Letters to my Berry #6

So you turn half today. And I’ll let you write this letter yourself, since over the last week or two you’ve been trying to get to the computer and operate it.

So long, bangalore. We're off to wash our arses in the Thames.

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OK I gave you two minutes, but unlike what you’ve been doing over the last one week, you didn’t try to get to the computer today, so I’ll write this myself.

This last month has been one of big change, as you made your first forin trip. It was a mostly peaceful flight from Bangalore to London, via Dubai. You hardly cried, though you kept screaming in excitement through the flight, and through the layover in Dubai. Whenever someone smiled at you, you’d attempt to talk to them. And it would get a bit embarrassing at times!

Anyway, we got to London, and we had to put you in day care. The first day when I left you at the day care for a one-hour settling in session, I cried. Amma was fine, but I had tears in my eyes, and I don’t know why! And after two settling-in sessions, you started “real day care”, and on the first day it seems you were rather upset, and refused to eat.

So I had to bring you home midway through the day and feed you Cerelac. It was a similar story on the second day – you weren’t upset, but you still wouldn’t eat, so I had to get you home and give you Cerelac. It was only on the third day, that is today, that you finally at ate at the nursery!

The biggest challenge for us after bringing you to London has been to keep you warm, since you refuse to get the concept of warm clothes, and refuse to wear them. And so for the last 10 days you’ve not only got a cold and cough for yourself, but you’ve also transmitted it to both Amma and me ūüôĀ

London has also meant that you’ve started travelling by pram regularly, though after one attempt we stopped taking it on the Underground since it was difficult to negotiate steps. When we have to take the train, I¬†thus carry you in your baby carrier, like a baby Kangaroo!

In the last one month, you’ve also made significant motor improvements. You still can’t sit, but you try to stand now! It seems like you’ve taken after Amma and me in terms of wanting to take the easy way out – you want to stand without working hard for it, and sometimes scream until we hold you up in a standing position.

Your babbles have also increased this month, and we¬†think you said “Appa” a few times in the last one week in the course of the last one week! Maybe I like to imagine that you say it, and maybe you actually call me that! It’s too early to say!

Finally, one note of disappointment – on Monday when you were all crying and upset and refusing to eat at the nursery, I rushed to pick you up, and hoped to see you be very happy when you saw me. As it turned out, you gave me a “K dear, you are here” kind of expression and just came home! Yesterday you actually cried when I came to pick you up!

It seems like you’re becoming a teenager already! And you’re just half!!

Letters to my Berry #5

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Your biggest milestone in your fifth month is that you started to eat. Beyond the milk that Amma directly provided you, and the formula milk that we had started you on after the doctor’s advice, the fifth month was when we started giving you what I called as “real food”.

You started with this thing called “ragi cherry” which I personally didn’t like too much – it was made out of a flour made by mixing ragi and other cereals with some nuts, etc. We would make a porridge out of this with some sweet element, and the first time I ate it, I said it tasted like soapnut powder.

Initially you made a fuss eating the ragi cherry, but to my utmost happiness, you seem to be yet another banana lover. After only two or three times of my feeding you bananas, all I had to do was to take your silver bowl and spoon and make mashing noises – and you’d immediately start salivating.

This was also the month where you started implementing Amma’s old company’s slogan “moving forward”. Given the size of your head you had trouble holding it up, but you invented your own way of moving forward while still keeping your head to the ground. I tried without success to draw an animal analogy – sometimes it seemed like you were like an ostrich with its head buried in the sand. Ranga said you were like an Aardvark, moving forward with your head on the ground.

One night I’d left you on the carpet with my house slippers at the other end of the carpet. I hadn’t been gone for a couple of minutes when I saw that you’d somehow traversed the length of the carpet and was about to eat my slippers! Yet another day, we had left you in your bouncer and gone somewhere, and you were trying to slide down. Amma stopped you, but the next time you attempted it, we let you slide. And we were amazed with the poise¬†with which you got down to the carpet, never once worrying us that you would hurt yourself!

