Hear it for Harriet
Though most people’s interest in the recently deceased Galapagos tortoise Harriet was because of her supposed association with Darwin, now debunked by Henry Nicholls, my interest was astronomical (15 July, p 21). No human was alive for the 8 June 2004 transit of Venus who had seen the previous transit in 1882, much less the one in 1874. So Harriet was a creature who may well have seen those transits and eventually got to see three.
My wife and I were glad to meet Lonesome George, the subject of Nicholls’s recent book, at last year’s Galapagos solar eclipse.
From Robert Senior, Science Centre, Woolsthorpe Manor
Nicholls lists the story that Newton was inspired by a falling apple as one of science’s myths. Including this particular story in his list is a little unfair. There are several published accounts that record Newton himself describing such an event. The first was by William Stukeley, who recalls sitting with Newton under another apple tree drinking tea and being told the story. John Conduitt records a similar story. So the story came from Newton himself. Of course he could have invented it, but why should he do so?
The event took place while Newton was at his childhood home of Woolsthorpe Manor during 1666 while Cambridge University was closed by plague. An apple tree there has long been identified as “the tree”. It was blown down in 1820, but the fallen trunk re-rooted itself. It is still flourishing and shedding apples. An analysis by the University of York, UK, of rings from the trunk taken in the 1990s dates the tree as well over 400 years old.
We are fortunate in having such reliable records of this delightful story and, through the re-rooted tree, a tangible link to the mind of our greatest scientist.
Uppingham, Rutland, UK
Rare Latin birds
Further to Elizabeth Bromham’s comment on the black swan (29 July, p 23), Wikipedia tells us: “Rara avis 鈥� ‘Rare bird’ 鈥� An extraordinary or unusual thing. From Juvenal’s Satires: Rara avis in terris nigroque simillima cygno (‘a rare bird in the lands, and very like a black swan’).”
The editor writes:
鈥� The full quote in the translation by Niall Rudd (Oxford University Press) is: “Suppose she is beautiful, graceful, wealthy, fertile, and also has ancient ancestors dotting her hallway; suppose she is purer than any Sabine with streaming hair who stopped a war 鈥� a rare bird, as strange to the earth as a black swan; who could endure a wife who was such a paragon?”
May I interrupt?
The graphic “Divided attention” in your article about interruptions at work shows that 49.1 per cent are initiated by the worker (24 June, p 46). While some of these may be aimed at helping with the task at hand (and therefore aren’t really interruptions at all), they are all chosen by the workers rather than imposed upon them.
How do these self-induced interruptions benefit the workers who initiate them? Perhaps they are simply a means of escaping the task, the work situation in general or the sheer deadliness of doing the same thing for hours on end?
Humans have been shown to induce variability into rigid situations so as to escape boredom, even to the extent of making mistakes. The challenge for workplaces may not be so much to reduce the overall rate of interruptions to workers but rather to allow them to have some that engender the kind of mental break that we all need. The water-cooler/coffee machine/short gossip may have a place in the modern workplace after all.
How many gods are there?
Feedback might be a bit quick to dismiss the idea of fractional gods (Feedback, 22 July). The Hindu Brihadaranyaka Upanishad certainly considers the possibility of one-and-a-half gods:
Then Vidagdha, the son of Sakala, asked him: “How many gods are there, Yajnavalkya?
Yajnavalky said, “As many as are indicated in the Nivid of the Visvadevas 鈥� 300 and 3003.”
“Very well,” said Sakalya. “How many gods exactly are there, Yajnavalkya?”
“Thirty-three.”
“Very well,” said Sakalya. “How many gods exactly are there, Yajnavalkya?”
“Six.”
“Very well,” said Sakalya. “How many gods exactly are there, Yajnavalkya?”
“Three.”
“Very well,” said Sakalya. “How many gods exactly are there, Yajnavalkya?”
“Two.”
“Very well,” said Sakalya. “How many gods exactly are there, Yajnavalkya?”
“One-and-a-half.”
“Very well,” said Sakalya. “How many gods exactly are there, Yajnavalkya?”
“One.”
“Very good,” said Sakalya, and he asked: “Which are those 303 and those 3003?”
Yajnavalkya said: “There are only 33 gods. These others are but manifestations of them.”
In Hinduism there are said to be 330,000,000 gods. Perhaps a really staunch atheist, who believes with 100 per cent conviction that there is no god, could count as a negative god (as opposed to the more common sceptical agnostics). How many such atheists are there? Well, if there were 330,000,000 of them, this would give us your “most likely” average of zero.
