM

      by cafebabe (894) on Saturday July 18 2015, @02:44PM (#210778) Journal

      At a guess, the milk from a spherical cow would taste smooth.

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  • (Score: 2) by c0lo on Tuesday July 07 2015, @07:38AM

    by c0lo (156) Subscriber Badge on Tuesday July 07 2015, @07:38AM (#206019) Journal

    It seems reasonable that a spherical planet will have the same gravity as a point paricle of the same mass but newton required twenty years to actually prove it.

    And it took some other years to Einstein to prove it doesn't - if you have a massive but small enough particle, you'd be dealing with a blackhole with a singularity at it centre.

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    • (Score: 0) by Anonymous Coward on Tuesday July 07 2015, @08:07AM

      by Anonymous Coward on Tuesday July 07 2015, @08:07AM (#206029)

      Which would have the same mass, therefore same gravitational pull. Just because there is less space being taken up by the same mass does not make gravitational forces on other objects increase. If it were so, then a compressing a marshmallow would increase it's weight.

      • (Score: 1, Funny) by Anonymous Coward on Tuesday July 07 2015, @08:22AM

        by Anonymous Coward on Tuesday July 07 2015, @08:22AM (#206035)

        Err...its. Dammit Jim I'm a physicist not a writer!

      • (Score: 2) by c0lo on Tuesday July 07 2015, @10:31AM

        by c0lo (156) Subscriber Badge on Tuesday July 07 2015, @10:31AM (#206053) Journal

        Which would have the same mass, therefore same gravitational pull.

        Outside. It is the centre of a blackhole where the singularity will lay.
        That's unlike the baricentre of a non-blackhole object, where the (integrated over the whole object volume) gravitational pull is zero.

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        • (Score: 0) by Anonymous Coward on Tuesday July 07 2015, @02:55PM

          by Anonymous Coward on Tuesday July 07 2015, @02:55PM (#206130)

          But for orbital mechanics, it doesn't matter what happens inside an object. All the planets are outside the sun and outside each other, and also the moons are outside their planets, and so on.

          Now strictly speaking, if what happens inside the object is asymmetric, it does matter; however for the planetary motion, the distance is so much larger than the size that you can neglect even that.

          Now what does matter is that gravitation is not exactly an 1/r² force even outside a perfectly spherical mass. As evidenced by the perihelion precession of Mercury.

          • (Score: 2) by c0lo on Tuesday July 07 2015, @09:36PM

            by c0lo (156) Subscriber Badge on Tuesday July 07 2015, @09:36PM (#206231) Journal

            Now what does matter is that gravitation is not exactly an 1/r² force even outside a perfectly spherical mass

            ???? Have some links, please?

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