This was also the month when you attended your first wedding – your aunt Barbie’s. You were such a centre of attraction¬†during some of the pre-wedding festivities that you were tired and slept through most of the wedding. Halfway through both the wedding ceremony and the reception, we sent you home so you didn’t tire further. So apart from the photos taken at the beginning of each session, you unfortunately don’t appear in any photos!

And of course, the biggest event in your fifth month was that you got named. While you had been named even before you were born, and your official name had been submitted to the municipality when you were a day old, we did a small naming ceremony for you. There, the family priest Nagabhushana Sharma made us give you several names.

So there was the maasa naama (month name) which the priest himself decided. You were “Shachi”. Then there was the nakshatra naama¬†(star name), which we had to come up with on the spot with the given starting letter. The starting letter for you was “Go” and Amma quickly came up with “Goda”, which she later elongated to “Godavari”.

And there was the vyavahara naama (trade name) which was supposed to represent one of your ancestors. The day I first met Amma in 2009, she had told me that she wanted to name her daughter Rukmini, after her grandmother. So there was no doubt about this one.

And then there was the¬†nija naama (real name), which of course had to be Abheri. I had to shout it loud three times, and I did that with my mouth close to your ear. Thankfully you didn’t get startled – suggesting¬†you like your name, and you won’t hate us later in life for it!

This is a monthly series that ordinarily runs on my wife’s blog, but since I wrote it this time (for the first time), I’m putting it here.¬†

Earlier editions:

Letters to my Berry ‚ÄstMonth#1

Letters to my Berry ‚ÄstMonth#2

Letters to my Berry ‚ÄstPrelogue

Letters to my Berry#4

 

Relative size of hand and mouth

So the daughter and I are playing a game where she makes a gesture and I try to imitate it (this blogpost is not part of the game, of course). Like me, and my mother before me, she’s an expert in contorting her face in all kinds of ways. So it is a fun game, to try and imitate each other in the way we contort faces.

One thing she does which I’m thoroughly incapable of replicating, however, is putting hands in mouth. She seems well capable of inserting her whole hand inside her mouth. On the other hand I struggle to even put in a finger or two.

This makes me wonder about the relative growth patterns in hands and mouths. As a baby, we are born with big heads and faces, and consequently big mouths. Limbs are tiny in comparison. As we grow, though, our limbs grow much faster than our heads, to the effect that soon we become incapable of putting hands in our mouths, and at best, can just suck on a thumb!

Another thing I’ve noticed in my daughter’s growing up is that she seems thoroughly incapable of putting her big toes in her mouth. It’s a well documented fact (with photos) that I used to do a fair amount of this as a baby. Even now, with some effort I can bring around my big toe and can suck on it if I want to. The daughter, however, seems thoroughly incapable of doing that.

Conventional wisdom is that as we grow older our bodies become less flexible. I wonder if it’s actually a curve that first increases, hits a maximum and then decreases slowly through life. So maybe my daughter can’t suck on her big toe because she’s too small for it (she’s three months old now)!

Whatever it is,¬†it’s fascinating to watch babies grow!

Damming the Nile and diapers

One of the greatest engineering problems in the last century was to determine the patterns in the flow of the Nile. It had been clear for at least a couple of millennia that the flow of the river was not regular, and the annual flow did not follow something like a normal distribution.

The matter gained importance in the late 1800s when the British colonial government decided to dam the Nile. Understanding accurately the pattern of flows of the river was important to determine the capacity of the reservoir being built, so that both floods and droughts could be contained.

The problem was solved by Harold Edwin Hurst, a British hydrologist who was posted in Egypt for over¬†60 years in the 20th Century. Hurst defined his model as one of “long-range dependence”, and managed to accurately predict the variation in the flow of the river. In recognition of his services, Egyptians gave him the moniker “Abu Nil” (father of the Nile). Later on, Benoit Mandelbrot named a quantity that determines the long-range dependence of a time series after Hurst.