鈥� Our spoof proof that the expected number of deities in our universe is zero (Feedback, 22 June) attracted many responses in addition to this one. Enough, possibly, to disprove Phil Adsley’s extension of precisely the same argument to life in general: “The number of life forms ranges from negative to positive infinity (leaving the philosophers to argue over negative life forms…) and therefore the expected number of life forms is zero.”
Several readers, like Chris Brooking, challenged our assumption that the number of deities is whole 鈥� some, with Dai James, pointing out, “The Greek heroes were the result of couplings between gods and mortals, thus producing demi-gods.” Over many generations this would produce hemi-demi-gods and so forth 鈥� beings whose deicity was a fraction with any whole number on the top and a number on the bottom that is a power of two: 2, 4, 8, 16 and so on. Those fractions would be what mathematicians call rational numbers, leading James to conclude: “The deities would thus be rational 鈥� a considerable relief as there are obvious dangers associated with an irrational god.” He goes on to reach a startling conclusion: “Since no gods can be irrational, none of them can be transcendental.”
We thank readers who made a similar argument based on the Christian doctrine of the Trinity 鈥� but we’re not going there. Archie Campbell suggests that the true number is “an imaginary number with no real part” and Vilnis Vesma elaborates 鈥� whooshing over our mathematical head 鈥� that imaginarily numbered deities “would only interact with the real world if there were zero of them”.
Luther Blisset also challenges our identification of deities with integers. Should we not count them using either the unordered cardinal numbers (as in, “Daisy the cow, Ermintrude the cow”) or the ordinals (as in “best cow, second-best cow, third…”)? Theologians may argue over which we should use, but in either case the range is from zero to infinity and so, assuming our universe is typical, the expected number will be one-half infinity which is, er, infinite.
Which brings us to Stephen Scott’s observation that we pre-answered ourselves on this matter, when on 22 April we quoted Neil deGrasse Tyson, director of the Hayden Planetarium in New York, responding to a discussion of the number of universes: “We live in the middle of infinity? Did those words really just come out your mouth?”
Trade in death
Duncan Graham-Rowe’s excellent and timely article on the problems created by ship-breaking in parts of Asia (22 July, p 39) underlines the need for strong international regulation of the industry.
However, the article only tells half of the tale. While the environmental toll is quite appalling, so is the human cost. Many tens of thousands of migrant labourers are employed breaking up ships in the Indian subcontinent. Usually paid little more than a dollar a day, they work in highly toxic and dangerous conditions with no or little protection.
A recent report by a number of organisations, including Greenpeace, showed that 372 workers have died at the Alang shipyard in Gujarat, India, over the past 25 years. A further 180 deaths have occurred in Bangladesh in the past 11 years. These figures are only the tip of the iceberg, however: many thousands more will die from cancers and other diseases caused by exposure to the huge quantities of asbestos, heavy metals and other toxic substances found in these ships.
The international community has a duty to stop this trade in death immediately and ensure that this work is done in an environment that is safe, for both the workforce and the planet.
Poison gas to blame?
You reported the first recorded death from chronic fatigue syndrome (CFS) (24 June, p 7). The symptoms of CFS can be very similar to the symptoms of carbon monoxide (CO) poisoning. CO is the most common poison in the UK: it can be emitted from faulty cooking and heating appliances powered by any combustible fuel. Even tiny amounts can kill, and low-level exposure over a long period can produce brain damage.
CO could well be ignored as a possible cause of symptoms attributed to CFS. There have been cases in which previously healthy children have died of CO in rented accommodation, but medics and at least one pathologist overlooked the gas as a possible cause of death until the rest of the family became ill.
We have been trying to find out whether patients presenting with symptoms of CFS have had CO ruled out as a possible cause. We are sure there are cases of CFS that have nothing to do with it; however, we ask experts in CFS to do their utmost to warn patients of the dangers of CO and to rule this out as a cause of their patients’ symptoms.
We invite readers to visit our website, , to ensure that they know how to keep safe from CO before the northern winter starts and heating systems are switched on.
Bug-free programs
I fear that the world’s computers 鈥� at least those operating Windows 鈥� are a long way from being immune to attacks by most viruses (22 July, p 46).
In spite of the efforts you outline to thwart these attacks, virus writers will eventually change tack and write more flexible code to get round the new defences.
The fact is that most viruses take advantage of software bugs to attack machines. They would have a much harder time if programs were written without bugs in the first place. Writing computer programs without bothering to iron out the bugs is akin to a surgeon not sewing up a patient after an operation.
