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Voiced and Unvoiced consonants

May 1, 2016 Leave a comment

I am reading “Words and Rules” by Steven Pinker, where I came across voiced and unvoiced consonants. The book explains some of the seeming idiosyncrasies of of the English language with the help of this categorization of consonants which is based on whether they are voiced or not.

Until now I had no idea what this distinction meant. When I looked it up, I learnt that the distinction was whether your vocal cords vibrate or not when articulating a sound. When you make the sound sssss, the vocal cords do not vibrate, while when you make the sound zzzz, the vocal cords vibrate. I do not know much about the anatomy of the voice box, but an easy way to identify whether the vocal cords are vibrating or not, is to feel your upper throat with your fingers while making the noise (as explained here on wikipedia).

If you actually try that while making the s and z sounds, you will feel the vibration for z but not for s. Since the vocal cords do not vibrate for s, it is called an unvoiced consonant, while z is a voiced consonant. Other such example pairs are p and b, f and v and k and g wherein the first of the pairs is unvoiced and the second is voiced.

The book is very interesting (I am only in the 3rd chapter now), but once I learned this voicing distinction, I see this distinction in Indian languages too (the 3 that I am familiar with).

Take Telugu consonants. The way the consonants are listed are as below.

క ఖ గ ఘ ఙ

చ ఛ జ ఝ ఞ

ట ఠ డ ఢ ణ

త థ ద ధ న

ప ఫ బ భ మ

This is exactly the same way in which Hindi consonants are listed too (In both the languages, there are other consonants that follow this set of 25, but I have not given those, as they do not follow this 5 letter pattern).

What is happening here is that the first two letters in each row are unvoiced, while the third and fourth letters are the voiced versions of the first two. Suddenly I realized that there are patterns in the way they are listed. While this is something that people with any interest in language probably already knew, it was completely new and exciting to me.

Curiously, the Indian language I am most familiar with, Tamil, is very different. Tamil maintains only one consonant for each pair. In all the 4 of the 5 cases listed above for Telugu, Tamil uses the same letter for both the voiced and unvoiced versions. For Pa and Ba, it just uses ப (called “pa”). Similarly Ka and Ga has only one letter க which is called “Ka” but used for both sounds. Ta and Da has the same letter டcalled Ta. Tha (as in Thailand) and Dha(as it The) has just one letter த.  But it does have different letters for cha (ச) and ja (ஜ), which is the exception of those 5. I have also heard people say that ஜ (Ja) is not a “true” Tamil character since words of Tamil origin do not have that sound and that it is usually used in words imported from Hindi/Sanskrit. I do not know enough of the language to confirm it (the few examples I know do indeed support this), but if so, there too, Tamil has only one letter.

F and V also constitute a pair of unvoiced and voiced consonants. In this case too, Hindi has separate consonants for each of them फ and व . Telugu and Tamil do not have letters for Fa, while they both have letters for Va. That is probably because Telugu and Tamil do not have words with the Fa sound.




Was Ramanujan Autistic?

April 24, 2016 Leave a comment

I recently read the book, The man who knew infinity . It was a real good book. Ramanujan was born in Erode (BTW, that name is the shortened form of eera odu, which means wet skull. It comes from a legend that Shiva tore off one of Vishnu’s heads), but spent a lot of time in Chennai (my home town) and so it had even more significance for me. It also, naturally, talked about his relationship with G H Hardy. So I highly recommend the book.

But what I want to highlight here is that the possibility that Ramanujan was Autistic. Given below is a page from the book.

A page from Ramanujan describing his childhood. There are some indications that he was probably autistic

A page from Ramanujan describing his childhood. There are some indications that he was probably autistic

The lining up of vessels is a tell-tale sign. If you see the wikipedia page for Autism, you will see that there are two pictures of kids lining up things. Moreover the talk about his tantrums, being self-directed, eating only at a temple (Autistic people are known to stick to a routine), being non-verbal till 3 years old etc suggest strongly that Ramanujan was Autistic.

All this should not be surprising since Autism has been with us for as long as we know. We have just started diagnosing it better. But, once I noticed this passage, I looked it up on the internet and soon found that many people have proposed the possibility that Ramanujan was Autistic. The author of this book though, was probably not aware of Autism (to be fair to him, the book was written 25 years ago, in 1991). There is no mention of it in the book. While the books takes lots of pain to try to understand Ramanujan’s genius and his awkward social capabilities, I wonder how different our understanding of Ramanujan would be, had historians acknowledge the possibility of his being Autistic. More importantly, makes us wonder, how much of his genius was because of his being Autistic. It is, in a sense, a futile exercise, since Autism is not something separate from the person. That is why, autistic self-advocates prefer the word “Autistic person”, rather than “a person with Autism”.

