We are complete strangers now.I don’t regret our time together or the separation.You have earned a status that nobody (myself included) can deny or take away.You are still my password.
We are complete strangers now.I don’t regret our time together or the separation.You have earned a status that nobody (myself included) can deny or take away.You are still my password.
Year end is about holidays and New Year wishes. But it is also about Calendars. I don’t know about others but I like to “read” new calendar, immediately check few dates or events, festivals!
I remember having written a couple of blog posts about Calendar. One, written in 2007, was a light take on Calendar – Calendar विषयी थोडेसे… (It’s in Marathi)
The other was written in 2010 about the mathematics behind the Calendar, or how to calculate day of any date. I was not able to find it in Archive – probably it got lost when I imported my old blog into this domain. So posting it here again. It was written on 13th February 2010:
Few years ago I was learning a programming language and was given an assignment to display calendar and tell day of date .
Let’s update this for today’s date i.e. 27th December 2017.
Srinivas Ramanujan, one of the best mathematicians the world has ever seen, was born on this day, 22nd December 1887. His birthday is observed in India as National Mathematics Day. He barely lived for 32 years (died: 26th April 1920) but the work he did in the short span continues to inspire mathematicians even today. Some of his conjectures were proven 80 years after his death, and some of them are being used in research work on Black Holes.
You can read book “The Man Who Knew Infinity” based on his life, or watch the movie with same title. But the movie is not quiet up to the mark. I would recommend this video discussing the movie and the genius of Ramanujan. Do watch this:
It is an amazing interview explaining the genius of Ramanujan through multiple perspectives and also elaborating on what makes him truly great!
Recently I received from a friend following story attributed to Ramanujan…
Mathematician Ramanujan didn’t have any close friends – someone asked him the reason. He replied that although he wanted to have close friends – nobody was up to his expectation. When pressed how he expected his friends to be – he replied – like numbers 220 and 284. The person got confused and asked what is the connection between friendship and these numbers!
Ramanujan asked him to find the divisors of each number!
With much difficulty – the person derived and listed them.
220 – 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220
284 – 1, 2, 4, 71, 142, 284
Ramanujan then asked the person to exclude the numbers 220 and 284 and asked the sum of the remaining divisors. The person was astonished to find:
220 – 1+2+4+5+10+11+20+22+44+55+110 = 284
284 – 1+2+4+71+142 = 220
Ramanujan explained that an ideal friendship should be like these numbers – to complement each other – even when one is absent – the other should represent the friend!
The person thought – no wonder this genius is on the world’s top list of mathematicians!
As far as I know this story is unlikely to be true. I tried to read through many Ramanujan anecdotes and didn’t find this story in any authentic source. The numbers 220 and 284 belong to the type of numbers described as Amicable Numbers. This is the smallest such pair and such numbers were knows since 1400+ years, dating back to Pythegoreans
However there is another anecdote about Ramanujan which is definitely true; in fact the number is now known as Ramanujan Number – and the number is – 1729. The story goes as follows:
I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. “No,” he replied, “it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.
The two different ways are:
1729 = 13 + 123 = 93 + 103
The story highlights greatness of Ramanujan. However it also misleads us to believe that Ramanujan was a math savant rather than math genius. If you have watched the above interview you would have known the difference.
So I won’t elaborate further and urge (or force!) you to watch the entire video!
Meanwhile, I will leave you with some of his amazing mathematical discoveries which are not only deeply complex but extremely elegant in form! (I am intentionally using word “elegant”, and if you have, by now, watched the above video, you would know the reference!)
Ramanujan once said “An equation for me has no meaning unless it expresses a thought of God“. It says a lot about how he viewed and approached Mathematics!
Title of this blog post is borrowed from Cyrus Brocha’s popular spoof on current news and affairs called “The Week That Wasn’t” where he mocks various news events of the week.
Yesterday the 2G scam verdict was announced by the special CBI court.
In a major setback to CBI and former CAG, a special court in Delhi acquitted all accused in 2G Scam including former telecom minister A Raja and DMK Member of Parliament A Kanimozhi.
