How to distinguish fake coin tosses...

Dilip posted an interesting problem the other day: if you were a professor teaching probability theory, and asked your students to toss a coin 100 times and write down the sequence of heads and tails that they obtained, and some of them cheated and simply made up a sequence of heads and tails, how could you tell?

It is interesting because, generically, very few sequences are truly random; and the human mind is certainly incapable of randomness. But what signs of non-randomness could you look for? The answer that Dilip, apparently, had in mind is that true random sequences will usually contain long "runs" of heads or tails (say, 6 or more heads, or 6 or more tails, in succession in 100 coin tosses). However, individuals generating random sequences will perceive such short "runs" as non-random and correct for them. But this is not a very reliable answer by itself: the probability of a run of 6 or more (heads or tails) in 100 tosses is about 80%, so a truly random run will fail this test about a fifth of a time, while a smart student will probably throw in such runs. I argued that if one combined this with various other tests, one should be able to tell quite reliably. But at the moment I am unsure whether 100 tosses are enough for this. Certainly nobody could say for sure whether a sequence of 5 tosses was generated by a coin or a human. Meanwhile, I strongly doubt that any human could generate a sequence of 1000 random symbols (coin-tosses, numbers, whatever) that would fool the statistical tests. But can one reliably tell which of the following two is "random" and which isn't?

Sequence 1:

tthhhhhtthhhhtthhthhhtthhhhttththhhtthhhhhhtthhhhh
htthhthhhthhhhthhththtttththtthhtthhhhhttthhththtt

Sequence 2:

hthtthhtthtthhhthtthtttththhthhththhhhthhttttththh
hthhhthtththhhthttththhthhhthththhhhthhthttththhth

Neither of these was generated by tossing a coin. One was made by me, by pressing "h" or "t" "randomly" on a keyboard (ie, I, a human being aware of the usual "pitfalls", was trying to generate a random sequence, fairly rapidly without thinking much about it). The other was made using the pseudorandom number generator in Python, which is based on the Mersenne twister. I would guess that the Mersenne twister is more random than I am: what I would be interested in knowing, from any experts reading this, is whether one of the above sequences can be demonstrated, statistically, to be so non-random that the chances are very high it was generated by me and not by the program. I am, moreover, interested in the method and not the answer (which you have a 50% chance of getting right randomly). If you confidently identify the Mersenne twister-generated sequence, it is safe to say that the problem is with your test and not with the Mersenne twister.

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The "bonus question" that came up in Dilip's blog is, what is the probability of observing a run of 6 or more heads or tails (let's call them 6-runs) in 100 coin tosses?

Kovendhan gave an approximate answer which seemed to work well in practice, but it turns out that he made two errors and a corrected calculation does poorly. The probability of a particular choice of 6 tosses (let's call it a 6-mer) being all heads or all tails is (1/2)⁵ (it is (1/2)⁶ for all heads, and the same for all tails). The probability then that it is not all-heads or all-tails is 1-(1/2)⁵. There are 95 ways to choose 6 successive tosses in 100. The probability of none of these 95 is all-heads or all-tails is ( 1-(1/2)⁵)⁹⁵ = about 0.049 approximately. The probability of at least one stretch of 6 identical tosses (all heads or all tails) existing would then seem to be 0.951 -- pretty near certain. The approximation consists of neglecting the fact that adjacent 6-mers here are not independent: eg, if your chain of tosses is HHTHTT, not only does this fail to give a 6-run, but it will also fail to do so on any of the next 3 tosses at least.

Meanwhile, Kovendhan used (1/2)⁶ instead of (1/2)⁵ for the individual 6-run, and 94 for the number of 6-mers, which yields 0.772, but he reported 0.781 -- I'm not sure how he got that. My numerical experiments suggested the true number is a little above 0.8, which is close to Kovendhan's fortuitously incorrect calculation of his approximate method, but quite far from what his approximation should really give.

