Learning to be Terse

An infinitely long Maxwell’s demon in a vacuum

Posted in Science by Croor Singh on September 19, 2014

There’s this article doing the rounds about the Indian central government getting a letter from a gullible Gujarati man who thought he had a brainwave when he realised that moving objects drag the medium they are in (air) behind them, and leave eddies of flow in their wakes. “All that wasted energy! Let’s put a windmill there and extract it all, why don’t we?”

So went he forth and sent a letter by post to the Prime Minister’s Office. (The article makes double mention of the fact that he sent his letter by post. That’s either wonderfully subtle mockery, or just blind luck.) And apparently the PMO saw fit to send this letter to the Railways asking for expert opinion.

The PMO, in turn, forwarded it to the Railways Ministry, asking it to explore the “techno-economic” feasibility of the idea, and sought regular updates.

The expert opinion was, of course, that this is a useless idea:

“A train will pass the windmill in less than 20 seconds. Even if there is a train every 15 minutes, a windmill can operate for only 25 minutes per day. This will not be viable economically. Further, the energy produced by the windmills would have to come from the trains only, which will consume extra energy[...]”

I have no problem with people sending silly ideas to engineers in the railways. I’m sure whoever got the job of explaining why the idea is silly had a lot of fun with it. I thought I would too.

So what’s wrong with sticking a windmill next to a train? The good people of the railways point out that this would be a huge investment that’s only ever going to be ‘switched on’ 25 minutes a day. Philistines, I tell you. What stops them from working with infinitely long trains and infinitely many windmills? Unfortunately, even with infinitely long trains and infinitely many windmills, there’s the little matter of the second law — the no-free-lunches law of thermodynamics.

Stick a windmill–indeed or any mechanism–next to a train and whatever energy the mechanism produces has to come out of the fuel the train burns. (There would be additional losses too.) As proof by reductio ad absurdum, imagine an ideal engine (a Carnot engine) running the train; i.e. the train’s already running at the maximum possible efficiency. The addition of the windmill draws extra work out of the fuel that the train is burning, and fucks with the second law. And as we all know, the second law is Tony Montana.

The infinitely long train idea is out, then. How about a mechanism that captures energy from the random motion of the turbulence that the (finitely long) train leaves behind in its wake? I can think of two inter-related problems with this.

The first one is logistical: what is the mechanism you have in mind that “knows” when the train has passed by? Because if the mechanism is in place when the train is passing by, it will affect the flow around the train, and therefore change the drag on the train, and therefore effectively draw energy from the train’s fuel source. At which point we’re back to fucking with Tony Montana.

The second problem is fundamental. Can you extract energy from the random motion in a medium? The idea of extracting energy from the wake behind a train is a rehash of the very old problem of Maxwell’s demon: a mechanism that can separate the ‘hot’, i.e. faster moving, molecules in a gas from the ‘cold’ ones. If you think about it, all you need is two compartments with a tube connecting them which only allows ‘hot’ molecules to pass in one direction, and only allows ‘cold’ molecules to pass in the other direction. And soon enough, one of the compartments will be full of ‘hot’ gas, and the other full of ‘cold’ gas. And of course, nothing of the sort is physically possible without violating the second law. Why this is so has to do with information and energy being equivalent, but I shan’t say more about this here.

In conclusion, windmills need large-scale movement of the air around them, i.e. they need wind, in order to extract energy. And changing the large-scale flow around a moving object has to be paid for with interest in increased drag, owing to the second law. The second law of thermodynamics also precludes any attempt at extracting energy from the small scales (albeit in a different way from above).

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Rape isn’t rape

Posted in Ethics, Society by Croor Singh on May 12, 2014

There are relics of colonial rule which we as a country seem desperately to want to cling to. The criminalisation of homosexuality is a perverse case in point, with the highest court in the land seemingly holding one fuck-awful section of the IPC a century and a half old above constitutional rights to freedom, dignity, privacy, life. The party which will presumably rule this country for the next five years has said it will continue this mockery of human dignity.

We’ve just been given another glimpse of what may be to come. A Delhi court has ruled that a man cannot rape his wife, lack of consent and the use of force be damned:

“The girl was more than 21-years-old at the time. Thus the girl and accused being legally-wedded husband and wife and the girl being a major, the sexual intercourse between the two, even if forcible, is not rape and no culpability can be fastened upon the youth,” Additional Sessions Judge Virender Bhat said while absolving the youth of the charge of rape.