But read the book. It is fascinating. Let me end it on one of the results that Ramanujan discovered which was that the sum of the infinite series 1+2+3+4… is -1/12. You can see the proof in this youtube video.


Categories: Uncategorized

Visualizing complex numbers

August 9, 2015 Leave a comment

I read a few books on math recently, and I learnt something about complex numbers that amazed me.

We are very used to the idea of thinking of real numbers as a line. We draw a line, mark its center as 0, mark all the positive numbers to its right, and the negative numbers to its left. Visualizing numbers as a line is rather obvious, but I have learnt recently that complex numbers can be visualized as points on a 2D plane (and also, more importantly, why that visualization makes sense, which we will come to later in this post). That reminded me vaguely that this was mentioned to me while at school, but I did not really understand the significance of it then (nor do I remember it being explained to me).

Just a quick reminder: complex numbers are the set of numbers which are of the form a+b*i. i here stands for square root of -1 while a and b are real numbers (real numbers include positive and negative numbers including decimal numbers). The key here is that we do not know how to take the square root of a negative number. But we denote it with i which stands for square root of -1. So, now, if you need square root of -16, it would be square root of 16 * square root of -1, which would be 4*i. You can also think of numbers like 3+4i or 2.75+2i and so on. Note that when b (in a+b*i) is 0, that just gives you the full set of real numbers.

Given that complex numbers are of the form a+b*i, with a and be being real numbers, you can start plotting these points on a 2D graph, by just plotting the points a,b on the graph. For example in the plot below, the blue point is the complex number 2+1*i (I will come to the red points in a second).


If you look at the red points plotted (starting with the one on the axis to the right of origin and going anti-clockwise), they represent points (1,0), (0,1),  (-1,0) and (0,-1). These are nothing but the complex numbers 1+0i, 0+1i, -1+0i, 0-1i. Or stated simply, they are :1, i, -1, -i.

All this is straightforward, but you might wonder what the big deal is with plotting complex numbers as points on a 2D graph. What value or what better understanding does it provide?

This is the most interesting part and I learnt about it a bit in the Imagining Numbers, which I linked to at the beginning of this post. Understanding it needs a re-thinking of what numbers really mean.

On the real number line (which would just be the x-axis in the above graph) addition would mean moving the number line to the right or left. For example, adding 2 to all the numbers, would just lead to the number line shifted to the right: 0 would have moved to the position of 2, 1 would have moved to the position of 3, 2 would have moved to the position of 4 etc. On the same lines, multiplication would mean stretching the line. In case of multiplication by 2, 0 would still be 0, 1 would become 2, 2 would become 4, 3 would become 6 and so on. If you plot this new line, it will be the old line but stretched on either side.

But what does multiplication and addition mean with respect to complex numbers? Let us take the simplest example. The number 1, when multiplied by i, becomes i. i when multiplied by i becomes -1 (this is the definition of i, because we defined i as square root of -1). Proceeding further -1*i would be -i and -i * i would be 1 (this is because -i*i would be -(i*i) which is -(-1) which would be 1). This we come back to where we started from.

These 4 points have been plotted in the above graph in red. If you see now, you will realize that multiplication by i just means that the plane is rotated by 90 degrees. Multiplicating again by i, will rotate the plane again, and so on till it comes back to the same position after doing it 4 times (by when we would have rotated it 360 degrees).

Now reading about it might be difficult, but I fully understood it when I saw this video below. The goal of the video is something different, but most of it is spent on explaining how to look at numbers in this new perspective. This video is extremely good and I have been sharing it with people I know. I have not understood this video fully (towards the end), but watch it till at least the 5 mins 10 seconds mark, it is a great explainer.

You might need to watch it a few times to grasp it fully, but please do so. I guarantee you that you will see a whole new way of looking at numbers, once you grasp the idea.

That is really all I have got for now. But it also makes me wonder, is there any sense in which we can extend numbers to use the 3D space or even more dimensions? What would such number systems be?

Categories: Math Tags: ,

Death sentences and the purpose of law

September 14, 2013 Leave a comment

Warning: Post contains graphic descriptions of a violent rape.

