Probably likely
As a scientist and engineer, I was amazed to find that the patterns described in Rachel Courtland’s article on Benford’s law came as such a surprise (16 October, p 10). It is only natural that numbers that are randomly distributed on a logarithmic scale translate into this observed pattern.
Compare the spacing between 1 and 2 on a logarithmic scale to that between 8 and 9. Between 1 and 2 covers a factor 2 increase but between 8 and 9 there is an increase of less than 13 per cent. Most laws of nature have power law relationships that cover multiple orders of magnitude, and there are also fractal patterns naturally present. This means that measurements tend to spread more naturally across logarithmic scales, and could explain why this “curious law” crops up in nature so often.
From Philip Hanser
Rachel Courtland writes that “Benford’s law states that for many sets of numbers, the first or ‘leading’ digit of each number is not random”, which implies that Benford’s law isn’t a characterisation of a probabilistic phenomenon. What I believe she meant was that each of the first nine natural numbers does not have an equal chance of being the “leading” digit in a set of numbers.
That a phenomenon is capable of being characterised by a probability distribution doesn’t mean that it is not random, merely that we can have some precision in describing its randomness.
Newton Centre, Massachusetts, US
From Donald Windsor
Benford’s law could have its basis in an inherent property of integers. I noticed this while running experiments simulating the evolution of birds in the 1980s. My description of this property is based on the partition of integers and was published in the Journal of the American Society for Information Science and Technology ().
Norwich, New York, US
Robots on the road
Google’s CEO Eric Schmidt says that the desirability of cars that drive themselves is a no-brainer (16 October, p 19). I disagree.
These cars, which Google has unconscionably put on the roads of California, cannot plan adequately for the unplanned. They can be programmed for varying traffic laws, but not for the multitude of different behaviours of other road users. These can only be assessed through instantaneous judgements of probabilistic functions 鈥� in plain English, stereotyping 鈥� based on qualities like the type of car, and observation of the other driver’s appearance and driving style.
Though the occupants of these automated cars can take control if necessary, it is almost certain that once these “drivers” get used to most of the driving being done automatically they will be less aware and responsive than if they were permanently in control. The time it would take for the car’s sensors to notify the unaware drivers of a problem, and for the drivers then to direct their attention to it, could be fatally problematic.
How will the system determine whether the car should hit the dog that runs out, or risk swerving to avoid it? And what algorithm will decide whether you should hit one person to avoid the possibility of hitting several?
Nobel controversy
I was surprised and disappointed by your coverage of the award of a Nobel prize for IVF pioneer Robert Edwards (9 October, p 7). I felt that you gave too much prominence to the criticism, especially that of the Catholic church. I understand that it was and is a controversial issue, but to put the Catholic criticism as the headline and not Edwards’s achievement emphasises the wrong aspect of the story; it is the sort of thing I would expect of the Catholic weekly, The Tablet, and not a science weekly of note.
From Colm Culleton
Thank you for quoting the Vatican’s spokesman on bioethics in your article about Robert Edwards’s Nobel prize, who expressed his concerns over the deadly fate of many frozen IVF embryos. A fertilised human egg is a human being from the very beginning, unless and until science can tell us definitively that it is not.
If it is human and if it is destroyed, that constitutes the destruction of human life, which is a moral issue. The Vatican’s role is to critique morals, just as yours is to critique the natural sciences. Its spokesman was correct to denounce the destruction of human life.
Bagenalstown, Co. Carlow, Ireland
Better nature
You quote Michele Aresta, Director of Italy’s National Consortium on Catalysis, who suggests that humankind “can fly much better than birds”, and can therefore supersede photosynthesis easily (25 September, p 48). Comparing our attempts at flight with that of birds tells us that attempting to out-do nature at photosynthesis is going to be considerably more challenging than he thinks.
We can undoubtedly fly faster than birds but can we fly more efficiently, with greater precision and manoeuvrability for longer times and over greater distances? Has Aresta watched a humming bird feed on nectar, a sparrowhawk manoeuvre at speed around trees and shrubs, or swallows arriving in the UK after migrating thousands of miles across deserts, mountains, oceans and forests?
