LearnNBlog: Fermat's Last Theorem

Recently read a news article about Prof. Andrew Wiles being awarded the Abel prize for his proof of Fermat's Last Theorem. I had first come across Fermat's Last Theorem in one of my mathematics textbooks in school. Apart from the various numbers and equations, each chapter had trivia about mathematicians. 

This was the theorem proposed by the French mathematician Pierre de Fermat in 1637. In the margins of the his copy of Diophantus's Aritmetica, he had left the following words 

"But it is impossible to divide a cube into two cubes, or a fourth power into two fourth powers, or generally any power beyond squares into like powers; of this I have found a remarkable demonstration. This margin is too narrow to contain it."

Enigmatic words, indeed!

For over 300 years, mathematicians across the world struggled with finding a proof of Fermat's last theorem. Empirical evidence could not disprove it either. But no proof could be found. The search for a proof of Fermat's Last Theorem became the quest for the Holy Grail for mathematicians. Many awards were announced for the person who cracked it. But Fermat's remarkable demonstration was not found since. In fact, it was thought that with the current available knowledge this theorem could just not be proved (or disproved).

In 1993, Prof. Andrew Wiles announced his proof of the theorem. However, soon after, an error was found in his proof. But Prof. Wiles was not to be deterred. He reworked and came back with a new proof, a year later. This proof was compiled over 150 pages and took in developments in mathematics from the 20th century (which would not have been  available to Fermat).

For his discovery of the proof of Fermat's last Theorem, Prof. Wiles was awarded the Abel Prize (considered to the Mathematics equivalent of Nobel prize) in 2016.

Prof. Wiles's proof was over 150 pages long, which explains why Fermat couldn't fit it in the margins of Arithmetia. Or maybe there is a simpler proof out there, which even the best minds have of the past four centuries haven't been able to resolve.

References

Fermat's Last Theorem (Wikipedia)

Prof. Wiles' Solution (Wikipedia)

The News Article on Abel Prize (The Hindu) 

P.S. With this post, starting a new section in the blog title "LearnNBlog", incorporating interesting (for me at least) learnings.

300

300 !!! This is the 300th post on this blog. So writing this "short" blogpost about the blog to mark the occasion.

Nishantzworld is now in its 10th year of existence. Did I ever think that the blog would still be running after nearly a decade? The honest answer would be "No". But it has survived taking its own course, going along with the times. Sometimes rapidly churning out posts, sometimes idling for a while. But the journey of the blogposts have continued. After all there is no dearth of topics to write about and the blog has churned out posts on almost everything under the Sun covering a whole gamut of subjects like movies, books, travel, politics, sports, social causes, industry news etc. 

The journey has seen its own little step changes. The appearance has changed dramatically from a s simple background to a white one with posts now popping out. Meanwhile the content has also gone through changes. Cricket, which initially provided bulk of the posts, has now its own separate platform, Slipstream Cricket. There is a dedicated MovieNotes section for reviewing Movies, while reviews of books find a place under BookMarks (or basically me showing off what I have been reading). There have been plans to include travel related posts under one heading, but it hasn't taken off yet. While photography has found a better platform on Instagram.

And now for the Fab 5, a list of my favorite posts from blogs #201-299, in chronological order. (An exercise which I had also done for my 100th & 200th posts as well).

• MovieNotes: Zalzala - Review of an old movie which I ended up watching one fine Sunday evening. My personal favorite MovieNotes till date.
• Rahul Speaks to Arnab - The one time I had to do a live blog. After all this was the event of the 2014 General elections.
• A Very Responsible Blogpost - Written (or not) with malice towards none. Even truer in our current "intolerant" times.
• Battle of the Bulge - Me showing off that I could complete a month long exercise regime.
• Falling Crude Prices - Turbulent times for the industry, and a more work-related post. How was I to know that this was still the beginning only and one year down the line things would be worse off. 

Hopefully, the blog continues towards Brian Lara's mark now. Once again, thanks to all the readers whose encouragement at different times have kept this blog going.

