The first Rubik solution
I read Jason Palmer’s article on Rubik’s Cube (9 August, p 40) with interest, principally because the three pages of text did not once mention , nor any of his reference works on the mathematics of the cube.
Palmer mentions that , created the “most common” speed-cubing method. I cannot dispute that her method may be the most commonly used by speed-cubers.
As a point of interest, Singmaster’s early books on the maths of Rubik’s Cube cited the earliest solution (which also happened to use “way-stations”, or intermediate positions), which was provided three years earlier in a private publication by Colin Cairns (my brother) and David Griffiths called Teach Yourself Cube-Bashing (September 1979). Over the next couple of years, I received several requests for photocopies of the text from Eastern European universities. So, this early solution was certainly known the length of Europe within a couple of years.
Teaching theory of knowledge
I was pleased to see A. C. Grayling highlight the International Baccalaureate Theory of Knowledge course in his commentary on “The Importance of Knowing How” (9 August, p 48).
As a Theory of Knowledge teacher, I couldn’t agree more with Grayling’s assessment that critical thinking needs to take centre stage in education. I am fortunate to teach some of the best students in New Jersey, US, but even my best students are absolute novices when it comes to defending their knowledge claims.
The easy access to all sorts of information via the internet can be, as Grayling mentions, an impediment to critical thinking. However, in my experience, the good-natured and all-pervasive relativism fostered by a well-meaning multicultural education may be the single greatest barrier for my students to overcome when weighing the merits of various knowledge claims.
Water not everywhere
I was shocked at the omission of some basic elements from Jonathan Chenoweth’s analysis of water consumption (23 August, p 28). His entire analysis is predicated on global trade in agricultural products constituting a trade in “virtual water” 鈥� insofar as arid countries may import foods that take a lot of water to grow, rather than addressing inadequacies in their own water supply 鈥� and that this virtual water can substitute for the real stuff. He also claims desalination is a “cheap” alternative.
There is the certainty that in the not-too-distant future oil will become scarcer and harder to access. Both desalination of seawater and the transport of “virtual water” will then become very expensive options. The ability of countries whose income depends on oil exports to trade for “virtual water” will reduce.
If Chenoweth’s analysis were implemented, it could easily tempt developing countries to abandon agriculture. This is happening in my country, Cyprus, which has suffered serious drought for two years. The government decided it was easier to compensate farmers than to develop water conservation. Land is not being cultivated, which means that erosion and water leaching are becoming worse.
If a poorer and less-developed country were to run down its agricultural resources in this way, and was then hit by rapidly rising food prices 鈥� due to sanctions or civil war, say 鈥� it would not be easy to restart widespread subsistence farming at perhaps only a few months’ notice.
Self-sufficiency in water, intelligent recycling and conservation measures remain the only sensible way to combat water shortages.
From Douglas Hawes
As a retired agronomist, I would say that the supposed high water efficiency of the Netherlands, the UK and Uruguay might be more due to the low evaporation rate and other climate factors of those countries than to real efficiency.
Water pricing probably plays a role, too.
Plano, Texas, US
Polypublishing
Perhaps one answer to the problems facing scientific publishing in the developing world that Priya Shetty reported (12 July, p 20) is to allow duplicate publishing 鈥� first in an international journal, then in a locally published title, with acknowledgement. Authors would gain recognition and leading publishers would maintain their position as the first to publish original content.
Reproducing the paper in the local language would increase exposure of local research to readers in the region, improving the viability of the local journal, particularly if it could establish partnerships with international publishers.
Anthropology on time
I agree with Hugh Gusterson’s view that it is improper to have anthropologists embedded within the armed forces in Iraq (2 August, p 20). I believe some field work before the invasion, however, would have quickly led to the conclusion that the war that the US had dismally in mind should have never been waged and that other strategies to remove Saddam Hussein and his cronies from power should have been considered.
History at stake
The brief contents-page listing for the two books in your Bookends section for 23 August states: “Warming death; on Giordano Bruno”. Taken together, this surely is a rather extreme understatement, given the recent discussion of why Bruno was sent to the stake (26 July, p 21).