You must have seen the news that the 4 men convicted for the rape and murder of a 23 year old student last december have been sentenced to death by a fast track court. It is natural for us to feel outraged at the incident, as it was a beastly crime. If you are in doubt, let me refresh your memory by quoting from the text of the judgment.

The facts show that entire intestine of the prosecutrix was perforated, splayed and cut open due to repeated insertions of rods and hands. The convicts, in the most barbaric manner, pulled out her internal organs with their bare hands as well as by the rods and caused her irreparable injuries, thus exhibiting extreme mental perversion not worthy of human condonation. As convict in pursuance of their conspiracy lured the victims into the bus Ex. P-1, brutally gang raped the prosecutrix, inflicted inhuman torture and threw the defenceless victims out of the moving bus in naked condition, profusely bleeding in a cold winter night ; their unprovoked crime demonstrated exceptional depravity of mind of the convicts.

…Further, the convicts did not stop after pulling out her internal organs after the crime of gang rape / unnatural sex but then had dragged the victims to the rear door of the bus Ex.P-1 to be thrown out and when the rear door was found jammed the victims were dragged by their hairs to the front door and thrown out of the moving bus. Her intestines were so severally damaged and the suffering inflicted on the prosecutrix was unparalleled. The brutality caused to her internal organs is extreme as is evident from the medical evidence on record and hence the act of convicts call for extreme penalty.

It is an act of unimaginable horror. No doubt about that. The death penalty was the correct sentence to be awarded considering the law of the land. I cant imagine what the mind of the perpetrators would have been like when they were doing the act. There are simply no words for such acts.

In spite of all that, something about the sentence left me uncomfortable.

Look at, for example, this part of the judgment which is a quote from an earlier judgment of the supreme court.

When the community feels that for the sake of self preservation the killer has to be killed, the community may well withdraw the protection by sanctioning the death penalty. But the community will not do so in every case. It may do so ( in rarest of rare cases) when its collective conscience is so shocked that it will expect the holders of the judicial power centre to inflict death penalty irrespective of their personal opinion as regards desirability or otherwise of retaining death penalty

It starts by saying that if the society feels the necessity of death penalty for the sake of self preservation, then the principle of sanctity of human life can be withdrawn, but follows it up saying, it may do so when the collective conscience is so shocked that it will expect the death penalty from the judicial arm of the government.

Similarly, look at this one.

The protection of society and deterring the criminals is the avowed object of law and that is required to be achieved by imposing an appropriate sentence. The sentencing court are expected to consider all relevant facts into consideration bearing on the questions of sentence and proceed to impose a sentence commensurate with the gravity of the sentence. Court must hear the loud cry for justice by the society in cases of the heinous crime of rape on innocent helpless girls of tender years, and respond by imposition of proper sentence. Public abhorrence of the crime needs reflection through imposition of appropriate sentence by the court. To show mercy in the case of such a heinous crime would be a travesty of justice and the plea of leniency would be wholly misplaced.

This too begins loftily saying the goal of law is to protect the society and deter criminals. But goes on to say that the court must hear the loud cry for justice from the society.

This is what makes me uncomfortable. However heinous the crime is, it cannot be undone. So we dont have any option but to look ahead. Thus when imposing a sentence, our only goal needs to be to prevent these four from repeating what they did, deterring other criminals and preventing similar crimes. There should not be any idea of a tit for tat or revenge when imposing sentences. But look around you honestly. Look at photos of protestors. Look at the media. Look at the judgment itself. Do you really think the motivation for the death penalty was to protect society or to prevent similar crimes happening in the future? I don’t think so. It was a collective act of revenge. That is all it is. When someone commits a crime on us, we instinctively feel an urge to get back at them. It is natural, but does not mean it is correct. Let me explain.

Am I saying no death penalty at all? No. My only point is that the basis for any punishment we impose, should be rational. It should not be driven by the fact that the society’s “collective conscience is shocked” or by the tendency of the court to take it upon themselves to “hear the loud cry for justice by the society”.

To drive home what I am arguing, let me give a hypothetical example. Suppose one week from now, a new fact emerges that, all these four people were, without their knowledge, given a drug by an evil neuro-scientist as part of an experiment (to be clear, I hate that stereotype of the evil scientist doing an evil experiment), that made them do such things. The way the judgment is written today, that new  fact should not affect the imposition of the penalty. After all it still was an unimaginably heinous crime, our conscience was indeed shocked, the society did cry out of justice and so all the necessary criteria for death penalty are met. But in the light of the new fact, the death penalty to those four people would definitely not be justice.

