Letters : McMaths
Farnborough, Hampshire
As a mathematician, I have been asked several times if the ad claiming that
there are 40,312 “combinations” of eight fast-food items was correct. Clearly
not鈥攂ut what is it? I awaited your take on the question, only to find that
you printed an incomplete solution
(Feedback, 9 February).
As a competent GCSE student can point out, 40,320 is the number of ways you
can arrange 8 objects in a line. As McDonalds reportedly subtracted 8 to exclude
the possibility of choosing just one item from 8, they should also have included
selecting any 7 from 8 (40,320), 6 from 8 (20,160) and so on, making a total of
109,592 permutations. I agree with Sally Baker that there are 255 combinations
(excluding the zero option). I also tried to use sub-options, like the 5
flavours of soft drink, but no matter how I tried, I failed to get to
40,312.
109,592 is indeed the number of options if you choose at least two items to
eat in any order. But the total number of permutations is 109,601. That includes
the number of ways of selecting only one item (8), and the one way of choosing
none at all, which may be many readers’ preferred option
(23 February, p 53)鈥抬诲
Letters : Greatest circles
Reston, Virginia
Moslems all over the world pray facing toward Mecca in their mosques. So why
does the mosque in New York city point toward Greenland rather than Saudi Arabia
(16 February, p 55)?
The reason is that the “great circle line” on the face of a sphere鈥攁
circle which lies in a plane passing through the sphere’s centre鈥攊s the
direct path, rather than a straight line on an arbitrary map. Thus the prayerful
in New York offer their prayers to the north-east to be received in the
south-east. For more information, see “Which way is Jerusalem? Which way is
Mecca? The direction-facing problems in religion and geography”, by Daniel Levin
(Journal of Geography, volume 101, p 27).
Letters : . . . . . .
Marleston, South Australia
Could there be a connection between the effect reported by Fox and the
research suggesting that we are attracted to people who look like our parents
(2 February, p 26)?
The semen of a genetically similar man will appear less foreign
than that from a man who is less genetically similar. It will provoke a less
vigorous immune response in the female鈥攚hose immune system will become
accustomed to it more quickly, with a lower chance of fetal rejection.
All this adds up to a better chance of having a healthy baby. Which is the
name of the game isn’t it? I do realise that there are other issues such as the
problems of being too genetically similar (as with siblings) and that genetic
dissimilarity provides the offspring with a greater immune repertoire. But the
idea is sound, is it not?
Letters : Why sex?
Hebden Bridge, West Yorkshire
Douglas Fox marvels at what he describes as one of the great mysteries of the
human condition: why do humans spend so much time having sex without resultant
pregnancy
(9 February, p 32).
The answer, it seems, is that it allows the
woman’s immune system to become accustomed to the man’s proteins, thereby
decreasing the chances of rejection of her fetus’s proteins when she eventually
becomes pregnant.
If such reasoning is correct, it still fails to explain the great mystery of
why this strategy is only adopted by humans (and a few other animals). If there
really was such a clear-cut evolutionary advantage in frequent sex, wouldn’t all
animals be at it like rabbits (and, indeed, humans)?
Surely there is a far simpler reason why we humans have so much sex: because
it’s so enjoyable.
Letters : . . . . . .
Epsom, Surrey
It is disappointing to see New 杏吧原创 publish an editorial that
so clearly fails to understand the evidence regarding the safety of MMR. The
vaccine has been used for over 20 years in more than 90 countries with over 500
million doses given. The scientific evidence for its safety and effectiveness is
enormous. Every reputable medical, nursing and scientific organisation in the
world that has looked at the allegations of a supposed link with autism have
declared that there is no such link.
Even if ileocolonic lymphonodular hyperplasia is associated with measles
virus, it is no more likely to be associated with MMR than with wild measles or
with single-antigen measles vaccination. And any scientist should know that
association is by no means proof of causation.
Research has detected and quantified a clotting disorder (ITP) that occurs as
a consequence of MMR in around 1 in 27,000 people鈥攁nd about 9 times as
often after measles. If autism arises as a consequence of MMR, we can be fairly
confident it occurs less frequently than ITP.
Because measles is so infectious, a very high vaccine take-up is required to
prevent outbreaks. Duncan Graham-Rowe and Debora MacKenzie show their ignorance
of vaccine programmes if they seriously believe that people will turn up for six
jabs instead of two. I know, from when I was a GP, how difficult it is for many
people to make it to the surgery, even when they want to have their children
vaccinated. Of course increasing the number of jabs required will harm take-up.
If parents can choose single-antigen jabs, many are likely to “cherry-pick” and
vaccinate only against whichever disease has most recently caused a scare in the
media.
