arithmetic – Pertinent Observations

Lifting and arithmetic

At a party we hosted recently, we ended up talking a lot about lifting heavy weights in the gym. In the middle of the conversation, my wife wondered loudly as to why “so many intelligent people are into weightlifting nowadays”. A few theories got postulated in the following few minutes but I’m not going to talk about that here.

Anecdotally, this is true. The two people I hold responsible for getting me lift heavy weights are both people I consider rather intelligent. I discuss weights and lifting with quite a few other friends as well. Nassim Taleb, for a long time, kept tweeting about deadlifts, though now he has dialled back on strength training.

In 2012 or 2013 I had written about how hard it was to maintain a good diet and exercise regime. While I had stopped being really fat in 2009, my weight had started creeping up again and my triglyceride numbers hadn’t been good. I had found it hard to stick to a diet, and found the gym rather boring.

In response, one old friend (one of the intelligent people I mentioned above) sent me Mark Rippetoe’s Starting Strength (and a few other articles on cutting carbs, and high-fat diets). Starting Strength, in a way, brought back geekery into the gym, which had until then been taken over by “gym bros” doing bicep curls and staring into mirrors.

It’s been a long time since I read it, but it’s fascinating – I remember reading it and thinking it reminded me of IIT-JEE physics. He draws free body diagrams to explain why you should maintain a straight bar path. He talks about “moment arms” to explain why the bar should be over your mid-foot while deadlifting (ok this book we did discuss at the party in response to my wife’s question).

However, two incidents that happened last week gave me an idea on why “intelligent people” are drawn to lifting heavy barbells. It’s about challenging yourself to the right extent.

The gym that I go to (a rather kickass gym) has regular classes that most members attend. These classes focus on functional fitness (among other things, everyone is made to squat and press and deadlift), but I’ve for long found that these classes bore me so I just do my own thing (squats, press / bench and deadlift, on most days). Occasionally, though, like last Friday, I decide to “do the class”. And on these occasions, I remember why I don’t like the class.

The problem with the gym class is that I get bored. Most of the time, the exercises you are doing are of the sort where you lift well below capacity on each lift, but you do a lot of lifts. They train you not just for strength but also for endurance and metabolic conditioning. The problem with that for me is that because every single repetition is not challenging, I get bored. “Why do i need to do so much”, I think. Last Friday I exited the class midway, bored.

My daughter is having school holidays, and one of the things we have figured is that while she has grasped all her maths concepts rather soundly (the montessori system does a good job of that), she has completely failed to mug her tables. If I ask her what is “7 times 4” (for example), she takes half a minute, adds 7 four times and tells me.

Last Monday, I printed out (using Excel) all combinations of single digit multiplications and told her she “better mug it by Friday”. She completely refused to do it. There was no headway in her “learning”. I resorted to occasionally asking her simple arithmetic questions and making her answer immediately. While waiting to cross the road while on a walk, “what is six times eight?”. While waiting for the baker to give us bread “you gave him ?100 and the bread costs ?40. How much change should he give you?”. And so on.

She would occasionally answer but again her boredom was inherent. The concept learning had been challenging for her and she had learnt it. But this “repetitive practice” was boring and she would refuse to do it.

Then, last Friday, I decided to take it up a notch. I suddenly asked “what is four and a half times eight?” (she’s done fractions in school). This was a gamechanger.

Suddenly, by dialling up the challenge, she got interested, and with some prodding gave me the correct answer. An hour earlier, she had struggled for a minute to tell me what 8 times 7 is. However, when I asked her “what is eight times seven and a half?” she responded in a few seconds, “eight times seven is fifty six..” (and then proceeded to complete the solution).

Having exited my gym class midway just that morning, I was now able to make sense of everything. Practicing simple arithmetic for her is like light weight lifting for me. “Each rep” is not challenging in either case, and so we get bored and don’t want to do it. Dial up the challenge a little bit, such as bringing in fractions or making the weights very heavy, and now every rep is a challenge. The whole thing becomes more fun.

And if you are of the type that easily gets bored and wants to do things where each unit is challenging, barbell training is an obvious way to exercise. and “intelligent” people are more likely to get bored of routine stuff. And so they are taking to lifting heavy weights.

I guess my wife has her answer now.