I know none of the particulars of the case, and the NDTV article does nothing at all to make anything clear (the woman met her husband in December 2013, but the marriage was solemnised in March 2013?). But what the judge said in his ruling will harm more than just this poor woman. This ruling will become another in the list of cases where nothing was found wrong with marital rape.

The judge is, strictly, correct. According to what is the law today, a man cannot legally rape his wife if she is an adult. (But, you say, how can a woman even be married if she isn’t an adult? The law until 2010 said that age limit was 15. Raising the age to 18 was the ‘compromise’ Indian lawmakers struck.)

Isn’t it time we fixed this stupid law? Sexual violence against women is staggeringly common(fn1). And a significant majority of the instances of sexual violence are committed by acquaintances. I don’t know what fraction is marital rape, but surely the only acceptable number is zero. (fn2)

I can’t imagine what the woman must have gone through. And she’s among the lucky ones who can get a case registered and take it to court. For every one of her, there are many others who either can’t or don’t report sexual violence against them, or aren’t even taken seriously enough to be given a hearing. (fn3) Or, if they are, they’re put through mind-numbing ordeals.

HT: Srikanth, who pointed me to the court ruling and hopes the Supreme Court will do something about this.


1) One in three women will face some sort of sexual assault in her lifetime. That number is just depressing.

2) Two-thirds of rapes are committed by people who aren’t strangers to the victims. The page at the link also says 28% of rapes are by an intimate.

3) 60% of sexual assaults aren’t reported. 97% of the accused will never serve jail time. India’s conviction rate (for cases that are actually reported) is 24%.

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The abuse of a raped woman

Posted in Ethics, Society by Croor Singh on May 2, 2014

When I wrote about Mulayam Singh Yadav and his ‘boys will be boys’ speech, I was trying to make the point that while Mulayam Yadav is an ignorant asshole, his views on sexual violence are representative of our culture of victim-blaming; that how the country’s law-enforcement and medical establishment treats victims of rape is symptomatic of this culture.

This misogyny is also inherent in the way we legally define rape. Indian law defines sexual violence in terms of whether the “modesty” of a woman has been “outraged”. Why every woman must be “modest” is something nobody writing the law seems to have bothered to ask. The worst manifestation of this lunacy was the two-finger test to determine whether a woman reporting that she’s been raped is ‘habituated to sex’. I say was; it was standard procedure until about a month ago; I have no doubt that there are doctors who haven’t got the memo. [Emphasis added.]

I suppose I shouldn’t be surprised that what I said I feared might happen is now happening to a woman in Kolkata. She is now the victim of an establishment that not only fails to provide adequate care or support, but on the contrary seems to be accusing her of making it up (the joint police commissioner of Kolkata has apparently held press conferences where he has said he finds the victims statements inconsistent). She has also been at the mercy of a doctor who clearly didn’t get the memo about what not to do during a medical examination of a victim of sexual abuse:

[...] the doctor asked the victim a few questions and took a vaginal swab which he gave to the police for forensic examination. However, the detailed protocols as mandated by the MoHFW guidelines (page 23-36) were not followed. Some key specimen (like pubic hair samples) were not collected/looker for and some outdated and irrelevant information (relating to the hymen, elasticity of vagina, admissibility of fingers etc.) was noted on the ‘report’ – clearly flouting the March 19 guidelines, which make us believe that the doctor who performed the preliminary examination is not aware of the MoHFW guidelines and protocols.

Besides, no steps were taken for the victim’s medical care, and health concerns. No urine test or testing for HIV was done and no psychosocial care was offered. When she requested the doctor to take samples/pictures of fingerprints of the culprit that might still be there on specific places of her body she was curtly told that the doctor knows what he is supposed to do. The doctor did not even use the correct and detailed form to record details of the medical examination. (page 62, MoHFW guidelines). It appeared that the hospital does not have a copy of either the new guidelines or the correct form.

That there are doctors who haven’t kept up with the law isn’t surprising. That this is happening in Kolkata’s second biggest government hospital is. That the doctor is either so much of an ass or so cynical that he can barely go through the motions even when faced with a woman who has been raped is both surprising and shocking.

I dare not imagine what the situation is in small towns and villages.

