Letters: Green sheep
All the familiar breeds of sheep we see today are the product of artificial
selection by generations of farmers, and have probably been bred for white
wool because it will take up dye more easily and is therefore more valuable.
Carole Nadin Ipswich, Suffolk
Letters: Tracing Eve
We should like to reply to ‘The case against Eve’ (22 June), in part
because Allan Wilson, who we know was distressed by the article, was unable
to respond himself before he died in July.
Wolpoff and Thorne seriously misinterpret the evidence from mitochondrial
DNA. The suggestion of replacement of populations, ‘probably in an abrupt
and violent manner’, is theirs, not Wilson’s. Basically, they have confused
the migration and extinction of genes with those of populations.
There is no suggestion that Eve was the first, and at one time the only,
woman. The results of a computer simulation may clarify the picture, as
it did for us. Begin with a population of (say) 15 mothers and set the rules
so that each generation remains the same size and the average number of
daughters produced by each mother surviving to reproduce is one, so that
in each generation some mothers leave no daughters (but any number of sons).
Run the program, and in about 15 generations, the 15 current adult females
will trace their maternal lineage back to a single ancestress; the mitochondrial
DNA of the remaining 14 founder-mothers has become extinct. This happens
without any selection or ‘violent replacement’. It’s just the process of
chance. The time span extrapolated back to the ‘African Eve’ is about 6000
generations.
In general, it seems that in human societies, as in the closely related
chimpanzees, men stay at home, in alliance with their male kin, and import
wives. Thus the mitochondrial DNA moves, with the females, from community
to community, in ordinary marriage transactions.
In the meantime, nuclear DNA is contributed to the next generation by
men as well as women. If genes controlling skull shape are in nuclear DNA,
which seems probable, they may locally change frequency as a result of drift
or local environmental selection pressures. Thus we see no incompatibility
in the African origin of all human mitochondrial DNA and the local continuation
of distinctive bone structure. The existence of both certainly strengthens
the view of the human race as one single interbreeding population.
A challenge to ‘Eve’ must come from finding mitochondrial DNA somewhere
in the world which does not conform to the patterns of descent proposed
by Wilson’s lab. And the best of luck!
Thelma Rowell, Mary-Claire King University of California at Berkeley
Letters: Killer disease
Thank you for a lucid and timely piece on the molecular genetics of
motor neuron disease and other progressive neurological disorders (‘The
mystery of motor neuron disease’, 17 August).
However, the piece perpetuated a widely held myth, namely that motor
neuron disease is rare. The disease in fact has a much higher incidence
than either multiple sclerosis or muscular dystrophy. It is people living
with the disease who are rare, because for 80 per cent of patients, the
trajectory is so rapid as to kill them within two to three years. For comparison,
MND is the second biggest neurological killer after Parkinson’s disease;
it causes a higher rate of fatalities (1 in 500 of all deaths in the UK)
than fatal accidents at work, or drink-related deaths on the roads.
Peter Cardy Motor Neurone Disease Association Northampton
Letters: Secrets in court
Christopher Price raises some important issues in his item ‘Forensic
science needs open minds’ (Talking Point, 20 July). Indeed it does, but
so does the whole judicial system.
The ‘narrow and dangerous psychological environment which (some) forensic
scientists and pathologists inhabit’ is a predictable though not defensible
product of the adversarial system of justice. This system gives pride of
place to legal rules rather than to the facts.
In 1987 a substantial group of New Zealand forensic scientists proposed
mandatory pre-trial disclosure of all scientific evidence to interested
parties, and the right for pre-trial discussions between opposing experts.
Both proposals were opposed by judges, prosecutors, the police and law societies.
Reasons given were many and complex, but the main threads were rights to
secrecy for tactical purposes, and commercial rights of ownership of evidence.
Not one of these groups gave top priority to exposing and probing all of
the relevant scientific facts. Perhaps I should not be surprised that we
were forced to yield to this powerful coalition, but it is still a source
of shame to me that we did.
The Australian and New Zealand Forensic Science Society has nevertheless
continued the drive for an even-handed approach to gathering and using scientific
evidence. We have adopted a voluntary code of ethics which focuses on high
quality forensic science and full pre-trial disclosure of scientific evidence.
The aim is to make expert evidence as sound, complete and clear as possible.
G. J. Sutherland The Australian and New Zealand Forensic Science Society
Petone New Zealand
Letters: Green sheep
Perhaps there are green sheep, but no one has ever noticed them.
