Growing up with mathematics

During my childhood, the honour of the most hated subject by far would have gone to Mathematics. I might have stood probably a hundred times in front of my father for learning the intricacies of the subject, standing was essential to prevent the consequences of my stupid muddled brain. With exams on the morrow, none of nocturnal visits had turned out pleasant to me. A boxed ear and a red bum were the bare minimum results of these necessary excursions. My father after a tiring days’ work, would have preferred to have his piping hot tea in front of doordarshan rather than end up as the tutor of the makeshift tuition. Mother forced these meet-ups on both of us and thus my father had no choice but to become my examiner before the actual exams. Given that, I did my own thing in the exams, I’m surprised how I usually ended up doing it decently. Considered to be the decent bum in school, my repertoire of curses and swear words were limited, thus mathematics managed to save itself from my insistent assault on its roots.

A score of 40 out of 100 in mathematics during my fourth grade brought out loud lamenting gasps from my parents. I had just managed to scrape through and it was also probably the day, when their hidden dreams of seeing me as a big bombing scientist ended.  But, it was also a day of liberation for me, since the dreamy stars were now absent in my parents eyes. I jumped around carefree with joy. The red bum and the boxed ears still made their presence now and then, but I was free now or rather I had a smaller chain of expectation tied around me compared to the heavy clunking metal which I used to lug around before this incident.

It took a beautiful geometry teacher to finally pull me into the whirlpool of mathematics during high school. The classes were now pleasant, the curses were gone. Soft brain petals started crashing on the hard rock faces of mathematics. Asking intelligent doubts inside and after class had become essential. Temporarily there was total malfunction and I scored lesser in the following exams than what I would have normally scored by mugging the whole set of sums. Before things started to take a nasty turn, the teacher left and was promptly replaced by a dour grunting male.  The soft brain petals chose to stay at home and the hard rock faces were left unbothered for years together.

Pre-university was the phase wherein I had mastered the art of solving problems blindly. My soft spoken mathematics tuition tutor made his class solve a barrage of problems in his two hour class every day. With such practise even the dumbest fellows get a hang of the subject and so was the case with me. Every sub topic had a fixed set of different kinds of problems, once I became aware of that fact, the going became easy. With such coaching going on, I decided not to attend the college maths class completely. Our college teacher, a giant of a fellow seeing his class dwindle down from 3 digits to single digits must have taken offence, after the exam results were out, he caught me on a by-lane near my home. Being sure that I might have flunked in mathematics, he took a very aggressive tone and started giving me advice on the need to attend classes. He didn’t know that the ace was up my sleeve. When I finally revealed it, he looked like a chicken caught under headlights. Quickly he simmered down and went back to his previous mode and demanded where I had lost the six marks (score was 94 out of 100), I rolled over my eyes, probably he might have given Kejriwal a run for his money today.

Engineering finally started to bring out the soft brain petals from their cosy spots. This time it was more of an internal drive than an external stimulationJ.  Looking at signals and their behaviours through the eyes of mathematics was probably my first aha moment in mathematics. The soft petals began their painful journey from hard to soft.  Endless hours in library to grapple simple integration over the sine wave and what not and as expected, my score bombed in that subject. Half of my time during that semester was spent on this subject. But, more than the score, it was that momentary joy of having understood something very intricate using mathematics, pulled me towards it. I tried to bring in my intuitive interpretations to the equations, many times I failed but there were few times where I really felt satisfied.

When I read technical papers and see a bunch of equations, the first response is that of fleeing. The fight part of the brain requires some time to wake up and override the flee response.  The grind then begins. Many of these grinds have shown how much an important role mathematics place in explaining phenomenon that is hard to explain intuitively. Looking back, it feels funny that such an important subject is taught in schools with so much apathy. Even the teachers don’t seem to have an idea on the end goal of mathematics. Even now, probably due to my long standing hatred, mathematics doesn’t sit easily inside my head. It looks around as if it is an unwelcome guest, but I have now closed all the doors tightly to make it stay there and give myself a better chance in wooing it. It is too important a guest to let go and I hope one day it will feel at home.

Start-ups & Products

Evolution is probably one of the most profound theories that one can see working in many spheres of life. The theory of natural selection bestows on the most adaptable, the crown of survival in a continuously changing environment.  In the technology industry many start-ups have come and gone and there are many more that will spring up in the future. In the garden of continuously changing environment of consumer’s tastes and preferences, seedlings spring up every now and then. Whether the seedlings manage to grow up into big trees having many branches or wilt under the changing tides is governed by the cycles of time. A vibrant start-up ecosystem will ensure that the technology garden is always ripe with fruits. The best possible idea among the many alternatives will emerge if the idea in its various forms germinates at the level of a startup. A big company pushing for a new product idea will muscle itself through to the consumers hand, who in turn will end up with a substandard product. Finally due to the network effect, the startup’s with good potential products are side-lined into oblivion.