The case and the verdict was significant for many reasons. First of all it had created sensational news when it first broke out in April 2011. The case was one of many which created negative perception about UPA-II as corrupt and mismanaged government and paved way for Anna Hazare/Kejriwal movement and later BJP’s “Modi wave”. The case was also sensational because of outrageous claims which were too too big to ignore. The accusation by CAG (Comptroller & Auditor General of India) that there was a loss to the nation of Rs. 1.76 Lakh Crore (~$33-35 Billion dollars!). Look at the headline how it was projected:
The case argued that there was loss to the nation by not auctioning 2G licenses and thus there must have been (or was) huge corruption and kickbacks. The Supreme Court took a note of this and immediately cancelled 122 telecom licenses, many prominent people (minister, MP, Corporate heads) were jailed.
After 6 years the Supreme Court ruled that there was no scam! All the accused were set free. Of course this is the trial court verdict and the matter would go to HC and SC. But the case as it stands today is important.
I had read in detail about how the loss figure of Rs. 1.76 Lakh Crore was arrived at. Right from the beginning I have maintained that the loss numbers were bogus. There was no scam to the tune of over-hyped numbers. Yes, there were irregularities in the process. But not a scam of the scale claimed. In fact if you read through CAG chief Vinod Rai’s claims you could see that there was no logic or conviction.
said Vinod Rai in one of the interview. Then at one occasion he said: “2G loss was pegged at Rs 4 lakh crore, I toned it down“. Contrast this with what CBI claimed as loss. Rs. 30,000 Cr. So there was no consistency in how to “value” the scam.
Moreover the case was no pursued properly and CBI failed to bring out evidence of any “scam”. The SC judge’s judgment is a harsh criticism of the CBI and the way the case was handled. Look at some of the quotes by the judge:
In his 1,552-page order, special judge O P Saini held that there was no criminality or conspiracy in spectrum allotment and said some people created a “scam by artfully arranging a few selected facts and exaggerating things beyond recognition to astronomical levels”.
Judge Saini also came down heavily on the CBI, charging the agency with shoddiness and approaching the case in fits and starts. The judge said he had “absolutely no hesitation in holding that the prosecution miserably failed to prove any charge against any of the accused, made in its well choreographed chargesheet“.
And these golden words: “For 7 years…I religiously sat in open court…waiting for someone with some legally admissible evidence in his possession, but all in vain”
How stupid can it get? This so-called “mother of all scams”. Now one may argue that the case was genuine but CBI messed it and didn’t do its job well. Let’s see, I hope Govt will pursue this in HC and up to SC. But given the harsh comments by the Judge, I would be surprised to see if there is any merit in the case and if upper courts give an contradictory verdict.
But look at the consequences of this false “scam”. It mobilized public opinion against the UPA and Congress in particular (they have never recovered from that blow yet). It strengthened the perception that UPA-2 was all about scams (BTW, the Coal scam, and the Commonwealth scams also were uncovered by CAG. So one can see how flimsy those cases would be). It gave way to BJP and Modi wave. It made Subramanian Swamy a hero-like figure in crusade against corruption (since he filed an individual case). And it established Rajeev Chandrashekhar, the formed owner of BPL Mobile and based on whose letter the “scam” was uncovered.
Of these Rajeev Chandrashekhar is worth discussing. I will do it in a separate follow-up post but let me articulate my position in brief. I feel Rajeev Chandrashekhar is no saint. He is equally dubious person. In his current role he is a BJP MP and majority owner of TV news channel Republic – yes the same shouting galore where Arnab Goswami puts 8 or 12 people in tiny windows and then constantly barks at them.
Rajeev Chandrashekhar, his role in 2G and his personal journey is worth elaborating on. Just to see 2G “scam” in perspective. Well, as of now it’s the scam that wasn’t…
Yesterday I was working on a stock idea for which I had to write analysis and fill in a template form. The form had couple of standard questions such as whether you are a SEBI registered investment professional etc. The last question on Disclosures was: “Have you invested in the stock you are covering? If yes, how many?”
