Indian kids are getting dumber at maths!

OK, that headline is a bit of a clickbait! They probably aren’t getting dumber, if anything it could be the opposite if the Flynn effect is really true. However, I specifically had the declining performance of Indian kids at the world’s foremost mathematics competition in mind, better known as the International Mathematics Olympiad or IMO, when I wrote that headline.

A bit of personal also-ran history is involved here as I did compete to join the Indian team at the turn of the millennium, but the competition was so fierce that I could not manage to get into the national-level top six that represent each country at the IMO. And that was just as well, as all the guys were clearly brighter and I did not deserve to be in that peer group. Nonetheless that teenage experience of competitive problem-solving (and failing to make the cut) informs my desire to keep a close watch on the Indian team’s performance at the IMO. I also occasionally try to solve IMO problems on boring London tube commutes, i.e. when I manage to get a damned seat, and share them with colleagues at work. Those interested can try them here.

The 2017 IMO recently concluded in late July, and the Indian team showed its worst performance this year since 1990 – the year it first started competing in this annual mathematical jousting event. Since this is brownpundits I tried to put the declining performance of Indians into context by comparing it, over the years, with our brown South Asian neighbours, Bangladesh and Pakistan. Throwing in Iran and United Kingdom as controls to add a bit of perspective. All the country-wise data can be accessed here.

Annual IMO Rank per country

The graphs are telling! India was up there with Iran and UK as its peers all through the 90s decade to the early 2000s. Indians were slightly worse-off than Iran, but by the turn of the millennium we were doing better. My own school-leaving cohort (and a couple of years around that) soundly beat both the Iranians and Brits. Yet 2005 marks a regime shift for the worse in average Indian performance at IMO and the data seem statistically significant.

I am at loss to explain this clearly worsening trend of performance by India’s brightest millennials. Did Indian parents really start begetting a dumber brood from the 90s onwards? I hope not! Good feeder schools and rigorous mathematical training play a big part in preparing high-school kids for such competitions and it is possible that some silly policy change (that I am unaware of) by the Indian government may have been a causal factor.

But there’s some hope in the same data for our Eastern cousins. Bangladeshi kids (and their mathematics training programme) seems to have shown phenomenal improvement(!) over the same period and now easily better India. India’s coincident decline does not help matters either. Bangladesh started competing at the IMO in the same year as Pakistan with similar laggardly results, but the subsequent improving trend in performance is clear as day. As for Pakistan, well, let’s just say that their national priorities leave a lot to be desired…

Why Democracy?

The idea to write this blog post on Democracy arose out of the need to describe what it is in context of Brexit. For more on the Brexit referendum itself see this. In this post I am trying to distill my own understanding of Democracy and have included the results of a numerical experiment I ran to quantify some ideas around the concept.

Democracy is essentially an algorithm to correct political error. In that respect Democracy belongs to a special class of algorithms, with Darwinian evolution, scientific peer review or machine learning being other notable members of the same class. The kinship between these disparate and very fundamental processes is not coincidental. It is explained by Popperian epistemology, which makes the existence and mitigation of error central to the idea of any knowledge generation.

Any discussion of the process of knowledge creation may seem like a digression at this point. However, please persevere for the next three paragraphs as setting this context is important for the central thesis on Democracy. According to Popper, knowledge itself can be understood as explanations, i.e. guesses or conjectures with two major criteria for goodness: falsifiability and parsimony. Any knowledge creator (sentient or otherwise) must therefore create knowledge in exactly this manner: creatively produce guesses or conjectures (including even, what look like, wild ones) and criticise them to remove those that are erroneous. Two immediate corollaries of this theory arise: a) existence of error is a permanent feature of any form of knowledge. Claims of knowledge that are perfect (e.g. a manual revealed by so-called prophets) are therefore, for want of a better word, baloney. And b) boundless knowledge-generation must require the ability or enabling culture to air seemingly wild guesses and criticise even ostensibly unimpeachable maxims. Continue reading “Why Democracy?”

India = Nigeria + Italy in terms of fertility

The map above shows the most recent district level fertility rates in India. It is immediately clear why comparing India to Pakistan and Bangladesh (let alone Nepal, Sri Lanka, or Bhutan) is a major error.

In some of the northern regions of the Hindi-speaking “cow belt” as well as the lightly populated Northeast the total fertility rate is similar to what you find in Nigeria, between 5 and 6 children per woman. For comparison the TFR for Saudi Arabia is 2.75. For Bangladesh it is 2.20 and for Pakistan it is 3.6. In contrast, much of the South, Punjab, and West Bengal have below replacement fertility.