As part of my daily readings of a couple of tech blogs, I thought of sharing some interesting product ideas from start-ups that was in news in the last month. I hope to put this up periodically probably for my own reference.

          Cube Sensors:

            http://www.youtube.com/watch?v=mE_5ZjEDImA

I liked the idea of having multiple sensors spread out at different locations in your home. Indirectly you have a spy in every room of your house if you want one. Connected seamlessly with your personal electronic device, these sensors can keep you updated instantaneously. This little things probably will revolutionize the way we see our homes if compelling use cases are found.

           Self-cleaning dishes:

               http://bit.ly/1a6uiqO

Doing the dishes always sucks. I don’t remember any particular day where I really enjoyed doing it. If the dish has been let out to dry then you end up pulling out the skin from your hand along with stuck gruel. This amazing company is developing dishes which will not allow anything to stick to it. So just pour some water to shake of the whole muck and you end up with sparkling clean plates.

3D keys:        

http://bit.ly/1dChp5o

This one in the outset may not look revolutionary. The option of printing your keys in 3D printer kiosks. Also I’m not so sure how will the business model will work, but they seem to be crazy enough to bring the 3D printer technology into the purview of the normal consumers.

Blood vessel 3D printing

http://bit.ly/1io4skl

Maybe a couple of centuries back people would have thought flying in the air is a crazy idea. A couple of days back, I would have said printing human organs is a totally outlandish dream. But a start-up in Japan is actually going out for trials of its bio printer which can print arteries of the heart. Soon, that long wait for the replacement body part faced by patients in hospitals will be a footnote in the book of history.

June: the wearable

http://www.youtube.com/watch?v=5U-5rgbnNuE

This one is not coming from a startup and probably that is why the utility factor is looking totally doubtful. A gem of a band will tell you how much sun exposure you have had. At least I don’t see women falling for it unless the gem is actually worth it. 

Rajasthan

Probably it is one of the most visited tourist places in India, so my eulogy of the place is one more drop in the huge ocean. In the dust and sands, we had a glorious history of kings and their life long gone and this trip was essentially an experience of reliving the past. The history lessons long forgotten made some comeback here and there. The guides were story tellers in their own right and every ruin, every palace needed their expert skill to make themselves appealing to the visitors.

 I and my wife went on this trip organised by Nirmala travels in the beginning of last year. The whole trip lasted more than two weeks. So we had our fill of sands and forts by the end of it.

The first place that we visited was the royal city of Udaipur. Flanked with hills in all directions, in the mornings it looked as if the misty mountains were not far away.

The most visible symbol of Udaipur is the palace which is built on a hillock. You can see sturdy trees on the top floor of the palace, the reason being the palace has been built around the hillock thus allowing for the soil to reach the top. The soul of the city mainly revolves around the exploits of Maharana Pratap, the memorial at Haldighati, the place of his fierce battle with raja maan singh and the memorial place for his Chetak horse on a small hillock near the big lakes of Udaipur are a proof of this. At the end of two days of sightseeing, I ended up eating hot pakoras and drank masala chai in the shopping hub of the city, with all shops closed for Sunday, I felt happy and my wife bewildered.

Chetak Ghoda memorial

Udaipur Palace

After Udaipur we visited Chittorgarh, the mighty fort situated on the top of the hill. The circumference of the fort is around thirteen kms and it contains in its belly history like no other place. From tales of Meera bhai to Rani Padmini, to the amorous Alaudin khilji and the brutal destruction caused due to Akbar’s attack on the fort, the whole place has a historic halo to it. The place looks sacrosanct and full of those past life that people had lived and sacrificed at its gates. You get an eerie feeling as you visit the jauhar sites where the women in the fort had immolated themselves whenever the fort was about to fall into the hands of the enemies. This had happened three times in the history of the fort.

Inside Chittorgarh Fort

Vijay stamb- Inside Chittorgarh fort

The next stop was Pushkar, the place with the only brahma temple. The climate had deteriorated to almost zero degrees and getting up in the freezing cold was an effort in itself.  Deciding against taking a dip in the holy lake in the freezing cold, we just sat on the banks enjoying the cold breeze. It is said that the lake is the symbol of brahma and the temple per se, doesn’t have much significance.

