Ramanujan and Shakuntala Devi

Ramanujan had a phenomenal ability in mathematical logic. Shakuntala Devi had the ability to perform mind-boggling calculations at a breath-taking pace.We can learn many things from knowing that humans like Ramanujan and Shakuntala existed. One is that there is a configuration of our brain that can result in such super-human abilities. Both Ramanujan and Shakuntala lived pretty normal life otherwise. This tells us is that a normal brain is not at a Pareto optimal level. Which is good news because it means that one does not have to sacrifice any mental functionality to achieve the abilities of Ramanujan or Shakuntala Devi. Another observation - they were both born in pre-independent India in poor families. Ramanujan received his education nothing out of the ordinary. Shakuntala Devi was not formally educated in school. This implies that starting your kids early in the tried-and-tested mechanisms of teaching so that they are successful in school early in their lives may not be optimal. It is low-risk strategy which will dumb down kids.

Brain is a physical object after-all. And, it operates by sending signals between its millions of neurons. This implies that there is a certain connectivity and configuration of neutrons that can allow one to think like Ramanujan or do calculations like Shakuntala. Can we design such a brain? Not at present, but maybe in the future. What do we need? We need to first figure out what is the critical size of the configuration of neurons that needs to be trained. Ideally, one would like to tailor the entire brain, but that may not be practically feasible. Once we know the critical size of connections that we need to optimize, then we need to figure out what to optimize. Which configuration results in a Ramanujan brain? Is that configuration unique? It is most likely not unique, because, first, in that case the probability of existence of Ramanujan becomes diminishingly small. Secondly, that would mean that any new experience or learning would change this configuration and the brain will become sub-optimal again. So, an ensemble of configurations should work. Great! But, what is the objective function that should be optimized? I do not think we know the answer of this one as well. Once we have figured out these questions, then it comes to the logistic part of physically designing such a configuration. How do we assemble neurons in a configuration? We will probably not start attaching single neuron to others from scratch. That's not possible. We will probably need to scan thousands of brains for their connectivity and select candidates that have closely related networks. This exercise will also tell us if the brain's ability correlates positively as we move towards the optimal configuration in a continuous manner, or will we see a step-change in the intelligence. If the process of optimization of networks is invasive, one needs to somehow grow that brain in-vitro. Then, we start optimizing the connections.

Rubik's cube: Marshmellow test for adults

I could never solve the Rubik's cube. What is it about this cube? The objective is to have all same-colored squares aligned in rows. So, one starts by aligning some of the same-colored squares. But then there is a catch: you need to destroy partially formed order/structure so as to further increase ordering in the cube. That is, in the intermediate steps, you need to undo what work you have done previously for reaching the globally optimum configuration. I think solving a Rubik's cube is a good measure of risk-taking mentality of people. Those who are scared to loose what they have for a better reward in distant future are unable to make such moves, and thus never solve the cube completely.

Politicians

Many years back when I was in India, I was watching an interview of Mr. Narayana Murthy, the chairman of Infosys. He was narrating a story about a meeting he had with the politicians of his state Karnataka. Apparently, the politicians were planning to promote their regional language, Kannada, while dissuading English education in state-funded schools. Murthy went around the table to ask each politician where do their kids go to school – all the kids either went to the best schools in India or abroad, and of course, they were all learning English. Amused, I told the maid in our house how the politicians in Karnataka are trying to promote their regional language in school over English. She replied that we should ask where do these politicians send their kids to school. So, one does not need to be chairman of a software company to figure out what the politicians are up to. It is in their favor to keep the population less educated, less equipped, economically weak and subordinate to them, as this will allow them to keep their powers unchecked and unquestioned. I had told the maid of this incident because I knew that she had made extra efforts to ensure that her kids learn English. Less education does not mean that a person is a fool to fall into the tricks of the politicians. Fools are fools. The people who look up to politicians as their leader for guidance in each step of their lives are the ones who are easily duped and manipulated. 

Fast forward to 2016. The prime minister of India announced one fine day that within a few hours, the currently circulating currency notes will no longer be valid. Everyone needs to get the notes exchanged with the new ones being issued by the RBI. This created a huge turmoil for many months with long queues in the bank, people losing their daily wages, small businesses suffering a loss in revenue, etc. The leaders claimed that this will clean the economy of black money. I was watching a popular news debate “The Big Fight” on NDTV – the topic was demonetization. A young girl from the audience said that “she is willing to stand in the line to get the notes exchanged. Our nation is being built and we should all look forward to that”. That comment sparked an emotion of hope and patriotism. Everyone clapped. I also felt a tinge of emotion. An year later, the Government admitted that they could not recover any black money. People had found ways to get their black money converted to white via many new avenues that had sprung up overnight. The entire experiment was simply like an ant colony optimization scheme – the conditions changed, a large number of people started figuring out the best possible way out, many loopholes and methods were identified and voila – we are rich as we were before. The young girl on The Big Fight was not from a poor family (people from marginal backgrounds hardly ever make up the audience of TV shows). She must have not suffered much. Who suffered were the poorest of the poor. They don’t have any say in the news channels as yet. In December 2016, just a month after the demonetization announcement, I was visiting some remote areas of Malwa region of India. The artisans over there gladly took a bank cheque as a payment for our shopping, but they told us that the nearest banks are many miles away. The workers they hire for block printing do not have access to banking – they get their wages in cash, they use boxes to store their money or sometimes dig pits in the ground to hide their savings. Most of them are not educated and are quite unaware of what is happening in the country. At the time of demonetization, they lost all their savings. To get their notes converted they had to walk many miles to queue up outside the bank. Those days banks were running out of newly issued notes. So, even if they spend their day not working but going to the bank, there was no certainty that their money will be exchanged. Great job Modi. 