The moral is, be aware of approximations and, if possible, have an estimate of their effect. Kovendhan's approximation is in fact very similar to Linus Pauling's when he calculated the zero-temperature entropy of ice. In the crystal structure of ice, each oxygen atom has four neighbouring oxygen atom, in a locally tetrahedral arrangement. Along each of these O-O bonds is a hydrogen atom, but not centrally located: two H atoms must be closer to the central O atom, and two must be closer to the neighbouring O atoms. Globally, there are many ways to satisfy this; to count the ways, Pauling essentially assumed that the configurations of the local "tetrahedra" could be counted independently. This is like Kovendhan's assumption about 6-mers; unfortunately, while two tetrahedra in ice share at most one corner, two 6-mers in the toss sequence can share up to 5 tosses, which makes the 6-mers much less independent than the tetrahedra in ice.

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I attempted an answer which I give below. A commenter observed that a formula exists for the probability of a run of 6 heads, and the same formula gives the probability of a run of 6 tails. However, the probability of six heads or tails is trickier.

My approach (which will be recognisable by physicists, computer scientists and others) was this: supposing we can calculate the probability P(N) that there are no 6-runs in N tosses, how do we calculate P(N+5), the probability that there are no 6-runs in N+5 tosses? If we can do this, we can start from P(5) = 1 (there are no 6-runs in 5 tosses, obviously) and build it up from there.

Naively, a 6-run can be built up at any of the five tosses between N and N+5: for example, if the previous five tosses up until N were all heads, then tossing heads again will give a 6-run. So we must consider all possibilities for both the five tosses from N-4 to N, and the five tosses for N+1 to N+5: ten tosses in total. There are 2¹⁰ = 1024 possibilities for these 10 tosses, so it looks like a counting problem. The number of possibilities of "successful" runs in these 10 tosses can be enumerated as follows (where "N" stands for "any", and one can replace H with T in all these examples):
HHHHH HNNNN (32 possibilities: 2⁴ for the last 4 tosses, times 2 for replacing H with T)
THHHH HHNNN (16 possibilities)
NTHHH HHHNN (16 possibilities)
NNTHH HHHHN (16 possibilities)
NNNTH HHHHH (16 possibilities)
for a total of 96 possibilities. There are then 1024-96 = 928 cases where there is no run of 6 heads or tails. So the "naive" answer is P(N+5) = P(N)*928/1024. If we want P(100), we can use this to go all the way back to P(5) = 1:
P(100) = P(95)(928/1024) = P(90) (98/1024)² ...
to get
P(100) = P(5) (928/1024)¹⁹ = 0.154 roughly
so the probability of at least one 6-run in 100 tosses is about 0.846.

Unfortunately, this is still not correct, because the 1024 possibilities -- and the 96 possibilities with runs -- are not all equally probable: they are conditional on the premise that there is no 6-run up until the N-5th toss. So, for example, the case "HHHHH TNNNN" should be weighted by the fact that it would be disallowed for half the possible sequences prior to this (the ones that ended with H); the case THHHH HNNNN would disallow far fewer sequences (the ones that end in TTTTT, which is only 1 in 32 sequences).

Therefore, I considered as prior possibilities, the five tosses numbered N-14 to N-10 (that is, the five tosses preceding the current ten-mer). There are the following ten possibilities that should be distinguished:
NNNHT, NNNTH, NNHTT, NNTHH, NHTTT, NTHHH, HTTTT, THHHH, TTTTT, HHHHH
and each of these has a "prior probability" (1/4 for NNNHT, 1/32 for HTTTT, etc), and each disallows a fraction of the 1024 10-mers we are considering, as well as a fraction of the 96 10-mers that contain 6-runs. If you do the calculation separately for each of these 10 prior possibilities, and then weight the average by their prior probabilities, you end up with
P(no 6-run in 100 tosses) = (1481219/1614480)¹⁹ = 0.195 roughly,
and P(at least 1 6-run) = 0.805 roughly.

This, as it turns out, is in excellent agreement with what I had previously obtained numerically.

