Pregnancy, childbirth, correlation, causation and small samples

When you’re pregnant, or just given birth, people think it’s pertinent to give you unsolicited advice. Most of this advice is couches in the garb ob “traditional wisdom” and as you might expect, the older the advisor the higher the likelihood of them proffering such advice. 

The interesting thing about this advice is the use of fear. “If you don’t do this you’ll forever remain fat”, some will say. Others will forbid you from eating some thing else because it can “chill the body”. 

If you politely listen to such advice the advice will stop. But if you make a counter argument, these “elders” (for the lack of a better word) make what I call the long-term argument. “Now you might think this might all be fine, but don’t tell me I didn’t advice you when you get osteoporosis at the age of 50”, they say. 

While most of this advice is well intentioned, the problem with most such advice is that it’s based on evidence from fairly small samples, and are prone to the error of mistaking correlation for causation. 

 While it is true that it was fairly common to have dozens of children even two generations ago in india, the problem is that most of the advisors would have seen only a small number of babies based on which they form their theories – even with a dozen it’s not large enough to confirm the theory to any decent level of statistical significance. 

The other problem is that we haven’t had the culture of scientific temperament and reasoning for long enough in india for people to trust scientific methods and results – people a generation or two older are highly likely to dismiss results that don’t confirm their priors. 

And add to this confirmation bias – where cases of people violating “traditional wisdom” and then having some kind of problem are more likely to be noticed rather than those that had issues despite following “traditional wisdom” and you can imagine the level of non-science that can creep into so-called conventional wisdom. 
We’re at a hospital that explicitly tries to reverse these pre existing biases (I’m told that at a lactation class yesterday they firmly reinforced why traditional ways of holding babies while breastfeeding are incorrect) and that, in the face of “elders”‘ advice, can lead to potential conflict. 

On the one hand we have scientific evidence given by people who you aren’t likely to encounter too many more times in life. On the other you have unscientific “traditional” wisdom that comes with all kinds of logical inconsistencies given by people you encounter on a daily basis. 

Given this (im)balance, is there a surprise at all that scientific evidence gets abandoned in favour of adoption and propagation of all the logical inconsistencies? 

PS: recently I was cleaning out some old shelves and found a copy of this book called “science, non science and the paranormal”. The book belonged to my father, and it makes me realise now that he was a so-called “rationalist”. 

At every opportunity he would encourage me to question things, and not take them at face value. And ever so often he’d say “you are a science student. So how can you accept this without questioning”. This would annoy some of my other relatives to no end (since they would end up having to answer lots of questions by me) but this might also explain why I’m less trusting of “traditional wisdom” than others of my generation. 

Half life of pain

Last evening, the obstetrician came over to check on the wife, following the afternoon’s Caesarean section operation. Upon being asked how she was, the wife replied that she’s feeling good, except that she was still in a lot of pain. “In how many days can I expect this pain to subside?”, she asked.

The doctor replied that it was a really hard question to answer, since there was no definite time frame. “All I can tell you is that the pain will go down gradually, so it’s hard to say whether it lasts 5 days or 10 days. Think of this – if you hurt your foot and there’s a blood clot, isn’t the recovery gradual? It’s the same in this case”.

While she was saying this, I was reminded of exponential decay, and started wondering whether post-operative pain (irrespective of the kind of surgery) follows exponential decay, decreasing by a certain percentage each day; and when someone says pain “disappears” after a certain number of days, it means that pain goes below a particular  threshold in that time period – and this particular threshold can vary from person to person.

So in that sense, rather than simply telling my wife that the pain will “decrease gradually”, the obstetrician could have been more helpful by saying “the pain will decrease gradually, and will reduce to half in about N days”, and then based on the value of N, my wife could determine, based on her threshold, when her pain would “go”.

Nevertheless, the doctor’s logic (that pain never “disappears discretely”) had me impressed, and I’ve mentioned before on this blog about how I get really impressed with doctors who are logically aware.

Oh, and I must mention that the same obstetrician who operated on my wife yesterday impressed me with her logical reasoning a week ago. My then unborn daughter wasn’t moving too well that day, because of which we were in hospital. My wife was given steroidal injections, and the baby started moving an hour later.

So when we mentioned to the obstetrician that “after you gave the steroids the baby started moving”, she curtly replied “the baby moving has nothing to do with the steroidal injections. The baby moves because the baby moves. It is just a coincidence that it happened after I gave the steroids”.