Cleaning the Augean Stables: Patna

As per Greek mythology, one of the labours of Hercules was cleaning the stables of King Augeas. The King owned thousands of heads of cattle, horses and goats. Every night they would be driven into a stable. which had become really filthy. Hercules managed to clean the place by diverting a river which flowed nearby through the stables and cleaned up the entire place in one go.

As part of the the ongoing Swachh Bharat Abhiyaan launched by our Prime Minister, a Swachh Survekshan has been conducted. The results are out and Patna comes out right near the bottom of this survey, ranked 70th out of 73 cities covered under the survey. The results are as expected. It just confirms what we already knew. The city lags behind on every single parameter covered in the survey (Details). 

On a recent trip to the city, found it filled with filth. Rubbish was thrown all around, there are open drains filled to the brim and mostly choked. All kinds of animals cows, buffaloes, dogs, chicken, ducks, goats were roaming around and eating from the same piles of garbage. Except for the modern cars plying on lanes meant for 2-wheeler's and bullock carts, it almost seemed as if the city was still living a couple of centuries behind the rest of the urbanized world, especially in matters of hygiene.

Below are few sample pictures from my recent trip.

(a) Housing complexes surrounded by standing water; (b) Cows munching in the garbage filled roads; (c) Unlit lanes; (d) Crumbling buildings - In all a picture of  complete squalor

Cleaning up Patna would be no less than the labour of cleaning the Augeon Stables. But we can't depend on a single Hercules to the task. A filthy garbage riddled city is not a unique problem. Most of the big European cities were in equally bad shape in the 19th and early 20th century. Urbanization had brought with it problems of waste management.  Lee Jackson's book "Dirty Old London" describes the state of squalor in London. London was described as having choking, sooty fogs; the Thames River was thick with human sewage; and the streets were covered with mud. (Sounds familiar). The book goes on to describe how the city came up with its innovations and fought its way towards cleanliness.

This is not just a European phenomenon. Though it is hard to imagine now, Singapore was equally, if not more filthy under the British rule (Singapore Sanitation). But the initiatives undertaken by former PM Lee Kuan Yew transformed it into one of cleanest countries in the world. The Singapore model was adopted by other developing South East Asian countries. It requires strong political leadership, public infrastructure development and strict implementation of rules to make the program a success.

Given Patna's size and population, the solutions would need to be even larger in scale.It is not as if nothing has been done in this regard. Patna has provided leadership in this regard earlier also. Dr. Bindeshwar Pathak and his foundation Sulabh International were the original Swachh Bharat Abhiyaan campaigners. The work done by Sulabh in building sanitation systems has been globally recognized. However, we can certainly do with more such sustained campaigns for cleaning up this mess. 

An example can be taken from the city which ranked bottom of the survey, Dhanbad (another place where I have a personal connect). Post the results, the students of my alma mater have decided to take up the matter in their own hands. A waste management start-up called Total Waste Solutions or ToWaSo has been launched by the Centre for Innovation, Incubation and Entrepreneurship at ISM, which is working on the theme 'Utilize the Waste before it gets Wasted'. 

More such schemes would be needed. Only a joint effort by the administration and the citizens can accomplish this seemingly Herculean task of cleaning up the city. It is possible. There are parts of the city, the so called VIP areas which are models of cleanliness with no garbage dumps and wide tree-lined roads. But they are only tiny pockets in a huge city. It is necessary to ensure that these areas expand further. It needs a strong political will, dedicated funding for the development of public infrastructure, and strict monitoring with heavy fines for rule breakers. Patna has recently deployed lots of traffic police in an attempt to decongest and manage the traffic. Sanitation department also needs similar manpower to drive the cleanliness initiative. And the efforts need to be sustained over years for results to come.

And yes, the Swachh Bharat Abhiyaan would be considered a great success if this task is accomplished.

P.S. An old blog post on the subject of sanitation (Link) 

BookMarks #10: Frankenstein

Title: Frankenstein (or The Modern Prometheus) 

Author: Mary Shelley 

Genre: Science Fiction, Horror 

Setting: Europe primarily Switzerland 

Published: 1818 

Summary 

The story is told in the form of letters written by Captain Walton, who is exploring the Northern Seas, to his sister Margaret, back in England. Captain Walton narrates the tale of a man named Victor Frankenstein, whom his crew had rescued during their expedition in the Arctic Ocean. The crew had also spotted a gigantic figure moving along on the ice earlier. 

