Do we live in a fractal?
Could the spatial expansion of the universe discussed by Amanda Gefter be explained if the distribution of galaxies were fractal (8 March, p 32)? That is, if the distribution were mathematically similar to the pattern found in “Cantor dust”, and the space interspersed within it were also fractal. This would imply that the number of its dimensions was not a whole one.
An apt description of the universe is that it resembles an expanding lump of dough on which “raisins” (stars and galaxies) grow more distant as the dough expands. If space is fractal, then its size increase should be non-uniform, because fractals scale upwards non-uniformly in comparison to normal geometrical expansion. The apparent rate at which galaxies move apart in space should similarly increase non-uniformly.
I wonder how this notion would affect our interpretation of the universe’s increasing velocity of expansion.
The editor writes:
鈥� David Wiltshire’s model, which we reported, is in fact consistent with a fractal galaxy distribution. We have also reported the search for evidence of space being fractal (9 March 2007, p 30).
How error takes flight
Charles Nightingale proposes a worldwide register of studies so negative results can be fully taken into account (8 March, p 20). I am not sure this would help.
Especially in my old field of experimental psychology, as soon as Bloobs and Carfoops report an interesting result, hundreds of young postgraduates searching for a decent and interesting thesis topic will launch studies on the supposed effect. If it is statistically elusive, negative results will probably be put down to poor experimental technique 鈥� and consigned to the waste-paper basket. The one or two that appear to confirm it will be registered and published with the respectable name of the supervisor as co-author.
Thus the “Bloobs and Carfoops effect” enters the annals of science, while those who have not found it are likely to remain very silent.
CO<SUB>2</SUB> is not the only gas
While I applaud your call for more rapid action from governments to reduce global emissions of greenhouse gases (1 March, p 5), you understated the urgency of the message by muddling the units used for greenhouse gas concentrations (p 14).
Jim Giles’s report says that to limit temperature increase to 2 掳C, “carbon dioxide concentrations in the atmosphere must stabilise at about 450 parts per million”. What it doesn’t say is that most modelling of the climatic effects of greenhouse gases uses the unit CO2eq: that is, the concentration of CO2 that would have the same effect as the sum of all greenhouse gases in the system.
This number is about 10 per cent higher than the concentration of CO2 alone, which as the article correctly states now stands at about 380 ppm. That means the current CO2eq is about 420 ppm.
It is calculations based on this composite unit which show that 450 ppm CO2eq is the highest concentration of greenhouse gases that leaves us a reasonable chance of limiting global warming to 2掳 C. If present trends continue, this threshold will be passed within five years. To assume that the threshold is 450 ppm of actual CO2 and not CO2eq overstates the time available to us to begin abatement by at least a decade.
Still unpredictable
Quantum mechanics may well rest on an underlying determinism, as Mark Buchanan suggests (22 March, p 28), but this does not imply that “predicting the future would be as simple as knowing the fundamental quantum rules and current conditions in enough detail”.
If the uncertainty of quantum mechanics is a consequence of a deterministic dynamic, then that dynamic must be chaotic. So, as in any chaotic system, the slightest inaccuracy would make it unpredictable in any practical sense. This does not imply that such a theory cannot be tested; just that its “predictions” must be more subtle than simply forecasting future behaviour.
Physicists often cite Bell’s theorem, which states that “No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics,” as proved. But this claims more than Bell delivers: his argument has several loopholes.
It involves hypothetical issues about what would have happened had an experiment been performed again under different conditions; it assumes that various mathematical averages exist and are unique; and it imposes strong restrictions on how the hidden variables behave.
In a paper published in 1995, Tim Palmer showed that deterministic but chaotic dynamics can model quantum phenomena without contradicting Bell’s theorem (). Whether such underlying deterministic dynamics can add some predictive element to the existing formulation of quantum mechanics is unclear, but we won’t find out by ignoring that possibility on spurious grounds.
Mathematically, the main circumstances in which probabilities can be derived from deeper assumptions, rather than simply assumed, is as “invariant measures” 鈥� averages that respect the dynamic behaviour 鈥� for a deterministic but chaotic system. It would be surprising if quantum theory did not possess an underlying determinism: in its absence, the system would not “know” what the probability of doing something ought to be.
Jaw-jaw, not war-war
Michael Brooks sensibly advises scientists to accept donations from groups such as the John Templeton Foundation and make good use of the money for science (15 March, p 20). I can’t help wondering why the Templeton prize is singled out, when adverts in New 杏吧原创 regularly offer money to scientists for working on nuclear weapons and other weapons of mass destruction, pesticides, and so on. Encouraging philosophers, scientists and religious people to communicate seems benign in comparison.
Back to the A-bomb
The problems currently being experienced by the Trident nuclear warhead programme (8 March, p 15) provide an excellent opportunity for a step towards eventual nuclear disarmament.
Instead of trying to make them operate as thermonuclear or hydrogen bombs, why not limit them to less-destructive fission or atom bombs only? The ability to destroy any target to the extent that Hiroshima and Nagasaki were destroyed ought to be more than enough.
Catholics fighting pain
It is outrageous for Carlo Bernardini to say that Catholics are averse to pain treatment for terminally ill patients (1 March, p 48). I am not a Catholic, but I worked for years with Catholic colleagues who have been in the forefront of pain control for cancer patients and others.