Final question for anyone who has read this far: is this the exact answer? (I posted on Dilip's blog that I think it is, but don't go by that.) It is, however, "good enough" in my opinion, by two measures: the remaining error is small; and the issues have (I think) been adequately illustrated that the answer can be (laboriously) improved, if need be.

I'd be fascinated, however, if there is an exact answer on the lines of the "run of heads" answer linked above.

Hand over the master keys, or else...

I find it comical that India's security agencies (now joined by several other countries) are demanding the "encryption keys" to BlackBerry devices. Can our government's security experts be ignorant of basic cryptography?

BlackBerry's encryption methods are not new, not novel, not unique, not even unusual. The technology to encrypt e-mail has existed since the early 1990s, and is called OpenPGP (after PGP or Pretty Good Privacy, the first program to implement it). It is usable on pretty much all e-mail systems and is built into Blackberries. There are no "master keys" here: each user has a public key and a private key, and messages can be encrypted with the public key but decrypted only with the private key. (Conversely, messages can be digitally "signed" with the private key and the signature can be verified with the public key). If A wants to send an encrypted message to B, A encrypts it with B's public key -- which A should have a copy of. The public key is meant to be public, and it is common for people to display it on their personal webpages and elsewhere. But B's private key is needed to decrypt it, and only B has (or should have) that key. Wikipedia has a good description of public key cryptography.

As far as I can tell, BlackBerry's "enterprise security" is a somewhat different system to secure communication between BlackBerry's servers and the customer's device, but it too is key-based cryptography (3DES or AES) that requires a private key for each device. RIM, the makers of BlackBerry, say they do not possess copies of customers' private keys, and indeed it would be alarming if they did. They are not being pioneers here (except, perhaps, in bringing it to wide use among their customers): this is standard practice in cryptography.

The government can ban BlackBerries, but it will have to ban e-mail: all email can be encrypted, using a method that dates back to 1991. And in fact it's easier than that: webmail providers such as Google Mail allow the entire session to be encrypted, and it is trivial to do this by clicking a few checkboxes (even my GMail app on my non-BlackBerry phone does this) -- so no agency can snoop without accessing Google's own servers. Perhaps our security agencies will next demand the root password for Google's data servers.

Alternatively, our government can try addressing our real security problems, and their underlying causes.

Yet more thoughts on Apple

It's been several months since we got our Mac Mini [1, 2]. Previously my wife used a Linux laptop. It worked well, except when it didn't, and I had to help out.

The Mac is just the same, except that when it works well, it works beautifully. Steve Jobs values aesthetics above everything else. But when it doesn't work...

So a few days ago she calls me to say the computer is not booting. I go over to look. Not only is she quite correct, but there's no way of telling what the problem is: all Apple gives you is a white screen with an Apple logo and an endlessly-spinning counter.

I go online with my laptop, and find that there are ways to boot differently by holding down various key combinations on boot. First I try "safe mode". It boots, and all seems well; but when I try the regular boot it fails again. And now "safe mode" doesn't work too.

Then I try "verbose" boot. This gives a scrolling screen of boot messages, of the kind familiar to Unix/Linux users. I see some messages about the filesystem but I don't understand them. The boot gets stuck at a point that I can't make sense of.

Then I try "single user". This time, I get a boot prompt that helpfully tells me to "fsck -fy". I do so, and after some churning, it tells me "filesystem cannot be repaired." I think, huh? I have seen serious filesystem errors on linux and unix, which can be repaired only at the cost of losing data: but I have never seen a filesystem that could not be repaired.

Googling gives me the dubious advice that repeatedly trying fsck should fix the problem, but it does not. I try the disk repair tool that comes from Apple's install DVD, but that too refuses to repair the filesystem.

Finally, "backup and reinstall" is the only way to go. I get a USB hard drive, use my unix skills to mount it and format it with the HFS+ filesystem in single-user mode, and back up all my wife's data (only a couple of unimportant files failed to get copied, luckily). And I reformat and reinstall, as any good Windows sysadmin would do.