Here she is, a politically aware, intelligent and brave young woman who was lucky to have so much immediate support from her student comrades and women’s organizations. Even she has to experience so many hurdles and so much of stigma and maligning attempts, just during the immediate aftermath of her traumatic experience. Justice remains elusive as ever. Her father wants justice for his daughter, but is extremely skeptical about the prospect of justice, going by the prevailing standards and conviction rates. One can imagine what women of lesser privilege and in places where even basic medico-legal infrastructure are missing, go through. Justice is a lottery.

From Kavitha, who pointed me to the Kafila article.

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Some thoughts on living in India and Sri Lanka

Posted in Politics, Society by Croor Singh on May 2, 2014

I started writing again on the blog about a month ago, after a hiatus of almost a year. Many things happened while I was away, not the least interesting of which was my voyage to the middle of the Bay of Bengal and my trip through Sri Lanka. Sri Lanka is a wonderful country in many ways, and the week or so I spent there was thoroughly enjoyable. I wrote the following while I was in Sri Lanka, circa December 15, 2013, and sent it to a few people I thought might be interested. I haven’t attempted to edit the essay from then.


Some thoughts on living in India and Sri Lanka

I guess most of you know about this, but the supreme court of India judgement on section 377 was handed down a few days ago. The supreme court reversed the stance of the Delhi high court that 377 has to be struck down because what happens in private between consenting adults cannot be punishable. Sri Lanka is very similar to India when it comes to how it deals with homosexuality. There is no gay-marriage, no civil unions. And, says wikipedia, there is a Sri Lankan law (like 377 a relic from the colonial age) that prohibits “grossly indecent” behaviour, something that’s conveniently left undefined (again, just like 377’s language of “against nature”).

What you may not know about the case is that nobody has ever been convicted under either the Sri Lankan law or the Indian law that make homosexuality punishable… Which is what makes the supreme court’s decision that much more frustrating. The court is seemingly saying that no matter how obviously unconstitutional a law in the (seriously outdated) book is, they will not strike it down, asking instead that Parliament pass a law amending section 377.

Jurisprudence comes in a spectrum, I guess, and there’s a case to be made against judicial activism (to wit: it interferes with the separation of powers). But judicial activism isn’t what we’re talking about here. Unless the supreme court of India professes to believing that every section of the IPC written in 1860 is magically compatible with the Indian constitution (i.e. that the Indian constitution is somehow magically backward-compatible with every section of the IPC), some parts of the IPC are going to be unconstitutional and it’s somebody’s job to clean up the mess. Shouldn’t it be the courts–the interpreters of the constitution–that do the striking down of decrepit laws when such laws are brought to their notice? Not that the supreme court is consistent in the matter of whether judicial activism is good or bad, by the way. In the 2G spectrum case, the court not only annulled what the government had done, but basically wrote procedure for an arm of the executive (saying public auction is the way to go, or else).

The mention of Sri Lanka comes from this: I’ve been in Colombo for less than three days now (a day and a half before I left for the ship, and today since the afternoon after I got back). I’d heard very good things about Sri Lanka before I came here. I also knew that Sri Lanka outranks India and the rest of the South Asia region by far when it comes to human development, even though Sri Lanka only has two-thirds the per-capita GDP of India.

The HDI shows on the streets of Colombo, I don’t think I’m being (very) obtuse in saying.

I went out drinking with friends from the ship tonight. Bars in Colombo are open until 12:30, clubs until 2:30am. There were no signs of the crowd thinning when we left the bar at close to midnight. The woman in the group says she didn’t feel a creepy stare because she was drinking or smoking or out past a ‘respectable’ time, I guess because she was by no means the only woman around. We went around midnight to a pier next to the bar. We again saw men and women of assorted ages at the pier, and no cops asking them why they were there. I took a bus (several of which run even past midnight) to my hostel from the bar. The cops were in their posts on the highway the bus takes checking for drunk driving, a vastly better use of police manpower than accosting people on the beach. I’ve also noticed that cars on Colombo’s streets stop for pedestrians instead of threatening to run them down (and everybody obeys traffic signals, which to somebody from Hyderabad means more than you think).

In summation, then, two points. First the obvious preach to the choir:

Colombo isn’t a cesspool of vice for allowing it’s bars to be open past 11. Or for allowing its women the freedom to do what they want. Or for making its policemen do what they’re meant to do.

