Tag: math

Card Games

So the other day, while playing rummy with the members of the in-law family, I figured why I suck so much at some card games despite having played them quite regularly when I was a kid. Back then, in family gatherings, it was common for the host to come up with a couple of packs of cards, and we would play either rummy or this game called donkey (some kind of variation of hearts is how I’ll describe it for those that don’t know it). Given how regularly we played it, I should have become rather good at either of them, which unfortunately is not the case.

Bridge was the first card game that I learnt “formally”, in the hostel blocks of IIT Madras. Soon after being explained the rules of the game, I was taught conventions, both in bidding and play. I was taught the math, the probabilities of various distributions and to make intelligent guesses. While I quickly became decently good at bridge, it didn’t help my game in any of the other card games that I’d learnt.

So while playing recently, I realized that I know little about the science of rummy. And then I realized the reason for it – we used to play with incomplete decks. The problem with old family-held packs of cards with which no “formal” games are played is that cards tend to go missing over the course of time (especially if there are kids around), and no one really bothers to check. And when you play with incomplete packs of cards, all the beautiful math and rules of probability go out of the window. And if you have learnt playing with such a pack of cards, it is unlikely you’d have figured out much math also.

Last night, while playing rummy with the wife, I tried my best to use math, to keep a careful note of discarded cards, the joker (for example, if seven of hearts had turned up as the joker card, that meant a six of hearts in hand was of less use than otherwise (we were playing with only one pack) ), mathematical probabilities of which cards are still available based on discards and stuff. Then, it turned out that there was too much luck involved in the distribution of cards, and I started missing the duplicate bridge games that we used to play back in IIT.

The wife has shown an inclination to learn bridge, and I’m trying to teach her. We’re also trying to learn poker (we’d bought this nice poker set in Sri Lanka last year but it remains unused since neither of us can play the game). Yeah, becoming really good at these card games is one of the aims of my “project thirty”.

Fractal life

Recently I finished reading Mandelbrot’s The (mis)Behaviour of Markets for the second time. Fantastic book. I think it is a must read for people who are interested in financial markets, and especially for those who work in capital markets. While it stays away from equations and “math”, and prefers to use pictures (or cartoons) to illustrate and show concepts (a method I definitely prefer to obscure math), it does raise a lot of very interesting fundaas.

So last week I was feeling stressed out. I realized that I had worked too hard on Wednesday and Thursday hence I got stressed out on Friday. A couple of months back, I took a couple of days of medical leave because I was stressed out. I reasoned that was because I’d pushed myself too hard the earlier two weeks. And thinking about all this today, I thought the incidence of stress has gone up over the last couple of months. This, I reasoned to pushing myself excessively for over a year now. And if I were to analyze my today’s work, I could probably say that I pushed myself too hard in the afternoon and hence got stressed out in the evening.

Same pattern, you see. At different scales.You get the drift, I guess. And stress is just an example I took. If I think about how my louvvu for my wife has evolved, again same pattern. There is a “global pattern”, and that same “global pattern” repeats itself over shorter intervals over the last two years. Irrespective of the quantum of time I look at, I see that same “global pattern” stretched or compressed to the appropriate time scale. In other words, love is also a fractal.

You can see fractals all around you. You can see self-similarity everywhere. And yet, even when you have small samples. you instinctively try to model it as a normal distribution. Without realizing that the “normal” distribution in life is the Power law.

Search strings – last one month

It’s been a long time since I’ve done this and I’m feeling bored now so thought I should write this. It’s the same old usual thing – unusual things that people have searched for and landed up at my blog. I used to compile these stats on a daily basis earlier but nowadays due to NED have abandoned it. So here is an attempt to revise it. This time it’s not for a particular month. It’s just over hte last 30 days. Here goes:

  • travelling on general compartment on shimoga express
  • “ramnath narayanswamy” sex
  • doctor is that the coin falls the right way
  • is token system better than queue in reception of hospital
  • where is kodhi math in karnataka??
  • women in skimpy cut offs

Ok I know the list is smaller than the usual, but I think people aren’t being that crazy nowadays, or for some reason the crazy people are being repelled by my blog! Hopefully next month I’ll have better stuff.

Anecdotes from school: Divisibility test for Seven

This is a new series on this blog, called Anecdotes from school. I realize I’ve had so many awesome anecdotes in school that I should tell you people about it. Of course I won’t write about the incidents when I beat up people or got beaten up by people (both were common). Even leaving them out, school was quite an awesome time so I think I should write about it.

One fine morning when I was in 9th standard, I arrived at school to find the rest of my class raving over this little guy called Ramu. He had apparently made some major mathematical breakthrough, and the school had called the Deccan Herrald to interview this prodigy. He is the next Ramanujan, people claimed (no, Ramu wasn’t short for Ramanujan). Efforts were made by all parties to hurt my class topper ego – what is the use of being a topper if you can’t come up with breakthrough discoveries, they said.