Thoughts:

• This has never happened to me on linux, which I've been using on my own computers for 10 years now, and on other computers for even longer. A couple of times the filesystem was sufficiently corrupted that some important system files got lost, but all I had to do was copy them over from another machine or reinstall the affected package.
  
  
• Linux, like OS X, typically uses a "journalled" filesystem (usually ext3 or ext4 on linux, HFS+ on Mac). This means that, after an "unclean" shutdown, the filesystem need not be thoroughly checked. But even when the shutdown is not unclean, Linux systems are usually set up to check the filesystem automatically once every 30 days, or once every 100 mounts (reboots), or thereabouts. This is just a precaution: hardware and software errors can always count problems. As far as I can tell, Mac is not set up to do this. In fact, as far as we know, the machine was not shut off "uncleanly" at any time recently: what probably happened was that undetected filesystem errors grew until they became unrecoverable. Why does Mac OS X not schedule a periodic filesystem check? Is it because Jobs thinks users will get frustrated at that informationless, spinning progress indicator? If so, why not just tell the user that the filesystem is being checked? I'm sure most users won't mind.
  
  
• My wife -- and other non-techie users -- could not have recovered the computer on her own. From all accounts, Apple's customer service is good and very likely they'd have done exactly what I did, but they would have taken a few days rather than a few hours.
  
  
• We should have taken backups, and got away very lightly considering we didn't. After this incident, we bought a new USB hard drive and set up Apple's "Time Machine" on it. This, like all Apple software, is slick and shiny; how well it works remains to be seen, or hopefully will not need to be seen for a while.
  
  
• I strongly suspect that the "filesystem could not be recovered" message was not the truth, but an example of Apple's control-freakishness. The filesystem could perhaps be recovered only by losing a few files (a common-enough situation). Rather than let the user make that choice, Apple wants you to call customer service at the slightest sign of trouble -- by escalating that trouble, and also by hiding all useful information from the user, making it available only via arcane key combinations at boot time.
  

So if anyone out there is thinking of buying Apple: it's slick hardware and software, but in times of trouble, it's probably much harder to fix than Windows. And harder than other Unix-like systems, because it hides so much of its Unixness on the grounds of being user-friendly, or something. Still, for many people, the slickness probably makes up for anything else.

Giant steps

Madhav Chari, jazz pianist, performed with an all-Chennai trio -- consisting of himself, Naveen Kumar (bass) and Jeoraj George (drums) yesterday at the Museum Theatre in Chennai. I have written about Madhav before, when he performed with a French rhythm section [1,2] (who also back him on his recent CD, "Parisian thoroughfares"); and had previewed the concert here. Suffice it to say that it lived up to its prior billing. In an e-mailed announcement Madhav had declared it to be "absolutely the very first international standard jazz group from India since the incpetion of jazz in the country in 1927." It was. He said "We play jazz music: thats what we do." That's what they did. Over half of the programme was of Madhav's own compositions, beginning with "Tales of the south" (a reference, he said, both to New Orleans and to Chennai) and ending with "Blues for Havana". In addition they threw in pieces by Charlie Parker, Thelonious Monk, John Coltrane, Cole Porter, and Sherwin/Maschwitz's "A nightingale sang in Berkeley square" (which Madhav played unaccompanied). They nailed all of them. Jeoraj took several drum solos, while Naveen played extended bass solos on Madhav's "Rejoice" and "Blues for Havana".

Madhav repeatedly said that the band is still feeling its way and is not really a mature outfit, which is why they chose not to play Ellington. But if there were flubs, I did not notice. The Parker was taken at breakneck speed, Porter's "Love for Sale" and Madhav's "Tango sentimental" were rhythmically very complex, and the chord changes in Coltrane's "Giant Steps" are a challenge for the best musicians. The band sailed through all of them.

But almost equally entertaining was Madhav's patter before the songs. He declared Chennai the most advanced city for percussion in Asia (previously he had said that though Chennai audiences may not understand jazz, they understand music better than anyone). He has a dim view of what has long passed for "jazz" in this country (perpetrated by people like Louis Banks), and took several potshots at the elites of Mumbai, Kolkata and Delhi; he challenged anyone from those cities to measure themselves against Naveen and Jeoraj; he conceded that the sizeable audience yesterday (well over 400) may be achievable for jazz in Kolkata, but declared that there is no jazz drummer in that city who can keep time, so Chennai is ahead on that count.