Adrian Bowyer University of Bath
Letters: Green sheep
It is evident that the lack of greenness amongst sheep has evolved as
a defence mechanism against ducks – sheep being permanently quadrupedal,
they are four times more likely than a flamingo to be bumped into by ducks.
If green sheep ever evolved, they would suffer substantially greater inconvenience
as they would be invisible against a background of duck-weed, thus provoking
even more collisions.
Tony Howard Norwich, Norfolk
Letters: Green sheep
Recently, Stephen Young showed in ‘How plants fight back’ (1 June) that
whereas lowlier aquatic animals like hydra do have green symbiotic algae,
there are no green herbivorous mammals or other terrestrial animals because
they have such a small surface area compared with that of plant-leaves that
they could never photosynthesise a square meal.
Michael Cotterill Freshwater, Isle of Wight
Letters: Green sheep
Sheep are green because they are not dyed-in-the-wool ecologists.
D. R. Bolton Manchester
Letters: Green sheep
Sheep are white so that they blend in with a natural limestone scenery
(eg the Yorkshire Dales). A white (or grey) sheep blends in perfectly with
a rocky background, whilst it looks more like a small rocky outcrop when
against a green background. Often a walker not used to the higher altitudes
and camouflaged sheep will stand on a ‘rock’ and find it moving quickly
from underneath him. The walker usually ends up feeling rather sheepish
after such an encounter.
Richard Marsden Leeds
Letters: Coral in danger
In discussing the precautionary approach in environmental issues, Paul
Johnston and Mark Simmonds (Talking Point, 3 August) emphasised the importance
of ‘an honest appraisal of a given situation’. Recent debate between overtly
‘green’ coral reef scientists and those who are much more cautious illustrates
this well. There is increasing evidence to link coral bleaching to abnormally
high sea temperatures but the available data still do not prove that bleaching
is caused by global warming. Of course it may be, and many reef scientists
are increasingly concerned about what they are seeing on reefs. Some are
already convinced. Equally, the data do not prove that bleaching is not
caused by global warming, as implied by headlines in the journal Science
(19 July).
Obviously such a correlation, or the proven lack of one, would make
better copy for journals like New 杏吧原创 and Science. But an ‘honest
appraisal’ of the situation, and one that needs communicating to the public,
is surely that we don’t know yet. Following the argument of Johnston and
Simmonds, this would then call for the precautionary approach – a view that
the majority of reef scientists would hold to, whatever their opinions about
the cause of coral bleaching.
Susan M. Wells Cambridge
Letters: Green sheep
In answer to S. P. Kingsley’s question, ‘Why aren’t sheep green?’ (Letters,
31 August), I believe the answer may be this: Sheep are most at risk from
predators when alone rather than when congregated in a flock. They are most
likely to be isolated during the winter months when they are often caught
in snowdrifts. Under such conditions the white fleecy coat would have two
advantages, warmth and camouflage. Such sheep would have an evolutionary
advantage.
Elaine Dignan Brooklands, Manchester
Letters: Naughty noughty
With regard to Richard Caie’s question about suitable names for the
next two decades (Letters, 24 August): considering the moral decline of
society as a whole, the next decade must surely be the noughties.
Cormac Neeson Birmingham
Letters: Fractal craft
It was a pleasure to see the feature devoted to ‘New-wave mathematics’
(3 August). But I was disappointed that William Bown and those he interviewed
described overly briefly the procedures followed in the actual practice
of experimental mathematics. As it is a new craft, it has few accepted rules
and can only be taught by example. Outsiders tend to think it is straightforward;
when they find that they do not necessarily see much on their own, they
tend to think it is ineffective, or even an imposture. To the contrary,
having practised it longer than anyone else alive, I know that it is truly
a craft: it requires a proper attitude and involves its own set of delicate
skills, but it is very effective.
Take the notion that there was a magical day when, to quote your feature,
‘suddenly, everyone could see the amazing things that Julia had conjured
in his head’. Such a day might have happened and perhaps should have happened,
but apparently it did not happen. I was not the first to use the computer
to draw Julia sets. The evidence is that Stanislaw Ulam was the first in
the 1950s. But Ulam thought that ‘mathematics is not really an observational
science and not even an experimental one’. Much additional evidence exists
to show that the computer was necessary to the new experimental mathematics,
but it was not sufficient. In my experience, to look at a picture very rarely
suffices to set out an ‘Eureka moment’ of any sort.