Double vision
Reading Jessica Griggs’s recent news story on visual illusions (4 September, p 14), I was reminded of a picture I painted as a student, some 50 years ago.
It started out as a picture of a man sleeping under one of those enormous hats in a typical “cartoon Mexican” pose: sitting on the ground almost completely covered by the hat, which takes up the top half of the picture. But when I returned to the room after a short break, I noticed that the lower half of the picture looked like a moustache with a pair of dark eyebrows above it.
So I completed it like that, with the possibility of it being seen either as a dark face under a reasonably sized hat or a small man sitting under a very large hat. By playing with the shapes and colours, it was relatively easy to create the illusion, despite it not being my original intention.
I entered the picture into a small exhibition, and it was the only work I ever sold. I never saw it again and would be most interested to know where it ended up.
From Peter Mitchell
The article on how the brain switches between two distinct interpretations of the same image prompted a quick experiment in my household.
I have identical twin boys. They are mirror twins 鈥� one is left-handed and one is right-handed. I asked each one in turn to describe what they saw when I showed them the image from the article.
The right-handed child saw the people under the arch but could not immediately see the skull. The left-handed child saw the opposite. Within a similar time frame the two boys began to see both images.
This is one of many examples of the twins doing something in the same way, but opposite to each other. Perhaps researchers may find this observation useful.
Ballymoney, County Antrim, UK
Silent soundtrack
My wife lacks the inner voice that most people have, just as David Dunthorn’s wife does (16 October, p 27). She does not experience any kind of inner dialogue, and when she reads she hears nothing.
She says that she knows what the words mean as soon as she sees them. She doesn’t have to recite them as if she were listening to an audio book. This reading method allows her to churn through books at an incredible rate, while still absorbing the detail. This phenomenon has prompted me to wonder how someone engages in abstract reasoning if they have never heard a spoken word.
Learning to see
I was surprised that David Robson should think it necessary to go back in time to test whether knowing a berry’s name might help someone find it more quickly (4 September, p 30). Modern bird watchers, botanists and other nature aficionados are all familiar with the way that one’s ability to identify species increases rapidly as one learns their names.
As someone who regularly leads and participates in nature tours with members of the general public, I am very used to hearing comments such as “I never knew there were all these plants in this area 鈥� I never even saw them before.” Being shown the species and told its name not only helps to fix it in one’s memory, but definitely increases one’s ability to see it in the first place.
Sweat and wine
It’s not only the Zulus in South Africa who treat fever by increasing body temperature (11 September, p 30). In the Piedmont region of Italy, the traditional treatment is to cover the patient in blankets and make them drink a full bottle of strong red wine 鈥� barolo for those who can afford it, but barbera may also suffice.
In my experience the treatment works for less serious cases.
From Peter Brooks
In my youth, medications such as paracetamol (acetaminophen) were not used to bring a fevered person’s temperature down, but to prevent it from rising dangerously high: it acted as a buffer, allowing the patient to “sweat it out” without the risk of an adverse event. At least, that was the information numerous doctors gave our family. Did they all have hold of the wrong end of the stick, or has the original purpose of antipyretics been lost?
Los Angeles, California, US
Esoteric physics
Is any other reader inexorably reminded of the medieval scholastics trying to calculate how many angels can dance on the head of a pin, when they read articles in New 杏吧原创 about cosmology and particle physics?
Rachel Courtland’s “Countdown to oblivion” 鈥� addressing a supposed paradox arising from a mathematical model of the multiverse 鈥� strikes me as the latest and most absurd example (2 October, p 6). A fudge factor introduced by mathematicians because they can’t think of any other way to solve their equations has real implications for the universe(s)? Give me a break. Did this fudge factor always affect the universe(s), or only after they thought it up?
For the record
鈥� In our article on endangered species (30 October, p 7) we mention the leopard magpie moth (Zerenopsis lepida, or Z. leopardina, depending on which lepidopterist we talked to). But any lepidopterist will tell you that it is not this species that we pictured, but a Millar’s tiger moth (Callioratis millari).