Randomising wear and tear of safety razor

A few months back, having mostly given up on my Gillette Mach 3, I decided to go all old school and get myself a safety razor. While I cut myself occasionally (one day I cut myself right on my Adam’s apple, giving me a minor scare that I’d slit my throat), I’m significantly happier with the results of this razor, compared to the Mach 3.

I find that I need to shave only a single time, compared to two rounds with the Mach3, and cleaning the razor in the middle of the shave is also far easier. And while it isn’t absolutely smooth, it leaves me mostly satisfied at the end of the shave. And I’m not even mentioning the cost saving here!

The only “problem” with using an old-school safety razor is that it takes in double-edged blades. Having used multi-blade cartridges all my shaving life thus far (my father had bought me a Sensor Excel when I was first ready to shave, which I later traded for a Mach3), I started using a single side of the blade to complete the entire shave.

In my experience, a decent blade should last about 6 shaves, as long as you use both edges of the blade equally. The challenge here was to know (visually) which side of the blade you had used, so that you could get the maximum out of the blade!

Initially I thought of using stickers or some such paraphernalia to indicate which side of the blade I’d used each time. After a little thought, however, I realised that if this was a common problem, the razor itself would’ve come with an asymmetrical head, so I could keep track. There should be a better way to keep track, I reasoned.

And so I decided that I would use each edge of the blade half-and-half in each shave. The first day, it worked. The second, I had finished shaving half my face, when I realised I’d suddenly forgotten which side I’d used. An improved method was required.

So the solution I’ve finally hit on is to randomise the edge of the blade I use each time I rinse my blade in the middle of the shave. So each time I rinse the blade, I give it a random twirl, and use whatever edge that twirl turns up for my next set of strokes. And so forth. This way, in terms of expected value, both edges of the blade are likely to wear by a similar amount by the end of each shave!

And so if I find one day that an edge is blunt, it is highly likely that the opposite edge is also as blunt, and it is a clear indication to put in a new blade!

It is remarkable how so often randomised algorithms can help you trivially solve problems that cannot easily be solved by deterministic methods!

Curation, editing and predictability

One of my favourite lunchtime hobbies over the last one year has been watching chess videos. My favourite publishers in this regard are GM Daniel King and Mato Jelic. King is a far superior analyst and goes into more depth while analysing games, though Jelic has a far larger repertoire (King usually only analyses games the day they were played).

In some ways I might be biased towards Jelic because his analysis and focus are largely in line with my strengths back during my days as a competitive chess player. Deep opening analysis, attacking games, the occasional tactical flourish and so on. He has a particular fondness for the games of Mikhail Tal, showering praises on his (Tal’s) sometimes erratic and seemingly purposeless sacrifices.

Once you watch a few videos of Jelic, though, you realise that there is a formula to his commentary. At some point in the game, he announces that the game is in a “critical position” and asks the viewer to pause the video and guess the next move. And a few seconds of pause later, he proceeds to show the move and move on with the game.

While this is an interesting exercise the first few times around, after a few times I started seeing a pattern – Jelic has a penchant for attacking positions, and the moves following his “critical positions” are more often than not sacrifices. And once I figured this bit out, I started explicitly looking for sacrifices or tactical combination every time he asked me to pause, and that has made the exercise a lot less fun.

I’d mentioned on this blog a few weeks back about my problem with watching movies – in that I’m constantly trying to second-guess the rest of the movie based on the information provided thus far. And when a movie gets too predictable, it tends to lose my attention. And thinking about it, I think sometimes it’s about curation or editing that makes things too predictable.

To take an example, my wife and I have been watching Masterchef Australia this year (no spoilers, please!), and I remarked to her the other day that episodes have been too predictable – at the end of every contest, it seems rather easy to predict who might win or go down, and so there has been little element of surprise in the show.

My wife remarked that this was not due to the nature of the competition itself (which she said is as good as earlier editions), but due to the poor editing of the show – during each competition, there is a disproportional amount of time dedicated to showing the spectacularly good and spectacularly bad performances.

Consequently, just this information – on who the show’s editors have chosen to focus on for the particular episode – conveys a sufficient amount of information on each person’s performance, without even seeing what they’ve made! A more equitable distribution of footage across competitors, on the other hand, would do a better job of keeping the viewers guessing!