Tailors

In a little street called Narayana Pillai Street, off Commercial Street in the Shivajinagar area of Bangalore there stands a building called “Ganesh complex” which can be called a tailoring hub. There are some ten to twelve shops (forgive my arithmetic if I’ve counted too low) all of which are occupied by tailors who stitch women’s clothes, primarily salwar kameez and its derivatives. I don’t know if there’s much to choose between the stores, and I think it’s a question of “tailor loyalty” the way it’s practiced among beach shacks at Baga beach in North Goa.

The wife is friends with a tailor called Ahmed, who runs a shop called HKGN tailors in this complex. Till recently (when he took two weeks with a consignment) his USP was “one hour tailoring”, where upon receiving cloth and measurements, he would stitch your dress in about an hour. I hear that there are a large number of tailors in the vicinity (though not sure if they’re in Ganesh complex) who offer the same terms. In fact, I know a lot of women who travel to that area to get their clothes stitched both for the quick delivery and also for the network of tailors that is present there.

While waiting for Ahmed to deliver the wife’s latest consignment yesterday (the one he took two weeks with), I was watching tailors in neighbouring shops working. The thing that struck me was that there isn’t much economies of scale in bespoke tailoring. Each piece of cloth needs to be cut separately, in its own size, and there’s nothing that can be “batch processed” across different samples. Of course, there is tremendous scope for specialization and division of labour, so you see “masters” who measure, mark out and cut cloth, and “stitchers” who stitch up the stuff together.

However, across the city, except for the handful of tailors in the Shivajinagar area, the standard turnaround time for stitching seems to be about two weeks. And given the wife’s experiences (I usually buy readymade garments so not much insight there) it is a fairly disorganized industry and requires several rounds of follow-ups and waiting at the tailor’s shop in order to get the goods.

The economics of the industry (that there are no economies of scale) makes me wonder why the two-week-turnaround time has become standard in this industry. Isn’t the turnaround time solely because of inventory piled up at the tailor’s? Can the tailor not manage his inventory better (like say going a few days without fresh orders or hiring a few extra hands temporarily or working a weekend) and thus lead to much shorter turnaround time? Given the individual nature of the job, what prevents tailors from offering instant turn-around like the handful of people in Shivajinagar do? Or is it that bulk orders (one person coming with a bunch of clothes to stitch) mess up any “quick turnaround model” the tailors could offer?

There is only one explanation I can think of. “Sales” and “production”, for the tailors happens at the same spot (their storefronts). For “sales” purposes they need to be there all the time, though they don’t need to be actively doing anything. Hence, it suits them if production is also a continuous full-time process, so that the time they spend at the storefront isn’t all “wasted”. By piling up an inventory of orders, tailors are always assured of having something to do even if no fresh customers are forthcoming.

So as the wife’s experience with Ahmed has shown, the “quick turnaround” hasn’t been sustainable at all.

Compensating Teachers

This is yet another of those things which I’ve been thinking about and have been intending to write about for a long time but have never gotten down to it. Pinky wrote this excellent post on the topic today and that has got me thinking. To quote her,

A bad teacher makes a bad student. A teacher who looks at teaching as just another job is doing no good to anyone. She neither grows in her life nor contributes to the positive growth of a kid.There have been a few teachers in my life who i have tremendous respect for, not because they taught me effectively enough to pass in their subjects but because they taught me to listen, think and speak!

I don’t have any solutions yet but I thought I should just put some bullet points here, just to try and give a structure to the problem. Let me know your thoughts