Victor begins telling Walton his story and how he came about to be on that icy landscape. He tells Walton about his family in Switzerland, his friends and early life. Then he went to university where the subject of chemistry and natural philosophy interested him the most. He develops a fascination for giving life to non-living things. He creates a large being to replicate human life and his experiments are successful. The “creature” as he refers to it comes into life. However he is repulsed by the creature’s hideous appearance and runs away. When he comes back the creature is missing. 

Victor falls ill from the results of his toils. However, his friend Clerval manages to nurse him back to health. Victor decides to go back to his family in Geneva. He then learns about the murder of his younger brother William and how the boy’s companion Justine has been implicated in it. On visiting the site of the murder, Victor spots his creature lurking around. He is convinced of the creature’s involvement in his brother’s murder and of Justine’s innocence. However, he is unable to stop Justine’s hanging. 

On a trip to the mountains, the creature corners Victor and then tells him his story. The creature has learned to speak and read from observing a family living in a cottage. His earlier interactions with humans had not gone well and he stayed in hiding in their cottage for some months while observing the family. Finally he mustered enough courage to meet the family but his intentions are mistaken because of his monstrous appearance. The frightened family runs away. The creature is angered by this reaction and sets the cottage on fire. Then he sets out in search of Victor, his creator. He also admits to the killing of William. After telling his story, he asks Victor to make a female companion for him, otherwise he would continue troubling Victor’s family. Reluctantly Victor agrees to this but seeks time. 

Victor and Clerval set out for England together. On reaching Scotland they separate. Victor sets to work on creating the female companion. One night he finds the creature watching him. Victor begins to doubt the monster’s promise and proceeds to destroy the female he was building. The creature is angered by his betrayal. He kills Clerval and implicates Victor in the murder. Victor is acquitted of the crime and he returns home. 

Victor gets married to his childhood friend Elizabeth, promising to tell her everything about his worries on the day after their wedding. On the wedding night, the creature comes and kills Elizabeth. Victor is enraged and vows to pursue the monster and destroy him. The pursuit takes him across the world and finally to the Arctics where he meets Walton. 

Fearing that his end is near, Victor makes Walton promise to destroy the monster. Walton agrees. Meanwhile the ship gets trapped in the sea ice. Walton’s crew is reluctant to proceed any further and although Victor argues otherwise, Walton is convinced to drop off the pursuit and return home. 

Victor succumbs to his illness. Walton finds the creature in mourning over Victor’s body. Walton hears the creature’s remorseful pleadings. The creature promises to destroy himself and end his own misery. Walton then watches the creature drift away into the sea. 

BookMarks 

Who is the monster here? Victor Frankenstein or his creation. While the creature commits the murders, he justifies himself due to him being abandoned by his creator, being rejected by the human society and his attempts at friendship being discarded all because of his hideous appearance. Certainly Victor is the one to blame for abandoning his creation. And also for keeping his family and friends in dark about this constant danger that he had created. 

Its a common misconception that the monster’s name is Frankenstein (although many may argue that Victor is the real monster in the tale), the creation is unnamed throughout the tale being referred to as creature or monster. 

Extras

Mary Shelley's original draft

Previously on BookMarks: Uncle Tom’s Cabin

Net Neutrality Wins

Net Neutrality: "the principle that Internet service providers should enable access to all content and applications regardless of the source, and without favouring or blocking particular products or websites."

For the past few months this had been a widely debated topic in India with Facebook's Free Basics campaign on one side, the average internet users on the other and the telecom operators and ISPs in the middle.

On 8th February, 2016 the Telecom Regulatory Authority of India ((TRAI) issued a notification on the "Prohibition of Discriminatory Tariffs for Data Services Regulation, 2016".

The TRAI order states that "no service provider shall shall offer or charge discriminatory tariffs for data services on the basis of content." Also "No service provider shall enter into any arrangement, agreement or contract, by whatever name called, with any person, natural or legal, that has the effect of discriminatory tariffs for data services being offered or charged to the consumer on the basis of content: Provided that this regulation shall not apply to tariffs for data services over closed electronic communications networks, unless such tariffs are offered or charged by the service provider for the purpose of evading the prohibition in this regulation." 