Now imagine the death penalty was given with the goal that such a punishment would deter future criminals*  or to prevent such crimes happening in future. Now if this fact of evil scientist comes to light, we can logically change the judgment, because our goal of preventing similar crimes in future can be easily achieved by sending the scientist to prison (or by hanging him).

To reiterate, I am not arguing that the death penalty should not be imposed because some future fact might come up which will clear up the criminals’ names (it has happened before+). My argument is that even in cases where the accused himself admits of the crime thus leaving no scope for any future change of facts, punishment should not be given just because it needs to be “commensurate with the gravity” of the crime, because it is nothing but a wordy way of saying I want an eye for an eye. It should be a logically thought out, well argued, evidence based judgment with our focus on the future.

Now, some of you might argue that I can make all these points just because it was not my own mother, or wife or sister who was the victim. I admit that if I was the guy with the girl on the bus that december night, it is highly probable that I would argue differently. But if I were personally involved in it, I should be the last person to be trusted to provide fair justice. So my opinion should matter less in such cases. In fact, that I am not personally involved in the case should make me more capable of rational discussion. So dont come back at me saying, I dont understand the nature of the crime.

Another aspect to be considered, that at first glance might look very silly, is very related to the points I am making here is that we do not have free will. So moral responsibilty cannot really be pinned on any person. Thus any legal system that depends on the criminal “deserving” the punishment, is a system based on the false notion of the person being responsible for what he does. I have written about that before, and hence will avoid going into detail here. When you understand that my brain functions, at the fundamental level as a physical machine, you realise that neither can I be blamed for the bad things I do, nor can I claim credit for the good things. That idea becomes extremely important when building a legal framework for the society.

Thus, when I see protestors baying for blood, the media pushing for death penalty and the judges writing judgments hearing the people on the streets, I feel very uneasy. Democracy is not always the ideal way to take decisions. If we always trusted the majority, the minorities will always get suppressed. So, trust not numbers. Always look for well reasoned arguments. In this case though, the legal system should be revamped. With cases like these, I only get the feeling that we are still letting ourselves be driven by the instincts of our humanity’s uncivilised infanthood. When will we, as a society, grow up?

* There is an important argument that there appears to be no evidence that death penalty does indeed deter criminals, but let us keep it aside for now. That is a valid argument, but that is not the point I am making in this post. So let us, for argument’s sake, assume that death penalty does indeed deter criminals.

+ This too is a very important argument, but again, not the one I am making now.

Categories: Ethics Tags: , , ,

An old article I wrote about language

September 7, 2013 Leave a comment

This blog has been in a coma for sometime, and I dont have any hope of writing anything new, in the near future. As I was listening to this podcast episode where Noam Chomsky was being interviewed about his work in linguistics, I was reminded about an article I had written a couple of years back for Science Reporter, a government run science magazine. It does not have a website where you can read the article online, but I have a scanned copy with me.

It is my longest article ever (and therefore the one with the maximum goof ups too, I guess), but given the drought on this blog, I thought I could inflict this upon you, just so you dont start raising your hopes of seeing the death of this blog. Not so soon, people, not so soon!

Here you go.

Categories: Biology, Writing Tags: ,

Does reduction in weight really help improve memory?

June 21, 2013 Leave a comment

I read an article in The Hindu today that reported a study that was presented at the The Endocrine Society’s annual meeting at San Francisco. The study claimed that in post menopausal women, reduction in weight led to improvement in memory. The study had very specific criteria of people who are eligible: post-menopausal women whose BMI (Body Mass Index) is greater than 27.

I tried to look for the source of this article. The results seem to have been presented at a meeting, and I could not claim my hands on the study (not for lack of access, I don’t see it published anywhere online). The closest I could get was to find the meeting abstract. I also found this article on Huffington Post that gave more details about the study.

I have multiple problems with the study (based on what I could gather from the articles and the abstract linked earlier).

What prompted me to find the source of the article was the sample size. Of late, I have learnt how to read science articles a little bit better. One of the key things to notice in such studies is the sample size. This study was done on 20 women. Yes, just 20. The Huffington Post article referred to an earlier study that claimed that obesity in post menopausal women leads to memory impairment. That study had more than 8000 subjects.

