Book Review - Music of the Primes by Marcus du Sautoy (2003)

I can say, with some modesty, that I am familiar with the subject of mathematics more than an average person is. Despite that I hadn’t ever read a non-technical book on mathematics, so this book ended up being a very engrossing and a pleasant surprise. Marcus has done a tremendous job detailing history of search of the proof of Reimann Hypothes: interspersed with personal stories and personalities of mathematicians involved – one person at a time.

What is Reimann Hypothesis? I am not smart enough to explain, but I regurgitate what I gleaned from the book. As mathematicians are wont to do, they wanted to understand what and why certain numbers are prime and what is the distribution of prime numbers across number line. When that proved to be tad difficult of an endeavor, one of them decided to find pattern in number of prime numbers less than a certain number, say primes less than 100, prime less than 1000, and so on. There was some success in generating a formula for such counting (see later), but it wasn’t exact. Meanwhile when a mathematician B. Riemann decided to pass on complex numbers to simple looking Zeta function (1+1/2^n+1/3^n+…) in 1850s, he observed that values of  “n” for which function takes value of zero relate to counting of primes (I don’t understand how, though!). Moreover, he guessed that all such “n” have the real part of 1/2. This guess is the Riemann Hypothesis. Line passing through this point is called Reimann’s critical line.

Book gave me a fascinating glimpse into how theoretical mathematicians work and how does mathematics advance. They often work by posing ad-hoc puzzles (“what happens when kick a rotating sphere of liquid”), trying new mathematical operations on existing formulas or statistics on existing numbers (“taking moments of function”, “passing imaginary numbers to known equations”), looking for patterns and trying to find equation and explanation of those patterns, translating numbers and equations from one branch of math to another (“from numbers to graph”), trying to prove intuitions, and finally aiming for elegant, closed form solutions and formulas to problems. To an application oriented engineer, this was delightfully ridiculous – trying anything to anything and spending decades trying to make sense of it toward no immediately discernible end!

In doing so, mathematical properties sprout starting with educated guesses on observed patterns called ‘conjectures’. When supported by available data become, conjectures become ‘hypotheses’ which make a novel yet untested prediction. Hypotheses graduate to ‘theory’ when the non-trivial novel prediction comes true and proven mathematically, and eventually to ‘law’ when validated in multiple domains across time to multiple level of rigour with no scope for any further enhancement or exception.

Growth of mathematics is also, surprisingly, driven by friendly bets between prominent mathematicians. Bets, often of little material value, but taken seriously enough, are reason for many important advancements in the field. For instance, 100 million Reiman’s zeros were calculated by costing CPU processing in 1970s just to (dis)prove a bet! I wonder if this is true of other disciplines of science.

Till very recently before advent of internet, exchange of ideas through letters was usual form of brainstorming and communication among mathematicians. Yet, many also worked in isolation through their rough sketches never sharing ideas till they were comfortable of elegance of proof, or of not being challenged or ridiculed, or not wanting to share credit of their discovery too early! Consequently, the amount of knowledge, which is lost to humanity, because their family couldn’t comprehend the importance of scribbles in their papers when they died (and just threw away) is heart wrenchingly disappointing. Ramanujan’s and Reimann’s notes on having figured out proofs but couldn’t be bothered to write them out because they thought them trivial have costed mathematicians efforts of centuries.

Book underscores a unique manner of working of theoretical mathematicians – their rigorous reliance on proof. Unlike other spheres of science, where theoretical predictions are useless unless observed under experimentation, mathematicians are content with solid proof despite lack of observations, and as corollary, they still do want solid proof despite what would be overwhelming experimental observations in other sciences. And why is it so? Because math being math, incongruence with theory may occur even after trillions of observations – 10^10^10^34 is theoretical number when Gauss’sPrime Conjecture is proven false. Does it matter in practice, though? This reliance of solid theoretical proofs also means that proofs once established don’t change forever. While theory of gravity has been refined every century, mathematical proofs established from 1600s have stood test of time.

Role of computers is hinted on later parts of books, but it is aptly concluded that computer can only help in disproving a hypothesis by providing counter examples but cannot prove a hypothesis simply because any number of matching examples (evidence) don’t count and cannot constitute a proof.

Now let’s come to the personalities of mathematicians narrated in the book. If you imagine mathematicians to be hard working geniuses & nerds, you will not be wrong, on average. Like all geniuses, most of them show their signs before they turn ten. For instance, Gauss (of the Gaussian distribution) was correcting his father’s math at age of three where normal children do not know beyond counting. Most mathematicians are pacifists reveling in their own cocoon with little care or awareness of the rest of the world. Some were eccentric – for instance, G H Hardy, lived his life fighting with, tempting, and challenging God, with often comical outcome where he ended up believing in God to prove that he didn’t believe in Him.

Ramanujan’s level of genius is, of course, unfathomable. If partition number is defined as number of ways to partition N things (partition number of 3 is 3, of 4 is 5) then he literally dreamt up formula to calculate partition number of any N just in flashing insight without intermediate steps which included square root, pi, sum, mod, natural logarithm, integration, differentiation, imaginary number, and trigonometry! If not Namagiri Goddess, then how?!

Of course, there are sprinkling of revolutionaries, womanizers, and partygoers. While the book does reference tumults in the rest of world – world wars, famines, Nazi politics – and their impact on mathematicians, and hence on mathematics, they are not dwelled into more than mere mentions.

Incentives for theoretical mathematics are few and far (are they?) – most of them do this simply for the joy and, occasionally, for the fame within mathematician community. There is no Nobel Prize in math. The highest award, the Field Medal is given only once in four years for living mathematics under forty years of age and accompanies just CAD 15,000. Opportunities for commercialization are rare – though of course, cryptography and encryptions are important exceptions. Makes you wonder how cheap and easy to sponsor a prize in math and yet why hasn’t anyone done so?

While reading the book, I also realized that my level of thinking as commoner, despite my admissions in the opening line of this review, is closer to what mathematicians were doing 400 years ago. Hence, what mathematicians are doing today, reflected in the later chapters of the book, went completely over my head! Marcus has done excellent job in talking about mathematics without using mathematics, but I do feel that book can be slightly better by exposing readers to real math – say equations or screenshots of seminal papers – even with clear expectations that reader won’t understand. Else there is risk of getting too lost in analogies!

Search for Reimann Hypothesis has led to multiple discoveries and developments on the way, and in recent years even found a connection to Quantum Physics, where distance between consecutive Reimann Zeros is found to mimic distance between energy levels in atoms! Was this coincidence or some universal pattern? Being able to predict next number in moments of Reimann Zeta function by observed energy level of atoms confirmed this as a tangible connection. Not only is the universe stranger than we imagine, but it is also stranger than we can imagine!