A few days back, we had studied divisibiility tests. Powers of two were simple, as were 5, and 3 and 9. 11 was also quite simple, and that left only 7 among the “simple primes” for which there didn’t exist an elegant divisibility test. “This is an unsolved problem”, Matki, our maths teacher, had declared. “Any one who can solve this is sure to win a Nobel Prize” (evidently she didn’t know that no Nobel is given out for Math. Of course, us 13-14yearolds also had no clue about such finer details.

So Ramu had woken up one morning with a divisibility test for seven. As I mentioned earlier, by the time I reached, the entire class had been convinced. I’m not sure if Matki had heard about it yet. It was a weird test, and I must admit I don’t remember it. It was extremely inelegant, with different operations to be done with different digits of the number. If it were elegant, I had reasoned, this problem wouldn’t have been unsolved for so long, I had reasoned. So inelegance would not really take away any greatness from the method.So I asked Ramu to demonstrate it to me.

He wrote down a few numbers on the blackboard – all known multiples of seven. Actually he picked only powers of seven (49,343 and 2401). The reason he did this (picking powers) is unclear. So he takes the numbers, puts his magical algorithm on it, and there it is. Done. Hence proved. QED.

Of course this was too much for my class topper ego to take, and I spent the rest of the day trying to find holes in this argument. In the meantime Matki and the other senior maths teachers in school had learnt about this, and had gotten convinced of the greatness of Ramu and his algorithm. The team from Deccan Herald was supposed to arrive at 4 o’clock, we were informed.

It was sometime in the afternoon. Maybe during the history lesson. My ego had been hurt so much that I obviously didn’t care about the lesson. All I cared for was to poke holes in Ramu’s algorithm. I decided to stress-test it. I picked 8. And ran the “divisibility test for seven”. The algorithm said “divisible”. I picked 9. Again the algorithm said “divisible”. 1. Divisible by 7. 2. Divisible by 7.

I had confronted Ramu during the lunch break regarding my “experiments” with his algorithm. “You obviously know that 8 is not divisible by 7. Why do you even bother running the test on that?” He countered. “Errrr.. Isn’t that the point of the divisibility test?”, I asked. I had already started to become unpopular in class. I then started picking random large numbers whose divisibility by 7 I had no clue about. According to Ramu’s algorithm, all were supposed ot be divisible by 7.

Deccan Herald was hurriedly contacted again, and asked not to come. I don’t know how Matki or any of the other maths teachers had reacted to this. I was “boycotted” by the class for the next one week for destroying the career of a budding mathematician. Ramu, however, wasn’t finished. A week later, he came up with an algorithm for trisecting an angle using only a straight edge and a compass.

On Being a Geek

I’ve always been a “topper types”. I started topping class when I was in first standard (and no, they didn’t announce ranks before that), and as if that wasn’t enough, my parents made sure that all relatives, and all teachers in school knew about my superhuman arithmetic skills. And as if even this wasn’t enough, I became the first guy in my class to wear spectacles. In a few years’ time, I went on to represent my school in supposedly intellectual pursuits such as quizzing and chess. I had been consigned to living life as a geek.

There were several occasions when I wasn’t really the topper; wasn’t even close to being a topper. However, something or the other ensured that I managed to maintain that geeky aura. In school, and at IIMB, I was supposed to be really good at math, and that made me geeky. Things were differnet at IIT – since a number of my classmates who trumped me in acads were also better than me at other geeky things. However, I think the fact that I was studying CompSci made me feel geeky, and I never lost any opportunity to show off my geekiness.

In this context, the last two years were quire awkward, as I was in a couple of non-geeky jobs. For the first time in almost twenty years, I had to go out of my way to demonstrate my geekiness, and given that those jobs didn’t need me to be a geek, things didn’t go quite well. I used to try and shove in lines into my conversation such as “we used to play chess in the classroom at IIT. since we couldn’t carry in chessboards, we used to imagine a board and play on that”.

It was very awkward. Thinking back, maybe that was one of the major contributing reasons to my not being too happy in the jobs. I wasn’t able to play my natural game. I had to invent a new me that would go to work daily. And it wasn’t just about the geekiness factor, but this was one of the important reasons, I believe.

Now, working as a strategy guy in a quant hedge fund, I feel I have every right to be geeky, and am well and truly back in form. I lose no opportunity to crack geeky jokes. I try to bring in analogies from various geeky fields I’ve been acquainted with – math, computer science, finance, and even physics. And I don’t mind making things complicated just so that I can slip in that geeky analogy that I think is “beautiful” and “elegant”.

Two days back, i was talking to Baada on the phone, and I smelt an opportunity to crack a geeky joke. We were discussing football while watching Liverpool play Chelski. And then suddenly I asked him if he knew the concept of inversion in geometry. When he replied in the negative, I spetn the next ten minutes explaining the concept to him, all so that I could slip in that one little geeky joke.

Beware of me, I would say.