I’ve written about Hurst once before, in the context of financial markets, but I invoke him here with respect to a problem closer to me – the pattern of my daughter’s poop.

It is rather well known that poop, even among babies, is not a continuous process. If someone were to poop¬†100ml of poop¬†a day (easier to use volume rather than weight in the context of babies), it doesn’t mean they poop¬†4ml every hour. Poop¬†happens in discrete bursts, and the number of such bursts per day depends upon age, decreasing over time into adulthood.

One might think that a reasonable way to model poop¬†is to assume that the amount of poop¬†in each burst follows a normal distribution, and each burst is independent of the ones around it. However, based on a little over two months’ experience of changing my daughter’s diapers, I declare this kind of a model to be wholly inaccurate.

For, what I’ve determined is that far from being normal,¬†pooping¬†patterns follow long-range dependence. There are long time periods (spanning a few diaper changes) when there is no, or very little, poop. Then there are times when it flows at such a high rate that we need to change diapers at a far higher frequency than normal. And such periods are usually followed by other high-poop periods. And so on.

In other words, the amount of poop¬†has positive serial correlation. And to use the index that Mandelbrot lovingly constructed and named in honour of Hurst, the Hurst exponent of my daughter’s (and other babies’) poop¬†is much higher than 0.5.

This makes me wonder if diaper manufacturers have taken this long-range dependence into account while determining diaper capacity. Or I wonder if, instead, they simply assume that parents will take care of this by adjusting the inter-diaper-change time period.

As Mandelbrot describes towards the end of his excellent¬†Misbehaviour of markets¬†, you can ¬†use so-called “multifractal models” which combine normal price increments with irregular time increments to get an accurate (fractal) representation of the movement of stock prices.

PS: Apologies to those who got disgusted by the post. Until a massive burst a few minutes ago I’d never imagined I’d be comparing the flows of poop¬†and the Nile!

Working women, maternity and all that

As I write this, my wife is at work. Though her official gainful fulltime employment starts only a few months later (her employers have deferred her joining date thanks to the baby), she is continuing with her work as Marriage Broker Auntie (which she is now pivoting into something like a “Love Training School“).

In fact, our daughter was barely a week old when my wife decided to get back to business, in her quest to get more people “settled down” and “find partners” (she even brokered a deal from her hospital bed as they tried to induce labour in her). And so I’ve been able to observe, at reasonably close quarters, what it’s like to work while having a tiny baby.

Some times, you think it just doesn’t matter. That she works mainly from home means that she’s always with the baby. There are always sufficiently long periods of time when the baby sleeps when she can do her emails and writing. While sleep is definitely disturbed (by at least two hour-long feeding sessions each night), that she doesn’t engage in other strenuous work means she can handle the work stress.

But then there are the minor irritants. Meetings are a no-no, for example, since she can’t go out, and it doesn’t always make sense to call business acquaintances home. She’s been trying to substitute it with Skype/Facetime calls, but the challenge has been in terms of timing.

Given that some of the people she works with are fairly busy, she needs to pre-schedule calls, and with the baby’s feeding and sleeping schedule being rather uncertain, this is not an easy task. And then there is the problem of having someone take care of the baby during the call, which means the call has to take place at a time when I’m at home.

And so she is on a Skype call now. As she went in for the call, she asked me to handle the baby until it was done, promising that it would be a short call. As it usually happens in such situations, Abheri decided to start crying some two minutes after Priyanka went in for the call.

I tried all my usual tricks. I lay her down on my chest, a technique that usually comforts her in no time, but to no avail (I’ve read about the merits of skin-to-skin contact with the baby but given up on it after she decided to eat my chest hair). I then tried this face-down neck-hold (that I’ve nicknamed “choke slam”), which again usually works in calming her. Again no luck.

Then I smelt shit and thought she was crying because she needed a change of diapers. That didn’t help either. Rocking and singing and swaying and talking – all usually have an immediate effect but none whatsoever today. It was obvious that Abheri was hungry.