Secondly, all this has still not meant that Sri Lanka’s “section 377″ is struck down. a) The gift of colonialism just keeps on giving. b) Popular opinion can change this in a hurry, one hopes, given how quickly progress has happened in the US recently. (Obvious caveat: the US was dealing with gay marriage rights, not gay existence rights.)

PS: The highest contribution to India’s HDI is from health, apparently. Which to anybody who knows what government healthcare in India looks like would be funny if it weren’t tragic. Our education index is well below our already pitiful overall HDI; Sri Lanka’s education index is on par with its overall HDI.

Your consciousness differentiates into boundless belonging

Posted in Skepticism, This and That, Weblogs by Croor Singh on April 23, 2014

Nothing is impossible. This life is nothing short of an ennobling uprising of spiritual empathy. We must develop ourselves and enlighten others.

It can be difficult to know where to begin. Although you may not realize it, you are dynamic. Being, look within and unify yourself.

We are at a crossroads of chi and ego. Our conversations with other beings have led to a summoning of ultra-sublime consciousness. Humankind has nothing to lose.

As you grow, you will enter into infinite growth that transcends understanding. The akashic record may be the solution to what’s holding you back from an unimaginable oasis of serenity. You will soon be aligned by a power deep within yourself —a power that is Vedic, powerful.

Greed is the antithesis of growth.

Without grace, one cannot believe. Yes, it is possible to disrupt the things that can exterminate us, but not without chi on our side. We can no longer afford to live with yearning.

It is a sign of things to come. The transmission of potential is now happening worldwide. Soon there will be a deepening of power the likes of which the planet has never seen.

This blogpost was generated by reionising its electrons. See also the random Deepak Chopra quote generator.

HT: Pharyngula.

Modi is India’s Reagan. Apparently.

Posted in Politics by Croor Singh on April 22, 2014

I haven’t written about the elections. They’re happening, and we’re polarised enough as a polity that nothing I have to say will change anybody’s mind about anything. But yesterday’s The Hindu op-ed page contains an article that I thought I’d say something about. I don’t think the article itself is insightful or original, but what it represents perhaps is.

First, about the article’s thesis that Modi is India’s Reagan, and (implicitly) that this is somehow reason for people to vote for Modi (or Modi’s model of development).

Reagan was a B-film actor who became governor of California and then the US president. Modi was an organiser for the RSS before he became the chief minister of Gujarat. Reagan was considered sunny and optimistic, even by his opponents (it’s morning in America, and all that). Modi is sullen and diffident at times, and a rabble-rousing demagogue at others. Very little similarity there, I think.

Where there does seem to be similarity is in the size of the respective personas in relation to what these men actually achieved. And, more importantly, in their policies. Reagan enjoys de facto sainthood, despite being the president whose tenure saw the enactment of game-changing financial legislation that led to the sub-prime mortgage crisis of 2008. Reagan was also the president who cut taxes on the rich while the middle class barely made any gains and poverty rose.  He started the restriction of the social welfare programmes that is now entrenched in US politics (think ‘no tax increase, ever’, or ‘Obamacare means death panels’).

And yet the hagiography surrounding Reagan–e.g. David Cohen’s article which prompted this whole blogpost–would suggest a very different picture.

Modi’s rise to stardom, if not sainthood, has been similar. Modi’s Gujarat has made great concessions to large businesses, and fared poorly in social indicators. And, just like Reagan, the hype about Gujarat is larger than life.

Reagan was opposed to the civil rights and voting rights laws protecting black Americans from discrimination. He was anti-abortion, and insisted on prayer in schools. Modi’s BJP wants to permanently criminalise homosexuality, and return India to its Hindu roots (we’ll say nothing right now about whether those things are in fact the same thing).

Like I said above, the David Cohen’s article isn’t very interesting; it’s the same ‘Reagan was called racist by elitists’ tripe. What is interesting is that such and article is now possible in mainstream news. Marx and Engels called for a global order of the proletariat; what we seem to have here is a global order of the rich and their minions.

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Sexual abuse, then and now

Posted in Ethics, Society by Croor Singh on April 18, 2014

I wrote the last time about sexual abuse and how what people in the public eye say about these things is only reflective of the society they are part of; that vilifying them without attempting to reform society is likely to do nothing. I have a couple of for-instances to show about what I mean.