Pushkar Lake

Jaipur, the city of the Marwari’s has again a rich tradition of rulers, with raja Maan singh being the most famous of them. Having accepted the Mughal overlordship over them, the Jaipuri’s had rarely faced any external dangers. Jaipur has a mix of Mughal and Rajasthani architecture in the buildings. The fort and the palace were impressive but it didn’t look as glamorous as the Udaipur palace. Jantar Mantar which is next to the city palace is a must visit site. Built in the 1700’s by Raja Jai singh, it is a place to be explored at leisure. The various instruments used to determine the accurate time and time of the year etc. makes you a wonder eyed kid looking at some magic happening. The Amer palace and the Jaigarh fort were pretty nice but the eye candy of the day was the giant canon which is on top of the Jaigarh fort. The canon has a range of 35 kms and it was used only once during its test fire. At the end of the city’s visit we had an evening free for shopping, I guess the normal tourists are royally screwed in these places. It is best to start bargain from say 20% of what the seller demands and be an obstinate buyer

Jal Mahal in Jaipur

The Big Canon

Amer fort- Royal Garden

Jantar Mantar

The next location was Bikaner, the place famous for its bujias. Closer to the desert area, Bikaner looked the driest place till now. The fort at the city center was nice, but by now since we had covered a pretty good amount of forts and palaces, there was nothing drastically new here. After the fort visit, we went to the Karni mata mandir. This place is an experience in itself. Thousands of rats scurrying in all directions. I mistakenly stepped on a couple of them, to pull my leg up instantly after feeling the furry touch. According to the local belief, the people who die in the town take birth as rats in the temple.

Bikaner Palace-Walls adorned with Gold

Karni mata mandir- where rats rule

Jaisalmer brought us next to the desert. Dusty and in a way quite sleepy, Jaisalmer seems to transport you back in time. Camels rule the roost in this place. One of the interesting places to visit here is the Patwaon-ki-haveli or the houses of the diamond merchants. Apparently lot of diamond trade happened in the bygone days at this place. The multi storeyed building gives a glimpse of the life of the rich in the times of the kings.

The vast expanse of the desert was finally in front of us. Sitting on the sand and watching the sun set on the sand dunes was quite a rich experience but almost all the tourists in Jaisalmer seemed to be present at the same place, diluting the richness to an extent. The camel ride was also fun, but considering the fact that only an 8 year old boy was guiding the camel, I was twitching in my seat whenever the camel grunted.

Gadisar lake

On the Thar - With the ship of the desert

Jodhpur the blue city has a majestic fort that looms over the city. Apparently some scenes of the movie Dark knight rises was shot in and around this fort including the famous pit scene. The fort is quite huge and the view of the city from the top is breathtaking.

Jodhpur Fort

Jodhpur Fort

The trip was rounded off by our visit to the only hill station of Rajasthan, Mount Abu. The Dilwara jain temples are majestic. The intricate carvings on the rocks requires time for the visitors to observe and see. It is unfortunate that photography is not allowed inside the temple complex.  Mount Abu is also a shopping haven for the ladies. Trinkets like earrings, bangles are pretty cheap if you bargain well.

Overall it was a nice trip. Having covered a significant portion of Rajasthan, there was lot to see, enjoy and experience. The experience with Nirmala travels was ok. Food was excellent as the cooks travelled with us and prepared nice south Indian food throughout the tour. Accomodation varied from very good to pretty poor. At least in a couple of places it was wonderful, average in around four places and pretty worse in a couple of places so much so that I had to get the sheets changed and in another place had to fight for a room change. The travel was done in a Rajahamsa kind of bus, whereas I was expecting an A/c bus, the younger people get to warm the last seats of the bus. So if you are not at least above 50, you are screwed. Lot of places were covered in the two weeks, probably it would have been impossible to cover so much if you travel on your own. In conclusion no more such travels for me in the future till I turn 60. I would rather spend double the money on a week long trip.

I would say we enjoyed Rajasthan a lot, it is mostly a history lesson that plays before your eyes. The sand filled forts and the run down relics look like the fast fading remnants of the glorious past that the place had seen.

Play the game, in theory

Game theory is a pretty fascinating subject. Even though I had spent almost three years in MBA classes, I somehow managed to evade it with one or the other interesting alternatives cropping up in the form of electives. Recently I picked up a book “The art of strategy” which was lying around in my brother’s book shelf. Based on game theory, it threw some pretty good insights about how the theory can be seen in the practical world.