So I had to call emergency. Thankfully Priyanka’s Skype call is voice only (or maybe she switched, since she typically prefers video), so she managed to take a little break from the call to take Abheri from my hands. She (Abheri) immediately calmed down – food wasn’t far away.

Priyanka is still on her call, cradling Abheri with one hand against her breast, as Abheri feeds. And Priyanka continues to work.

Major level up in respect for her to see her work this way.

And major envy as well – that she can hold the baby and simultaneously work – nearly four weeks in and I’ve still not mastered the art of holding the baby with one hand, so I can’t work while carrying her!

PS: As for the new law that increases maternity leave, I’m sceptical, since I believe that full-time employment is something that will soon be history. More importantly, the law raises the cost of hiring women, so I’m not sure it will have its intended consequences. Read Priyanka’s excellent analysis here.

Bayesian recognition in baby similarity

When people come to see small babies, it’s almost like they’re obliged to offer their opinions on who the child looks like.¬†Most of the time it’s an immediate ancestor – either a parent or grandparent. Sometimes it could be a cousin or aunt or uncle as well. Thankfully it’s uncommon to compare babies’ looks to those who they don’t share genes with.

So as people have come up and offered their opinions on who our daughter looks like (I’m top seed, I must mention), I’ve been trying to analyse how they come up with their predictions. And as I observe the connections between people making the observations, and who they mention, I realise that this too follows some kind of Bayesian Recognition.

Basically different people who come to see the baby have different amounts of information on how each of the baby’s ancestors looked like. A recent friend of mine, for example, will only know how my wife and I look. An older friend might have some idea of how my parents looked. A relative might have a better judgment of how one of my parents looked than how I looked.

So based on their experiences in recognising different people in and around the baby’s immediate ancestry, they effectively start with a prior distribution of who the baby looks like. And then when they see the baby, they update their priors, and then mention the person with the highest posterior probability of matching the baby’s face and features.

Given that posterior probability is a function of prior probability, there is no surprise that different people will disagree on who the baby looks like. After all, each of their private knowledge of the baby’s ancestry’s idiosyncratic faces, and thus their priors, will be different!

Unrelated, but staying on Bayesian reasoning, I recently read this fairly stud piece in Aeon on why stereotyping is not necessarily a bad thing. The article argues that in the absence of further information, stereotypes help us form a good first prior, and that stereotypes only become a problem if we fail to update our priors with any additional information we get.

The one bit machine

My daughter is two weeks old today and she continues to be a “one bit machine”. The extent of her outward communication is restricted to a maximum of one bit of information. There are basically two states her outward communication can fall under – “cry” and “not cry”, and given that the two are not equally probable, the amount of information she gives out is strictly less than one bit.

I had planned to write this post two weeks back, the day she was born, and wanted to speculate how long it would take for her to expand her repertoire of communication and provide us with more information on what she wants. Two weeks in, I hereby report that the complexity of communication hasn’t improved.

Soon (I don’t know how soon) I expect her to start providing us more information – maybe there will be one kind of cry when she’s hungry, and another when she wants her diaper changed. Maybe she’ll start displaying other methods of outward communication – using her facial muscles, for example (right now, while she contorts her face in a zillion ways, there is absolutely no information conveyed), and we can figure out with greater certainty what she wants to convey.

I’m thinking about drawing a graph with age of the person on the X axis, and the complexity of outward information on the Y axis. It starts off with X = 0 and Y = 1 (I haven’t bothered measuring the frequency of cry/no-cry responses so let’s assume it’s equiprobable and she conveys one bit). It goes on to X = 14 days and Y = 1 (today’s state). And then increases with time (I’m hoping).

While I’m sure research exists some place on the information content per syllable in adult communication, I hope to draw this graph sometime based on personal observation of my specimen (though that would limit it to one data point).

Right now, though, I speculate what kind of shape this graph might take. Considering it has so far failed to take off at all, I hope that it’ll be either an exponential (short-term good but long-term I don’t know ) or a sigmoid (more likely I’d think).

Let’s wait and see.