So in effect, it has declared that the entire internet content is same, whether its a video on youtube, a news channel site, live scores site, a social media site or even this blog. No particular content can be promoted by telecom operators through special plans like zero charges for certain sites/apps while charging different amount for others.  Although there are still some grey areas and some loopholes still need to be sorted out it was a first major notification in the net neutrality debate.

This notification has effectively stopped the Mark Zuckerberg's Free Basics campaign. Zuckerberg has been championing the cause of Free Basics to get more people on board the internet by providing certain websites free of costs (i.e. without any data charges). They had also conducted a major newspaper and billboard campaign for Free Basics. However the effort wasn't enough to covince TRAI or the net neutrality activists. Here is what Zuckerberg had to say in his Facebook post

"Everyone in the world should have access to the internet.

That's why we launched Internet.org with so many different initiatives -- including extending networks through solar-powered planes, satellites and lasers, providing free data access through Free Basics, reducing data use through apps, and empowering local entrepreneurs through Express Wi-Fi.

Today India's telecom regulator decided to restrict programs that provide free access to data. This restricts one of Internet.org's initiatives, Free Basics, as well as programs by other organizations that provide free access to data.

While we're disappointed with today's decision, I want to personally communicate that we are committed to keep working to break down barriers to connectivity in India and around the world. Internet.org has many initiatives, and we will keep working until everyone has access to the internet.

Our work with Internet.org around the world has already improved many people's lives. More than 19 million people in 38 countries have been connected through our different programs.

Connecting India is an important goal we won't give up on, because more than a billion people in India don't have access to the internet. We know that connecting them can help lift people out of poverty, create millions of jobs and spread education opportunities. We care about these people, and that's why we're so committed to connecting them.

Our mission is to make the world more open and connected. That mission continues, and so does our commitment to India."

His intentions might be completely altruistic but Free Basics isn't cutting any ground with net neutrality activists. In fact the TRAI ruling has been welcomed all across. For those in doubt on the correctness of the ruling, here is a tweet from Tim Berners-Lee.

"Well done India! passes strong #netneutrality rules, stands up for open Web. See @webfoundation -> http://tiny.cc/ftmy8x #savetheinternet"

Coming from the man who built the world wide web, that should end the debate on Free Basics vs Net neutrality. 

Now, the implications of this ruling. All existing data plans with prioritized access will go for a toss. Alongwith Free basics, Airtel Zero kind of services will also get shelved. This would lead to changes in the tariff plans by all telecom operators. Could be interesting times in the Indian telecom space where data and net speed are becoming the dominant sectors ahead of voice calls and messages.

Technology has been moving at a pace much faster than the regulations. This ruling by TRAI is a major step in ensuring net neutrality and keeping pace with the rapidly evolving connectivity needs.

MovieNotes: Airlift

Title: Airlift (IMDB)

*ing: Akshay Kumar, Nimrat Kaur, Purab Kohli
Language: Hindi with mix of Arabic

Director: Raja Menon

Genre: History, Drama

Basic Premise

Airlift tells the story of the evacuation of nearly 170,000 Indian nationals from Kuwait after the country had been invaded by Iraq in August 1990.

MovieNotes

What Works
The movie never goes over-the-top in its patriotism. The protagonists aren't shown doing "heroic" things (except for one climatic shot). They are just trying to make sense of the sudden change in their environment while attempting to survive this unexpected ordeal. Also we get to see varied reactions from different people all trying to make the some sense of this sudden trauma.

Akhsay Kumar as the lead protagonist Ranjit Katyal. He is simultaneously understated and the reluctant leader of the Indian community. His slow transformation from a self-centred "Kuwaiti" to an "Indian" who is concerned about the whole community is beautifully depicted. As is Mrs. Katyal's slightly slower acceptance of the situation.

The movie shows the tensions of the situation without going into the details of the prevailing politics.

The time period of 1990 is also referenced nicely. We get to see an upcoming Sachin Tendulkar giving an interview, late-80s Bollywood music playing in the background, people fiddling with audio cassettes.