The second problem was the ease with which it has been suggested that it was the reduction in weight that led to better performance. The memory test given was to remember picture-name pairs and to recollect them later. The study says that after reduction in weight, FMRI scans revealed higher activity while storing the memory, and lower activity while retrieving it, suggesting that once weight was reduced, it was storing well (using more resources) and recollecting easily (using very little effort). There is nothing to indicate that it was weight loss that caused this improvement. What if the women were feeling more confident and happy after losing weight and so performed better? What if they knew that this was a post-evaluation and so had to do better as they felt obliged to show improvement? What if the post-weight loss memory assessment showed better performance merely because they had already done the same activity before losing weight and so were better at it a second time?

I am also surprised that all the 20 women they chose did indeed stick to their diets and lost weight. The probability of that happening, appears very less to me. If it were so easy to induce people to stick to a diet (this study seems to have done it with 100% success), there would be a lot less number of fat people. If this 20 was only a subset of the people they chose (the subset that did indeed lose weight), then why was that not mentioned in the abstract? Also, if they chose the people who lost weight, did they exclude anyone after post-weight loss assessment?

All of this makes me wonder whether the study established anything at all. I would say no. Of course I have not seen the study itself, but a sample of 20 is too low to establish or even suggest any sort of causality, much less suggest something about our famously complicated brains.

Categories: Uncategorized Tags:

I demand that my workplace offer me a room to worship Sachin Tendulkar

April 26, 2013 Leave a comment

I read an article some months back and wrote this  then. For some reason (I dont remember now), I did not post it. Hence doing it now.

I was reading this article “Muslims from abroad are thriving in catholic colleges” from the New York Times which, for some reason, stayed in my mind for long. The article is about how Christian colleges in the USA are turning out to be more attractive to Muslim students. And the extent to which some colleges go to accommodate religions are surprising. But it actually should not be news. After all, it is a Christian college and so they already believe that religion is inseparable from any aspect of life and so they can easily empathise with similar importance that others give to their religion. But somehow there were many aspects of the article that made me extremely uncomfortable.

“I like the fact that there’s faith, even if it’s not my faith, and I feel my faith is respected,” said Maha Haroon, a pre-med undergraduate at Creighton University in Omaha, who was born in Pakistan and grew up in the United States. “I don’t have to leave my faith at home when I come to school.”

Has carrying your faith to school become a good thing now? And this:

Muslim students here cite the accommodations Dayton has made, like setting aside spaces for them to pray — a small room for daily use, and two larger ones for Fridays — and installing an ablution room for the traditional preprayer washing of hands and feet.

The university also helps students arrange celebrations of major religious holidays, and it contracts with a halal meat supplier for special events.

Manal Alsharekh, a Saudi Arabian graduate student in engineering at Dayton, said, “I was in another university before that did not respect us so much.”

Wait, what? Is giving in to your every little fantasy, what you call respect? Why do you stop there then? Why don’t you ask for more respect saying they need to build a mosque in the college playground? Their sense of entitlement amazes me. Do they also want every student including non-muslims, the staff etc., also fast with then during the month of Ramzan? You might think I am exaggerating, but imagine a college that actually does that. Then, I am sure there will be somebody who will move from Dayton to that college and say “Dayton did not respect us so much”.

Being an Indian, I have been brought up with the idea that Secularism is accepting and embracing all religions. Thus if having a symbol of an om or a cross or a crescent at an event is considered communal, but having all three makes it secular. Looking back, should not that have made the event three times more communal? Only recently have I learnt that Secularism, in the west, means keeping religion out of public life. And that I think is a more sensible definition.

The problem with the Indian definition of secularism is that it will lead to public institutions yielding to every silly fantasy that could be held by any citizen on the planet. If I seriously believe Sachin Tendulkar is god and get a sizeable following to believe the same, then the Indian definition of secularism does not know how to handle this. Should they start having a photo of Sachin Tendulkar too whenever they have an om, a cross and a crescent. How far can this go? Do they declare his birthday as Tendulkar Jayanthi. Naturally, the best way out of this is to say, if you like Tendulkar, keep it at home. If you believe in Allah, pray to him at home. Nobody is stopping you, or will stop you, or will be allowed to stop you. But you cannot others to share your passion, or to make special concessions to suit your personal interest.

I realise that private colleges can do what they want and nobody from outside can dictate what they do (I have no clue about the US education system and so cant say if Dayton is funded by tax payers’ money). But this kind of bending over backwards, only adds to the idea that religion is some special fantasy (very different from someone devoted to Harry Potter) deserving something extra wherever they go. That should not be done.