If we consider a person’s salary as Society’s recognition of his/her worth, school teachers are not recognized enough
Abysmal salaries drive away a large number of potential school teachers away from the profession
Love for teaching is important, but if teaching pays as abysmally as it currently does, the opportunity cost of doing what you love is way too high for some people, and so they end up in other professions
We have a market failure in teaching – how do we run a school profitably while paying teachers competently while on the other hand keeping fees reasonable, and not resorting to any subsidies?
India suffers from what I call the “official’s wife bug”. In the 60s and 70s, the teaching profession got flooded by women who weren’t really looking to make much money, but more to just pass some time and use their bachelor’s degrees rather than being housewives. This has fostered a culture of low schoolteachers’ salaries in India. People who weren’t looking to make money out of teaching crowded out those who found the opportunity cost of the low salaries in teaching too high.
McKinsey interview level arithmetic: assume a school having classes 1 to 12, 4 sections per class, 40 students per section. 8 periods a day 5 days a week gives a total of 12 * 4 * 8 * 5 = 1920 periods per week. Assuming each teacher can take 5 classes a day (or 25 a week) we will need 77 (round it off to 80) teachers. Number of students is 12 * 4 * 40 = 1920, so essentially 25 students have to pay for one teacher’s salary, and this is apart from expenses towards school building, maintenance, overheads, etc. McKinsey level handwaving. 10 students have to pay for one teacher’s salary. Doesn’t sound feasible
Primary and secondary education is simply way too important to be left in the hands of unmotivated disinterested people, but that seems like the situation we are in (I dont’ mean to say all teachers are unmotivated or disinterested; just that the situation doesn’t incentivize talented motivated people to enter the profession).
Universities attract talent by allowing faculty to make money by other means such as consulting and organizing for-profit courses. Will something like that work for schools? And no, I’m not talking about private tuitinos as the other source of income. Is there something else?
Government intervention is not a solution. In a place like India it will only end up messing up things further and draining more money from the system.
In the pre-IT era, teaching salaries were more competitive (with respect to competing jobs) than they are now, so they could attract better talent
I wonder if it is only in India that such a large proportion of school teachers are women. This is just a general pertinent observation, and has nothing to do with the rest of the post
The officer’s wife model was good when it started off – some motivated people came into the system because fo that. Just that the system is not sustainable and we’re facing the problems of that now and because a lot of school managements fail to take into account that the model isn’t sustainable

Any thoughts on this? Any possible solutions? Of course it’s not possible to implement any macro-level solution. All I’m looking at is a school-level solution. How do you plan to run one school (of size I mentioned in my bullets) sustainably while ensuring teachers are paid adequately enough to not scare away interested people?

Gyaan From a Former All India Topper

CAT is less than a month away. Or more, depending on when you’re writing it. If any aspirants are reading this, I have just one piece of advice for you – which no one in any CAT Factory will give you. It’s about going for it. About batting like Sehwag. About reaching out far outside the off stump and playing every ball. I just want to assure you that percentages are in favour of this kind of a game.

In my zamaana, every correct answer in CAT gave you one mark, and every incorrect answer took away a third of a mark. Every question had four possible answers of which exactly one was correct. This negative marking had a completely psyching out effect on most takers, and people are afraid to go for it. And six years back, I liked it. For it made my own risk-taking strategy much easier – since I could now afford a larger number of errors.

The arithmetic is simple. Even if you have no clue about the question, and just put inky-pinky-ponky (or even better mark ‘C’, since years of research has proven that it’s the statistically most probable answer in CAT) you have one-fourth chance of getting it right – which gives a three-fourth probability of getting it wrong. And given the payoffs for correct and incorrect answers (1; -1/3) you can clearly see that the expected payoff of taking a completely random guess is ZERO!

So while this obviously rules out insane inky-pinky-ponkying, what it does tell you is that if you can eliminate at least one of the four choices, you are in the money! If you have to pick one of three possible answers, the expected payoff is 1/9 which is greater than zero. Yeah it doesn’t look very high but then the expected payoff is positive! So you need to go for it.

Back when I was in my 3rd year, there was some free mock CAT at IITM. And some of us 3rd years went just for the heck of it. I attemped 130 out of 150 questions, getting 90 right and 40 wrong. It still gave me a significantly higher score than any of my seniors (who were writing CAT that year) – most of whom attemped not more than seventy. Later that day a senior called me aside and told me that the art of CAT was about leaving questions. And that it was all about the questions that you left.

Leaving the ball makes sense in cricket where one mistake ends your innings. What if instead of ending your innings you were just deducted 2 runs everytime you got out? Would you still leave the balls outside off and play the waiting game? How on earth would you score runs if you were to leave every ball? It’s all about scoring, and you can score only if you attempt a shot.

I understand that CAT format has changed now and you have 5 possible correct answers for every question while the negatives are still at 1/3. Even then, if you can eliminate two out of the five answers (shouldn’t be too gouth), you have a positive payoff. And you must go for it. Keep in mind that you can’t score if you don’t play the ball.

I leave you with a video. The message is in the name of the song. Idu One Day Matchu Kano. This is a one day match dude. So you must go for every ball. And look to score.