This question got me thinking. The question was plain and simple: “Are you eating your own dogfood?” Or, since I am a vegetarian, the question was: “Do you eat your own pudding?”
The question has two sides or themes: Skin-in-the-game and Vested Interest – which are two sides of the same coin.
A typical stock analysis and recommendation is for identifying multi-baggers or stocks with huge upside potential.
If you recommend a stock because the stock, according to you, is going to go 5x, and at at the same time you disclose that you don’t own a single stock, the obvious question would be – “How come you don’t own a stock which you believe would go up 5x?”. It means two things: (1) Either you are sure or there is no conviction OR (2) Maybe you have another 20x stock idea which you are not disclosing. Whatever maybe the case, this lack of “skin-in-the-game” makes the stock recommendation suspicious.
On the other hand, if you recommend a stock and disclose that you have a significant position in it, and you have invested a lot of personal money in it; the obvious thought would be that your recommendation is biased. Since you have “vested interest” in seeing to it that the stock is bought by people you would give a positive analysis/report.
So it’s a catch-22 situation. Is there any way out?
There is. But it is a process and not one-time activity. First of all, you should buy the stock. Skin-in-the-game is absolutely important. You have to share the risk and reward of your recommendation. Secondly, if the stock has significant upside (say 5X) you should also buy and keep buying while it moves up. It shows conviction on your part that you are super-bullish. At least, you should never sell.
This dilemma is not only about investing; it is true about many other walks of life. For example, if some Indian living permanently in the US, having no investments in India, constantly lectures on what India should do and how it should improve systems, sooner or later people are going to shut him up. He has no skin-in-the-game. He should not preach from outside. If he cares, he should be in India improving things from within.
Now take case of Office of Profit. If you are part of Government or a Ministry that can decide fate of an industry and thus a specific company, and you also happen to be beneficiary in that company (stakeholder or a Director), then you clearly have vested interest. That is strictly unethical and illegal and not allowed.
All such matters are very subjective and there is a fine line between right and wrong, accepted and not-accepted. Skin-in-the-game can be a virtue in some cases and a vice in others. Ditto with vested interest.
Nassim Taleb, the famous author of books such as Black Swan and Fooled By Randomness has written a book titled “Skin in the Game: Hidden Asymmetries in Daily Life” which is on the same theme. I haven’t read it yet but going by other books of Taleb it should be an interesting read! Look forward to reading it soon…
The last year, and the last week week was amazing!
It rekindled my two old love interests: Mathematics and Music…
Interest in Mathematics was revived long back…on 31st December 2016, to be precise. And since then I have spent quite some time in 2017 on Mathematics (on the book I am contemplating) – and enjoyed every moment of it!
I had never really lost interest in Mathematics. It was just dormant or less prominent. But reviving interest in Mathematics has helped me a lot during the last one year when I was feeling very lonely and had many negative and depressing thoughts and grudge against my own shadow.
Interest in Music was rekindled yesterday! And that is an amazing feeling! I had practically lost interest in Music for last few years. Didn’t enjoy listening to music, exploring it, sharing with others, discussing with close friends – all of which I used to do a lot…really a lot till few years ago.
yesterday and day before yesterday I was awake till 4-5 AM listening to music on iPod/Youtube from 11 PM or so. It was not because I couldn’t sleep. It was because I didn’t feel tired/ didn’t want to sleep.
I am feeling very energized. I was wandering clueless since last 31st December, trying to fill the vacuum, healing the hurt and trying to forget and forgive.
Hopefully these two old love interests can fill the vacuum created by my other love, and heal the wounds, at least to some extent.
Few weeks ago I wrote about Misha Osipov – the new chess prodigy. That was an amazing feat by a human in chess!
This week something equally or more significant has happened in chess. Google’s AI, AlphaZero, developed a “superhuman performance” in chess in just four hours. After being programmed with only the rules of chess (no strategies), in just four hours AlphaZero had mastered the game to the extent it was able to best the highest-rated chess-playing program Stockfish.
