Infinity's end
Amanda Gefter’s exploration of infinity, mathematics and physics (17 August, p 32) arouses my bewilderment that people believe mathematical constructs like infinity are realised in the world. Where theory predicts infinite density, I see a breakdown of the theory.
Mathematical concepts don’t need to be part of physical reality. I can conceive of always being able to add another pebble to a pile of pebbles while recognising that it is practically impossible to do so.
Removing infinity from a particular cosmological theory is interesting as a way to overcome the problems arising from it, but it does not follow that infinity or similar constructs should be removed from mathematics.
Canberra, ACT, Australia
Infinity's end
Infinity does not have to defy imagination as Gefter suggests. It is sometimes possible to see the beginning and the end of an infinity at the same time, as in the infinity of the number of numbers between 1 and 2.
Now let us ask how many minuscule “pieces” make up a length of 1 metre. The answer is 6.19 脳 1034 because that is how many Planck lengths (1.6 脳 10-35 metres) would fit in it. It is my understanding that anything smaller than that does not physically exist.
Infinity exists only in maths, not in the real world.
Sunbury-on-Thames, Middlesex, UK
Infinity's end
Gefter deals with two different things: on the one hand, classical concepts of number and geometry; and on the other, the reality that physicists attempt to explain. There may well be only a finite number of objects in the universe, but a mental construct, namely the mathematical concept of integers, allows an infinite sequence of integers. Likewise in geometry, we have the idealised concept of a circle.
More generally, any mathematical or theoretical physics explanation of physical reality is no more than a descriptive language that offers a portrayal of that universe’s features. Description and reality are not the same thing, any more than a portrayal is the same thing as the person portrayed.
Ripon, North Yorkshire, UK
Loony names
I agree with the views of my fellow Apollo 8 crew member William Anders on the naming of lunar landmarks (14 September, p 30). The International Astronomical Union (IAU) disregarded his suggestion, even though we discovered them on the far side of the moon.
On the near side of the moon, on the shore of the lunar plain known as the Sea of Tranquility, there is a small triangular mountain that had no name. I first observed it on Apollo 8 and called it , after my wife. It was used as the starting point for the descents of Apollo 10 and 11.
Although the IAU does not officially recognise the name, it is embedded in spaceflight history.
Lake Forest, Illinois, US
Vaccine bonus
Vaccines influence the immune system in more ways than Michael Brooks describes (17 August, p 38). They can give a useful degree of protection against certain cancers. Studies in several countries have demonstrated that the tuberculosis vaccine BCG, when given early in life, confers some protection against acute leukaemia .
There is also evidence that BCG or smallpox vaccination early in life reduces the subsequent risk of melanoma, an aggressive skin cancer, by around half. Moreover, vaccinated people who do develop melanoma have a better prognosis than their unvaccinated counterparts ().
Preliminary evidence indicates that yellow fever vaccine given to adults also gives some protection against melanoma ().
We need to do more studies to determine the full spectrum of health-enhancing effects of vaccination strategies.
London, UK
Stem cell worries
Peter Aldhous’s article discusses US restrictions on patients being given treatments based on their own stem cells (10 August, p 42), but it is worth noting that ordinary cells are touchy about being manipulated, and stem cells especially so. They are designed to match the environment in which they find themselves, and once removed from their home niche, they change fast.
If you are quick and careful, you may be able to deliver an effective stem-cell therapy to the donor. But we really don’t know how to be that quick and careful just yet.
Stem cells that proliferate in cell culture certainly don’t fit the quick and careful label: they could be many things by the time they are returned to the donor. In short, using cultured stem cells is biological Russian roulette.
It is easy to criticise the US Food and Drug Administration for regulating their use, especially if one takes a libertarian stance, but the FDA does play a useful role in inhibiting potential abuses of stem cells. The desperately ill will grasp at any straw, and untested treatments are simply straws. Whether they prove to be last straws, that’s the question.
Griesheim, Germany
Third twin
I read with interest Helen Pilcher’s report on different “identical” twins (31 August, p 44), and was surprised that she did not allude to the possibility that the twin born with two vaginas, two colons and a split spinal cord might have absorbed a third fetus.
Some form of fetal resorption is, according to Charles Boklage of East Carolina University in Greenville, North Carolina, not uncommon, and may occur in one in eight multifetus pregnancies.
Silver Spring, Maryland, US
Hot tip
The valiant efforts of the Syracuse University Lava Project researchers to understand and control lava flows (3 August, p 40) might benefit from a look at what happens inside an industrial smelter. Integrated steelworks produce lots of slag, a waste product of smelting ore. As the researchers know, slags are not so different from lava in their physical properties, and are very well studied.
My years as a geologist working in ferrous metallurgy gave me many blissful moments studying the behaviour of slags. Whether a slag solidifies as a dense rock or porous pumice determines its suitability for use as an aggregate for road construction. As for the need to scale up experimental lava pits, industrial plants could supply researchers with an order of magnitude more material if slag were used.
Medowie, New South Wales, Australia
Angry eyes
Martin Van Raay says he would like the computers he uses to be able to recognise anger (24 August, p 30). He may be interested to note that Google recently patented a system that observes .
Fans of sci-fi author Philip K. Dick, meanwhile, would be amused if computers could carry out Voight-Kampff tests, as featured in his story Do Androids Dream of Electric Sheep? In the tale, the test was a way to distinguish between androids and humans by observing changes in the eye brought on by emotions.
Glasgow, UK
The threat remains
Our world appears fairly benign, according to Nicholas Humphrey (3 August, p 28). He argues that “placebos at large”, constructed by big government and religion, help us overcome our overcautious nature, which evolved when big threats were more common.
However, I’d argue that for many people substantial threats do remain, even if our innate systems are not geared up to assess and respond to them in the same way as those ancient threats.
These include the consequences of global climate change, the potential for financial meltdowns, and wars involving weapons of mass destruction.
Chirn Park, Queensland, Australia
Dark life
Robert Adler reports that in the hunt for dark matter some researchers are considering the possible existence of dark atoms, dark chemistry and even dark stars and planets (31 August, p 36).
If so, there may equally well be dark aliens living ever unseen and undetectable alongside us, and who are puzzled by the 15 per cent or so of matter that is missing from their universe.
Carrick-on-Shannon, Leitrim, Ireland
Logged off
Facebook founder Mark Zuckerberg seems to think that there is a human right to internet connectivity (31 August, p 22). Here in rural Somerset, 11 miles from Bristol, we have had no access to cyberspace for two weeks because of a cabling fault.
Could I take the telecoms company to court for infringing my human rights?
Bishop Sutton, Somerset, UK
Silver lining
Your article on the legacy of acid rain points out that measures to combat the problem have led to rivers in the eastern US becoming too alkaline (31 August, p 7).
Although there may be a downside, such as the overgrowth of algae, might the alkalinity of these rivers not help ease the problem of ocean acidification?
Wellington, New Zealand
I will be free
I agree with reader Sadie Williams that “whether I am obeying laws of probability or causality, or both, I am still not free” (31 August, p 31). But I am complex enough for my behaviour to be ultimately unpredictable, which is good enough.
Peaslake, Surrey, UK
For the record
鈥� We added a dash too much salt to our feature on the use of methane hydrates as a fuel source (31 August, p 40); freshwater Lake Baikal does not contain sea life.
鈥� The demon worm Halicephalobus mephisto seen haunting our feature on deep life (27 April, p 36) was discovered by Gaetan Borgonie, not Tullis Onstott.