For the record
鈥� We should have said that arsenic occurs naturally in groundwater as a result of minerals leaching from rocks (30 August, p 7).
鈥� Scott Tremaine is the Richard Black Professor of Astrophysics in the at the (6 September, p 19). Though located in Princeton, New Jersey, the Institute is not affiliated with Princeton University. We also said that black holes could grow to 30 times the width of the solar system 鈥� that should have been three times.
鈥� The correct DOI for the study of cyclones by James Elsner and colleagues is (6 September, p 20).
鈥� The correct DOI for the paper by Hasse Walum and colleagues on vasopressin and pair-bonding is (6 September, p 16).
Risk rank
Michael Bond encourages us to assess risk numerically 30 August, p 34. But how are we to “weigh up all the facts”? Bond says that after the 9/11 terrorist attacks it was “irrational” for people to drive rather than to fly. But the rationale is based on the fact that no further such attacks actually occurred, which was not knowable at the time.
We did know that flights had been grounded, which I “weighed” as suggesting that the government thought that the risk of another incident was significant. I weighed the resumption of flights as suggesting that the government considered the overall risk of flying to be reasonable compared with driving, not that it was back to a very low level.
It seemed to me that the risks of flying were much less quantifiable than those of driving. With no “facts” to suggest that flying was once again significantly safer than driving, I think that travellers’ weighing of risk would depend on the extent to which they trusted the government’s judgement 鈥� and they had just had some evidence to suggest it wasn’t wholly reliable.
I continued to fly as normal, but I would not wish to criticise those who made a different call. It seems quite reasonable to choose a known and tolerable risk (driving) over an unquantifiable and potentially high risk (flying).
Some of the article’s other recommendations are very important, so it was a shame to confuse the issue. Statistics should be used whenever they are meaningful, but in unexpected new situations such as 11 September 2001 it is surely reasonable to supplement out-dated statistics with other heuristics. Maybe the concept of “weighing the facts” merits a fuller discussion for cases in which one encounters such novelty.
From David Bailey
Michael Bond possibly overestimates people’s irrational responses to various threats. I flew to the US in October 2001, and thought about my emotional reactions during the usual long waits. People don’t just fear death, they also fear being trapped for a long period of time in a dangerous or inevitably fatal situation. It is this, I think that made many Americans wary of flying after 9/11. Was that so irrational?
People may also fear the prospect of committing to a journey, only to find that some political (or other) change has severely increased the risk. I, for one, do not wish to fly to the US until George W. Bush is out of office 鈥� thus reducing (I hope) the risk of a surprise attack on Iran, with the nearly inevitable terrorist (that is, low-budget military) response.
I must also say that I expected the aircraft and US airports to be pleasantly half-empty, but the crowds seemed as bad as normal 鈥� so the 9/11 effect was obviously not that great!
While I am sure that a greater public understanding of statistics would be useful, I think it is worth realising that judgments made on the basis of probability of death alone can be naive.
Hyde, Cheshire, UK
Risk rank
In the table of transport risk accompanying Michael Bond’s article on risk perception (30 August, p 34), a more meaningful statistic than passenger deaths per distance travelled would be deaths per passenger journey: I am interested in my chance of arriving safely, no matter how far I have travelled. And for aviation, most deaths occur at or near take-off and landing, rather than in the long distances travelled in flight.
Looking for data, I found instead another interesting comparison. According to a 2003 report by the European Transport Safety Council () there are 0.035 passenger deaths per 100 million kilometres of air travel but 16 per 100 million travel hours.
From Roger Pither
We generally use air travel for very long distances, and walking for very short ones. According to the figures for the relative risk of transportation-related death in the US in 2000 at you are far more likely to die in a car than walking, and the “average person’s” lifetime risk of dying during air travel is greater than that for bicycle, train or bus.
Ottawa, Ontario, Canada
From Tony Williams
Michael Bond is being unkind in criticising the move away from air travel in the US immediately following the 9/11 terrorist attacks. The use of commercial airliners as suicide weapons was entirely new 鈥� there was no evidential basis for calculating the risk that it might happen again. For all the US public knew, there might have been many more terrorists awaiting their chance.