Longevity of Reimann Hypothesis has given it an enigmatic status. Some mathematicians take this as challenge of ultimate proportion. Others shy away knowing that it may as well be the end of their careers. Many proofs in other areas of mathematics depend on Reimann Hypothesis being true. Will we ever prove this almost 200 hundred year old hypothesis? There were 300 million zeros discovered which follow Reimann Hypothesis – as of book’s writing in 2003 – and 10 trillion as of writing of this review, giving overwhelming evidence about its truth, but alas no solid conceptual proof exists yet (how Reimann Zeros look?). It’s even proved that there are many more zeros within an arbitrarily small band around critical line than outside, but that doesn’t prove that all zeros are on that line. It’s even proved that there are infinite zeros on the Reimann’s critical line, but that still doesn’t prove that all zeros are on that line.

Godel’s incompleteness theorem says that we cannot prove that same set of math axioms won’t lead to two different answers (contradictions), and there are going to be some true statements which cannot be proven. It’s amazing how mathematical logic can even prove such abstract generalized statements! A possible consequence of this is that Reimann’s Hypothesis may be one of those statements which cannot be proven. But mathematicians believe in elegance of solution and haven’t yet surrendered that such important hypothesis won’t have a proof.

A person like me who doesn't understand Reimaan Hypothesis, has no comprehension of its importance or role in the world, cannot even being to understand even after trying - and I did try, during and after this book, and still ended the book feeling the sadness one feels when one departs from a lovable character at the end of the book: feeling of parting the long journey and deep melancholic awareness that next chapter of that story may never come within my lifetime. This is the power of well told story written by Marcus du Sautoy.

***

Below are some noteworthy facts about Prime numbers and Reimann hypotheses which have nothing to do with the book review but elicited aha for me and documented just for fun.

• Number of primes up to number N is approximately 1/ln(2) + 1/ln(3) + … + 1/ln(N)
• Harmonic series, 1/n, is called so because pot filled with water up to 1, 1/2, 1/3, … levels produce harmonious sound but not at other levels!
• Mathematicians have created a 26 variable equation to generate all primes. This works when results are positive numbers, but most often, they are not.
• AT&T played key role in mathematical research, even as telephone company they had little applications for mathematics, but it was not purely altruistic behaviour towards science & humanity, but a commercial and public relation consideration since they had restrictions on how much profit to absorb because they were a monopoly.
• How to test if a number is Prime, without necessarily trying out all divisors? X^p=X(modulo p) only if p is Prime for any X. This is important to find keys for Public Key Cryptography.

Breaking the Bias – Lessons from Bayesian Statistical Perspective

Equitable and fair institutions are the foundation of modern democracies. Bias, as referring to “inclination or prejudice against one person or group, especially in a way considered to be unfair” is naturally anathema to such ideals. Unfortunately, efforts to reduce impact of bias have been slow and difficult. This is because it is scientifically acknowledged that humans are innately inclined to bias. A significant share of those biases isn’t even known to persons who are supposed to hold them: hence called ‘unconscious bias’. It is also established in many scientific studies that members of a group which was supposed to be biased against also hold the same biases towards their own group (e.g., women being biased against women). So why is bias so inherent part of our biology?

Consider the early man in Savannah. He is suspicious of – as in, biased against – people who don’t look like him, bcause people who don’t look like him are usually from different tribes and people from different tribes are usually at war with his tribe. It’s s survival heuristic his brain has evolved. This is no different from other heuristics we are still encumbered with in the modern world which have roots in the early environment, such as ‘fat is tasty’, ‘sweet s edible’, etc. One way we can model bias is by borrowing from one of the canonical formulae in statistics: Bayes’ Law.

In English, and in the context of this discussion, this means that my magnitude of bias against a certain group, after observing an incident related to that group, is the output of multiplication of two numbers: what’s the magnitude of bias I held against that group before the incident (“prior”), and how directionally aligned that incident was to direction of bias (“evidence”). This change in magnitude of bias is called Bayesian update. In other words, if I was highly biased against the group, but recently observed an incident where a person/group behaved in the way opposite of what bias would have expected, then my bias against that group will reduce.

How can we leverage this Bayesian perspective to understand our fight against bias? One way focuses not on reducing bias, but on reducing the impact of bias: by reducing reliance on human decision making by better use of data; and by tracking the impact of bias on outcomes, and aiming for equity in outcomes by giving preferential treatments to protected groups. However, the majority of sociological and psychological methods of reducing bias typically focus on making people aware of biases, reiterating the need for reducing bias, and counting on the moral compass for people to behave differently (first two articles on the Google search). In Bayesian formulation, these efforts focus on reducing prior and are valid means to combat bias. Yet, prior is often formed in early childhood and adolescent experiences, and is heavily influenced by family, upbringing, and peer group. Hence, changing the prior when the employee joins the corporate workforce may be a tad too late.

However, little effort is done on exposing more favourable evidence. Occasionally there is a conversation to have biased people interact with people from the protected groups so that they realize that their biases are not fair. This largely occurs in a context where people are not just biased but actively antagonist to each other, but rarely in a corporate context. Nevertheless, the value of this in reducing bias cannot be underemphasized. Some ways evidence can be introduced in the workplace setting to counteract against prior is by designing teams and interactions which forces different people to interact with each other. Multiple repeated interactions will help move prior sufficiently to reduce bias over time. Reshuffling teams or seating to make them mix-gendered teams, for an instance, could achieve this outcome.

There is a different Bayes’ Law in mind of each person holding bias for each of the protected groups. While we talked about affecting prior and evidence, we shouldn’t forget the concept of ‘group’. Workplace efforts to reduce biases are competing from Bayesian update of bias from evidence/incidents from the external world as well, which makes this a challenging task. Hence reframing the group into smaller groups actively can also reduce bias, at least in the workplace setting. For instance, group of “women” can be reframed as group of “working women”. Generating positive evidence for working women can be easier in business settings – and will have less competition from the external world – and so will help in reducing bias faster, even as we may not be able to reduce bias against all women”. How to do that in practice? We will have to modify our language, word choices, and reframe the context. While this is not ideal – none of this really is – but we are working with what we can manage effectively, and hopefully eventually reach the ideal outcome in long term.

In the end, we must remember that tendency to be biased was a useful primordial heuristic, thus innate in human nature, and can only be reduced to the extent of the world we live in, but continuous focus on bettering prior, positive evidence, reduced level of human involvement in decision making, and reframing the group context will surely make a dent. It already has.

