## 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.

## Hooke’s Curve, hooking up and dressing sense

So Priyanka and I were talking about a mutual acquaintance, and the odds of her (the acquaintance) being in a relationship, or trying to get into one. I offered “evidence” that this acquaintance (who I meet much more often than Priyanka does) has been dressing progressively better over the last year, and from that evidence, it’s likely that she’s getting into a relationship.

“It can be the other way, too”, Priyanka countered. “Haven’t you seen countless examples of people who have started dressing really badly once they’re in a relationship?”. Given that I had several data points in this direction, too, there was no way I could refute it. Yet, I continued to argue that given what I know of this acquaintance, it’s more likely that she’s still getting into a relationship now.

“I can explain this using Hooke’s Law”, said Priyanka. Robert Hooke, as you know was a polymath British scientist of the seventeenth century. He has made seminal contributions to various branches of science, though to the best of my knowledge he didn’t say anything on relationships (he was himself a lifelong bachelor). In Neal Stephenson’s The Baroque Cycle, for example, Hooke conducts a kidney stone removal operation on one of the protagonists, and given the range of his expertise, that’s not too far-fetched.

“So do you mean Hooke’s Law as in stress is proportional to strain?”, I asked. Priyanka asked if I remembered the Hooke’s Curve. I said I didn’t. “What happens when you keep increasing stress?”, she asked. “Strain grows proportional until it snaps”, I said. “And how does the curve go then”, she asked. I made a royal mess of drawing this curve (didn’t help that in my mind I had plotted stress on X-axis and strain on Y, while the convention is the other way round).

After making a few snide remarks about my IIT-JEE performance, Priyanka asked me to look up the curve and proceeded to explain how the Hooke’s curve (produced here) explains relationships and dressing sense.

“As you get into a relationship, you want to impress the counterparty, and so you start dressing better”, she went on. “These two feed on each other and grow together, until the point when you start getting comfortable in the relationship. Once that happens, the need to impress the other person decreases, and you start wearing more comfortable, and less fashionable, clothes. And then you find your new equilibrium.

“Different people find their equilibria at different points, but for most it’s close to their peak. Some people, though, regress all the way to where they started.

“So yes, when people are getting into a relationship they start dressing better, but you need to watch out for when their dressing sense starts regressing. That’s the point when you know they’ve hooked up”, she said.

By this point in time I was asking to touch her feet (which was not possible since she’s currently at the other end of the world). Connecting two absolutely unrelated concepts – Hooke’s Law and hooking up, and building a theory on that. This was further (strong) confirmation that I’d married right!

## Discrete and continuous diseases

Some three years or so back I got diagnosed with ADHD, and put on a course of Methylphenidate. The drug worked, made me feel significantly better and more productive, and I was happy that a problem that should have been diagnosed at least a decade earlier had finally been diagnosed.

Yet, there were people telling me that there was nothing particularly wrong with me, and how everyone goes through what are the common symptoms of ADHD. It is a fact that if you go through the ADHD questionnaire (not linking to it here), there is a high probability of error of commission. If you believer you have it, you can will yourself into answering such that the test indicates that you have it.

Combine this with the claim that there is heavy error of commission in terms of diagnosis and drugging (claims are that some 10% of American kids are on Methylphenidate) and it can spook you, and question if your diagnosis is correct. It doesn’t help matters that there is no objective diagnostic test to detect ADHD.

And then your read articles such as this one, which talks about ADHD in kids in Mumbai. And this spooks you out from the other direction. Looking at some of the cases mentioned here, you realise yours is nowhere as bad, and you start wondering if you suffer from the same condition as some of the people mentioned in the piece.

The thing with a condition such as ADHD is that it is a “continuous” disease, in that it occurs in different people to varying degrees. So if you ask a question like “does this person have ADHD” it is very hard to give a straightforward binary answer, because by some definitions, “everyone has ADHD” and by some others, where you compare people to the likes of the girl mentioned in the Mid-day piece (linked above), practically no one has ADHD.

Treatment also differs accordingly. Back when I was taking the medication, I used to take about 10mg of Methylphenidate per day. A friend, who is also on Methylphenidate and of a comparable dosage, informs me that there are people who are on the same drug at a dosage that is several orders of magnitude higher. In that sense, the medical profession has figured out the continuous nature of the problem and learnt to treat it accordingly (a “bug”, however, is that it is hard to determine optimal dosage first up, and it is done through a trial and error process).

The problem is that we are used to binary classification of conditions – you either have a cold or you don’t. You have a fever or you don’t (though arguably once you have a fever, you can have a fever to different degrees). You have typhoid or you don’t. And so forth.

So coming from this binary prior of classifying diseases, continuous diseases such as ADHD are hard to fathom for some people. And that leads to claims of both over and under medication, and it makes clinical research also pretty hard.

Do I have ADHD? Again it’s hard to give a binary answer to that. It depends on where you want to draw the line.

## Narendra Modi and the Correlation Term

In a speech in Canada last night, Prime Minister Narendra Modi said that the relationship between India and Canada is like the “2ab term” in the formula for expansion of $(a+b)^2$.