And while Bernardini is critical of “indoctrination” of children by Catholics, he seems unable to make the connection between his beliefs and those of his father who “greatly despised priests”.
Meanwhile, Lawrence Krauss pokes fun at the “intelligent design” crew 鈥� I am not one 鈥� as incapable of following his views on the long-term survival of life (p 53). Who says they can’t?
Creationism in decline
Contrary to the fears of many, including Michael Zimmerman (2 February, p 16), creationism is not gaining popularity in western democracies. Anyone tempted to spread claims that its popularity is rising would be wise to check the numbers.
The Gallup polling organisation has been asking a consistent set of questions for decades. Since the 1980s in the US the fundamentalist opinion that Adam and Eve were created a few thousand years before the pyramids has held fairly steady at between 43 and 47 per cent, with the lowest value occurring in 2007. The number believing in human evolution under the guidance of God has stayed between 35 and 40 per cent.
The number agreeing with the scientific consensus that evolution occurred without a god has risen from 9 or 11 per cent at the end of the 20th century to a high of 14 per cent in 2007.
In that time those who believe in human evolution, with or without the assistance of God, have twice edged into the majority.
Remarkably, the number taking the Bible literally has steadily sunk from about 40 per cent in the 1970s 鈥� nearly matching those who then favoured the Genesis story 鈥� to between a third and a quarter. So a large portion of those who now tell pollsters they believe in Adam and Eve no longer believe the Bible to be absolutely true.
The struggle between creationism and evolution is not a great ideological battle in which the most persuasive side wins the public over. In the online Journal of Religion and Society that levels of belief in evolution in first-world nations depend, logically enough, on the level of belief in God, and that rising levels of atheism and agnosticism keep creationist opinion at low levels (1 September 2007, p 32).
Fossil help
Donald Prothero concludes his discussion of the numerous transitional fossils: “Creationists simply have no answer to such irrefutable evidence” (1 March, p 35). Oh, but they think they do!
In the course of a long online debate I was repeatedly challenged to demonstrate transitions within a species. The examples I provided were dismissed as a series of steps up to modern whales, but with no progression within the species itself to the next one. What we require is a photo display of actual fossils showing the most complete progression available of one species into a new one.
On the telepathophone
You report that the Ambient Corporation is developing a device to convert thought into words through the use of sensors (8 March, p 23).
The obvious next step is to transmit this signal to a similar device worn by someone else, which would send it to their brain as a thought message.
T-mail, perhaps?
Musical discrimination
Recent issues have underlined how much information our brains have to handle when listening to music (23 February, p 34) and how much our perception depends on filtering (1 March, p 44). This may explain some puzzling features of deafness.
I have been deaf (“moderate” tending towards “severe”) all my life, and have used hearing aids since I was 17 (I am now 75). All this time I have enjoyed music and I sing in a choral society, but I find it almost impossible when listening to distinguish lines other than the melody.
When listening to a symphony orchestra, for example, it is the overall body of sound that I enjoy. I can appreciate a quartet more, or a soloist with accompaniment 鈥� so long as the accompaniment is not too loud.
The articles referred to prompt me to suggest that the brain may have discarded the process for distinguishing the parts, in order to cope with the extra demands imposed by deafness. This would explain why simply increasing the volume of sound, even with binaural hearing aids, does not improve matters. The same is true of the familiar problem for deaf people of trying to follow conversation in a room where there are many competing sounds.
The majority, for whom the ability to “distinguish the parts” is second nature, may find it almost impossible to realise the difficulty faced by the deaf. The Royal National Institute for Deaf People is currently campaigning on the issue of music in the background to speech on television. Producers appear quite unable to appreciate that this can completely obliterate intelligibility for many people.
Conversely, we deaf people find it very hard to comprehend that fully hearing people can easily pick out speech (or individual parts in music) against a background of other sound, when this is a brain process that we completely lack.
Seeds of hunger
Your timely commentary on hunger neglected to mention the fact that the rapid spread of wheat rust reflects the way that plant breeding to create successful “green revolution” crops has narrowed their genetic base (15 March, p 5 and report, p 14). Nor did you mention that much public crop-breeding science has now been privatised. Poor farmers have become deeply dependent on manufactured seeds, and vulnerable to their weaknesses.
We need crop science to pay more attention to resilience, and to serve public interests before private ones. The question is, how to make that happen when there is little profit in selling seeds to the destitute.
Forestall not forecast
What a horrific concept conflict forecasting is (15 March, p 26). It is surely obvious that unstable societies in which violence is likely are a result of deprivation, unemployment, hunger, lack of opportunity, insecurity and a visible gap between the rich and the poor.
Detecting the places where violence is most likely to occur may bring protection to the better-off, and add security for those who already live more secure lives. It will do nothing for those who already live in terrible hardship.
What is needed instead is effort dedicated to the task of better sharing the world’s resources, so that there are no longer vast numbers of deprived people who can be recruited to violent causes. Rather than trying to forecast the sites of social instability, so that forces can be moved in to control desperate people and those that use them for their own ends, we need to work to remove the causes of social instability.