What Doesn't
Not showing the real extent of the work done by the Indian government in the background. The movie gives the Indian bureacratic machinery far less credit for the rescue than it deserves.

The sheer scale of 170,000 stranded people somehow never shows up on screen. It just seems to be number thrown up without any logistical back-up.

Rating - 8/10. Overall a good film, with heart.

Previously on MovieNotes - The Motorcycle Diaries

MovieNotes: The Motorcycle Diaries

Title: The Motorcycle Diaries (Diarios de motocicleta) (IMDB)

*ing: Gael Garcia Bernal, Rodrigo de la Serna

Language: Spanish

Director: Walter Salles

Genre: Biography, Journey

Basic Premise

It narrates the journey made by Ernesto "Che" Guevara when he was a medical student alongwith his friend Alberto and how the journey shaped his life.

MovieNotes

"This isn't a tale of heroic feats. It's about two lives running parallel for a while, with common aspirations and similar dreams"

Thus begins the tale of an epic journey. A journey which sowed the seeds of a revolution into the mind of a medical student. A student who would go on to become one of the most famous revolutionaries of the modern times. 

The move begins on a light-hearted vein with Alberto and Ernesto commencing their trip across the length of South America. They say their farewells and have their little funny adventures on their motorcycle "The Mighty One". However as the journey progresses, the mood of the film changes from fun to seriousness. Their encounters with the different folks awakens them to hardships of the world. The fun-seeking youth who are travelling for the sake of travelling run into people suffering all kinds of hardships and being exploited by those around. The economic inequalities and the sufferings he witnesses makes Ernesto believe that only a revolution (and an armed one) can truly bring about justice.

The movie is a brilliant depiction of the journey and not just in the physical sense. It is more a  story of the transformation within the minds. The sale of the motorcycle half-way through the tale provides an inflexion point in the story from where the movie adopts a more serious tone with the focus shifting from the tale of Alberto and Ernesto to the sufferings of the people they meet. The movie does not tell of any heroic feats but gives an inkling of the the revolution about to come. 

It is one those rare movies which make you think about the injustices around you. 

Rating - 9/10. A tale which begins on a light-hearted note but progresses into something far more serious without losing pace and grip.

Previously on MovieNotes - 12 Years A Slave

The Big Oil Drop: Free fall continues...

Almost a year back, I had written about the falling crude prices. Since then the free-fall has continued with oil trading in the low to mid 30s. Alarm bells are ringing across the industry. The time for trying to figure out the reasons for the slide is long gone, though everyone has their own. The sharp slide is already having its impact. Projects worth nearly $35 Billion have been shelved; 200,000 jobs have been cut, the M&A market is warming up for the bloodbath. And the situation is likely to worsen. 

The US Congress has agreed to allow sale of crude outside US lifting a 40-year ban. The Shale boom made US less dependent on external producers. Which was one of the main reasons for bringing the prices down. However with prices down, the producers are in for a hard time, some having shut shop, most cutting activity levels to the bare minimum. Thus the US Congress decision is an attempt to ease the producers as their domestic market is already having a glut. This move might stabilize the US market but is unlikely to lift the prices.

The lifting of sanctions on Iran is likely to bring more cheap oil in the global market this year. Thus putting more pressure on the oil producers. Supply increases further with demand staying same or even worsening given the global economic slowdown.

The sharp drop has resulted in Saudi Arabia having a huge deficit in its budget. The Saudis, who are the only ones with swing capacity, have steadfastly refused to cut production to boost the price. Instead they have taken an interesting decision to publicly list Saudi Aramco.The listing of the world's biggest company could be the biggest financial event of the century, making up quite a bit of the Saudi deficit. Although it would also open their economy to more scrutiny, something which is against their secretive ways. But then tough times do call for drastic measures.

The emergence of Australia as a source of LNG would shift the direction of the global LNG trade away from Qatar. However the low prices have resulted in delays in some of the projects. Thus enabling Qatar to retain its hegemony for a while longer. Meanwhile, Qatar has been doing its bit to retain its market renegotiating supply contracts with the likes of China and India.