Unfortunately for him, this has been widely lampooned on twitter, with some people seemingly not getting the mathematical reference, and others making up some unintended consequences of it.

In my opinion, however, it is a masterstroke, and brings to notice something that people commonly ignore – what I call as the “correlation term”. When any kind of break up or disagreement happens – like someone quitting a job, or a couple breaking up, or a band disbanding, people are bound to ask the question of whose fault it was. The general assumption is that if two entities did not agree, it was because both of them sucked.

However, considering the frequency at which such events (breakups or disagreements ) happen, and that people who are generally “good” are involved in such events, the badness of one of the parties involve simply cannot explain them. So the question arises – if both parties were flawless why did the relationship go wrong? And this is where the correlation term comes in!

It is rather easy to explain using vector calculus. If you have two vectors $A$ and $B$, the magnitude of the sum of the two vectors is given by $\sqrt{|A|^2 + |B|^2 + 2 |A||B| cos \theta}$ where $|A|,|B|$ are the magnitudes of the two vectors respectively and $\theta$ is the angle between them. It is easy to see from the above formula that the magnitude of the sum of the vectors is dependent not only on the magnitudes of the individual vectors, but also on the angle between them.

To illustrate with some examples, if A and B are perfectly aligned ($\theta = 0, cos \theta = 1$), then the magnitude of their vector sum is the sum of their magnitudes. If they oppose each other, then the magnitude of their vector sum is the difference of their magnitudes. And if A and B are orthogonal, then $cos \theta = 0$ or the magnitude of their vector sum is $\sqrt{|A|^2 + |B|^2}$.

And if we move from vector algebra to statistics, then if A and B represent two datasets, the “$cos \theta$” is nothing but the correlation between A and B. And in the investing world, correlation is a fairly important and widely used concept!

So essentially, the concept that the Prime Minister alluded to in his lecture in Canada is rather important, and while it is commonly used in both science and finance, it is something people generally disregard in their daily lives. From this point of view, kudos to the Prime Minister for bringing up this concept of the correlation term! And here is my interpretation of it:

At first I was a bit upset with Modi because he only mentioned “2ab” and left out the correlation term ($\theta$). Thinking about it some more, I reasoned that the reason he left it out was to imply that it was equal to 1, or that the angle between the a and b in this case (i.e. India and Canada’s interests) is zero, or in other words, that India and Canada’s interests are perfectly aligned! There could have been no better way of putting it!

So thanks to the Prime Minister for bringing up this rather important concept of correlation to public notice, and I hope that people start appreciating the nuances of the concept rather than brainlessly lampooning him!

## Sigma and normal distributions

I’m in my way to the Bangalore airport now, north of hebbal flyover. It’s raining like crazy again today – the second time in a week it’s raining so bad.

I instinctively thought “today is an N sigma day in terms of rain in Bangalore” (where N is a large number). Then I immediately realized that such a statement would make sense only if rainfall in Bangalore were to follow a normal distribution!

When people normally say something is an N sigma event what they’re really trying to convey is that it is a very improbable event and the N is a measure of this improbability. The relationship between N and the improbability implied is given by the shape of the normal curve.

However when a quantity follow a distribution other than normal the relationship between the mean and standard deviation (sigma) and the implied probability breaks down and the number of sigmas will mean something totally different in terms of the implied improbability.

It is good practice, thus, to stop talking in terms of sigma and talk in terms of of odds. It’s better to say “a one in forty event” rather than saying “two sigma event” (I’m assuming a one tailed normal distribution here).

The broader point is that the normal distribution is too ingrained in people’s minds which leads then to assume all quantities follow a normal distribution – which is dangerous and needs to be discouraged strongly.

In this direction any small measure – like talking odds rather than in terms of sigma – will go a long way!

## The moving solstice

Today is “Makara Sankranti”. If the name doesn’t already strike you, “Makara” is the Sanskrit name for “Capricorn”. The Makara Sankranti is supposed to represent the Winter Solstice in the Northern Hemisphere, or the day when the Sun is directly over the Tropic of Capricorn.

However, we know that the winter solstice falls on the 21st or 22nd of December every year. Then why is it that the Indian version of the Winter Solstice falls on 15th of January?

I’m not sure if you remember, but a few years back, Makara Sankranti would usually fall on the 14th of January. After some back-and-forth movements, it has now settled on the 15th of January. You might have already noticed that this is unlike other Indian festivals such as Deepavali or Ganesh Chaturthi, whose dates according to the Gregorian calendar move every year (typically in a -11, -11, +19 cycle) over three years). This is because unlike Deepavali or Ganesh Chaturthi, which are observed according to the Lunar calendar, Makara Sankranti follows the solar calendar!

I recently read a book called “Solstice at Panipat”, about the third battle of Panipat in 1761 (my review is here). The Marathas went to battle four days after celebrating the Winter Solstice. The battle was fought on the 14th of January 1761, which means the solstice was observed that year on the 10th of January. So you see that the solstice, which is supposed to be observed on the 21/22 of December, was observed on 10th of January in 1761, and on the 15th of January in 2014.

