posted by
n1
on Tuesday July 07 2015, @05:55AM
from the a-taurus-is-not-a-torus-but-it-can-make-donuts-in-a-car-park dept.
from the a-taurus-is-not-a-torus-but-it-can-make-donuts-in-a-car-park dept.
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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Solving Problems in Robotics and Sensor Networks with Algebraic Topology
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(Score: 2, Funny) by Anonymous Coward on Tuesday July 07 2015, @06:11AM
Unconventional mathematician loves money and secretly yearns to work in quantitative finance instead of algebraic topology.
(Score: -1, Spam) by Anonymous Coward on Tuesday July 07 2015, @07:00AM
Let me see your sack! I know the drippin'ness is coming from you, and it's driving me insanyoly! You're the one who possesses the papoohiesack. It'll only take me a second to check your sack...
(Score: 2) by MichaelDavidCrawford on Tuesday July 07 2015, @06:43AM
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.
Yes I Have No Bananas. [gofundme.com]
(Score: 0) by Anonymous Coward on Tuesday July 07 2015, @07:04AM
But what does the milk from a spherical cow taste like?
(Score: 2) by cafebabe on Saturday July 18 2015, @02:44PM
At a guess, the milk from a spherical cow would taste smooth.
1702845791×2
(Score: 2) by c0lo on Tuesday July 07 2015, @07:38AM
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.
https://www.youtube.com/watch?v=aoFiw2jMy-0 https://soylentnews.org/~MichaelDavidCrawford
(Score: 0) by Anonymous Coward on Tuesday July 07 2015, @08:07AM
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
Err...its. Dammit Jim I'm a physicist not a writer!
(Score: 2) by c0lo on Tuesday July 07 2015, @10:31AM
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.
https://www.youtube.com/watch?v=aoFiw2jMy-0 https://soylentnews.org/~MichaelDavidCrawford
(Score: 0) by Anonymous Coward on Tuesday July 07 2015, @02:55PM
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
???? Have some links, please?
https://www.youtube.com/watch?v=aoFiw2jMy-0 https://soylentnews.org/~MichaelDavidCrawford
(Score: 5, Funny) by KritonK on Tuesday July 07 2015, @07:52AM
What difference? Coffee cups and doughnuts are homeomorphic [wikipedia.org] surfaces with a genus [wikipedia.org] of one. Even I know that, and I'm not a mathematician!
(Score: 2) by Dr Spin on Tuesday July 07 2015, @10:10AM
The difference is: <drum roll> Coffee on the nuts or not!
Warning: Opening your mouth may invalidate your brain!
(Score: 3, Funny) by FatPhil on Tuesday July 07 2015, @10:45AM
Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
(Score: 0) by Anonymous Coward on Tuesday July 07 2015, @02:59PM
Neither the coffee cup nor the doughnut is a surface. Both are solid bodies with a non-empty interior. Although I'm not sure whether they are open or closed sets.
(Score: 2, Informative) by khallow on Tuesday July 07 2015, @07:07PM
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.
(Score: 2, Interesting) by khallow on Tuesday July 07 2015, @07:13PM
(Score: 2, Interesting) by khallow on Tuesday July 07 2015, @07:32PM