Let me also sharpen your feature on another point. Quite a number of
major fractal conjectures have already been vindicated by a full proof admired
by connoisseurs of mathematics, both ‘old-wave’ and ‘new-wave.’ The connectedness
of the M-set has long ceased to be an isolated example. Dr Tai Lai has proven
a refined form of one of my first observations, namely, that there is an
astonishing resemblance between a J-set and the corresponding piece of the
M-set. And just last month, Dr Shishikura proved an even more difficult
item on my list of observations-conjectures: that the boundary of the M-set
is of Hausdorff dimension 2. However, these proofs have done little to reduce
my personal collection of difficult mathematical conjectures involving fractals.
When one includes topics other than iteration, this list grows faster on
one end than it shrinks on the other. The best path to understanding continues
to be pluralistic. It uses observation and proof hand in hand, as described
in your feature.
Benoit Mandelbrot Yorktown Heights, New York
Letters: Corny fractals
The burden of proof seems to us to rest with those who wish to claim
hoax; and we feel it would be necessary for those arguing this case to indicate
plausible techniques by which a fraud was perpetrated. The Centre for Crop
Circle Studies would be willing to indemnify against all claims anyone who
is willing to explain his methods and to reproduce the occurrence at CCCS
expense.
Ralph Noyes Centre for Crop Circle Studies London
Letters: Corny fractals
Unfortunately New 杏吧原创 has only seen fit to print one article on
crop circles (‘Circles in the corn’, 23 June 1990) which put forward Terence
Meaden’s now discredited theory of the ‘plasma vortex’ as the causative
agent. If people unfamiliar with the subject could only think beyond the
trivial approach purveyed by the popular press that crop circles are caused
by (1) hoaxers (of course there are some hoaxes which are generally easily
recognised), or (2) aliens in spacecraft, or (3) plasma vortices (which
simply don’t fit the facts), then perhaps we would make some progress towards
understanding this phenomenon.
George Wingfield Shepton Mallet, Somerset
Letters: Corny fractals
I was interested to see your news item about the Mandelbrot crop pattern
(In Brief, 24 August).
Although the article points out that the Mandelbrot has theoretically
to be built up dot by dot, I can think of at least one way to lay out this
shape, since the basic shape of the main body of the set is a cardioid.
One definition of this curve is as the locus of a fixed-length chord,
length 4x, which passes through a point on the circumference of a circle,
radius x, while the chord’s mid-point moves around the circle. (See the
diagram, below.)
This suggests a routine that could be used by three people armed with
a rope knotted at the mid-point. After laying out the generating circle,
one would be stationed at the cusp O, a second would walk round the circle
holding the rope’s mid-point P, and the third hold the end Q. O would feed
the rope through or take in the slack as necessary.
At times, O would be in between P and Q. As long as the rope were kept
straight, PQ would sweep out the cardioid.
Add a few circles, and you’d have a reasonable Mandelbrot look-alike.
Ray Girvan Birmingham
Letters: Crafty crow
Ian Stewart’s review of the problem of sphere packing, including Wu-Yi
Hsiang’s recent solution (‘How to succeed in stacking’, 13 July), might
have mentioned a well-known situation where packing density would make the
difference between life and death. This occurs in Aesop’s fable, The Crow
and the Pitcher:
‘A crow, ready to die of thirst, flew with joy to a pitcher which he
beheld at some distance.
When he came, he found water in it indeed but so near the bottom that
. . . he was unable to reach it . . . At last, seeing some pebbles lying
nearby, he cast them one by one into the pitcher, and thus, by degrees,
raised the water right up to the rim, and satisfied his thirst.’
What Aesop may or may not have realised is that, if the pebbles are
spherical and equal in size, and the water level below a threshold, the
crow would die of thirst. Ignoring boundary effects, if the crow drops pebbles
to achieve a ‘random close-packed’ geometry and the water occupies less
than 39 per cent of the volume of the pitcher, the water level will not
reach the surface when the pitcher is full of pebbles. If the crow could
achieve a truly close-packed geometry, now known to be optimal (concededly
a difficult feat dropping the pebbles through water), still if the water
occupies less than 26 per cent of the volume of the pitcher the crow must
go thirsty.
Depending on the material at hand, other strategies might present themselves
to a thirsty crow. It is known, for example, that mixtures of spheres of
different volumes can achieve higher densities than assemblies of equal
spheres.
Arthur Lesk University of Cambridge