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Joe Philip Ninan
Works at Tata Institute of Fundamental Research
Lives in Mumbai
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Joe Philip Ninan

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Inverse cube force law

Here you see three planets.  The blue planet is moving around the Sun in a realistic way: it's going around an ellipse.

The other two are moving in and out just like the blue one, so they all stay on the same circle, which shrinks and expands.  But they're moving around this circle more slowly.   In fact the red planet isn't going around at all: it only goes in and out!

In 1687, Isaac Newton published his famous book, the Principia Mathematica.  And one thing he did here is figure out what extra force, besides gravity, would make it move like these weird other planets.

According to Newton, gravity obeys an inverse square force law.  For example, if you move a planet 3 times as far from the Sun, it feels a force that's 1/9 as strong.  Figuring this out and using this to explain the motion of planets is one reason Newton is so famous.

But he also showed that if you add an extra force obeying an inverse cube law, and adjust the angular momentum of your planet, you can make it planet move in and out just as it did before... but make it move around at a different rate!  

This goes to show that Newton had intelligence to spare.  He didn't just solve the important problems that made him famous, he also had lots of minor ideas that still required amazing cleverness.

And turns out this strange fact he discovered is just one of several weird and fascinating things about the inverse cube force law.  For example, the so-called 'centrifugal force' obeys an inverse cube law.  It's not a real force; it's sometimes called a 'fictious force'.  But you can still describe it using an inverse cube law, and this ultimately explains Newton's discovery.

And a quantum particle in an inverse cube force behaves in a truly bizarre way, which people have been struggling to understand for decades.  If you think you understand quantum mechanics, this may make you reconsider.

I recently learned a lot about these things while writing a chapter for a book called New Spaces for Mathematics and Physics.

Why?  Well, it's a long story.   I've decided that most of what I learned doesn't belong in this paper.  But I had to write it down before I forgot it!  So I wrote this blog article:

https://johncarlosbaez.wordpress.com/2015/08/30/the-inverse-cube-force-law/

Go there if you're curious for more. 

Puzzle: how many times does the blue planet orbit the Sun for each time the green one does?

The animation was made by ‘WillowW’ and placed on Wikicommons:

If you can make a version of this animated gif that takes less than 1 megabyte, I can feature it on Visual Insight and credit you!

But the one I really want has a green planet going faster than the blue one.  It's here:

https://en.wikipedia.org/wiki/File:Newton_revolving_orbit_3rd_harmonic_e0.6_240frames_smaller.gif
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Joe Philip Ninan

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I'm quite hopeful that Internet will one day save science from the current ugly system of paper journals. Github like collaborate research networks is how future science should be done, replicated, discussed and published.
 
If a scientist is judged by the quality of research and not the results of that research, the final moment of publishing a paper becomes less important.
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Functional Composition

I was first introduced to the beautiful structural layer of symmetries in canon music from the famous GEB book by Douglas Hofstadter.

This talk by Chris Ford, combines the power of Lisp family languages, and  structures in Bach's famous crab canon.
This is a match made in heaven of all things beautiful!

h/t to Harshant Singh
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I was inspired to think differently when I read Barbara Ehrenreich's Nickel and Dimed in America. If you don't have time for the book, read this Atlantic article, which brings the story up to date. I love her notion that minimum wage workers are philanthropists, giving their work to the rest of society for less than it costs to provide.
Minimum-wage jobs are physically demanding, have unpredictable schedules, and pay so meagerly that workers can't save up enough to move on.
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A great quote from what I found to be a very interesting article:

Tao now believes that his younger self, the prodigy who wowed the math world, wasn’t truly doing math at all. ‘‘It’s as if your only experience with music were practicing scales or learning music theory,’’ he said, looking into light pouring from his window. ‘‘I didn’t learn the deeper meaning of the subject until much later.’’
A prodigy grows up to become one of the greatest mathematicians in the world.
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Four and a half years of violent conflict have destroyed entire regions of Syria. Caught in the middle of all this horror are the children of Syria, relying on parents who have lost control of their own lives and are now being forced to make difficult choices in desperate circumstances.
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In case of Syria, I don't know any way we can help. But what these photos portray is true story of every single war on earth. Especially those fought in areas where civilians live. I hope these kind of photo journalism as well as social media will help in lifting the abstract cold feeling people have when they hear about wars in distant countries. Hopefully in future humanity will stop glorifying wars and move on to more peaceful coexistence strategies!
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Convincing 1 out of 6 people on this earth to click the "I agree" button to forsake all my privacy! Now that is an unparalleled achievement in human history!
 
A million users isn’t all that cool. You know what’s cool? One billion users.
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True, no doubt google knows a lot more, thanks to gmail!
Problem with facebook is that, they give data to third party advertising companies. Google atleast claims they don't do that in their ads.
My major issue with fb is that, their network is too big. When one company has a graph which shows how almost 99 % of the Internet users are connected to each other, it is impossible for the remaining 1% to find something anonymously on internet (especially if the content is in fb).
No matter how anonymously we create an account in fb, accidentally typing name of two persons or two fb group pages is typically enough for fb to interpolate the graph and identify who the anonymous user is.
Which is scary, since more and more people are putting useful content/discussions in fb pages instead of good old emails/blogs.
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This is a great explanation of why the train is always late, the plane is always too full, and why everyone else has more friends.
The following is a draft of an article I have submitted for publication in CHANCE Magazine, a publication of the American Statistical Association. With their encouragement, I am publishing it here to solicit comments from rea...
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Issued in the public interest of Astronomers!

Credits: Original Infographics taken from :http://visual.ly/circles-hell-dantes-inferno (Durasova et. al)

Edited in Gimp
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The Blender Institute folks keep cranking out some gorgeous results... 

#foss   #blender   #3D   #animation  
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  • Tata Institute of Fundamental Research
    2010 - present
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