Here is 2017 data by state:

State/UT Fertility rate 2017
Sikkim 1.2
Andaman & Nicobar 1.5
Chandigarh 1.6
Kerala 1.6
Punjab 1.6
Puduchery 1.7
Goa 1.7
Daman & Diu 1.7
Tripura 1.7
Delhi 1.7
Tamil Nadu 1.7
Karnataka 1.8
Andhra Pradesh 1.8
Lakshadweep 1.8
West Bengal 1.8
Telangana 1.8
Maharashtra 1.9
Himachal Pradesh 1.9
Gujarat 2
Jammu and Kashmir 2
Arunachal Pradesh 2.1
Haryana 2.1
Uttarakhand 2.1
Odisha 2.1
Chhattisgarh 2.2
Assam 2.2
 India 2.2
Mizoram 2.3
Dadra Nagar Haveli 2.3
Madhya Pradesh 2.3
Rajasthan 2.4
Manipur 2.6
Jharkhand 2.6
Uttar Pradesh 2.7
Nagaland 2.7
Meghalaya 3
Bihar 3.4

What kind of a language is Kashmiri?

I want to begin a series of posts on Brown Pundits on culture, history, language and politics of the Kashmir valley – a bit of an insider’s account. When writing about Kashmir it is unfortunately very easy to get drawn into, rather inextricable, India-Pakistan political tangles that the Valley has suffered from. I will try to describe the modern Kashmiri politics too (against the larger Indo-Pak backdrop) and its evolution since the early medieval period in one of my posts. However, for the rest I’ll try my best to steer clear of such political discussions when discussing the local culture and people.

Please note that when I speak of Kashmir, I speak only of the Valley of Kashmir – for that is what Kashmir really is. It is not Jammu, it is not “Azad” Jammu & Kashmir, it is not Gilgit-Baltistan and it is not Ladakh.

So, with that little introduction, let me begin by discussing a topic that is after my heart – my mother tongue, Kashmiri, or as we call it in Kashmiri: Koshur

Kashmiri language is primarily spoken in the Valley of Kashmir and by Kashmiri ethnic diaspora communities in other parts of India or abroad. It is one of official languages recognized by the Indian state and typically written in three scripts: Sharada (the original and oldest-known script used for the language), Devanagari (used today mainly by Kashmiri Pandits with some vowel modifications) and Nastaliq (used by both Pandits & Muslims). Due to its Constitutional status, one can find Kashmiri written (in Nastaliq) on any Indian banknote along with a dozen other languages. The use of Nastaliq for Kashmiri differs markedly from its use for, say, Urdu or Persian, in that the modified-Nastaliq used for Kashmiri always marks vowels and diphthongs.

Kashmiri is not similar to Hindi/Urdu (or to Punjabi, Pahari or other north Indian languages) at all. Needless to add that it isn’t mutually intelligible with any of them. Kashmiri is a member of the wider Indo-Aryan family of languages – but the kinship almost ends there. In terms of its development from early Vedic dialects, Kashmiri (and Dardic branch in general) split off very early compared to the Sauraseni Prakrit – which gave rise to modern-day Punjabi/Pahari/Hindi/Urdu/Gujarati etc.

Kashmiri preserves many archaic features of Sanskrit speech – lost in a majority of languages of the plains. Kashmiri is semi-inflected, more like Sanskrit, and unlike Hindi.


Skt. “drakshaH khadam” > K. “dachh khyeim”

Compare with “Mainey angoor khaye” in Hindi. Note that Kashmiri, like Sanskrit, inflects the verb “khyon” (to eat) and there is no need of the pronoun equivalent of Hindi “mainey”.

Skt. “tatra ma gatchha, tatra aast siMhaH” > K. “tot ma gatshh, tatyi aos suh”

Compare with Hindi “wahan nahin jao, wahan sher tha”. Again Kashmiri uses the verb “gatshh” (to go) in imperative tense just like in Sanskrit.

Kashmiri has a very different and much more extensive vowel system and uses the schwa and diphthongs (i.e. combinations of vowels) a lot compared to Hindi/Punjabi, which makes it sound very different (some say like Russian/Slavic languages).

E.g. no word in this ordinary Kashmiri sentence has a simple vowel – they are all long vowels or diphthongs:

“tsooraa, daeris dyoo shyenah-shyenah tsyal, makaana-maelyikh ha bozyee”

“O thief, to-window give slowly push, (or else) house-owner may-hear”

Note how the non-native Arabic loanword “malik” (lord/owner) has been changed in Kashmiri – by changing /a/ to the diphthong /ae/ and /i/ to /yi/.

Kashmiri also changes all word-final /k/, /t/ and /p/ to aspirates /kh/, /th/ and /ph/. Hence the final -k in “malik” changes to /kh/.

Skt. “taapa” (heat) > K. “taaph”,
Skt. “ropya” (silver) > K. “roph”
Skt. “taraka” (star) > K. “taarukh”
Skt. “prati” (every) > K. “prath”
Skt. “shata” (hundred) > K. “hath”
Skt. “pata” (fallen, behind) > K. “path” (behind, trailing, remote)

Also, notice the addition of the schwa, i.e, the (semi-vowel) -a ending, as in “makaan” > “makaana”. This is another feature that Kashmiri preserves from Sanskrit. Hindi, on the other hand, tends to delete the schwa endings in Sanskrit, e.g. Skt. “yoga” > Hindi “yog”.

