Schoolkid explosions
I was amused to read of Michael Frayn’s unpromising starting materials 鈥� chalk and elderberries 鈥� for making explosives at the age of 7 (23 September, p 50). I recall similar researches on my own part at a similar age. I, at least, had paraffin as an available ingredient, but I, too, failed to make anything go bang.
Then I thought a little more about it. Elderberries are pretty acid, especially before they are ripe. Maybe if I had ground some chalk and added plenty of crushed elderberries, and sealed the jar…though please don’t try this at home, kids.
For the record
鈥� Due to an editing error, our article about snake venom (30 September, p 51) stated that it is possible to receive a deadly bite from garter snakes, American racers and radiated rat snakes, all of which are kept as pets. This is not true. Even if you put your hand into those snakes’ mouths, you would not get a deadly bite.
鈥� In the feature “Never say always” (23 September, p 30) we mistakenly obeyed the “i before e” rule and misspelled the name of philosopher Charles Peirce.
Understanding mathematical proofs
In his article on mathematical proofs, Marcus du Sautoy raises the issue of the acceptability to mathematicians of computer-assisted proofs: “the possibility remains that a glitch is hiding somewhere in the mass of computer code that could kill the proof” (26 August, p 41). The correctness of the proof is the issue that is usually raised when custom-built programs are used to generate parts of proofs that would otherwise be beyond human capacity. However, I don’t think that this is the only, or even the main, issue. The ability of humans to understand computer-generated proof steps is, in my opinion, far more important. Mathematicians want to know not only that a theorem is true, but also why it is true; they want to mine the proof for new methods that they can add to their own arsenal.
To address the negative reception to his computer-assisted proof of the Kepler conjecture, Thomas Hales has recruited the assistance of the automatic theorem proving community (to find it, look up “Flyspeck” on the web). By generating proof steps only via a small core of logical rule applications, automatic theorem provers provide a high degree of assurance in the correctness of their proofs. Hales’s Flyspeck project is making steady progress. It will be interesting to see how well its computer-generated proof is received by the mathematical community. Despite its almost certain correctness, it will still be huge, making human understandability just as daunting a challenge.
Du Sautoy is wrong when he claims that mathematicians are used to 100 per cent certainty. At a 2004 Royal Society meeting on the nature of mathematical proof, Michael Aschbacher, an expert on the classification of finite, simple groups, claimed that the probability of an error in the proof of this classification was 1. This certainty of error has not persuaded Aschbacher, nor any of his colleagues, to abandon this proof. In fact, a tolerance of minor or correctable errors is normal in mathematics. This also suggests that it is not the correctness of computer proofs that is the main obstacle to their acceptability.
A simple corrollary to the undecidability of provability suggests that there is no limit to the size of proof that mathematicians must cope with, even if they limit themselves to short, simple theorems. So either large areas of mathematics must be abandoned as beyond the scope of humans, or computers must be enlisted to assist with the generation of huge proofs. This puts a premium on enlisting computer science techniques for presenting such proofs in a way that humans can explore them and achieve some level of understanding.
Bump up the fibre
In my view, the conclusion reported in your article on food fads that “you might as well not bother” to increase fibre intake to reduce your risk of colon cancer remains premature until investigators have studied the effects of long-term fibre consumption from natural foods, in amounts approximating to 100 grams per day (23 September, p 42). This is the amount that human physiology has arguably adapted to through millions of years of natural selection among the hominin ancestors of humans.
Biofuel fallacies
The article about biofuels unfortunately repeated uncritically some naive ideas suggesting that the interests of the global poor are served by cheap food produced on agricultural land in rich countries (23 September, p 36). The reverse is often the case, as potential exports by Third World farmers 鈥� who constitute most of the world’s poor 鈥� are blocked, and even their domestic markets are taken over. The Oxfam campaign to “make trade fair” focused on this issue.
The Doha round of world trade talks has recently collapsed following the rejection by Europe and the US of developing countries’ demands that they stop subsidising and protecting their farmers. If rich countries were to shift their agricultural support and production from food to biofuels, we might see reduced dependency on fossil fuels, new markets for developing countries, continued support for farming communities and a new growth of world trade.
How effective this would be in limiting greenhouse emissions is a separate question.
The planet has only a limited carrying capacity, and land has an aesthetic and practical value for the human population and the ecosystem that far exceeds its ability to produce energy from crops or wind farms. Before we go barrelling down the biofuels route, there needs to be a sustained and creative effort at reducing the energy intensity of every aspect of our lives. Someone has to convince me why my local heathland should be replanted with switchgrass to fuel the school run or the weekend city break.
