Time to P=NP
There are a few problems with the technique used by Samuel Arbesman and Rachel Courtland to predict when the mathematical problem of “P versus NP” will be solved (25 December 2010, p 24). Most obviously, it assumes the rate of mathematical progress has been constant, whereas there are vastly more working mathematicians today than there were even 100 years ago.
More fundamentally, to answer the question of when we should expect a solution to a 40-year-old problem, we should not take into account any problem resolved in less than 40 years. Instead, you could take problems posed between 1800 and 1970 that took more than 40 years to resolve. For the probability of a resolution of P versus NP in 2011, find the fraction resolved within a year of turning 40.
Rachel Courtland writes:
鈥� This method would indeed allow us to calculate the probability that P versus NP might be solved in 2011, but we were unable to implement it due to the paucity of data. Instead, we decided to create some perspective by supposing it will be solved this year and ranking it alongside other long-standing mathematical problems.
Positive presents
Our family and friends have been playing the secret Santa game for years. We do it for reasons exactly opposite to Graham Lawton’s premise that each person really wants to win by ending up with the best possible present (25 December 2010, p 58).
Everyone knows that if they don’t end up with the gift that particularly takes their fancy, then they could just buy one later for a few dollars. Hence the lessons of loss and non-attachment lose their sting, and promote an atmosphere of general hilarity around the thieving, horse-trading and open plotting.
Altruism always makes an appearance when someone stuck with an undesirable gift has it stolen from them just so that they can re-enter the game.
The purchase of a single cheap item takes the anguish out of gift selection and prevents ugly comparisons. Now we all look forward to present-giving at Christmas instead of dreading it.
Hangover chemistry
Roger Highfield writes in his myth-busting article on alcohol that “anyone… turning to hangover cures is going to be disappointed” (25 December 2010, p 53). However, there is hope for drinkers.
In an earlier edition of New 杏吧原创 (20 December 1997, p 46), Andy Coghlan described the biochemistry of ethanol metabolism and advocated the amino acid supplement N-acetyl-cysteine (NAC) as “a top tip for a scientific cure” for hangovers.
In a later article, Coghlan, with co-author Jens Thomas, described his own less-than-scientific research over four drunken weekends, where NAC once again proved effective (27 November 1999, p 34).
When alcohol is metabolised, a compound called acetaldehyde is formed, which is thought to be behind the unpleasant symptoms associated with hangovers. NAC has been shown to be an efficient acetaldehyde scavenger, especially when combined with vitamin C, which accounts for its reported booze-busting qualities.
From my own experience, 1 gram of NAC combined with a vitamin C tablet, before and after drinking alcohol, seems to work as a prophylactic. Any hangover symptoms present the following morning can be treated in the same way.
If the results of this treatment are simply down to my imagination, then I am happy to benefit from the placebo effect.
Happy headache pill
The observation by Linda Geddes that there is “growing evidence that cytokines associated with inflammation can cause depression” (15 January, p 30) got me wondering whether there might be a connection between inflammation, depression and a growing consumption of over-the-counter painkillers.
Are we seeing large-scale self-medication against depression with non-steroidal anti-inflammatory drugs (NSAIDs)? Maybe NSAIDs are being used to suppress inflammatory reactions to environmental factors that have triggered depression.
Innovative accounts
It is tempting to use the measure of patents per million people to compare countries’ levels of innovation 鈥� as did, for example, your Insider special on Switzerland (UK edition, 6 November 2010, p 46). But non-Swiss technology firms establish parent companies in Switzerland for tax reasons. These hold the company’s patents and charge royalty revenue to non-Swiss “subsidiaries”, minimising tax burdens in their home countries.
So Switzerland’s nice-looking statistics are explained by inventiveness, but not the technological kind.
Humans 1 鈥� Robots 0
Anil Ananthaswamy’s article about robotic astronomers (15 January, p 20) omitted to mention that the Palomar Transient Factory also uses human volunteers to analyse some of the data. The volunteers, of which I am one, are credited with having identified over 1200 supernovae in the past year.
Human volunteers are better than computers at abstract pattern recognition, necessary for analysing this type of data.
Alien invasion
Garry Hamilton’s article, “Aliens to the rescue” (15 January, p 34), rang bells for me here in the Lake District. For the past year, the local Alien and Invasive Species Eradication Officer has been trying to remove skunk cabbage (Lysichiton americanus) from the valley of the river Crake.
This North American wetland plant has colonised the river banks since it escaped from a garden upstream. The newcomer is claimed to threaten endangered species and sensitive habitats, but when challenged to provide evidence of ecological damage, its detractors tend to reply with assertion and hearsay.
In fact, the flowers of this plant are used by many species of insect, and its powerful root system helped to protect the river bank from erosion during recent floods.
The arrival of a new species cannot be rejected merely on the grounds that it is alien. After all, the Lake District was once covered by glaciers and ice fields; few of today’s species were present. The entire ecosystem has built itself up from nothing, and long may this process continue.
Chinese sewage
The Chinese plan to divert up to 45 cubic kilometres of water a year from the south of the country to the north, reported in Fred Pearce’s IBM-sponsored article (UK edition, 18 December 2010), prompts the question of what happens to that water after use in urban centres.
It is estimated that less than half of Chinese sewage is treated in any way. The extra water will surely cause an explosion of algal growth in the shallow Yellow Sea at the mouth of the Yellow river.
The editor writes:
鈥� The water will, in the short term at least, be replacing water that is currently pumped unsustainably from underground. It is unclear whether it will of itself cause an increase in sewage.
Grand-patricide
John Healey asks why people speak of the grandfather paradox, involving a person travelling back in time and killing a grandparent, rather than the mother or father paradox (18 December 2010, p 29). Surely it is to minimise the emotional baggage connected with the problem. Real-life cases of someone murdering their grandfather must be much rarer than patricide or matricide.
Reality tales
Melanie Keene’s article on the Victorian fashion for scientific fairy tales (25 December 2010, p 42) reminded me of an American theme park in the 1980s that promoted the notion that plants grow because little people living beneath the Earth’s crust push them upwards from their roots. As if the truth of how plants really grow weren’t wondrous enough.
I do think all our lives, whether child or adult, can be enriched by at least a spoonful of imaginative sugar, but learning the truth about how the natural world works is the best prescription for living in harmony with it.
Electric life
Having just read your excellent article about the electrical connections formed by specialised bacteria when they are placed under stress (18 December 2010, p 38), I was left wondering if anyone has suggested this as a possible mechanism for the evolution of multicellular life.
Kicking up a stink
As an owner of four pet skunks, three of which are “fully armed”, I must debunk your claims that skunk spray almost always causes vomiting (25 December 2010, p 63).
The closest description of the smell I can provide would be that it is similar to burning rubber. I have found that a quick spray of air freshener allows me to keep my last meal firmly down.
Left, right, left
Apparently the cultural association of height with virtue is borne out by experiments which show that positioning people higher up can make them more compassionate, helpful and virtuous (15 January, p 10).
So maybe we should now look to see whether actions related to the right-hand side of a person are associated with righteous and correct behaviour. We could also investigate whether those related to the left-hand side are associated with being left behind, left out or even something more sinister.
The results might help us decide once and for all whether to support right or left-wing political parties.
For the record
鈥� We tied ourselves in knots over Borromean rings (8 January, p 10). Their key property, as our diagram showed, is that if you remove any one of the rings from the linked set of three, the remaining two are unlinked. Contrary to what we said, none of the rings is threaded through any other.