In a series of 100 games against Stockfish, AlphaZero won 25 games while playing as white (with first mover advantage), and picked up three games playing as black. The rest of the contests were draws, with Stockfish recording no wins and AlphaZero no losses.
This is a very significant development in the field of Artificial Intelligence and Machine Learning!
Chess programs and softwares so far used to work as a combination of “Huge database of Chess games + Rules/Analysis Engine + Brute force of computing power”. So the programs were “fed with” chess games and rules; they didn’t “learn” chess. Of course that was also a tremendous achievement. You should read Garry Kasparov’s book Deep Thinking to read about his match with Deep Blue and the future of Man vs Machine chess.
But Google’s AI is altogether different! Few months ago Google’s AI beat the best human in a Chinese strategy game called Go. Watch a short video explaining Google’s Deep Mind here.
Google AI is trying to develop a general purpose machine learning software that can learn things on its own and then excel. In the recent game of chess the Google AI learnt the game of chess in just 4 hours; not just learnt, it mastered the game of chess in 4 hours! The program AlphaZero then played with another strong program Stockfish in 100 games and destroyed it 64-36!
Look at reactions of some of the best Chess players in the world today
You can read an academic paper on this Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm
The world around is us changing rapidly! Driverless cars, Drones, Hyperloop, Self-learning AI, Machine learning, Blockchain, Robots performing human tasks and posing threat to jobs…disruption is inevitable in all spheres of life!
One can only imagine how these changes would impact us in year 2030 or 2040! Embracing the technology and facing disruption is not an option; welcoming it and adjusting ourselves, and keeping ourselves up-to-date is the only option! Gone are the days when you could leave University with a degree and spend the rest of your life without upgrading your skills, learning new things. You must earn all your life just to keep pace with the world around you! Because now the threat is not only from other humans, but from machines as well!
Remember the Red Queen quote from Alice In Wonderland?
During World War II, lots of fighter planes were getting hit by anti-aircraft guns. Air Force officers wanted to add some protective armor/shield to the planes. The question was “where”?
The planes could only support a few more kilos of weight. A group of experts were called for a short consulting project. Fighter planes returning from missions were analyzed for bullet holes per square foot. They found 1.93 bullet holes/sq. foot near the tail of the planes whereas only 1.11 bullet holes/sq. foot close to the engine.
The Air Force experts thought that since the tail portion had the greatest density of bullets, that would be the logical location for putting an anti-bullet shield.
One of the experts named Abraham Wald said exactly the opposite; more protection is needed where the bullet holes aren’t – that is – around the engines.
His judgment surprised everyone. He said “We are counting the planes that returned from a mission. Planes with lots of bullet holes in the engine did not return at all”.
Einstein had said: Not everything that counts can be counted, and not everything that can be counted counts”.
I got this interesting story as a forward. It is a very good example of second level thinking.
In his exceptional book, The Most Important Thing, Howard Marks hits on the concept of second-order thinking, which he calls second-level thinking. Here is an interesting blog on Farnam Street on the concept. You can also read a Memo by Howard Marks on this here.
One of the important tools in second-level thinking or second-order thinking is Inversion. I briefly touched upon Inversion when I mentioned Charlie Munger’s story and quote of mathematician Jacobi. You can read the reference here.
The above fighter plane story is another example of second-level thinking using principle of Inversion. Others were looking at planes that returned safely and trying to identify which are they should protect. Abraham Wald rightly applied the Inversion principle and thought: “We should focus on the planes that didn’t return, and think why they didn’t and protect them from getting gunned down!”
Another example of principle of Inversion which many of you would know if you are fans of Amazon founder Jeff Bezos. When asked about what is the purpose or goal of life, most people would give answers which could be summarized as follows:
Jeff Bezos was asked similar question about his goal and what motivated him to found Amazon; and his answer was very interesting. He applied principle of inversion and said: “My idea was to minimize regrets in life when I am 80 years old!” This is a “Regret Minimization” approach as opposed to “Pursuit of Happiness” approach. Jeff said that giving Entrepreneurial instincts a shot was one of his life goals. If he had failed at Amazon he would have happily gone back to his previous career and would have scaled up there. But he wouldn’t have regretted at age of 80 that he had aspirations to start his own venture but he didn’t.