The preference for travelling by car rather than by air is also influenced by two important psychological factors. If people are unlucky enough to be involved in a car crash, they are far more likely to walk away from it than from a crashed aeroplane. Another factor, probably even stronger, is that car drivers feel they have some control over events and that they can take action to avoid accidents. In an airliner in trouble, everyone except the pilot is helpless.
Whaley Bridge, Derbyshire, UK
From Ron Holley
Personal perceptions are more likely to be based on the nature of individual journeys. Every time you board an airliner you are surrendering your personal freedom to the airline, regardless of the length of the journey. Using your car, you feel in command of the situation. That too is a false perception, because air traffic control is intrinsically safer than venturing onto the highways 鈥� but we cannot easily overcome the feeling of helplessness.
But this all seems rather academic when there is seldom any choice between being a pedestrian, driving your car, taking the train or flying: the nature and length of the journey determines the solution.
Gosport, Hampshire, UK
From John Davnall
Michael Bond reports that US television coverage of homicide increased by 483 per cent between 1990 and 1998. During this period, US television may have provided an increasing choice of channels, including a greater number of 24-hour “rolling” news channels. This may account for much of the increase in coverage, but the viewer can only watch one channel at a time and so will have their TV-based perception of risk informed only by that exposure.
Stockport, Cheshire, UK
Life under several suns
Quoting work by Margaret Turnbill and Jill Tarter, Marcus Chown writes: “Then they looked for stars whose radiation level has not varied by more than 3 per cent over a period of at least 3 billion years, like the sun” (23 August, p 40).
What they must mean is that, during the 3 billion year period, no short term variability (pulsation, outburst and so on 鈥� with periods of a few months or years) of that order is likely to have occurred.
Stellar evolution calculations show that the sun has increased in luminosity by some 25 per cent during the last 3 billion years 鈥� i.e. since life appeared on our planet.
Its ongoing evolution will make our environment distinctly uncomfortable within the next billion years.
We owe our existence to the fact that our sun is not a “variable star”.
From C. E. Steuart Dewar
Would the inhabitant of a multi-star system ever even think that there might be life outside of their world?
We are fortunate to see night skies with thousands of suns (if we aren’t in a light-polluted city). We can well imagine that there might be intelligence out in the universe. But if we had two suns that left Earth eternally lit, would it even occur to us that there might be other suns, with other planets, and intelligent life?
This has interesting implications for the search for extraterrestial intelligence. In our own system, there might be life in the suspected under-ice seas of Europa, or perhaps some heat-resistant life form on Venus 鈥� but neither would likely think of life existing outside their environs either.
Perhaps the reason that we have not been contacted by alien intelligence is that the occurrence on the surface of a planet of a life form which can also see stars and therefore envision that life might exist on other worlds is rare indeed.
Morganton, Georgia, US
Placebo envy
Michael Brooks is amazed at the power of the placebo effect and even found a clinical trial where a placebo performed better than a known effective drug (23 August, p 36). He should not have been so surprised.
Attached to every clinical trial are two types of errors: type I error, which occurs when an effect is found where none actually exists; and type II error, which occurs when the positive effect of a drug is missed.
These errors arise because of the considerable variability amongst humans in their responses to drugs and to pain and illness. They occur regardless of any placebo effect.
In designing clinical trials, an allowance is often made for 5 per cent type I error 鈥� for every 20 trials carried out, one is expected to produce a false positive. The power of the trial to detect an effective drug depends on its sample size size (the larger the better) and the variability between patients (the smaller the better).
The double-blind placebo-controlled trial provides important evidence but is not the last word on its own. Many such trials need to be carried out. I suggest that the placebo performing better than a standard drug was a false positive. However, a placebo has one great advantage over a drug 鈥� no side effects!
From Mary Mulvihill
If the efficacy of some drugs depends so strongly on the placebo effect that they work only if a patient knows they are receiving the drug, as seems to be the case with diazepam, for example, then surely this has implications for drug discovery research. Should researchers take the placebo effect into account when looking for candidate drugs and drug targets? And, given the differences between men and women when it comes to pain relief (19 July, p 28), should we be doing this separately for men and women?