It is similar in the case of Jelic’s videos. There is a pattern to the game situation where he pauses, which biases the viewer in terms of guessing what the next move will be. In order to make the experience superior for his viewers, Jelic should mix it up a bit, occasionally showing slow Carlsen-like positions, and stopping games at positional “critical positions”, for example. That can make the pauses more interesting, and improve viewer experience!

What are other situations where bad editing effectively gives away the plot, and diminishes the experience?

Brexit

My facebook feed nowadays is so full of Brexit that I’m tempted to add my own commentary to it. The way I look at it is in terms of option valuation.

While the UK economy hasn’t been doing badly over the last five years (steady strictly positive growth), this growth hasn’t been uniform and a significant proportion of the population has felt left out.

Now, Brexit can have a negative impact on two counts – first, it can have a direct adverse impact on the UK’s GDP (and also Europe’s GDP). Secondly, it can have an adverse impact by increasing uncertainty.

Uncertainty is in general bad for business, and for the economy as a whole. It implies that people can plan less, which they compensate for by means of building in more slacks and buffers. And these slacks and buffers  will take away resources that could’ve been otherwise used for growth, thus affecting growth more adversely.

While the expected value from volatility is likely to be negative, what volatility does is to shake things up. For someone who is currently “out of the money” (doing badly as things stand), though, volatility gives a chance to get “in the money”. There is an equal chance of going deeper out of the money, of course, but the small chance that volatility can bring them out of water (apologies for mixing metaphors) can make volatility appealing.

So the thing with the UK is that a large section of the population has considered itself to be “out of the money” in the last few years, and sees no respite from the existing slow and steady growth. From this background, volatility is a good thing, and anything that can shake things up deserves its chance!

And hence Brexit. It might lower overall GDP, and bring in volatility, but people hope that the mix of fortunes that stem from this volatility will affect them positively (and the negative effects go to someone else). From this perspective, the vote for Brexit is a vote of optimism, with voters in favour of Leave voting for the best possible outcome for themselves from the resulting mess.

In other words, each voter in the UK seems to have optimised for private best case, and hence voted for Brexit. Collectively, it might seem to be an irrational decision, but once you break it down it’s as rational as it gets!

Movie plots and low probability events

First of all I don’t watch too many movies. And nowadays, watching movies has become even harder as I try to double-guess the plot.

Fundamentally, commercial movies like to tell stories that are spectacular, which means they should consist of low-probability events. Think of defusing bombs when there is 1 second left on the timer, for example, or the heroine’s flight getting delayed just so that the hero can catch her at the airport.

Now, the entire plot of the movie cannot consist of such low-probability events, for that will make the movie extremely incredulous, and people won’t like it. Moreover, a few minutes into such a movie, the happenings won’t be low probability any more.

So the key is to intersperse high-probability events with low-probability events so that the viewer’s attention is maintained. There are many ways to do this, but as Kurt Vonnegut once wrote (in his masters thesis, no less), there are a few basic shapes that stories take. These shapes are popular methods in which high and low-probability events get interspersed so that the movie will be interesting.

 

Kurt Vonnegut’s Masters Thesis on the shapes of stories

So once you understand that there are certain “shapes” that stories take, you can try and guess how a movie’s plot will unfold. You make a mental note of the possible low-probability events that could happen, and with some practice, you will know how the movie will play out.

In an action movie, for example, there is a good chance that one (or more) of the “good guys” dies at the end. Usually (but not always), it is not the hero. Analysing the other characters in his entourage, it shouldn’t be normally hard to guess who will bite the dust. And when the event inevitably happens, it’s not surprising to you any more!

Similarly, in a romantic movie, unless you know that the movie belongs to a particular “type”, you know that the guy will get the girl at the end of the movie. And once you can guess that, it is not hard to guess what improbable events the movie will comprise of.

Finally, based on some of the action movies I’ve watched recently (not many, mind you, so there is a clear small samples bias here), most of their plots can be explained by one simple concept. Rather than spelling it in words, I’ll let you watch this scene from The Good, The Bad and The Ugly.