Weight loss with low carb diet, or How I lost 15 kgs in 15 months

I've always struggled with mild overweight. It's nothing to worry about, but I've been pushing 24-25 BMI for most of my life. While I have always had a strong understanding of the theory of nutrition and theory of exercising - something which is part of my scientific and rational way of thinking - I struggled to put them in practice. For instance, I have tried and given up on more exercise regimes then I can remember in the last 20 years. Of course, I also know that while exercise is awesome for your health and must for your body, it's not a solution for weight loss. Nutrition it is.

And like everyone I knew the basics - avoid sugar, fried stuff, packaged food, more vegetables, etc. I just had difficulty sticking to a routine. I have been averse to fad diets and wanted to take a moderate and slow approach towards better health, hence I was focusing on "reduce" rather than "avoid" for all the bad stuff. Unfortunately for my temperament, reduce just didn't work, since there was no intuitive measure of how much is enough or when to stop. Avoid turned out to be better since that forces black and white distinction. Long story short, I began hearing about low carb and low dairy diets for the last 3-4 years and after looking into multiple scientific research into and consistent anecdotal evidence, I decided to look into the Keto diet. It quickly dawned to me that Keto is not just suitable or feasible for vegetarians. I modified this to low carb, low dairy version for me, and after sifting through my notes and reading created by diet program.

Results? I lost about 15 kilograms in 15 months straight as the weight chart below shows. I wasn't starving, I wasn't going hungry, but I watched what I ate and results gave the confidence to say no to candy or ice cream or pizza which tempted me. My customary before-and-after pictures show some change, albeit not as drastic as before-and-after pictures are wont to do, but the change was visible and noticeable by family and friends alike. In fact, slight uptick you see on weight graph is intentional as I felt it's going too low for my preference. I was content to be around BMI 18-20.

My weight loss journey for the last 6 years, and drastic loss in last 1 year

Before (Oct 2018) and After (Mar 2020) - from 78 kgs to 65 kgs

Here is my diet plan

Main principles

• Avoid junk food, processed food, packaged food
• Minimize refined/white sugar as much as possible, including honey
• Increase portions of nuts, vegetables, and fibers in the diet
• Reduce carbohydrate intake, specially avoid bad kind of carbohydrate during dinners
• Reduce milk intake as much as possible, limit to buttermilk, curd, and paneer wherever possible
• Increase protein intake significantly
• Eat very healthy breakfast, in a small portion, or skip the breakfast altogether and don't eat till noon
• Eat moderate portions during lunch
• Eat light dinner, and do not eat anything after 8pm
• Take fixed portions in the plate, and don't go for second serving
• Chew slowly, enjoy the food, avoid distractions
• Drink lots of water, about 4-6 liters daily
• Keep 3-4 hours gap before mealtime and bedtime

Good kind of Fat & Protein

Walnut, Almond, Peanut, Chickpeas, Flaxseeds, Paneer, Cheese, Tofu, Mushroom, Lentils/Daal, Pumpkin seeds, Soy chunks, Sprouts, Clarified butter/Ghee, Coconut/Olive/Peanut oil

Good kind of Carbohydrate

Sweet potatoes, Brown rice, Oats, Corn flex, Millets, Lentils/Daal, Sprouts, Banana, Broken Wheat/Daliya

Good Vegetables

All kinds are good but Avocado, Brocolli, Carrots, Green peas, Lemon, Guava, Gooseberry/Amla, Beetroot, Spinach, Lettuce, Cucumber, Tomato, Capsicum, Brinjal are better

Things you can drink

Green tea, Lemon juice, Curd

Things you can eat A LOT

Paneer, Cheese, Soy chunks, Peanuts, Peanut butter, Almond, Walnut, Flaxseeds, Mushroom, Tofu, Avocado, Brocolli, Lettuce, Chickpea, Green pea, Spinach, Pumpkin seeds, Cucumber, Tomato, Capsicum, Brinjal

Things you can eat A LITTLE

Sweet Potato, Banana,  Coconut, Brown rice, Oats, Corn flex, Lentils/Daal, Broken Wheat/Daliya

Taking all this together, here is what my day looked like:

Breakfast - skip or small fruit or small portion from Good Carbohydrate list

Lunch - 2 roti, 2-3 bowls vegetable curry, (if you want to taste anything else, take 1 teaspoon only)

Mid-day - dry fruits, small fruit, 2-3 cups of coffee (coffee is not advisable)

Dinner - Sprouts, or Soy chunk, or Salads, or grilled Vegetables, or Paneer, or Peanuts

And trust me, your body will adapt to this. This may look like meagre diet but I never felt hungry. Any pangs were soothed by a handful of sprouts/peanuts which are both filling and incredibly tasty. I discovered 3-4 ways to cook sprouts in the process.

Planning your own foreign trip, with Sri Lanka as example

Cross-published at https://www.tripoto.com/trip/planning-your-own-foreign-trip-with-sri-lanka-as-example-5bfb9f5804051

This guide is about how I went about planning my own Sri Lanka trip. My actual itinerary and travelogue will be published in a separate post after I complete the trip. This is supposed to help you provide resources and steps in planning any trip your own, and is based on a series of steps I follow when I need to plan any foreign trip.

When and Duration

The first thing to plan is when you will travel, and for how long. Open-ended search on Skyscanner (e.g. from Chennai) can tell you what's the cheapest airfare you can expect to your desired destination. Now you can compare your own airfare for the proposed period against this to decide if your period of travel and any excess airfare is acceptable for you or not. Based on your vacations, leaves, personal desires, and so on you can choose to pay little (or very) more than the cheapest fare for your proposed period. You can also play around a few other months to check what's suitable costing for you. You can also go to Wikitravel to find if your period will have good enough weather. This decides your when.

New go to few tour operators to find out duration of ready-made packages to your destination. Selecting your holiday destination on (e.g.) MakeMyTrip, TravelTriangle, ThomasCook, and SOTC can give you idea of typical duration (and cost) of trip. For Sri Lanka, this was about 4-7 days. Quick Google search or Tripoto search can confirm your decision. This whole thing shouldn't take more than 15 minute as our focus is just overall duration and not cost and not itinerary. For Sri Lanka, I realized that less than 5 is too short and more than 10 is probably too long. This decides your duration

Flight Tickets

Flights being most expensive component, you want to nail this down first. Create permutations for duration based on your decision, say 22-28, or 23-29, or 22-29, etc. to find suitable option based on fare and convenience. I usually look at few websites like paytm.com, easemytrip.com, goibibo.com, airline's own website, and few offers if available on credit cards I hold and book the tickets. This step can take 1-2 hours across days.