The first video below is a movie review of what seems like a horrendously bad movie called Jaani Dushman. I’d call this the Gunda of the noughties, but I probably don’t know enough. The bit of interest to me is from 0:43 to 2:30. (But go ahead and watch the rest of the video too. They’re good, the reviewers.)

The last thing the reviewers say about the  attempted rape is significant: “this was in 2002.” And here we are, a decade later. Should we be pleased that at least some people find what is said in the movie about rape obviously idiotic? Should we be distressed that a decade later, leading politicians seem to be saying the same thing that the movie did?

The second video below is a short film called Bol, by a filmmaker called Pooja Batura Pathak. The short film portrays graphically what I suggest above about how we don’t, as a society, seem to have changed at all in how we deal with sexual abuse. (fn1)

One in three women will experience sexual abuse or rape in her lifetime, statistics say. A large fraction of this will be abuse by somebody known to the victim. And the woman will be blamed for it. We can do better. We must do better.

HT: Sharmila pointed me to the review of Jaani Dushman. I can’t remember where I found the short film.

fn1: I do have some quibbles about the short film. Is it important to show the girl in the short shorts doing a silent prayer as she passes a temple? What does religious belief have to do with what the girl goes through later? But, like I said, these are quibbles.

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Bloody red tape (Rant)

Posted in Campus, Personal by Croor Singh on April 18, 2014

The centre is holding interviews today and we’re short-staffed since today’s officially a holiday. I was asked to help out with office work. Shouldn’t be hard, should it?

One part of the office work I was assigned was to look at train tickets for reimbursement. Interview candidates are given sleeper class fares for train/bus journeys from wherever they currently study/reside to Hyderabad and back. In order to make sure that this provision isn’t misused, the rules say the journey has to be made by the shortest route. You’d think that the “shortest” would be interpreted liberally. After all, train journeys between the same two locations can be shorter in one direction than the other.

For instance, a sleeper class ticket from Bombay to Hyderabad is Rs. 345. A sleeper class ticket from Hyderabad to Mumbai is Rs. 350. There seems to be a small difference in the distance travelled (8km or so) and an even smaller difference in the fare. What would you say is the reasonable response to this?

One response is to say nobody is trying to cheat anybody, and the difference of five bucks hardly matters. The time it would take to check whether the train the candidate took was indeed the shortest journey (there are 15 trains between Hyderabad and Bombay) is worth more than the five bucks that the centre would save by skimping on the reimbursement.

The other response… well, you can probably guess what the other response is. We’ve all been to government offices at some point. Unsurprisingly, I got told to go away for arguing this point. Typical.

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Boys will be boys

Posted in Ethics, Society by Croor Singh on April 12, 2014

Mulayam Singh Yadav, once a possible candidate for the Prime Minister’s post, has basically said of rape what you or I might say of the pulling of pigtails on a playground. He wants to abolish the death penalty for rape–but not because he thinks the death penalty is unconscionable. He also wants to, and this is more important, punish women who ‘falsely’ claim rape (footnote 1). If it comes to pass, what this might do to the prevention and punishment of crimes that are rarely reported, and even more rarely prosecuted successfully is anybody’s guess.

Mulayam Singh Yadav is a patriarchal insensitive ignorant asshole. Unsurprisingly, lots of people have said this in the two days since his statement (footnote 2). To stop there, however, is to vilify one man while letting the rest of us off the hook. The culture of abetting rape does not begin and end with one clueless politician.

We live in a culture that normalises the objectification of women but shames them if they revel in their sexuality; a culture that  will call a woman a prude for not accepting the objectification of women in public, but will call the same woman a slut  for being in charge of her own sex life; so much so that victims of rape are told they “brought it upon themselves.” Mulayam Yadav’s is only the latest (and not necessarily the worst) restatement of this sentiment. And the culture of rape is only the worst symptom of the underlying misogyny that women endure every day. (footnote 3)

This misogyny is also inherent in the way we legally define rape. Indian law defines sexual violence in terms of whether the “modesty” of a woman has been “outraged”. Why every woman must be “modest” is something nobody writing the law seems to have bothered to ask. The worst manifestation of this lunacy was the two-finger test to determine whether a woman reporting that she’s been raped is ‘habituated to sex’. I say was; it was standard procedure until about a month ago; I have no doubt that there are doctors who haven’t got the memo.