Llangollen, Denbighshire, UK
Your article is misleading about ethanol energy efficiency calculations. As two thorough, independent metastudies conclude, the research by David Pimentel that the article cites is in the minority. Pimentel’s is the only one of six major research groups to suggest that corn ethanol requires more energy to produce than it provides.
The links to the metastudies can be found at and .
Taken back to basics, biofuels are merely a means of bottling solar energy. This energy can be collected directly, or via the wind, from areas that provide minimal economic returns 鈥� certainly deserts, and possibly tidal estuaries, hilltops and, ultimately, Earth orbit.
Windmills might, to some people, be something of an eyesore but they sure beat the pollution-belching stacks of even the best coal-fired power stations. Developing solar in all its forms is at present the only potentially viable way to solve the energy problem for all humanity.
I wish to take issue with a point made with respect to oil palm plantations in Indonesia and Malaysia. It is not the extension of these plantations that is, or has been, the cause of the destruction of large areas of rainforest. These were destroyed, and still are being destroyed, by logging for timber for sale mainly outside these countries, much of it still being done illegally. The great majority of plantations are created by planters on land that has been logged out beforehand.
Heavily logged forest left unattended will usually degenerate into scrub with some short-lived light-demanding trees whose seeds have been blown in from elsewhere. Fires in the scrub will reduce the whole lot to sheets of Lallang (Imperata cylindrica) over a period of a few years. The soil will degenerate and erosion may set in as a result, along with flooding during heavy rains.
In such circumstances, the planting of oil palms for biofuel and other “permanent crops”, including reafforestation with economically viable non-native species, with the provision of beneficial covers, usually legumes, can prevent the total destruction of the land and much reduce the effects of flash flooding. The plantings should be designed to minimise erosion and by providing good access facilitate disease control, fire control and the economic benefits of income and employment for the local populations. This is what has been going on in many parts of Malaysia and Indonesia and is, in my opinion, something to be encouraged rather than condemned.
Rudgwick, West Sussex, UK
Biofuels and the other renewables cannot replace fossil fuels because renewable energy budgets are so unfavourable. Mechanical devices converting wind, water or sunlight to electricity are currently constructed courtesy of cheap fossil fuel. Reproducing and servicing them using only the electricity they produce would leave little if any surplus energy for public supply. Most biofuel crops need huge energy inputs in the form of fuel and fertiliser every year.
Wood was the main biofuel before 1750. Unfortunately, it cannot energise a world population of many billions. If our descendants want to enjoy a good quality of life sustained by forest industries, they will have to number less than about 200 million.
There was no mention of biofuel from algae in your biofuels article. While it is not yet a major source, it appears quite promising, especially for sewage treatment, fish farming, smokestack exhaust remediation and other synergistic applications.
Fall City, Washington, US
We waste a lot of sewage by letting it run out to sea. It would be a perfectly good fertiliser, except for the fact that people don’t want to eat food nourished from this source. Why not use it to fertilise crops for biofuel?.
Chatswood, New South Wales, Australia
Mutable laws
I was fascinated by Lee Smolin’s article on the mutability of the laws of nature (23 September, p 31). He says that the question that keeps him awake nowadays is: “Is there a way to represent the laws of physics mathematically that retains the notions of the present moment and the continual unfolding of time?” I would suggest that cellular automata seem the natural choice.
A cellular automaton is a model consisting of an infinite grid of cells each of which can adopt more than one discrete state: for example, either black or white. Simple rules dictate the state of each cell at a given instant, based on the states that it and its neighbours were in an instant earlier. While this sounds simple enough, cellular automata are capable of producing enormously complex patterns. Starting with the system as it is currently configured (“now”), you can follow it forwards through time. You can’t, however, go backwards 鈥� or at least not without guessing and ambiguity.
In this sense, the one-way nature of the “arrow of time” is mirrored in the behaviour of cellular automata. They make their own contingent laws that are consequences of the way the system has evolved, rather than being written into the machinery of the automaton itself. Even such a simple automaton as John Conway’s Game of Life (21 June 2003, p 32) displays this kind of behaviour, it seems to me.
It seems very natural to think that the underlying nature of the universe could be a cellular automaton, and that laws such as Newtonian physics, relativity and the standard model are higher-level descriptions of typical behaviour in that automaton.
Smolin’s evolutionary perspective on natural laws seems like good physics. It even includes some refreshing “don’t knows”. But he skates over an important issue. From Newton’s laws, it is not possible to predict an object’s movement indefinitely into the past or future. Doing so would require us to specify the initial conditions with infinite precision. Weather forecasting is an obvious counter-example, in which imprecise initial conditions limit how far ahead a forecast can be accurate.