It is said that Modi is a PM who connects with the people. I heard a part of the speech he delivered at the Madison Square Garden. He made two jokes, one that man is now a slave to the mouse (referring to a computer mouse), and the second that it costs more money per mile to take an autorickshaw in Ahmedabad than the per mile cost of ISRO’s Mars mission. I did not laugh. Thanks to Whatsapp, I had heard these jokes before. So, we have a PM who goes center-stage and cracks whatsapp jokes. Not surprisingly, he connects to the people, as that’s how we do small talk in our drawing rooms. All fluff and no substance. As an example, when Raghuram Rajan talked about buying and selling of dosas to explain an economic concept, it became famous as Dosanomics. The leaders of yesteryears apparently made the mistake of presenting political, social and economic issues as serious matters. 

EDX

It is 9.30 AM and I know that there are a hundred things I should be working on right now. But sometimes you feel inspired, and then those hundred things wait and you write a blog. EDX is the newest online teaching website.  A couple of months back, I registered for a course in Physics taught by a professor at MIT. It was a 5 week course, with new course material released every week and a problem set to be submitted weekly. I struggled to keep up the pace. Missed a few deadlines. Managed a few. Then we had the final exam. I got 80% and that took my aggregate grade to 63%. Just above 60% and I passed! That's not the point. The point is the elegant manner in which the professor taught the course. The beauty of how he developed a complicated theory for the students bit by bit. And, it is all available for free. The best thing about EDX is the software which allows you to submit answers even when they are as long equations. Online learning has come a long way. EDX has emerged as the leader. It's the future.

Orange

Everytime I eat an orange, I get fascinated by its amazing design. To start with, there is the skin. It is porous, hydrophobic, squishy, and sticks to the fruit with a mesh of fibers. The inside has spherically arranged packets holding liquid and covered with a thin fibrous layer. If we open a packet, we find small spheroid bulbs filled with beautifully colored liquid and covered with a delicate layer. Orange grows symmetrically out from a small bud, becoming enlarged as it adds cells in a defined structure, it is not assembled piece by piece like the way we manufacture items. And, if left alone, it seamlessly mixes into the ground. An amazing beauty, an intricate balance, a piece of art, and zero pollution. It is produced by a small plant not more than 6-7 feet in height, 3 feet in diameter. No raw materials to be shipped in, no workers doing 3 shifts - just an un-disturbing existence. Humans are in the stone-age of manufacturing. We lack the intellect to design. We are struggling.

"Parallel lines meet at infinity"

"Parallel lines meet at infinity", my cousin in class 10 told me, and also that his teacher had mentioned that if one cannot understand this apparently simple concept then one can never hope to understand mathematics. I was in class 8 at that time. I wonder why did the  teacher say so. The concept is still not obvious to me. By linking an obscure statement to the ability to understand mathematics, the teacher very effectively killed any uncomfortable questions about it from the students.

Suppose I am standing near a  set of parallel lines, say a railroad. I look towards positive infinity - the lines meet at some point. We will never reach that point and the point is not a well-defined point, but the lines do meet as per the statement. Now, let me gaze towards minus infinity. Again, the parallel lines meet at minus infinity. Now if two lines meet at two distinct points, then they are nothing but the same line. So, we arrive at a contradiction, and parallel lines do not meet at infinity.

My mathematician friends tell me that this line of reasoning is not quite correct, as one cannot have a well defined point at infinity and that the statement that "parallel lines meet at infinity" is only valid in projective geometry. 

A monkey and a surahi

This is a story I read when I was a small kid. It goes like this: A man wants to catch a monkey. He places some chickpeas (chana) in a surahi (surahi is a Hindi word for a thin, necked flask, usually to store drinking water), leaves it in a park where monkeys frequently visit and hides behind a nearby tree. In some time, a curious monkey approaches the surahi and inserts his hand inside the neck of the surahi to grab as many chickpeas as his fist can hold. But the monkey's fist is too big to slide out of the neck of the surahi. The man starts running towards the monkey. The monkey sees the man but out of greed does not open his fist to remove his hand and is caught. Interesting story - monkeys are fools, and humans are clever. Clap. Clap. Just that, the story is only a figment of one's imagination and, in reality, monkeys are smarter than this. One would notice that a monkey, while attempting to scavenge food from a waste-bin or while attempting to open a container, would run away at the slightest hint of someone approaching him. In fact, I have seen clever monkeys who manage to steal bread-pakoras from kids but do not approach a heap of bread-pakoras in the nearby shop because they know that the shopkeeper will not let them steal.

Humans are different though. They are the greedy lot. And, they are so greedy that if monkeys could understand their behavior, they would be the ones writing stories about them. If one replaces chickpeas with something that humans care more about, say, a legacy like a house which can be sold to make some money. Humans will put on a nasty show and will fight tooth and nail to get a hold of it or a piece of it. One cannot reason with them, and to even attempt such a thing is naivete. Quite an entertainment for monkeys, I must say.