All this may have something to do with the fact that the laws we’re talking about were written in 1861. The IPC criminalises adultery (and treats women as if they were their husbands’ property), but–and this is still true, in 2014–has no punishment for marital rape. (footnote 4)

Is it surprising that men who’ve grown up in such a culture treat women like crap? Or talk flippantly about rape in political speeches?

fn1: I am not saying here that “he promised to marry me” should make somebody guilty of rape. The ‘reneging on a promise to marry is tantamount to rape’ doctrine comes from the law’s attempt to define sexual abuse in terms of the damage to the ‘modesty’ of the woman. The sooner we do away with this the better.

fn2: Mulayam Singh Yadav is by no means the only ignorant asshole. His partyman Abu Azmi wants to hang women who get raped. I would point out that he wants us to become one step worse than Saudi Arabia where rape victims are lashed publicly. A parliamentarian from the BJP has called for women to not be allowed to use mobile phones or wear jeans.

fn3: This paragraph is an excerpt from something I wrote with a friend about Steven Pinker’s AMA on reddit. Pinker’s position, we thought, was short-sighted. We didn’t get it published anywhere, but some of you may have seen it.

fn4: If a married man sleeps with an unmarried woman, it isn’t punishable; but it is punishable for a single man to sleep with a married woman, because he would be infringing on another man’s property rights.

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The deterministic equations of life, the universe, and everything

Posted in Science by Croor Singh on April 4, 2014


In principle, the equations of classical (or quantum**) mechanics completely determine the future of every particle in the universe given the present state of every particle. This has two implications: one, that the universe is deterministic (with attendant restrictions on what “free will” can mean); and two, that the physical law that entropy in the universe always increases requires serious explanation. I recently attended an interesting talk on the second of these by a philosopher of science. Even more recently, a chat with a friend turned to the determinism of the physical laws.

If you accept that the basic laws governing the motion (and therefore the time-evolution) are deterministic, does that mean, given that there was a definite beginning, that every one of us is unique? Can there be somebody else who is exactly like you? If that question seems leading, that’s because it probably was. In order to answer that question, however, you’d have to define what “exact” means. Now, it may seem like I’m splitting hairs here, but bear with me.

What’s a good definition of “exact”? Clearly, I know the universe exactly if I know where every molecule of the universe is and how fast it is moving. You might think this is an extreme demand and you’d be right. You would need a computer larger than the universe to keep track of all the data. (Why? The simplest “computer” that can do this is the universe itself. Any device with a more complicated process for tracking every molecule will have to have many times the number of molecules the universe has. And universes are hard to come by.) If this is your definition of “exact”, then, it is meaningless (and perhaps trivial) to ask if somebody else can be “exactly like” you.

Luckily, this level of detailed knowledge is not only impossible, but also unnecessary. I don’t need to know what every molecule on Earth is doing in order to predict that the Earth will go around the Sun in a slightly eccentric circle. This is the salvation of the scientific enterprise. Emergent phenomena can be studied without needing to know every detail of the underlying physics*.

Phrased slightly differently, it is indeed true that you are “unique”; both in the sense that there’s nobody else whose molecules are exactly like yours (i.e. we’re all snowflakes), but also in the more important sense that the arrangement of molecules that makes you could be no other way.

But even this more correct interpretation is meaningless for the reasons I’ve given above: what matters are some aggregate properties of the molecules that make up you and me. In general, whether or not these macroscopic properties are uniquely determined by initial conditions is not a question that has an answer. You might think the answer is what you choose it to be, the answer that lets you sleep at night.

UPDATES: When I say above that you can choose the answer you want, I mean you can’t get to the answer by pure rationalism. We don’t, of course, have to answer this question “rationally”; we can find the answer empirically.

*I say underlying physics, not in support of the sentiment that “it is all physics underneath.” In fact, this is not only wrongheaded, but also counterproductive. The wrongheaded bit is illustrated (as only Randall Munroe can do it) here.  I know of at least two prominent examples of people taking “everything is numbers” to idiotic heights: Steven Levitt of Freakonomics, and now Nate Silver of Five Thirty-Eight.

** Srikanth points out that since quantum mechanics is inherently probabilistic, what I say here may not hold. I think it still might, but I realise that it’ll take more than one blogpost to sort this out.

HT: Aanveeksha, who brought this topic up.


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