This is such a novel approach! It frees you from the burden of pursuing your dreams and fearing failure and enables you to just enjoy what you want to do and not have any regrets. Many things could be turned into success if we approach life with this philosophy!
Warren Buffett has often said that his biggest mistakes in life were not errors of commission, but the errors of omission. That is, Buffett regrets the opportunities he missed far more than his investing bets that went wrong. Because, according to him, in many cases of omission he had enough knowledge, insights, wisdom to make a right decision and yet for some reason he didn’t and then the missed opportunities turned out to be multi billion dollar “errors” – which never show up anywhere in the Books of Accounts.
Hope this highlights the power of second level thinking and principle of inversion as tools in thinking and decision making…
A couple of days ago I wrote a blog titled “I Teach. Therefore I Learn” which was a twist on a maxim by famous French philosopher and mathematician Renee Descartes (1596-1650) which says: Cogito ergo sum. (I think; therefore I am.)
In a Discourse on the Method, Renee Descartes questions the world and his surroundings by doubting and re-evaluation everything. By doing so, he aims to gain a fresh perspective without any preconceptions. Through the different parts of the discourse, Descartes questions the reality and incontrovertibility of his surroundings and comes to the conclusion in part 4 of, “I think, therefore I am.” He believes this is the only incontrovertible truth he can actually prove, the logic being that since he has the ability to recognize that other things may not be the true, he must exist to have the ability to do this in the first place. If he didn’t exist, then he would not recognize not doubt his surroundings. His maxim not only conveys his skepticism of the surrounding world but also explains the only truth he knows.
“I think; therefore I am” is such an intriguing quote that there are many layers to it. The deeper you peel, the more meaning and leading thoughts you can generate!
Though I like philosophy and serious thinking, I also like satire, humor, and, at times, even non-sense jokes! Some friends call me “the funny guy with a poker face”. Anyways, so what I found interesting was that how this famous quote by Descartes has been turned and twisted in some most hilarious and intelligent ways! I liked one, in particular, and used it as a tag line for my blog – “I Doubt. Therefore I Might Be?” It goes with my nature of being skeptical and suspicious about things and habit of questioning or debating everything! 🙂
Here are few more:
And there is an entire parody song written by The Comedian group. It is published on http://www.amiright.com/ whose mission is “Making fun of music, one song at a time. Since the year 2000”!
Here is the song “I Think Therefore I Am”:
That French philosopher Descartes
Listened to his pounding heart
He thought a bit and he felt a spark
Tingle in his spine
‘Twas then he coined the line
His fame be-gan
That pompous line —
“I think, there-fore I am!”
They walked along drinkin’ rum an’ coke
A little confused, they remembered jokes
And passed around a joint for tokes
In a roach-clip burnin’ bright
They drank whiskey through the night
The big ex-am
Then they cried —
“I drink, there-fore I cram!”
A hurricane someplace far off blew
As he was workin’ wind-jammer’s crew
As the tide bust through a big gust threw
His sailboat upside down
He dropped into the sea to drown
But he was a
And he shouted out —
“I sink, there-fore I swam!”
(harmonica & guitar instrumental)
He walked up, her back was bare
He didn’t see hair anywhere
He told himself he’d charm her there
Push in-to her open thighs
Felt a gassiness inside
Blew wicked gust-ings from his can
Coughed and cried —
“I stink, there-fore I scram!”
He hears the ticking of the bomb
And works along with a careful aplomb
Shuts it down with a wonderful calm
‘Til the timer’s stopped its spin
Maybe it’s ticking loud again
His last thought —
“I think, there-fore I–” BLAM!!
People tell me
I’m a fool
To waste what I
Did learn in school
I still believe that this is cool
I’ll write more of these
Was born a man
Whose motto’s —
“I think, there-fore I can!”