You may be tempted to try out many websites and offers, but my lesson is that these days prices are pretty consistent across portals and any offer is mostly teaser and benefit will be lost in transaction fee or convenience fee. Prices tend to go up (Murphy's law) during your search period so you should just book within 1-2 days. Do keep in mind arrival and departure times of flights and travel times too (and not just airfare) since odd timings may add to hotel cost at origin station, or have the inconvenience of night wait at the airport, or cost of an extra meal, or unreasonable cost of airport transfer, and so on. Airfare cost alone isn't everything!

Your Itinerary

This is biggest and most time consuming process. Goal of this is to come up with cities you will stay in, and the number of days within each, and transport between cities. This step may take 4-40 hours of time depending on how much in detail you want to go!

You will have to read a lot! Refer itineraries on tour operators websites, pickyourtrail.com, tripoto.com itineraries, and TripAdvisor forum's to identify potential cities you may be interested in. You can plot these on Google Maps to plan a route which is roughly circular and doesn't require returning back, and minimizes overall travel distance and time. You can also get a broad sense of distance and travel times between places so that you can incorporate travel time between cities in your daily plans. You need to decide if the day of travel can also accommodate some sightseeing or will only be spent on travel due to distance and exhaustion.

Refer to TripAdvisor's Things to Do for those places to decide for yourself what things will interest you — not every tourist spot works for everyone, I like slow paced vacations, and not much interested in historical buildings, for example — and how long you think you need to cover those. Read TripAdvisor reviews of tourist spots and see pictures. Split things into 'Must See' and 'Good to See' and 'Avoid' options based on your preference, cost and reviews. This will broadly inform how many days are needed to cover each city. Do note that many places may have ticket cost which isn't easily available (may have to read few reviews), or free days (may have to check attraction's website), or closed days (e.g. every Tuesday), or limited opening (e.g. morning 10am-2pm) which you need to factor in deciding your local route. Use existing itineraries to double-check you duration at each city. At this stage, you can also drop a city from your plan, or choose between cities if you are in two minds. You will have to decide if you want to shift hotel at each city, or can cover one city with another city as base in day's round-trip.

For each place of stay, plot your sightseeing places on Google Maps to broadly understand the density of activities which will, later on, help guide your hotel location and need for local transport.

Based on previous itineraries, your comfort level, and cost comparison you can also decide if you will drive your car (not an option for Sri Lanka), take public transport (an option if you are adventurous, in Sri Lanka), or have dedicated cab for the full duration. Documents on TripAdvisor's Sri Lanka forum have good information on this. Given that I was travelling with family and prioritized convenience, I chose to go with a dedicated cab.

Once your itineraries and places of interest are finalized, you will have to decide if you need to pre-book anything. For instance, Safari at National Parks in Sri Lanka may be pre-booked (but will cost extra) or booked via hotel or done on the spot. Similarly for Whale Watching tours at beaches.

Local Transport

Every country has different options with different cost, and you need to read a lot to find out what will work for you. Rome2Rio is a good portal to quickly get a list of various available options for local transport. As mentioned above, I decided to go with dedicated cab and hence shot an email to key tour operators Tangerine Tours, Red Dot Tours, Walkers Tour, and few others from google search. I also dropped an inquiry at srilankacaranddriverhire.com which is an informal collective of non-branded operators (link found from TripAdvisor's forum).

After comparing cost, few Q&A based on what is covered and what is not covered, and comparing cost of all day hire, or partial hire I decided to go with one operator. Before finalizing the operator, I read its review on Facebook and TripAdvisor, wherever possible, since not all operator have reviews. Be careful to not just go by star-rating but read reviews. It takes time but there are lots of fake reviews! Reviews which are not accompanied by description, or timed in short duration are suspect. You can even click on reviewers on FB to see their profile and ascertain if they are genuine tourists or not. I found many times operators or drivers or folks based in Sri Lanka themselves were giving 5 star to their page. I also found few operator having multiple FB pages. All these are unreliable in my mind, though of course I cannot claim that for certainty as I didn't avail their services.

You can also search on airport transfer options, based on your flight timings. Most airports will have taxis available 24x7 but public transport may be cheaper. You can go through the airport's website or search the internet to find suitable options. Your hotel may offer too though that's likely to be expensive. Pre-booking may work, or maybe expensive. Uber is omnipresent but every country has it's local taxi network as well.

As everywhere, evaluate options holistically for convenience and freedom and not just on price. You don't want to spoil you 100k vacations for saving 5k. Since vacations are experiences, day to day convenience matters a lot in making those memories happy or unhappy!

Hotels

Hotels may not be very expensive in overall cost of the trip, but have undue influence in your vacation experience. Different countries have different hotel booking websites which work better. booking.com, agoda.com, and kayak.com are good ones to start wtih. Airbnb can be explored and can come out cheaper for Europe and US, but for Asia, hotel operators have flooded listing on airbnb.com and it's not much different. Your map of tourist spots will come handy here and you can select few hotels based on budget, amenities, views, breakfast, and location on the map. Go through pictures and customer reviews of the hotel on TripAdvisor and Facebook to filter out some, and do remember to keep you 'fake review' detector on.

Do remember to email or call the hotel to confirm the booking, and don't just rely on booking portal's confirmation. Many a times inventory is not be updated or hotel may simply overbook and refuse you. You don't want to stuck searching at last minute in the foreign country. If you are staying longer at one place, or like to cook in, you can search a hotel with a kitchen. Hostels and dormitories are good options if you are single or have a tight budget.

Visa, Forex, and SIM Card

There are multiple guides on this on the web and this is a standard official process so you have to do what you have to do. For Europe, I have heard that some countries are more lenient than others in granting Schengen Visa so your itinerary should keep that in mind as a port of entry. For every other country, your Visa is specific to that country so you follow the official process. Sri Lanka Visa is online approval which took less than 30 min to fill and 5 min for approval.

These days you will be carrying a combination of foreign-currency pre-paid card and foreign-currency cash for your trip. Based on hotel cost, local transport cost, meal cost, attraction fee, and a healthy buffer you can estimate how much to carry. Depending on acceptance of card vs cash you can split your amount. For Sri Lanka, you need to convert into local currency in destination only and carrying USD is recommended, though INR may also be acceptable. TripAdvisor forums had good information on where to exchange money.

Similarly, local SIM card from airport, city, or pre-paid SIM card from your origin country can be taken based on price and convenience. For Sri Lanka, generally advise is to take local SIM from the city. You may search for telecom operator with decent coverage at cities in your itineraries. Google, google and google away!

