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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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Never knew Tug-of-war can be this dangerous when the rope snaps and releases all its potential energy!
 
Tug-of-war (വടംവലി) is a dangerous game that has killed and maimed participants :-o

Source: https://what-if.xkcd.com/127/
Ignore simple physics and your appendage could be amputated by a tug of war rope.
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Joe Philip Ninan

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We don't say "I runned a marathon," but why not? Regardless of how they started, irregular verbs seem to persist, despite the continual influence of children, who prefer regular verbs. A new model shows that irregular verbs can continue based entirely on the interactions of speakers, and it also reproduces the observed patterns of regular and irregular verbs.
Interaction among speakers of a language may explain why frequently used verbs tend to remain irregular even as language evolves over generations.
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Yes. True
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Joe Philip Ninan

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A cute and adorable simulation of how racial / religious segregation are resulted from seemingly harmless small individual biases. (Based on Famous Game theorist, Thomas Schelling's work on Dynamic Models of  Segregation)

Also shows the importance of  active cultural demand for diversity, which can help in desegregating a society.
 
"Parable of the Polygons" is a playable post on how harmless choices can make a harmful world.
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A new improved 2nd law of thermodynamics

The 2nd law of thermodynamics says entropy increases.  This is a powerful and useful idea, because you can compute the entropy of different things, like different mixtures of chemicals, and use this idea to see which things can or cannot turn into which other things.  But is the 2nd law always true?  And if so, why?

People have studied this for over a century.  It's clear by now that the 2nd law is only true under certain conditions... which happen to include the conditions we usually see around us.  That's no coincidence.  These are the situations that allow for life as we know it!  

But the laws of physics allow for situations where entropy is very high and occasionally decreases for a short time, then comes back up... and also situations where entropy starts out high and decreases

In the second case, we can just stick a minus sign in our definition of time and save the 2nd law that way: now entropy increases.  The first situation can't be saved that way.  And even in our universe, there will be tiny patches that work like this: if you've got a box of gas in equilibrium, there will be tiny patches where by random fluctuations, entropy decreases for a little while. 

Can we prove theorems saying that under certain precise conditions, the 2nd law of thermodynamics is true?   Yes!   Boltzmann did it a long time ago, and by now there are several theorems like this.   These theorems are limited in their power - they haven't put an end to the mysteries surrounding the 2nd law.  But they're useful because they let us see what's the logic behind the 2nd law, and where are the loopholes. 

Theorems say "if X then Y".   This doesn't mean Y is always true.  It means that if you want Y to be false, you need X to be false too!

One loophole is that the 2nd law only applies to 'closed systems' - systems that don't interact with the rest of the world.  You can lower the entropy of an 'open system' by transferring entropy to the rest of the world.  That's what you're doing whenever you clean your room! That's what the guy in this cartoon should do.

My student +Blake Pollard has a new paper where he generalizes the 2nd law to certain open systems called open Markov processes.   They're like random walks where the walkers can walk in and out of the room.  Very roughly speaking, he shows that for these systems, entropy can only decrease if it flows out of the system.    But he's written a great blog article that explains it more clearly than I just did:

http://johncarlosbaez.wordpress.com/2014/02/16/relative-entropy-part-4/

Check it out!
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All games have rules and goals are counted only when those conditions are met! Every bottle has a volume as long as it does not leak out- closed systems are like that! Unfortunately, many theorems are used without considering the laws and those leads to the flaws! Normality in statistics is such a condition and many of the users do not bother about it at all!
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David Mumford has a new blog, and one of his first posts is about understanding Feynman path integrals in a finite-dimensional setting. I had seen a nice treatment of this topic that treats time and space as both being discrete, but this approach treats time as being continuous, and leads to a formula for exp(tH) for any matrix H.

  http://www.dam.brown.edu/people/mumford/blog/2014/FeynmanIntegral.html

I can't seem to find an RSS feed for this blog, though...
Like many pure mathematicians, I have been puzzled over the meaning of Feynman's path integrals and put them in the category of weird ideas I wished I understood. This year, reading Folland's excellent book Quantum Field Theory -- A Tourist Guide for Mathematicians, I got a glimmer of what was ...
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The power of Occam's Razor!
Recent Comments. Bunny on #250: Empiricist Man; chaospet on #248: The Ultimate Excuse; ben on #248: The Ultimate Excuse; chaospet on #250: Empiricist Man; E.L.F. on #250: Empiricist Man. Latest Comics. #250: Empiricist Man · #249: Robots… from Mars!! #248: The Ultimate Excuse · #247: Useless ...
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Hahaha! This is awesome! Resharing it!
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The number of children living at the al-Amal Institute for Orphans has nearly doubled since the 2014 war.
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+Ninan Sajeeth Philip That would have been a real surprise for all of us, missed it we would have been happy to meet you better luck next time

Happy journey back Take care 
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More on math of segregation...
 
