P = NP?
Your article “The hardest problem” (4 June, p 36) made it sound as though proving P=NP would immediately allow us to solve many problems that have stumped computer science, whether timetabling, travelling salesman routes or sudokus. But actually it would only tell us that an algorithm to solve the problem quickly exists in each case.
So with P=NP proved, how hard would it be to find the algorithms? If we knew, for a given problem, that we could check a proposed algorithm was correct in polynomial time, then, by virtue of having proved P=NP, we would also know the algorithm could be found in polynomial time 鈥� but still wouldn’t know how to find it.
From Richard Willis
As a former computer designer, I know that many computer architectures and the languages used to program them have limitations. Despite this, I still believe that logic circuitry can be configured to solve unique problems, including sudoku, packing and routing. In their simplest form, these are problems of permutations and combinations, and knapsack packing, for example, can be solved by a normal PC using just a few lines of an Excel spreadsheet.
However, with , it may be advantageous to implement a solution that uses iterative methods.
Kingston upon Thames, Surrey, UK
鈥� The editor writes:
The examples given in the article were intentionally small so that they could be easily explained. General versions of these problems with a larger n are much more difficult: while you can solve simple versions using Excel, it is not going to be able to crack a travelling salesman problem with 85,900 nodes any time soon.
Man bites dog
When talking about the reasons for domesticating animals, why assume that dogs were not eaten by early humans (28 May, p 32)?
Dog meat is on the menu in many parts of the world. In fact, since domesticated dogs soon reach sexual maturity and reproduce rapidly, an early human family would have been overrun by a pack of carnivores if some puppies were not culled.
Suckling puppies, like suckling pigs, gain weight quickly and do not affect food resources until they are weaned. At that point, they begin to compete with humans for food 鈥� and we know what happens to suckling pigs.
I suspect that researchers will eventually find prehistoric puppy bones marked with signs of human consumption.
No silver lining
Did Erle C. Ellis have his rose-tinted spectacles on when he wrote “A world of our making” (11 June, p 26)? While his analysis of the evolution of the Anthropocene is coherent and informative, his acceptance of it, which is more political than scientific, is baffling.
Anyone who can write, “It is no longer Mother Nature who will care for us, but us who must care for her”, lacks knowledge of history and anthropology. Humanity’s record defines a belligerent, warlike and rapacious species. There is little sign of this destructive nature abating.
The chances of us creating “a better Anthropocene” are negligible, as we see the global economy hell-bent on burning every last vestige of fossil fuel. Unless we switch away from current business-as-usual trends, an atmospheric CO2 concentration in excess of 400 parts per million by volume appears to be a foregone conclusion. That spells climate disaster, not in the distant future, but for the generation now at school.
Reading minds
Duncan Graham-Rowe suggested that understanding how the brain turns thoughts into words will pave the way for machines that read minds (28 May, p 40).
However, much of thinking is imaginal. Einstein, for instance, said in a letter to mathematician Jacques Hadamard published in (Dover, 1965): “The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be ‘voluntarily’ reproduced and combined.”
So to “read” thoughts, one should study brain signals not only in Wernicke’s area, which is important in language, but also in the occipital lobe, the visual processing centre. However, deeper thought processes are essentially sensorimotor, relying on neural hierarchies distributed over the whole body. That means even looking in the occipital lobe will not reveal much of what is going on in our “mind”.
Not so heavy
In your article on the possibility of cellphones being carcinogenic (11 June, p 7), the researchers class using a phone for 30 minutes a day as heavy use. It may well have been in the late 1990s, but not any more; now that many people use only cellphones, a couple of hours a day isn’t unusual.
This sounds a bit like saying “smoking might be risky, but only for heavy users who have more than two cigarettes per day”.
Apocalypse thinking
Michael Shermer is spot on about the human brain’s pattern-seeking abilities, but not about the reasons why people engage in “apocalyptic thinking” (4 June, p 30). When we test imaginary scenarios in the theatre of the mind, as philosopher Karl Popper said, we are “letting our ideas die in our stead”.
Apocalyptic thinking is just another imaginary scenario on a larger scale than usual. It’s a thought experiment that cranks up the “what if?” anxiety that comes with the territory for volitional creatures like ourselves.
For thousands of years, people have sought to control the credulous through fearful imaginings. We now live in an age of rational, scientific scepticism, and each generation can emerge safer and wiser as successive doom scenarios are dispatched to “die in our stead”.
Low-fat worries
Reading that the hunger hormone ghrelin can be suppressed just by believing a low-calorie drink is a high-calorie treat (4 June, p 21) reinforces my concern that the opposite may happen, and that foods labelled as low fat may do more harm than good.
Consumers may believe such foods contain fewer calories than they do, so their ghrelin levels do not drop as much as they should, and they may eat more. As many low-fat foods seem to contain more sugar than their standard counterparts, this extra sugar can end up increasing fat deposits.
Could this help to explain why, despite there being so many low-fat products, the number of people classed as obese keeps rising?
The cost of money
With all the number-crunching on power-hungry computers needed to run the virtual money mentioned in your technology special (4 June, p 23) I have a question: just what is the carbon footprint of a bitcoin?
Decades ahead
In “When science gets it wrong” (21 May, p 28) you presented the excellent example of the diffraction limit in microscopy, surpassed in 1984 by the invention of the near-field scanning optical microscope.
At a conceptual level, this technique was described in publications by Edward H. Synge, who corresponded on the subject with Albert Einstein, . Synge will be celebrated in a symposium at Trinity College Dublin in 2012, as a late recognition of this achievement, among others, with which few are familiar.
Hot wheels
Martin Savage, in his Pythonesque theorising on the difference in train speeds in summer and winter (21 May, p 25), forgets that not only will the metal rails be longer in summer, but the metal wheels of the engine also get bigger to compensate. Therefore, provided the wheels are rotating at the same speed in summer as in winter, there will be no difference in journey time.
鈥� The editor writes:
…and this is the last stop for this surreal journey.
Wow!
I was impressed to see on the back cover advertisement (28 May) that Mercedes-Benz is celebrating “125! years of innovation”. Factorial 125, the number of years claimed, is more than 10200, so the company started to innovate unimaginable aeons before the big bang.
Canon fodder
One wonders what ecclesiastical diet is responsible for the proposal to use a “high-powered propane canon as a sound source” for mapping caves (4 June, p 26).
Got the T-shirt
On the same day as “The grand delusion” feature (14 May, p 35) appeared, I collected a T-shirt I had ordered.
Uncannily, its logo is: “What You Know, Ain’t So”.
Robo sock
I was puzzled at the idea of having to program a robot to recognise a pair of slippers or an article of clothing (21 May, p 18). Surely the answer is a washing label with instructions for the robot.