Other Things

For some countries, you will be required to, or advised to take travel insurance and health insurance. Find suitable insurer from your origin country, or compare with WorldNomads. If you are self-driving, you need to find a convenient, reliable and cheap car rental company. Few other things to bother are transit visa, luggage allowance on your flight, and frequent flyer miles for your trip.

Plan and Unplan

There are generally two types of people in travel — those who plan everything, and those who leave everything impromptu. Depending on your persona and comfort level, you can plan further minute details of your day, or leave everything unplanned except flight tickets. Despite all the planning, you have to remember that things may take longer than expected, or unexpected hiccups may occur, or unplanned activities may be found interesting. Travel is for fun, and you shouldn't have to skip fun because you planned way too much! On the other hand, after visiting you may realize that somethings could have been done differently and better, and that's okay! Not everything will be perfect, and least you can do after coming back is to put your advise in travelogue to help someone else next time around!

Getting LL, DL, IDP in Bangalore without Agent

I tried, and succeeded, in getting Learning License and Driving License in Bangalore without any intermediary and without any "under the counter" fee. Here is my experience related to Electronic City (KA-51) RTO in past one month.

Learner's License

1. Fill online application at Karnataka Transport portal.
1. You will have click on 'English' at top right few times to get the page in English. I filled application under Sarathi-3 system.
2. Really all they need is Application Number and few basic details. Application can only be done online and not on paper. You can either fill online and get printout or fill basic detail, submit, get application number, and then fill paper application.
3. If you need standard license, select MCWG (Motor-Cycle With Gear) and LMV (Light Motor Vehicle, Car, etc.). I had to make extra trip because I filled both Motor-Cycle With Gear and Without Gear but apparently first covers the second so both weren't wanted.
2. Provide supporting documents
1. Get right proof of age and address (original and copy)
2. Attach one photograph to application. Even though it asks you for 3 copies, they aren't required because you get photographed at RTO.
3. Go to RTO. Cash (Fee) counter opens until 12:30pm on Saturday and 2:30pm on Weekdays so you want to have 2-3 hours with you for whole process. Try to reach by 11am. New location in Begur Rd has functioning Enquiry counter so they try to help.
4. First pay the fee in Cash Counter 2 or 3 showing your application. I was charged 30/- for each class, 60/- in total. This was before fee hike happened in early January 2017. They will provide require receipts, called "challans". Cashier didn't try to overcharge me, but is direct and not-friendly. Given his workload though, I wouldn't complain, and he will answer question if you ask.
5. Get into huge queue to get your documents verified at Room 1. Staple (or Pin, available at Enquiry desk) your documents with challan at top, application in middle, proofs in the end. While your time reading about road signs hanging around.
6. In about 30 minutes you will enter room, and get your turn with Assistant Inspector of some sort. This guy was very particular about anyone not stepping an inch ahead of yellow waiting line but was clinical about process. If your documents are in order, he will tick or sign on papers. He will ask to see both your hands flattened out on desk, perhaps to do "high quality" medical due diligence about your driving abilities. If you are missing a paper, he will ask you to get one. Anything forms, envelopes, etc. which you need to buy can be obtained from tea-shops outside, of course, at heavy premium. You can usually skip the long queue if you are coming with additional documents on the same day.
7. Next you will go to Biometric Room 2 (nearby Room 1) where after showing your packet, and waiting few minutes, you will be photographed and thumb-printed. This shouldn't take much time.
8. You will be asked to go down (find stairs) and go to a place which is crowded with people waiting for their LL Test. Guy outside on desk will check your papers again and ask you to sign in register. As this stage they made me buy prepaid postage envelope (17/- Stamp, 30/- price, a trip to tea-shop again) but I realized that it's not required and others didn't have it.
9. Test is, of course, a joke. I had imagined computerized or written test, but I just got into Inspector's room with 50 others and he spend next 15 minutes explaining and asking to random people meaning of various signs. No one failed, and he was very particular about cautionary signs indicating caution "200 meters before". If you stay towards end of crowd, you can just get by mumbling something and trying to appear inconspicuous.
10. End of session, he will collect the document packet and you are done for the day. 2 sheets of LL, one for each MCWG and LMV will be available in a week's time. If you need to learn or take classes, you need to collect these and go about practicing. I didn't so I could've just collected them on day I applied for DL, and saved myself a trip to RTO.
11. If you don't make errors, you can do all this in one visit and 3-4 hours, which is achievement of the sort. Collect your LLs from Room 4 in few days. No identification needed really nor any register entry made, so anyone can collect anyone else's.

Driving License

1. Fill the same application at same portal, except choose DL as purpose of application. You only need application (with photograph) and previous LLs as documents.
2. Buy stamped envelop (30/-) and a transparent pouch (3/-) from tea-shops outside. Also get Form-4 (3/-) for Driving Inspector to provide feedback.
3. Pay fee at Cash Counter, which will include license, smart card, and testing fee. Exact 1000/- for two classes of vehicles. This was after fee hike in early January 2017.
4. Get your documents verified in Room 1. Staple everything with Both challans at front, Form 4, DL application, previous LLs, envelop, transparent pouch in that order.
5. Go to Room 8 upstairs for Biometric and then Room 4 downstairs for some computer entry.
6. Then you have to go a Driving Test area which is outside RTO office in nearby street. Ask at Enquiry desk and get there. You will have to have your own Car and Gear Bike for testing.
7. There was only one inspector who had asked all Bikers first, and Cars later, to get in line. Only thing he asked on both occasion was hand signs: right (right arm stretch, palm facing front), left (circular motion with right hand), slow-down (up-down motion with right arm, palm facing down), stop (right arm up at elbow, palm facing front). Then he asked me go to dead-end and come back. No one really checked anything and unless you hit someone or something or fall down within 20 feet of him, you cannot fail. Meanwhile he will have scribbled something on your application which you can collect. You will have to do this twice for both (bike and car) vehicles.
8. Go to RTO Room 9 to get another register entry and submit all document packet. They will ask vehicle number (Registration Card) and insurance validity to note in register. I had worked myself into panic in getting RC, PUC and Insurance for Car and Bike but really PUC was not asked and you could just give any RC or Insurance details irrespective of vehicle you gave test in. They didn't keep copy but noted down in register only, so even phone picture did it for me. I had also wondered about getting additional driver for car and bike apart from me in case genuine question comes up about who drove the test vehicle (since you are supposedly still don't have license) but then nobody bothered asking these, so you could get one too. Also rental bike is okay too since no documents asked during testing and no bike verified during register entry.
9. You are done, in about 4 hours. License should come to your house in 4-6 weeks. If not, go there and remind them! It did for me in 4 weeks.