This shows that there is an error in the Indian solar calendar. This error amounts to about 20 minutes a year, which means that the rate at which we are going, about 10000 years from now the Makara Sankranti (“Winter Solstice”) will fall in June, the middle of the summer!

That we know that the error in the Hindu solar calendar is 20 minutes a year allows us to calculate the last time the calendar was calibrated – we can date it to around 285 AD. Back in 285 AD, the calendar was calculated accurately, with the Winter Solstice falling on the actual Winter Solstice. After that, the calendar has drifted, and one can say, so has Indian science.

I’m informed, however, that this 20 minute error in the Hindu solar calendar is deliberate, and that this has been put in place for astrological reasons. Apparently, astrology follows a 26400 year cycle, and for that to bear out accurately, our solar calendar needs to have a 20 minute per year error! So for the last 1700 or so years, we have been using a calendar that is accurate for astrological calculations but not to seasons! Thankfully, the lunar calendar, which has been calibrated to the movement of stars, captures seasons more accurately!

Update: The link to the tweet doesn’t show the entire thread. See that here.

Update: Here is a piece by astrophysicist Jayant Narlikar on the Makara Sankranti. Basically due to a change in the earth’s axis, our divisions of the night sky into 12 constellations are not stationary, and hence the date when the sun moves from “Dhanur” to “Makara” is no longer the solstice date.

## Festivals and memes

We don’t normally celebrate festivals. We don’t particularly enjoy them. The only festival we celebrate to some degree is Dasara, when we set up dolls and invite people home to view the dolls. Of course, the last couple of years it’s been similar arrangements and there hasn’t been much innovation in what we do, but we enjoy it as a process and hence take forward the festival. Last year, we even got some fireworks during Deepavali and burst them. Again – it was a fun element. We aren’t too enthused by rituals and since most other festivals are little more than rituals we don’t celebrate them.

The wife, however, sometimes have existential doubts. “There must be a reason that our ancestors celebrated these festivals”, she pops up from time to time, “so it may not be correct on our part to simply stop celebrating. We should take forward the tradition”. This is question that comes up each time we don’t celebrate a festival (which you might guess is fairly often). Before today I hadn’t been able to give a convincing reply either way – whether it makes sense to follow our instinct or if it’s a cultural duty to take forward the tradition.

Towards the end of his classic book The Selfish Gene, Richard Dawkins introduces the concept of the meme.  In fact it was Dawkins who “invented” the concept of the meme. It is meant to be a cultural analogy to the gene, and it’s a “cultural’ concept that propagates like biological concepts are taken forward through the generations via genes. Given the multitude of so-called memes that keep popping up every other day, I’m sure all of you know what meme means. I’m just providing the context here since my argument depends on the original Dawkinsian definition of the meme.

Let us say that there is a genetic attribute I inherited from my father, let’s say it’s my height (my father was 5 feet 10 inches, and I’m an inch taller than that). Now, it is not necessary that this particular gene is passed on to my progeny. It is not even necessary that the corresponding gene from my wife gets passed on – there might be a mutation there and despite the wife and I being fairly tall (by Indian standards) we cannot rule out producing a short child. The point I’m trying to make is that while genes propagate, not every trait needs to pass on from you to your offspring. Only a few traits (chosen more or less at random when your and your gene-propagating partner’s genes undergo meiosis) get passed on. Yet, through the network of you and your siblings and cousins and extended family, the family’s genetic code gets passed on.

Now, festivals and other cultural practices can be described as memes. We in the Indian society have a set of memes, which are called “Ganesh Chaturthi”, “Deepavali”, etc. That these memes have survived through the generations shows their strength – who knows about festivals that had been invented but didn’t survive. Now, the fact that we have inherited this meme doesn’t necessarily mean that we need to propagate it. Unlike genetics, the choice here is not random combination – it is our personal choice (we can’t decide what genes our offspring inherits from either of us or through a mutation).

So, just like every genetic trait doesn’t need to be propagated from a parent to an offspring, not every cultural trait needs to be passed on. If I were to pass on every cultural trait I inherit irrespective of whether it is desirable, even when circumstances change, undesirable cultural traits continue to exist. This is not efficient. As a society, we have bandwidth only for a certain number of cultural traits, and if traits are passed on without much thought, the bad ones won’t die. And will crowd out the good ones.

So if you were to look at it in terms of responsibility to society, you need to propagate only those cultural traits that you deem to be relevant and important. “So what if everyone stops celebrating Ganesh Chaturthi?” you may ask. If that would happen that would simply mean a vote of no confidence for the festival and an indication that the festival needs to be phased out. If everyone were to propagate only those cultural traits they find useful, traits that a significant proportion of society finds significant will continue to survive and thrive. For Ganesh Chaturthi to exist 30 years hence, it isn’t necessary for ALL families that have inherited it to celebrate it now. As long as a critical mass of families celebrate it, the festival will survive. If not, it probably doesn’t need to exist.

(the choice of Ganesh Chaturthi for illustration is purely driven by the fact that the festival is today).