Preventive altruism
Routine HIV testing would indeed help prevent the transmission of the virus (22 July, p 8). You make the point 鈥� as I did some years ago in New 杏吧原创 鈥� that those who know they are infected tend to do more to avoid passing on the virus than those who think they aren’t do to avoid catching it (21 March 1998, p 50).
It should also be recognised that cultivating such “preventive altruism”, with interventions aimed at infected individuals rather than at the wider uninfected population, would be likely to have a disproportionately greater effect in stemming the spread of HIV. This is because HIV-negative people just about always outnumber HIV-positive people, usually many times over, and the impact of any particular individual taking up a preventive measure would reflect that disproportion. If, for example, the prevalence of the virus is 1 per cent, 99 negative folk would need to be persuaded to take up condom use to have the preventive impact of persuading a single positive person to do the same 鈥� a task which would generally be easier anyway, given the tendency to preventive altruism.
An important opportunity has been missed through the overwhelming emphasis of HIV prevention work on uninfected populations. Routine testing would make it easier to start redressing that imbalance.
Water is no fuel
Your article on the zero-emission car being developed by Tareq Abu-Hamed and colleagues is titled “Power on tap” and says in the first paragraph that such a car could run “with nothing more than water in its fuel tank” (29 July, p 35).
Why is it deemed necessary to put such outrageous claims in the titles and beginnings of articles? Saying that the car discussed in the article runs on water is equivalent to saying that the internal combustion engine runs on air. The water would more accurately be described as a catalyst (as it is regenerated), or maybe a means of chemical energy transduction and transport. What it isn’t, though, is a fuel. The fuel is boron.
Beating the air
Darwin wrote in On the Origin of Species: “It is certain that many forms, considered by highly competent judges to be varieties, resemble species so completely in character that they have been thus ranked by other highly competent judges.” A century and a half later, the atmosphere is still being agitated by debate over the reality of a subspecies of meadow jumping mouse (15 July, p 12).
Most biologists regard “subspecies” as a nearly useless category, to be replaced by quantitative data on geographic variation in morphology and genetics. Either the US Endangered Species Act exists to preserve the ecosystems and genetic diversity that will allow local populations to persist in their natural ranges, or it does not. But, as Darwin himself added to his statement above, “to discuss whether they ought to be called species or varieties, before any definition of these terms has been generally accepted, is vainly to beat the air”.
Sliding passengers
I liked the article about Einsteinian aeroplane boarding (29 July, p 42). Another solution might be to remove the fuselage from around the seats. Passengers could then walk directly to their seat without having to go down any aisles or doors. The practical version of this would be to have all the seats and lockers on a “tray” that could slide out of the nose (or tail) of the aeroplane. Passengers could get to their seats from any direction in an open departure lounge 鈥� and everyone would not “board” at once 鈥� they would just find their seat as they arrived at the lounge. When everyone was seated you would slide them back into the plane.
Precocious puberty
Alison Motluk suggests that the processes of sexual and social maturation are distinct and that the gap between them is problematic (22 July, p 34). This is at best naive. At worst it is something New 杏吧原创 is usually critical of: the medicalisation and pathologisation of normal social issues.
Historically, the notion of a gap between the attainment of sexual maturity and social maturity is not unusual. A Roman boy donned the toga of manhood during his teen years but was not considered a full social and political citizen until about 30.
Further, part of becoming a socially mature person is knowing how to conduct a mature sexual relationship. To delay the onset of puberty would simply push back the development curve, leaving a person in their early 20s trying to deal with puberty and all its pitfalls along with the battle of starting a career. Surely the middle school years, when the young person is relatively sheltered economically, is a much more appropriate time to undergo this transition.
From Ian Rickard, University of Sheffield
Peter Gluckman claims that in the pre-agricultural past it would have been usual for girls to begin to reproduce at the age of 12 or 14. Studies of contemporary hunter-gatherers worldwide provide no support for this.
In such populations, age at menarche (first menstruation) may typically be anything between 12 and 18. However, there is commonly a time lag between the age at which girls begin to menstruate and the age at which they begin to have babies. This lag can be between two and eight years. It is rare for girls to become mothers in their early teens.
In addition, age at menarche is unlikely to be a valid indicator of a girl’s readiness to reproduce, since there are other important factors, such as skeletal growth, which have consequences for successful reproduction. Girls who do reproduce in their early teens are at a high risk of experiencing childbirth complications, including stillbirths. Natural selection is unlikely to have strongly favoured reproduction at such a young age and may instead have favoured delay.
While it could be argued that the lag between age at menarche and age at first giving birth is an artificial, cultural constraint, its apparent ubiquity suggests it may in fact have played an important role in human evolution.
Sheffield, UK