The Maths of Segregation

A lot of people today are playing this excellent game by +Vi Hart  and Nicky Case: http://ncase.me/polygons/

It very clearly shows how even low levels of racial intolerance among citizens can cause high levels of segregation to emerge in the city.

The appeal of the game is that it's so simple. It's based on an equally simple model of segregation devised by the economist Thomas Schelling, which as it happens, I have spent the last year or so studying in some detail with my collaborators +George Barmpalias and +A.E.M. Lewis .

We've made several interesting findings, including the fact that in a particularly simple version of the model, making the citizens more tolerant can actually cause higher levels of segregation to emerge.

How? I explain it in this blog-post:
http://richardelwes.co.uk/2013/06/18/schelling-segregation-part-2/

(H/T +Matthew Daws who was the first of several people to point me towards the polygon game.)
I talked in Part 1 about a model of racial segregation devised by Thomas Schelling in 1969 [original pdf]. This post will describe how the model works, in its simplest 1-dimensional incarnation, and what we've discovered about it. (I hope this post is also accessible to everyone, ...
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Ramanujan's nested radical

In 1911, the mathematician Srinivasa Ramanujan (1887–1920) posed a problem in the Journal of the Indian Mathematical Society: to find the value of the radical expression √(1 + 2√(1 + 3√(1 + ...))). After six months, nobody had been able to solve the problem, so Ramanujan revealed the surprisingly simple answer, which is 3.

One strategy that mathematicians sometimes use when they are struggling to solve a problem is to generalize the problem. This sounds like a counterintuitive thing to do, but it is useful in this situation, as follows.

Define the function f(x) = x + n + a, where n and a are numbers. It can be easily checked that f(x)^2 = ax + (n+a)^2 + x(f(x+n)), because both sides of the equation are equal to x^2 + n^2 + a^2 + 2an + 2ax + 2nx. Taking square roots of each side shows that f(x) = √(ax + (n+a)^2 + xf(x+n)). This expression also gives a formula for f(x+n), which can then be substituted into the right hand side of the expression for f(x). Doing this recursively and then setting x=2, n=1 and a=0 gives the required identity, because f(2)=3.

This sketch of a proof has some loose ends. For example, the square roots are intended to be positive square roots, and it is not completely clear that the infinite expression given converges to 3 in any reasonable sense. However, the convergence turns out to be fast, as +John Cook demonstrated in a blog post from last year: http://www.johndcook.com/blog/2013/09/13/ramanujans-nested-radical/

In the same 1911 journal contribution, Ramanujan asked another similar question about nested radicals. This turned out to be the case x=2, n=1, a=1 of the same identity, which results in a nested radical expression that evaluates to 4. Ramanujan made a total of 58 such contributions to the Journal of the Indian Mathematical Society, including the famous Rogers–Ramanujan identities.

Relevant links
The 2005 paper On Ramanujan's nested roots expansion by K. Srinivasa Rao and G. Vanden Berghe explores this identity and some related results in detail: http://zariski.files.wordpress.com/2010/05/sr_nroots.pdf

Wikipedia on nested radicals: http://en.wikipedia.org/wiki/Nested_radical

Wikipedia on the Rogers–Ramanujan identities: http://en.wikipedia.org/wiki/Rogers–Ramanujan_identities

My post from Pi Day about Ramanujan's approximation to π: https://plus.google.com/101584889282878921052/posts/74oomcTuJoV

(Found via Cliff Pickover on Twitter.)

#mathematics #scienceeveryday  
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Joe Philip Ninan

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The flight path taken by Rosetta from launch to landing on the comet.

We are mindbogglingly good at orbital mechanics.  I imagine some small course corrections were applied en route, but even so, it does seem a little like firing a rifle in LA and hitting a target in New York, while requiring that course correction can only be done by people breathing on the bullet as it whizzes past.
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Landing on Moon, Mars, Venus, Titan, asteroid and now soft landing on a comet by harpooning it! We humans surely are living in interesting times !!

Attached, is a picture of the comet 67P/C-G taken by Rosetta two months ago,
The small rock pieces on the comet looks like stuffs clinging on to a big magnet! It is really magical to actually see such a real world example of  irregular gravitational field!

ESA has also made a series of cute cartoons on the mission, which are very entertaining, #arewethereyet  
Links to the videos of the series are given below.

#WakeUpRosetta -- Once upon a time...

Are we there yet?

#RosettaAreWeThereYet - Once upon a time...

#RosettaAreWeThereYet – Fabulous fables and tales of tails

Preparing for #CometLanding

Comets hold the keys to unlock the mysteries of our solar system's origins. Eagerly waiting for science results..
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  • Tata Institute of Fundamental Research
    2010 - present
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