Towards the end, he recounted a lady at a recent party asking him why he blew his own trumpet so much, and asked the audience (to resounding cheers): "Well, if I have the greatest jazz band in the history of India, am I supposed to keep quiet about it?"

Indeed, a few years ago I marvelled that there was a jazz pianist in this "conservative" city who was the equal of the best in New York. Now I find that there is an entire world-class jazz piano trio in this city -- but it now seems exciting rather than surprising. My opinion is that Madhav really does not need to blow his own trumpet. His piano, and his new rhythm section, are eloquent enough.

Should one pray for Hitch? - continued

Christopher Hitchens' own answer to the question is here, along with much other interesting stuff. In Hitch's words,

Well look, I mean, I think that prayer and holy water, and things like that are all fine. They don’t do any good, but they don’t necessarily do any harm. It’s touching to be thought of in that way. It makes up for those who tell me that I’ve got my just desserts... I have to say there’s some extremely nice people, including people known to you [interviewer Hugh Hewitt], have said that I’m in their prayers, and I can only say that I’m touched by the thought.

Yesterday I received my copy of his new memoirs, Hitch-22. The immediately striking thing is that he has chosen to be photographed smoking a cigarette for its cover. This was before the cancer diagnosis, and he does like to be considered a contrarian, but if he were superstitious I wonder whether he would now think of it as tempting fate. Hitchens is also known for his prodiguous consumption of alcohol (I am surprised that the book cover does not portray him holding a glass of Scotch); and smoking and drinking are both significant risk factors for oesophageal cancer, especially in combination in large quantities.

If I were religious, I'd pray for him. As it is, I (like millions of other strangers) offer him my best wishes: I hope that he recovers fully and, meanwhile and afterwards, suppresses his contrarian urges sufficiently to obey his doctors when they ask him to stop poisoning his body in this way.

As for the material between the covers of his book: I have only read as far as the beginning of the third chapter (on his father). The "prologue with premonitions" is not his most memorable piece of writing, but that is only because his standards are so high. It is, however, sprinkled (as one would expect) with interesting anecdotes and thoughts. His portrait, in the next chapter, of his mother Yvonne -- her life, her death, his relationship with her, and his thoughts on her after she died -- is stunning and harrowing: if the book maintains that sort of intensity, it would be a life-altering experience for any reader, I would think. I have a large and growing pile of books that are only partially read, but despite the considerable bulk of this book, I will not be surprised if I finish it sooner than many other recent purchases.

Reading comprehension in Open magazine

Today I read this article in Open magazine, on allegations that Sharad Pawar's daughter, Supriya Sule, is a citizen of Singapore and therefore should have her Indian citizenship revoked. The article unquestioningly quotes Mrunalini Kakade, who lost the election to Sule in 2009.

However, nowhere in the article is there evidence that she is a citizen of Singapore: the phrase used, consistently, is "Permanent Resident" which is a status for non-nationals, short of citizenship (Singapore Government web site, Wikipedia; links produced by a few seconds on google). What Open's rather breathless article says is

According to [Kakade's] petition, Supriya Sule holds 'Singapore citizenship'--Permanent Resident Identification Number S 69726251--in addition to her Indian one. This is against domestic rules that do not permit dual citizenship.

The giveaway, as Mrunalini Kakade tells Open, was Supriya Sule’s disclosure that she owns property in Singapore. Under the law of that country, only a permanent resident of Singapore is allowed to purchase property there...

"Besides, she is also the director of Laguna International Pvt Ltd. In this context, her nationality is shown as a 'Singapore Permanent Resident'... "

So, all the evidence that Kakade has supplied, at least as quoted by Open Magazine, suggests that Sule is a "permanent resident" of Singapore -- not a citizen -- just as thousands of Indian citizens are permanent residents of the United States. There is nothing in India's laws that prohibits citizens from permanent residency of another country.