Then, the Paris agreement on Climate Change. If every country keeps their end of the promises, their would be shift from hydrocarbons to alternate energy sources. However, the low crude prices have made the alternate energy sources less attractive. We are reaching a stage where the oil is unlikely to run out but environmental concerns would reduce its consumption.

However, the tensions in the Middle East over Syria and the Saudi Arabia-Iran stand-offs might spike the prices up. Throw in further uncertainties like the possibility of Saudis acquiring a nuclear deterrent from North Korea or Pakistan, further escalation in the so called fight against Islamic State (which has captured a big chunk of the oil trade) or the migrant situation blowing up in Europe  But hoping for a war to jack up prices is certainly not good karma. 

Low prices are welcome news (for now) for an energy-importing country like India. The export bill reduces and with it the foreign exchange outflow. However, it comes at the cost of its domestic production which needs a much higher price to be commercially viable.

Times certainly are tough for the people in the oil sector.

Resolutions Time

A new year has dawned upon us and ‘tis time when resolutions are made. Most of which broken by this time of the year. So instead of making resolution for a year, me decided to make some resolutions for the future (no time frame). And helping me in framing the words is a famous playwright from some centuries back. 

Give thy thoughts no tongue,

Nor any unproportion'd thought his act.

Be thou familiar, but by no means vulgar.

Those friends thou hast, and their adoption tried,

Grapple them to thy soul with hoops of steel;

But do not dull thy palm with entertainment

Of each new-hatch'd, unfledged comrade. Beware

Of entrance to a quarrel; but being in,

Bear't that the opposed may beware of thee.

Give every man thy ear, but few thy voice;

Take each man's censure, but reserve thy judgment.

Costly thy habit as thy purse can buy,

But not express'd in fancy; rich, not gaudy;

For the apparel oft proclaims the man,

And they in France of the best rank and station

Are of a most select and generous, chief in that.

Neither a borrower nor a lender be;

For loan oft loses both itself and friend,

And borrowing dulls the edge of husbandry.

This above all: to thine own self be true,

And it must follow, as the night the day,

Thou canst not then be false to any man. 

These were the words of wisdom imparted by Polonius onto his son Laertes as he is leaving for France to attend university, covering a whole gamut of subjects from friendships to fighting to finances (Hamlet Act I, Scene III). Though written over four centuries ago, the words still hold good, although some of the contexts may have changed. So on the lines of Shakespeare, here are my resolutions. 

1. Listen to varied opinions but do not put anything on any social media without verifying it through other sources. And certainly not indulge in hate-mongering. 
2. Be financially prudent. Not be a miser nor a spendthrift. Save first and then spend. Invest after due research and not just a hunch or a tip. Do not get swayed by any get-rich-quick-schemes nor panic on every news event. Keep track of the finances. 
3. Do not procrastinate. But on the other hand, do look before you leap. Many things sort themselves out with time but many go worse as well.
4. Spend time with those who really matter. Take more holidays. 
5. Do my bit to save the environment.
6. Keep Learning.
7. And finally “to thine own self be true”. The most important one. After all everything else falls in line after this.

Cheers to a new year and new resolutions

Goodbye 2015

The year MMXV A.D. approaches its end. It’s time to reflect on the year gone by and decide the course for the year to come. The more things change, the more they remain the same. Yet, every passing year leaves behind its own share of memories. Overall it wasn’t a very likeable kind of year with issues snooping around at the back of the mind. 

• Major change: Shifting to another place and hunting for a new one, a major exercise in itself.
• Memorable Experience – River rafting in the Ganges and having to hang on to dear life in the rapids as the raft overturned and people getting swept away to the next raft. More adventure than we had bargained for. But memorable all the same. Then there was the musical concert, the play seen on a screen and finally being part of mega service launch. And securing a phone invite via social media. And some more dentist trips.
• Achievement of the Year – Completing a month long fitness challenge. And feeling quite good about it. Although other attempts did end midway.
• BookMarks - Started a new section on the blog, dedicated to the books I complete reading. 9 entries made this year.

Now for the resolutions for the next year: Be Healthy & Happy and keep everyone around happy. And I am certainly looking forward to 2016. After all it has that one extra-special day. 

Wishing all readers a very Happy and prosperous 2016.