And K. “shyenah-shyenah” is also from Skt. “shanaiHi-shanaiHi”, which translates to “slowly-slowly”.

Another overwhelming characteristic of Kashmiri is its frequent use of the voiced sibilant /z/ in native words (i.e. words it has not borrowed from any other language). Hindi-Urdu also uses /z/, but only in non-native (borrowed) words.

So, the verb “bozun” (to hear or see, to perceive) used in the above sentence is just the Kashmiri form of Skt. ‘bud/bod’ – 1st conj. parasmaipada (transitive) verb. cf. Skt. ‘bodam’ (I perceived) > K. ‘boozum’
Similarly, we have many other examples of Skt. /d/ or /j/ (and sometimes /s/) changing to /z/ in Kashmiri:

‘adya’ (today, now) > ‘az’ (today)
‘dvi’ (two) > ‘za’
‘raja’ (king) > ‘raza’
‘bhaja’ (cook) > ‘vaza’
‘vajra-mala’ (lightning) > ‘vuzmal’
‘puja’ (worship) > ‘pooza’
‘jivha’ (tongue) > ‘zyav’
‘jnana’ (knowledge) > ‘zaan’
‘jana’ (to generate, give birth) > ‘zyon’
‘jeeva’ (life) > ‘zoo’, ‘zuv’ [Cf. Greek ‘zoo’ which also means life and is a cognate]
‘dhyana’ (consciousness) > ‘zoan’ [Interestingly that the same Skt. word gives rise to Japanese ‘zen’]
‘jala’ (water) > ‘zal’ (urine)
‘maMsa’ (meat) > ‘maaz’

Finally, Kashmiri has no voiced aspirates /bh/, /dh/ or /gh/ – all of which change to /b/, /d/, /g/.

E.g. Skt. “bhavami” (I am) > K. “ba” (I)
Skt. “bhrhaspativara” (Thursday) > K. ‘brasvar’
Skt. “bhruma” (brow, eyebrow) > K. ‘buma’
Skt. “dhuma” (smoke) > K. ‘duh’ [Note Hindi “dhuaN” preserves /dh/]
Skt. “ghana” (viscous, thick) > K. ‘gon’ [Again Hindi “ghanaa” preserves /gh/]
Skt. “gharma” (warmth, sunshine) > K. ‘garm’ [Note Hindi “garmi” is via Farsi, not Skt.]

While there are many other aspects and complexities of the Kashmiri language which I have not mentioned here, the above details are enough to give most people a flavour of the language: how it sounds and why it sounds so different from Hindi or Urdu. I would urge people to visit the following extensive resource on the Kashmiri language for more details:
An Introduction to Spoken Kashmir

There are some differences in the usage of Kashmiri depending on whether the person speaking it is a Kashmiri Pandit or Muslim. Nonetheless, this division is not nearly as material as say that between (Sanskritized) Hindi and (Perso-Arabized) Urdu. The dialectical categorization of Kashmiri is more based on region (e.g. Anantnag vs. Srinagar) or economic/social status (as spoken in cities vs. as spoken in villages) rather than religion.

Of course, there are specific words in the language that specify religious concepts – and they are bound to be different for Pandits and Muslims. But for non-religious concepts the words used by Pandits or Muslims are essentially the same.

As an example of what spoken Kashmiri sounds like, I will end with a fantastic rendition of classic Kashmiri love poetry, sung by the inimitable Shameem Dev Azad – considered to be one of the best singers Kashmir has ever produced. She is married to ex-CM of J&K State, ex-Cabinet Minister and senior leader in the Indian Congress party, Ghulam Nabi Azad (whence Azad), though she was unmarried at the time this programme was produced.

This particular clip is from an episode of a series called Anhaar that was produced by Doordarshan Srinagar and ran from 1978-1980. The conductor (also the producer of this series) is Padma Shri Pandit Bhajan Sopori, a santoor maestro of the sufiyana mousiqi gharana of Sopore, Kashmir.

The song itself is a poem composed by the 19th century Kashmiri poet Rasul Mir. It expresses a sentiment very common in Kashmiri love poetry, about the woman pining for her beloved (K. madano < Skt. madana lit. beloved, god of love). In that respect, Kashmiri literature clearly continues the Sanskrit tradition of love-poetry (ghatakarparaH*, vikrama-urvashiyam etc) where it is always the woman singing about lost love, as opposed to, say, Persian poetry (of Khayyam or Sa’adi) which is typically from the male’s POV.


[*] A correction to meghadutam, which, as Pramathanath Sastry points out below, is from the male’s POV.