What should we make of a news magazine that writes a 1300+ word on this issue without addressing this point, or asking Kakade to clarify?

Kashmir

Cross-border terrorism is almost dead. Pakistan is engulfed in its own problems. So why does the Kashmir problem not die too?

Could it be because ordinary people do not like living in a police state? And, when they protest, they do not like being treated as terrorists and fired upon?

The local media is prevented from doing their jobs, and the "national" media (ignorant of Kashmiri, and broadcasting to those who are ignorant of Kashmiri) is free to lie. (Link via Shivam)

We shoot down unarmed protestors. Which incites more protest, and we shoot them down too. (Even unarmed motorcycles are not spared.) We ban the media. We squash civil liberties. And all this is "legalised" by the draconian Armed Forces Special Powers Act (which was originally framed for the north-east, and extended to Kashmir in 1990). Our "law" allows the army to fire on protestors, invade people's homes, search them, take people away without warrant, and be immune from prosecution for all this. That's the law that has ruled the north-east for over 50 years, and Jammu and Kashmir for 20 years.

Now, why do we call ourselves a democracy? Why do we pretend that we have a free press? And why do we expect the people of those states to be grateful for these things?

Should one pray for Hitch? And should he know?

The question is engaging the religious. Christopher Hitchens has been diagnosed with cancer. Given his well-known atheism, should a religious-minded well-wisher pray for him?

On the religious side, Rabbi David Wolpe, who has debated Hitchens frequently on religion, puts it very well (as quoted on Goldblog) in my opinion: "I would say it is appropriate and even mandatory to do what one can for another who is sick; and if you believe that praying helps, to pray. It is in any case an expression of one's deep hopes. So yes, I will pray for him, but I will not insult him by asking or implying that he should be grateful for my prayers."

I wish all religious leaders were so open-minded: too often, religious impositions are accompanied by the implication that one should be grateful for the favour, or the threat that one is condemned if one is not grateful.

A scientist on the Dish goes a bit further in asserting that one should not even inform Hitchens (let alone demand his gratitude) that one is praying for him: to do so would be "malicious". In support, he links this randomized trial on the effect of prayer on patients who had undergone coronary artery bypass graft surgery. The study showed that, on patients who did not know whether or not they were being prayed for, prayer had no effect; but patients who knew with certainty that they were being prayed for did significantly worse (exhibited more complications within 30 days of the procedure).

So there you have it. Pray if you like, but don't tell.

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(Actually, I'd be surprised if those results were replicable with other ailments: the only explanation that I can think of is that patients who know they are being prayed for believe that their prognosis is particularly poor, and therefore are under more stress -- which is particularly relevant here since they are heart patients. In particular, patients were told, via messages in envelopes, either that they "may or may not be prayed for" or that they "will be prayed for". Perhaps the latter statement was truly frightening to a lot of the patients. I'm unconvinced that the study was ethical: at the minimum, they could have chosen a different ailment, on which stress would not have such a direct and obvious effect.)

Jazz in Chennai

Madhav Chari, who is in my opinion easily India's best-ever jazz musician and pretty much the only one of international standards that I have heard, has put together a new trio. The other two members are Naveen Kumar (electric bass) and Jeoraj George (drums).

Though his colleagues in the trio are little-known, Madhav says this trio is of "international standard". And knowing him, if he says that, I believe him. He does not give compliments readily, but he has praised these members to me in the past.

They play a concert on July 22 at the Museum Theatre, and Madhav conducts three workshops in the preceding weeks. The details are below.

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WORKSHOPS:

(1) JAZZ AND WESTERN CLASSICAL MUSIC
JUL 3 SATURDAY 5.00 - 6.30 PM
VENUE: MUSEE MUSICALS

The main emphasis will be on the European roots of jazz music, western classical harmony and its development, jazz harmony-melody-rhythm configurations.