Brooks suggests that the “conditioning effect” of a placebo “could be exploited to reduce doses of painkilling drugs with potentially dangerous side effects”. But this risks triggering the nocebo effect 鈥� the converse of the placebo effect, in which patients experience adverse side effects even when given only a sugar pill.
Finally, could there be any connection between the placebo effect (which seems to entail some form of belief), and religion? Religious people might conceivably exhibit a stronger placebo effect. If so, clinical trials might have to become even more complicated, to take account of whether or not participants are “believers”.
Dublin, Ireland
Hidden code-breakers
Public-key cryptography was not first invented by Whitfield Diffie and Martin Hellman at Stanford University as your interviewee Jacques Stern, and many others, believe (16 August, p 42). The late James Ellis of the UK Government Communications Headquarters (GCHQ), a friend and colleague, told me in 1995 that in 1969, bound to secrecy and working alone, he developed an “existence theorem” for encipherment using separate public and private keys. For three years GCHQ struggled to find the one-way function needed, then Clifford Cocks, a Cambridge mathematician, joined and together they solved it.
The Stanford team reached the same point in 1975. By the early 1980s the US National Security Agency knew of James’s work and Diffie came to meet him at GCHQ.
Sadly the political climate of the time meant that the idea was never patented in the UK. The matter is well covered in Simon Singh’s The Code Book (Fourth Estate, 2000). James died just one month before Cocks was allowed to break the long silence by giving a talk at GCHQ.
The green stuff
I read with dismay the claim that phytoplankton could be the fuel of the future (16 August, p 34). My career started in the early 1960s, researching the prospect of cultivating plankton using warm water and carbon dioxide discharged by Poole power station. The project fizzled out for lack of support.
Producing phytoplankton to feed bivalve molluscs is now vital to my business. It is possible to sustain production of around 100 grams per cubic metre per day in sterile, sealed containers, using a cocktail of nutrients ranging from large amounts of nitrogen to traces of B vitamins. If I could sustain cultures like this in open tanks, the aquaculture world, including China, would beat a path to my door to see how I do it.
Self-organisation
Your coverline “Hands off! Why things work better if you just let go,” and its teaser on the contents page 鈥� “Sometimes life runs more smoothly when you relinquish control” 鈥� misrepresent what Mark Buchanan’s article establishes (9 August, p 28). He compares attempts at centralised planning and control with local, decentralised or self-organised control, not with no control: the traffic lights he described worked more effectively when they shared traffic information with neighbouring sets of lights.
We have learned that centralised planning, with its five-year plans, cannot begin to cope with the variety of conditions on the ground. Also, no control 鈥� i.e. the “free market” 鈥� is a major cause of our current environmental and financial crises, and applying central regulation or control to this is not likely to help. A more promising alternative is a locally cooperative and self-organising market based upon principles such as . Your headline should really have read: “Local self-organisation does better than central planning and control”.
Irrational? Me?
I can hear the sound of babies being thrown out with bath water in Pete Lunn’s claim that “people don’t behave the way economic theory predicts” (30 August, p 16). It is true that certain quirks of economic behaviour in specific examples do not follow the predictions of more generalised macroeconomic models, but it should come as no surprise that aspects of economics that are most affected by psychology are better explained by including, yes, psychology. This does not mean that at the higher macroeconomic scale, current economic principles do not apply. It is normal in all fields of research to refer, at the boundaries of predictable behaviour, to neighbouring specialities.
Lunn says “economics students are still taught to start with the unquestioned assumption that people are rational”; yet two decades ago, before I passed my economics O-level aged 16, I was taught about “goods of ostentation”, whose demand curve is upside down.
From Elizabeth Barron
Pete Lunn describes a specific example of trust between individuals and then uses it to explain an aspect of how markets function in general. But consider what happens if you alter his example of cooperation for mutual benefit to: “Imagine a company awards you 拢10. You can keep it, or you can give some to another company. The first company will treble what you give to the second, and the second may or may not give you some back.” Would you be so trusting in this situation? Or if you replace “company” with “government”?
Inverness, UK