For starters, consider a situation wherein there are two sailors competing with each other in a race. Since sailing involves several strategic decisions that needs to be taken, what is the best way to succeed? The answer depends on whether you are leading the other person or trailing. If you are leading, then you have to just copy the strategies that the trailing person is employing, because no matter what, if those strategies speeds up his boat, then your boat would also speed up by the same amount or in case the strategy completely flops then also you are ahead of him and you are bound to win the race anyway. This effectively kills the strategy of the trailing guy. So taking lead in such a situation becomes very critical. This strategy would not work if there are multiple players in the game though. Some traces of this strategy can be seen in our telecom domain as well. Samsung and Apple are in a neck to neck race with the former slightly ahead, but they are always looking back towards Apple for guidance, be it in curved phones or smart watches. Companies like Nokia and Sony are right now far down in the horizon, so even a 41 MP sensor or a complete water proof phone doesn’t muster any notice by the leader.

Traffic is technically a collection of humans sitting in tin boxes called cars doing nothing much till the car in front moves. But in India it takes a completely different meaning, It stands for huge mass of completely disconnected individuals doing their own things in a larger setup. How many times have we faced the frustration of standing orderly in a traffic jam and a slick cab driver would come in the wrong side and nuzzle into the traffic at the front. Our frustration level increases crazily. The cab driver reaps a significant savings in time whereas all the other drivers in the traffic would suffer a minor time cut. If the drivers breaking the law increases, then the incentive for the obedient drivers to break the law also increases, so much so that going in the proper lane would generate more reward than breaking it, but this equilibrium is not a good one to have. The vehicles coming in the opposite direction would also suffer at the hands of these law breakers. What is the best way to curb this practice? Imposing severe fines or probably penalizing them on time is the best way, the level of these fines should be so heavy that more than 99.9% of the drivers should conform to the rules. Even if you get caught once, it should be enough to make you think ten times before breaking the rule again. The same thought can be applied to shortcuts as well. Shortcuts saves time, even though in terms of distance it will usually be a little longer. There will be an optimum capacity for this shortcut beyond which the incentive to take it would decrease rapidly. How to preserve the sanity of the shortcuts? Once you discover one, keep it to yourself.  In similar ways, if you have an expressway along with a alternate toll free route, it is important to price the toll for the expressway such that the traffic doesn't go beyond a point. The optimum equilibrium needs to be critically analysed.

Another interesting concept is that of mixed strategy. Here you let chance to make a decision rather than actually thinking through an outcome. Consider the case of a football player trying to take a goal kick, assuming he can kick the ball to the right, or to the left. How should you choose among these two options? If there are different payoffs associated with each of the options, then choosing the correct proportion in terms of chance is important. It would not be just feasible to select either right or left based on chance (coin flip). An optimal randomization would be needed based on the payoffs.  Say if the striker can hit the net 58% of the time when going for the right and 85% of the time when he hits left then a 50: 50 chance will give a payoff of 71.5 (average of the two). The above score is for situation when the goal keeper has dived to, say his left side. Now if the payoff for the striker is 70% for the right side kick and 55% for the left side kick when the goalie has dived to his right, then the strikers combined payoff will be 62.5%. We can clearly see that with 50:50 chance the strikers combined payoff can be kept to 62.5% by the goalie by diving to the right always. So the optimal mixture where the striker maximizes his payoff would be the percentages where the left and the right payoff are the same for him and the goalie remains indifferent to both directions. Thus optimal mixture turns out to be 72:28 for the striker to choose between right and left.

Taking a revolver with one bullet and rotating it randomly before the hero and the villain alternately put it on their head and pull the trigger is often seen in our Hindi films. This act has a name in game theory, it is called as brinkmanship. Brinkmanship exploits the increasing tension with each act in the game. The probability of failure goes on increasing with each small step the opposing parties take. Thus in a way both the players are on a slippery slope, the person who blinks first will lose everything that he is playing the game for.

Finally one of the most effective strategies that one can use practically is what I would call “cut the oxygen strategy”. Facing a difficult challenge such as reducing weight, a person would come up with umpteen excuses to eat what he/she likes.  But if you make the alternate route of not reducing weight very painful such as paying a terribly huge fine to a friend if the set target is not met is pretty effective. It will push the lazy self towards action. So if want to be an entrepreneur, before thinking of what to do just resign from your job, go down to the street and start off, your probability of success is the highest this way.