IDP

IDP, aka International Driving Permit, is document stating that you hold valid DL in your home country. This is often required if your DL is not in English. Since Indian DL is usually in English, this doesn't serve any additional purpose but still some country and states in USA require one. Here is process of how to get one.

Note that you will get IDP from RTO only if your DL is also from same RTO. I didn't expect this given DL is for whole of India and chip DL is connected to computerized network, but then whole IDP process is exercise in redundancy, so there you have it.

1. Documents you need are:
1. Application for IDP, Form-4A (pdf here)
2. Original DL, Original Passport
3. One photocopy of DL, Passport front/back/visa page, flight tickets on your name (to and fro)
4. Medical declaration and certificate from registered medical practitioner, Form-1 and Form-1A (pdf here)
5. Paste passport size photos in application and medical certificate
6. 3 additional passport size photographs
2. For RTO Electronic City, signed medical declaration and certificate is available at xerox shops opposite RTO for 100/- (yes, Indian jugaad) where you can fill your name and details.
3. Pin all documents and go to RTO Room 12 for verification and signature. There is unlikely to be any queue here. There is a rule that you need to reappear for driving test if DL is issued within last 3 months but they didn't seem to notice or mind this in my case, so nothing was asked.
4. After signature, pay 1000/- at Cash Counter against fee and obtain challan.
5. Include challan and submit documents again at Room 12, and obtain acknowledgement slip
6. Collect your IDP after 1-2 weeks.
7. When I went to collect IDP they informed me for need for additional driving test since my DL was less than 3 months old. [Yeah, they don't read application when they accept and only later when they process it.] Even though IDP was already ready, I was asked to go for driving test. After requests to hurry, I was informed to just pay fee for test (visit to cash counter, challan for 300/-) and then collect the IDP.

Why should I care about the future generations - what have they ever done for me?

Cycle of re-incarnation would have you believe that you will reap, as early as within next life, what you sow. While this is certainly a fancy notion, this isn’t truth by any notion of reasonableness. Hence even if you wouldn’t have enjoyed what you do now – for example, luxuries of material progress, benefits of freedom struggle, developments of modern technologies – there is hardly an obligation, let alone nagging sense of guilt, for doing something for future generation.

May be I am selfish but I’ve got only one life. Barely 40 years of pleasurable existence (excluding pre-puberty and senility). There is nothing wrong in me to want to live only life the way I like. I didn’t ask to born, so there isn’t any purpose I am supposed to fulfill. If I am dead tomorrow, why should I even care what happens to rest of the world and rest of the people (and ants, mosquitoes, etc. for that matter). I wouldn’t even know and feel ever.  Why should my narrow sense of kinship with fellow humans overshadow my sense of connectedness with the entire Universe? Should I feel depressed by falling of a star somewhere?

Admittedly, my progeny and kins will inhabit this planet after I’ve departed. Yet, what I do for future generation wouldn’t benefit them as much as what I do for my kids directly. If I think about it, I haven’t even met my descendants and I am not kind of person who gets worked up on what his bloodline is going to suffer in future. In that way, I am kind of a model citizen, beyond narrow interests of family and clan, equally indifferent to all.

Some will say that had this attitude been taken by our forefathers we wouldn’t have had what we do. But, who really knows? Could we have not been better? Did all those who worked on what they did do it for future generation i.e. us? What they did was their choice. My choice is to make optimal decision based on information in my hand at this juncture of my existence.

Assuredly, do what you like, and if it benefits next bunch of people in the world, well and good, but if it doesn’t, don’t worry. Want to buy plastic bags and drink water in paper cups? Be my guest (though you might want to check if it will start hurting you in this generation!) It’s a beauty of this big world that there will be some people who will disagree with even the best construed arguments. My role is to convince you that I (and you too) shouldn’t worry about future generation, with awareness that some of you wouldn’t get convinced, and end up doing (possibly) something good for future generation, which makes my not worrying not as troublesome as I could be. Ironically, success of my argument depends on the failure of my argument. But, either way, who gives a damn?

Every conversation with Child

This has to be saved. Yes, this represents almost every conversation with our daughter too.
http://www.slate.com/articles/life/low_concept/2015/10/every_conversation_between_a_parent_and_a_child_in_four_conversations.html

1.

Child: Can I have this?

Me: No.

Child: Ah, perhaps I’ve miscommunicated. I’m asking for it because I want it.

Me: I understood that, actually.

Child: I think maybe you’re not hearing me. I’d like it because I want it.

Me: I’ve heard you quite well, I’m saying that’s not actually an argument.

Child: PERHAPS IF I SAID IT LOUDER.

Me: There’s no problem with my hearing. The problem is that your argument is, as the Romans would say, circulus in probando.

Child: Well then, let me offer this new information: I want it.

Me: That’s the same information. That’s what you just said, and it’s also the information I assumed when we started.

Child: Well, can I watch YouTube?

Me: You also can’t watch YouTube.

Child: If I can’t watch YouTube, then can I have it?

Me: No! Sorry. No. Why would you think you can have it now?

Child: What if I ask more politely?

Me: I support your decision to behave more politely, and it might increase your chances of getting the next thing you want, but it won’t affect your access to this thing now.

Child: Can I have part of it?

Me: No. No, the having of it is what I’m saying no to. Having part of it is the same as having it.

Child: So can I have all of it?

Me: No! I’m answering the same question. The answer is no.

Child: Why not?

Me: BECAUSE I—Look. No.

Child: But, OK, look, here is some new information.

Me: Yes. What is it?

Child: I need it.

2.

Me: Put your shoes on.

Child: Let the games ...

Me: Nonononono ...

Child: BEGIN!

Me: Just put your shoes on.

Child: In the vacuum of space, are there free-floating molecules?

Me: Put your shoes on.

Child: Did you know that we don’t actually vote for president, we vote for people who vote for president?

Me: I don’t care, put your shoes on.

Child: I am.

Me: You’re not. Put your shoes on.

Child: Why do we have shoes anyway?

Me: Just put your shoes on.

Child: That reminds me, where are my shoes?

Me: What? They’re right there! Right next to your feet!

Child: Oh, these shoes?

Me: YOU ONLY HAVE ... I’m sorry. Yes. Those shoes. Your only shoes.

Child: Why don’t I have more shoes?

Me: No more questions, just put your shoes on.

Child: I can’t. I’m not wearing socks.

Me: Did you take your socks OFF?

Child: Well, I’m not wearing them any more, so it’s a fair bet.

Me: Put on your socks and then put on your shoes.

Child: I am!

Me: You’re not! You’re just sitting there!

Child: This is me putting on my shoes! This is part of it! All of this, this is the putting on of the shoes. It says in the I Ching ...