More optionality in startup valuations

Mint reports that Indian e-commerce biggies Flipkart and Snapdeal are finding it hard to raise more money at the valuations at which they raised their last funding rounds. One line from the report:

Despite Morgan Stanley’s markdown in February, Flipkart is still approaching investors asking for a valuation of $15 billion, but it hasn’t had any takers yet, the first two people cited above said.

The problem with the valuations is that it includes significant option value. It is common in startup funding to include implicit options in favour of the new round of investors to protect them from the downside of any future decrease in valuation.

Typically designed in the form of “ratchets”, when the firm raises a fresh round at a lower valuation, the investors in the previous round will get additional shares so that their overall share in the investment remains the same (won’t go into the exact mechanics here). This downside protection allows investors to be more aggressive on their valuations of the company, and the company is able to report higher headline numbers.

Ratchets have two problems, both of which are illustrated in the difficulty of Flipkart and Snapdeal in raising more funds. Firstly, optionality in funding means an automatic markdown of funds held by investors in progressively earlier rounds. This is not explicit, but a ratchet is basically existing investors writing an option in favour of the new investors. While the cost of this option is not explicit, it is the earlier investors who bear the cost.

So Series C (and earlier) investors bear the cost of the optionality given to Series D investors. Series B and earlier investors bear the cost of Series C’s optionality. And so on. Notice that this telescopes, so the founders (original owners of equity) have written options to everyone who has invested (of course they also benefit from the higher overall valuation).

Now, if a “down round” (funding round at lower overall valuation than previous round) happens, this optionality gets immediately gets “paid out”. So if the Series D valuation is lower than Series C valuation, Series B and earlier investors (and founders) immediately “pay” the difference to the Series C investors (these options are American, and usually without an expiry date). So Series B and earlier investors (and especially founders) will not like this round. And they will hunt around for offers that will ensure that they don’t have to pay out on the options they’ve written. I suspect this is what is happening at Flipkart and Snapdeal now.

The second problem with ratchets is that stated valuations are inflated. A common share in Flipkart (don’t think one exists. All investors in that firm are effectively either long or short an option in the same stock) is not valued at $15 billion, so that valuation is essentially a misnomer. When Morgan Stanley says on its books that Flipkart is actually worth $11 billion, it is possible that that is the “true value” of the stock, without accounting for the optionality that latest round of investors receive. In other words, the latest round of investors invested at a price, which if extended to all stock, would value the company at $15 billion. But the rest of the company’s stock is not the same as the stock these investors hold! 

The problem, though, is that the latest “headline valuation” (inclusive of optionality) is anchored in the minds of founders and other earlier investors, and they see any lower price as unacceptable. And so the logjam continues. It will be interesting to see how this plays out.

With IPO being way too far off an event for determining if a company has “arrived” I propose a new metric, with shorter horizon. A company can be declared as having arrived if it manages to raise a round of equity with no embedded options. Think about it!

Why authors need convertible debt

At the end of a recent blogpost, I had referred to a piece by Matthew Yglesias where he refers to author advances as “convertible debt”.

 An advance is bundled with a royalty agreement in which a majority of the sales revenue is allocated to someone other than the author of the book. In its role as venture capitalist, the publisher is effectively issuing what’s called convertible debt in corporate finance circles — a risky loan that becomes an ownership stake in the project if it succeeds.

While I agreed with Yglesias’s piece when I had first read it (around the time it was published), I’m not so sure I agree with it now. As I approache the “home stretch” with the first draft of my first book (it’s a popular economics book on liquidity and market design), I’m plunged in self-doubt every time I sit down to write it.

The problem with writing a book is that the author needs to work for months together without any feedback whatsoever. It is occasionally possible for the author to take feedback from a few family members and friends. While such feedback is sometimes useful, the problem is that the people providing the feedback represent only a very tiny fraction of the book’s overall client base (I hope lots of people will read my book once it gets published).

So there is always a reasonable chance that months of effort might result in an absolute dud, implying zero returns. It is also mildly probable, of course, that these months of efforts might result in a blockbuster, but while you are producing it you have no clue which way it will turn out.

This can create serious motivation issues, and on the occasional bad day at work you might be tempted to abandon the project altogether and get back to doing something more predictable. You can have some internal deadlines but they need not be binding (like I’d set the deadline to finish my first draft as the day I went for my vacation to al-Andalus. However I’ve already reneged on that and given myself a further fifteen days). Unless there is extremely strong internal motivation, it is hard to sustain your effort.