(2) JAZZ, ROCK, GOSPEL AND BLUES MUSIC
JUL 10 SATURDAY 5.00 - 6.30 PM
VENUE: MUSEE MUSICALS

Emphasis on the African cultural roots of jazz music, blues music and gospel music as twin music forms: one sacred the other "profane", blues as the basis for jazz and rock music. Swingin' the blues.

(3) JAZZ, HINDUSTANI AND CARNATIC MUSIC
JUL 17 SATURDAY 5.00 - 6.30 PM
VENUE: MUSEE MUSICAL
THIS WORKSHOP IS A CO-PARTNERSHIP WITH SRUTI MAGAZINE

The art of improvisation: what is necessary: similarities in process between carnatic/hindustani and jazz music. Actual differences between the music forms. Differences in cultural configurations between the west and India (jazz is essentially a western musical idiom even if part of its roots lie in Africa). Fusion and Con-Fusion: Pitfalls in thinking that is endemic to jazz and carnatic collaborations.


CONCERT:

(4) MADHAV CHARI PERFORMANCE WITH A JAZZ TRIO
JUL 22 THURSDAY 7.00 PM
VENUE: MUSEUM THEATER
PRESENTED BY MUSEE MUSICALS
CO-SPONSOR: K. BALAJI

Please be seated at the venue no later than 6.45 PM.

In what sense are we a "socialist" republic?

In 1976, Indira Gandhi amended the Preamble of the Indian Constitution to insert the words "socialist" and "secular" in the description of the Indian republic. It is not clear to me what she meant by "socialist", but 34 years later, we still don't have a social security system or any kind of safety net for the vast majority of our people. We have a "public distribution system" for essential commodities, that is decrepit and corrupt but is pretty much the only resource for the poor. Our healthcare and education are terrible. We know that Mrs Gandhi, like her father, admired the Soviets, but in what respect, other than autocracy and midnight arrests, did she attempt to emulate them? (Mrs Gandhi made this amendment at the height of the Emergency. She did not choose to remove the word "democratic" from the Preamble, presumably because the Soviet bloc had its own definition of that word, as in "German Democratic Republic" -- the former East Germany. Why change words when you can merely change their meanings?)

The motivation for the above reflections was the recent decontrol of petrol prices. Now, subsidising petrol is the sort of broad-based subsidy that makes no sense to me: it benefits the rich as much as, or more than, the poor. I am all for removing such subsidies. I think we should also be charged more realistic amounts for water, electricity, and other things that we take for granted. I seldom pay more than Rs 5 for parking my car, and usually I pay nothing: our cities could earn huge revenue by just charging parking fees that bear a closer relation to the price of real estate. There is no possible argument for subsidising car owners to this extent.

But the question is, what will we get in return for removing the subsidies? Can the poor be assured of affordable food, good healthcare and education? The government has passed the "Right to Education" act but there is no clarity on how it is to be implemented, and I am worried that the only effect of the act will be to hamstring the existing private schools without providing any alternative. There seems to be zero movement, and indeed zero interest, on any of the other things that an allegedly "socialist" government should be providing to its needy people.

Balancing the budget is all very well, but there is surely no short-term rush for that: if we manage to lift 300 million people out of poverty in the next generation, the government's tax revenues will shoot up too. As George W Bush said, we need to make the pie taller. Besides, there are enough wasteful government schemes that we can trim without hurting millions of people in the process. But I do not for a moment believe that the poor will become magically prosperous via GDP growth alone. Thanks to India's spectacular recent growth, the urban middle class earns ten to fifty times as much as it used to a generation ago; but we remain every bit as stingy in paying servants and workers, haggling for the last rupee. That's not going to change.

Meanwhile, without an education, the poor simply face no better prospects than unskilled labour -- whether in farming, industry, construction or homes -- and no means of fighting exploitation.

So while I am, in theory, happy to pay more for my petrol, I want to know what the government plans to do with my money, other than cut the deficit. Indira Gandhi made "Roti, kapda, makaan" a slogan: a generation or two later, a huge number of Indians lack even those essentials of life. Healthcare and education? Perhaps a century or two from now.