Me: NO. NO MORE I FRIGGIN’ CHING. PUT YOUR ... I’m sorry. I’m sorry. Just ... put your shoes on.

Child: I found my socks. They were right here next to my shoes.

Me: If you put your shoes on by the time I count to five, I’ll let you choose what we do next. One ...

Child: (with socks and shoes already on) YouTube.

3.

Me: OK, come eat dinner.

Child: This is dinner?

Me: Yes.

Child: I see. I see. So you’re saying this is dinner.

Me: It’s getting cold.

Child: But this is whole pieces of food that you’ve just … cooked.

Me: Yes. We’re eating something healthy for dinner.

Child: How can we be sure this is healthy?

Me: It’s healthy. And it’s dinner. Eat it.

Child: I had cold pizza and Skittles for breakfast, and then I got a 100 on my spelling test.

Me: You’ve stumbled into post hoc ergo propter hoc there, buddy, and that hasn’t worked since the second century.

Child: PERHAPS IF I EXPLAINED THAT I DON’T WANT IT.

Me: You can yell all you want, this is dinner.

Child: I think it’s cold.

Me: It’s not cold.

Child: Look at it. It’s cold. It’s gone cold.

Me: Eat it, it’s not cold.

Child: I’ll eat it if you eat it.

Me: No! That’s not the way it works!

Child: Why not?

Me: BECAUSE I’M THE GROWN-UP AND I SAID SO NOW QUIT ASKING ME AND GO DO SOMETHING ELSE BESIDES TALK TO ME FOR THE LOVE OF GOD OR I WILL LITERALLY BLOW UP FROM SITTING ON MY ANGER AND IMAGINING HOW MUCH TROUBLE I WOULD BE IN IF I PULLED THIS SHIT WITH MY PARENTS IN 1978!!!!

Child: Why are you yelling?

Me: I’m sorry, I’m sorry, I didn’t mean to yell, I’m really sorry. I’ll order pizza.

4.

Child: Where is Mom?

Me: Why do you need her?

Child: Sometimes one just needs one’s mother.

Me: I’m standing right here, perhaps I can help you.

Child: This falls under Mom’s purview, so …

Me: She’s busy right now, and I’m taking care of you.

Child: Busy where?

Me: Upstairs. But don’t go there.

(Child leaves room)

(Long pause, muffled discussion from upstairs)

(Child returns)

Child: I spoke with mom.

Me: So I gather.

Child: Mom says to ask you. Where is the thing from before?

Me: The thing I wouldn’t give you before?

Child: Yes.

Me: Why do you want to know?

Child: I’m a curious person. I thirst for knowledge.

Me: But you can’t have it.

Child: Boy, you are really jumping to conclusions here! I know I can’t have it! OF COURSE! I’m just curious.

Me: If I tell you where it is, will I find out that at some future time, you have the thing?

Child: Does anyone truly know what the future holds?

Me: So, there is a future where you’ve gone and gotten the thing.

Child: Hold that thought.

(Child leaves room)

(Long pause, muffled discussion from upstairs)

(Child returns)

Child: Mom says she’s busy and that you should just tell me where the thing is, because I promised not to get it.

Me: You promised.

Child: As Mom is my witness.

Me: You know you aren’t getting it, right?

Child: I just like to know where things are, in our house.

Me: The thing is on top of the refrigerator.

Child: Why did you put it there?

Me: Because I don’t trust you.

Child: But … how is that possible? I trust YOU.

Me: Thanks.

Child: I trust you so much that I know when I go and get a stool and bring it over by the refrigerator, and climb up it, the thing will be there.

Me: You promised you wouldn’t do that.

(Child leaves room)

Me: DO NOT GO TO THE KITCHEN. I SWEAR TO GOD IF I HEAR THAT STEP STOOL—

(Child comes back into room)

Child: Why were you yelling at me?

Me: I’m sorry. I shouldn’t have yelled.

Child: Can I play on the computer?

Me: Yes.

(Child opens computer and begins watching videos on YouTube)

(Mom walks down stairs)

Mom: I specifically told you not to get on the computer.

Child: Dad said I could.

My favourite Podcasts

I've been listening to various podcasts while commuting to and fro from work for last couple of months, and I couldn't be happier.

Before I discovered podcasts, my options of utilizing a considerable amount of my daily waking life were limited to music from FM radio station or music from my USB stick. Former were annoyance due to abundant number of advertisements, which are often repeated, and limited selection of latest songs, which were also repeated, and which were less of musical delight but more driven by latest movie marketing. Later was considerably preferred, but became boring due to my inability to update my collection often and hence repeating same collection. I tried audio-books few times but quickly discarded the option for they required too much concentration detrimental to safe driving.

Enter world of podcasts! Podcasts are best described as audio blogs. They are delight because they are almost inexhaustive, being updated weekly, and are not as distracting in effect being similar to listening to radio news, and are wildly interesting, entertaining, educational and useful. In some way, I feel they have made my driven less stressful since I am no hurry to reach my destination, instead preferring continuation of my favourite show.

Below is collection of some of my favourite podcasts, in decreasing order of my preference, alphabetically within each sub-group, and my commentary on the same:

List Updated on 11th June 2020

Great:

• Anthropocene Reviewed — Host's personal opinion on various random things, often including esoteric history and personal anecdotes, told in soothing narrative
• EconTalk (Library of Economics and Liberty) — This isn't very entertaining but if you want your mental horizon to be stretched with very deep fundamental concepts, this it it. Falls into a category of podcast you should listen to but probably you won't.
• Every Little Thing — is discussion on minor topics and histories of science.
• Futility Closet — Extremely affable narratives from history of world telling history of minor things and incidents. As they describe themselves, will suit you if your mind is curious about oddities and find pleasure in information for sake of it.
• Indicator from Planet Money — News and stories around current economic metrics from USA.
• Planet Money — Stories of past and present things that make modern economy.
• Radiolab from WNYC — Interesting informative stories about various themes, primary around science and technology.
• Science Vs — This is one the best show to learn about the scientific basis of many common conceptions and misconceptions. Each episode looks at academic literature and tries to synthesize positive, neutral, or negative decision on key questions. Examples of questions explored are the effectiveness of vaccines, diets, multi-vitamins, political questions on abortions, gun control, etc.
• What Trump Can Teach Us About Con Law — Show talks about various topics in US Constitution Law and how they are interpreted in the current environment, their history, their usefulness, key cases, etc. and ties them back to US President's Trump's actions.