This is where convertible debt, in the form of a publisher’s advance, can help. On the upside, the advance will guarantee you some returns (however meagre) from the project. On the downside, the advance from the publisher comes with a deadline, which acts as a Damocles’s sword to ensure you are motivated and finish your book on time.

As a first time author however, whose only published work so far has been 2000 odd posts on this blog and a 100 odd articles for Mint, I didn’t give myself too good a chance of snagging convertible debt, and so I soldier on, hoping my book turns out well.

Soon, once I finish the draft, I hope to start taking the book to publishers. If any of you has leads on who to approach, do let me know. It’s a non-fiction (popular economics) book with an Indian core but written for a global audience. For now I’m ruling out self-publication, since I’m looking at this book as providing me far more than royalty revenues and can do with some publisher validation.

Also, that might help me get some convertible debt for my next book!

Sudden death and the discount rate

It’s six years today since my mother passed away. She died in the early hours of Friday, 23rd October 2009 following a rather brief illness. The official death summary that the hospital issued reported the cause of her death as “sepsis”. She only officially died on the 23rd. As far as I’m concerned, I’d lost her two Mondays earlier, on 12th October 2009, when she complained of extreme breathing difficulty and was put on ventilator in the ICU.

Looking back (this year’s calendar is identical to that of 2009, so memories of that year have been coming back rather strongly this year), I realise that the suddenness with which it all happened have left me with a deep sense of paranoia, which can be described in financial terms as a “high discount rate”.

Having moved back from Gurgaon in June of that year, my mother and I had settled down in a rented house in Tata Silk Farm (she didn’t want to go back to our own house in Kathriguppe where we’d lived until 2008). She had settled well, and living not far from her sisters, had developed a nice routine. There were certain temples she would visit on certain days of the week, for example.

And then suddenly one day in September she complained of breathing trouble (she took thirty minutes to walk from our then house to my aunt’s house, which is only a ten minute walk away). Initial medical tests revealed nothing. More tests were prescribed, as her breathing got worse. There was no diagnosis yet.

She started seeing specialists – a pulmonologist and her cardiovascular surgeon (she had had trouble with some veins for a few years). More tests. Things getting worse. And before we knew it, she was in hospital – for a “routine three day admission” for an invasive test. The test got postponed, and the surgery finally done a week later. She got out of the ICU and remained there for hardly two days before she complained of insane breathing trouble and had to be put on ventilator – the only purpose the 12 days she spent on that served was to help me prepare for her impending death.

In all, it took less than a month end to end – from initially complaining of breathlessness to going on ventilator. What seemed to be a harmless problem leading to death.

I realise it’s caused insane paranoia in me which I’m yet to come out of. Every time I, or a relative or a friend, show minor signs of sickness, I start fearing the worst. I stop thinking about the symptoms in a Bayesian fashion – by looking at prior probabilities of the various illnesses that could be causing them – and overweight the more morbid causes of the symptoms. And that adds paranoia and anxiety to what I’m already suffering from.

Like two weeks back I had a little trouble breathing, but no apparent cold. It wasn’t something that happens to me normally. A quick Bayesian analysis would have revealed that the most probable cause is a sinus (which it was), but I spent half a day wondering what had become of me before I applied Vicks and quickly recovered. When my wife told me a week after she reached the US that she had got a high fever, I got paranoid again before realising that the most probable cause was a flu caused due to a change of seasons (which it was!).

Another consequence of my mother’s rather sudden death in 2009 (and my father’s death in 2007, though that was by no means sudden, as he had been diagnosed with cancer two years earlier) was that I suddenly stopped being able to make plans. I started overestimating the odds of something drastic happening, and planning didn’t make sense in such scenarios, I reasoned. As a consequence I became extremely short-term in my thinking, and couldn’t see beyond a few days away.

There have been several occasions where I’ve left a decision (such as booking tickets for something, for example) until it has been too late. There have been times when I’ve optimised for too short a term in some of my decisions, effectively jacking up my “discount rate”.

I’d written a while earlier about how in case of rare events, the probabilities we observe can be much higher than actual probabilities, and how that can lead to impaired decision-making. Thinking about it now, I’ve seen that playing out in my life over the last six years.  And it will take a considerable amount of effort to become more rational (i.e. use the “true” rather than “observed” probabilities) in these things.