Changing the past
Patrick Barry’s article describes John Cramer’s proposed experiment to delay one of two entangled particles by sending it on a longer journey than its twin, then forcing the delayed particle to choose wave or particle form in order to find out if the choice forced upon it controls the form of the twin particle, detected earlier (30 September, p 36). If you think this through, it turns out that either the delayed particle has the same form as its partner, in which case you cannot say that the past has not controlled the future, or the delayed one has a different form, in which case you cannot say that the future has controlled the past.
The proposed experiment has even farther-reaching implications than described. If it shows a retrocausal effect, it will also show that quantum entanglement only affects the photons and not the whole experiment.
My prediction is that there will be no measured retrocausal effect because the whole experiment is in quantum superposition. This means that changing the movable detector changes the state of the experiment, so the photon arriving at the other detector matches the current measurement, not the measurement that was taking place when the photon beam was split.
Charcoal sinks
Burying carbon dioxide is being promoted by some sections of the coal-fired power industry as the solution to climate change. Aside from the massive technical hurdles to be overcome, one of the problems with such techniques is the limited availability of suitable geological structures in which to store the enormous quantities of CO2 we produce each year. There is also the risk that the pressurised gas will leak at some point in the future.
Production and burial of charcoal as part of a biofuel cycle, by contrast, allows carbon to be permanently removed from the atmosphere and stored in a relatively stable form. The technology is simple and available, and the process could be implemented immediately. Charcoal is 85 to 98 per cent carbon, and 4 kilograms of wood produces around 1 kilogram of charcoal. Other useful products are obtained, some of which, such as methanol, can be used as fuels. The charcoal can easily be compressed and buried in the voluminous holes left by centuries of coal mining. Combined with coppicing, suitable land could be turned into effective and permanent carbon sinks.
Suicide robots
I refer to your article on military robots (23 September, p 28). Is it just me, or can anyone think of an easier way to get a munition into a US base than by attaching it to a robot with an autonomous “return home” function?
So, military robots might be developed by the Pentagon with a capability for speech, face and gesture recognition. Will these be based only on the characteristics of people who might be found in a Midwestern shopping mall, or more broadly? If the former, what will such a robot make of the Greek negative of the head nodded upwards, the Indian head waggle to indicate a reluctance to say no, or an Indonesian with eyes downcast in deference to authority?
Genius unfulfilled
The main thing that your report on how to be a genius missed was the other, unsuccessful side of the coin (16 September, p 40). While the genius-level achievers mentioned in the feature all had the work ethic, the inspiring tutor and so on, we didn’t see how many others had the same opportunities, worked just as hard and were equally inspired by their tutors, but failed to make the genius grade. Without knowing that, I don’t think the study says anything at all.
Also, there are clearly exceptions to these rules. There are differing accounts of Srinivasa Ramanujan’s rise to acknowledged mathematical genius, but the consensus seems to be that he came straight out of left field. I’m quite sure he worked hard, but he didn’t have access to great mathematicians or texts. Nevertheless at a young age he came up with extraordinary results from his own intuition.
In the realm of sport, I don’t believe for a second that the only difference between an internationally recognised soccer genius such as Zin茅dine Zidane and, for example, Steve Fletcher of relatively lowly AFC Bournemouth 鈥� a cult figure with a legendary work ethic and commitment to the cause 鈥� is that Zidane worked harder or had a better coach at a young age. Or, to take the example of Andre Agassi and Pete Sampras: in no way did the article provide any evidence that it was solely Sampras’s greater work rate that led to his greater haul of titles.
The assertion that geniuses are made not born assumes that talent and IQ are inherited while qualities of character 鈥� such as determination, persistence, diligence, ambition and the ability to concentrate for long periods 鈥� are not. It is quite likely that those qualities are also inherited to a significant extent and cannot be built upon by teachers or will power if not there in considerable measure to start with. These qualities may well be gifts just as much as musical ability or IQ.
Peterborough, Cambridgeshire, UK
The article on how to be a genius reminded me of Buckminster Fuller’s views on the subject (16 September, p 40). This is from his last book, Cosmography: “All children are born geniuses, but are swiftly ‘degeniused’ by their elders’ harsh or dull dismissal of the child’s intuitive sense of what could be relevant. Children spontaneously weigh all information from their immediate experience and try to relate it to other experiences of some time before. The incipient geniuses must somehow weather, year after year, the barrage of admonitions to ignore what they spontaneously think, instead only paying attention to what others think and are trying to teach. The human mind inherently seeks comprehension of the topological interrelationships of all experiences. Geniuses discover, speak out on, and mathematically formulate the generalized principles they find underlying all experience.”
Penngrove, California, US