Very Good:

• 60-Second Science — Quick bites into latest scientific research. Mildly interesting.
• 99% Invisible — Short stories about man-made things that shape the world, and design consideration thereof.
• Completely Optional Knowledge — Simple explanation of science queries. Can be too simple and verbose at times for my knowledge.
• Criminal — Stories of crimes, laws, and their history from USA
• Freakonomics Radio — Logic and data driven look at almost everything in world around us. Built from book of the same name, this is absolutely wonderful podcasts which brings out best practices in various fields from all over the world. Intelligent and stupid questions, all are honored.
• Linear Digressions — Discussion on recent paper in Machine Learning space, or general topic related to Data Science world in simple to understand language.
• The Allusionist — Etymology of words explained in saucier language.
• The Data Skeptic Podcast — This just fits into my groove of analytic science, so I love it for its discussion and references. Will work if you have interest in the science of data driven decision making.
• The History of India Podcast — No one told story of ancient India sourced from ancient text better than this! Making history informative and fun.
• The Infinite Monkey Cage — This is general discussion, with some comedic input, on scientific concept done in live stage setting.
• Reply All — This is discussion on internet, technology and social issue surrounding them. Fairly humour, creative, except for its 'Yes-Yes-No' segment where conversation on dissecting an viral tweet.
• Science Friday — Interviews on cutting edge research or latest discovery in world of Science.

Good:

• A Skeptics Guide to Conspiracy — This is very good in content but not so much in editing. I think they could say that same in half the time as there is a lot of repetation in conversation. However, this discusses latest research in science, with few good puzzles thrown in.
• HBR IdeaCast — Management gyaan isn't my cup of tea, but listening to key stories of Harvard Business Review is still worthwhile.
• Hidden Brain — Anecdotes from behaviour science and psychology.
• Inside Forbes India — India related stories from business world.
• The Economist — Weekly round of world new and explanations on money, market and science. Useful for getting critical international news, and free! Content is heavily biased towards US and UK with bit of Japan, China and Europe but then one can assume it's driven by where money is.
• This American Life — Interesting, emotional and amusing stories from various walks of life, on varying theme
• Sawbones — Humour filled history of medicines and surgery
• StarTalk Radio — This has decent enough content on astronomy, astrophysics, and anything Universe related, but there is lot of banter and chit chat which makes it inefficient for me.
• Stuff You Should Know — This is 'how things work' of podcasts. It's mildly entertaining but content is too low key and slow for my taste.

Good but Defunct:

• 30 Animals that Made Us Smarter — How science and tech uses "biomimicry" to learn from nature and animals.
• 50 Things That Made the Modern Economy — Stories of small things and their impact on world.
• Dissecting Love — Science and biology of relationship and sex. Need I say more?
• More Perfect — This show goes into the story behind pivotal cases in front of US Supreme Court, past and present, and how law and precedent and arguments are shaping the legal opinion.
• Invisibilia — Bit verbose and emotion insight into hidden psychological narrative governing current world and human life.
• It's Your Universe — Journey into Solar System. It's only one season though!
• Serial — This is a serialized radio show with one story. First season presented a true murder mystery thriller. Very gripping.
• The Intersection — Melting pot of Science, History, and Culture in this Indian quality podcast.

If you can recommend any other, I will be really thankful!

Vedika - Day 825

I've not been able to update this blog and my frequency is dwindling. It may die natural death. Hence, I've moved to Twitter. That is, Vidhi is on twitter since 13th Jun'14. Follow her (but who is reading this blog anyway?) at here handle: VG01AG01. This gives me incentive to post because (1) posts are smaller (2) it's new platform. Let's see how long I stay there.

Below is screencap of tweets in last one week.

Vedika - Day 784

Vidhi understands that she has many names. She responds to them well. She connects Vidhudi to Chachu. Vedika Gupta to formal name when asked by stranger. And more. Her emphasis on Vedika Gupta, not yet uttered clearly enough to let stranger understand completely, is absolutely adorable.

As her vocabulary increases, she often corrects us. Having forgotten teaching her, we sometimes slip in something simpler for more complicated word, giving her opportunity to correct us. And her correction takes always the form: <full wrong phrase> NOoooo, <full right phrase>. For example, when inquired about whereabouts of her Chacha by her, we may respond that he has gone out. She quickly chimes, "chacha gone out, No..., chacha gone to gym". As she has started talking, her voice and dialogues are source of surprise and joy, and worthy of recording for preservation. We have not found a quick way to record her utterances, unlike quick video shooting by phone. Unfortunately, she has become conscience of videographing, and immediately stops whatever she is doing and demands to be shown what is being captured.

In a new twist — which her mother finds corruption of her English grammar, and I find sign of her ability of go beyond specified words and understand deep context — she has started making-up fake words. Specifically, fake verbs. She announced other day that she is "office kaaming" when pretend working her mother's laptop. Looking at cats sleep, she said that they were "needing". When her toys fall down, she rues that they are "bumbing." She has, for reasons unknown, also started adding "only" to end of each setence. We worry her deviation from grammatically English to Indian English! Her most common sentence these days is: "They are bumbing only!".

She has picked up names of most vegetables, fruits, letters, numbers, days of the week, months of year, seasons, opposites, and shapes by now. She has even started recognizing letters in written form even when presented out of sequence. Her favourite, now, being letter A. Her understanding doesn't disassociate 'A' from 'Apple' now. So, as she spots an A, on keyboard often, but also in newspaper, she shouts that there is Apple there.

Her sentence structure of some of common phrases brings out hilarity. As perhaps mentioned earlier, she declared few weeks ago that vidhi ke ghar main to daadi bhi hai as way of saying that there is dadi in the house. Yesterday, she went on sing-song about vidhi bhi su-su karti hai, chacha bhi su-su karte hai, papa bhi...you get the drift.

In playgrounds, I find her silent and non-interactive. She is timid, and doesn't reach out to, nor responds when reached out to by, other children. She prefers going one round on each of two identical but different coloured swings and see-saws. She avoids slides, for reasons unknown. I want her to run and do bit of body movement, which she avoids. If, and when, she runs, it is hilarious with her both arms raised and bent at elbows, whole body shaking.

Her nightly tantrums are still ongoing. She not only wants things to be done in certain very very precise way to her, but also wants you to align yourself to her precise specifications. That means direction of sleep, where your body parts lie, speed of fan, presence and location of her soft toys, and whether or not you use blanket. She instruct once, and then cries till her demands are met. Which are often, but when not, can lead her to cry for hours, and then fall asleep sobbing. This happening every night is naturally source of huge annoyance to her mother and I. Once in a while she would get a slap for it. That is more of outlet of our frustrating demeanor rather than any step towards solution. And solution, most of the nights, is none, for it feels that she wants to cry.