If a woman catches rubella (German measles) during early pregnancy, her child
will have congenital rubella syndrome, which causes deafness, blindness, heart
defects and brain damage. Indeed, the syndrome is one of the known causes of
autism. Before MMR was introduced, and despite rubella vaccination, there were
up to 50 cases of congenital rubella syndrome each year in Britain鈥攁nd
many more abortions were performed to prevent it. Mumps, meanwhile, was one of
the commonest causes of meningitis. With MMR we almost eradicated these
conditions.
The risks of changing to single-antigen vaccines far outweigh any conceivable
risk from MMR. The safest thing any parent can do is to ensure that their child
receives the MMR vaccine.
Letters : Too many wars
Clearwater
As Britain and other countries in Europe continue to change their drug
policies away from criminalisation toward a more health-based approach, we in
the US can’t help but be a little envious
(2 February, p44).
European “harm reduction” approaches actually produce far lower rates of
illicit substance use than here in America, and you also enjoy far lower rates
of property crime and violence associated with criminal drug dealing.
This is despite the fact that we have federal task forces devoted to raiding
medical marijuana operations and we arrest over 700,000 citizens every year for
marijuana alone. We also have the dubious distinction of incarcerating twice as
many of our citizens as does the entire European community, whose population is
a third greater than ours. Meanwhile, our government officials wring their hands
and lament that current drug treatment is only available on demand in about 15
per cent of cases.
An aggressive advertising campaign authorised by Bush’s Office of National
Drug Control Policy was released during the telecast of the Super Bowl (an
American football championship game). In it, the ONDCP attempts to tie the War
on Terrorism to the War on Drugs. While the connection is extremely dubious, it
clearly illustrates that our current President is less interested in policies
that work than in waging worldwide war on whatever front he can find. America’s
very real problems with drug abuse bear the heavy burden of such a myopic
mindset.
Letters : Look north
London
I read with interest your article about virtual particles
exerting macro effects on suspended gold foil
(2 February, p 17).
This reminded me of E. A. Reeve’s “north-seeking force” of the 1930s, a
heretic effect consigned to oblivion along with perpetual motion and
anti-gravity. Reeve, who was the Royal Geographical Society’s librarian, claimed
that thin, non-magnetic sheets lightly suspended from a single point in a vacuum
and exposed to daylight eventually aligned themselves with true north. Despite
the apparatus being reasonably easy to duplicate he could get no serious
scientist interested in replicating and confirming his results because there was
no obvious mechanism.
He was so convincing that I have always thought there might be something in
it, and that it ought to be followed up. Now we have “dark energy” and “virtual
Brownian motion”, perhaps it is not quite as stupid as was thought.
Letters : Beware the quietly thawing North Sea gases
Norwich
The relationship between rapid global warming and mega-tsunamis would not
be the simplistic cause-and-effect sequence outlined by Paul McCrory
(16 February p 54),
but a feedback loop. McCrory suggests the giant waves could
disturb methane hydrate deposits on the seabed and release methane, which is a
greenhouse gas. However, the initial rise in global temperature would trigger
“outgassings” from frozen methane hydrate deposits, which in turn would
accelerate the warming, and so on until the critical temperature was reached
that thawed out the bulk of methane deposits鈥攁t which point we could
expect a runaway greenhouse effect.
There may be some evidence of a truncated sequence like this in the record of
tsunami strikes on the east coast of Britain since the last ice age. These were
caused by the Storegga slides off the west coast of Norway鈥攍arge-scale
disruptions of the bed of the Norwegian Sea between 11,000 and 8000 years ago
that were probably triggered by hydrate outgassings as a result of rising sea
temperatures. These outgassings, which were probably not localised, were
followed by the prevailing mild climate of the Bronze Age. On average it was 3
掳C warmer over Britain than today. However, it would be very difficult to
establish a causal link after this time.
If the Storegga slides were to reoccur today they would inundate the entire
British east coast from the Shetlands to Norfolk, as well as most of the
Netherlands. This is a salutary reminder that the consequences of global warming
may not be gradual.
Attention has been focused on the long-term threat to the south coast from
mega-tsunamis originating in a volcanic cataclysm at La Palma, but a more
immediate threat鈥攐nly decades, not centuries off鈥攎ay lie to the
north, in the quietly thawing gases beneath the North Sea.
Letters : Jab and parry
New Barnet, Herts
Why are the media and the British government, amid the MMR controversy
(16 February, p 5
and 12),
quietly ignoring the potential consequences of routine
BCG inoculations having been suspended a number of years ago? Unless there has
been an extensive and unreported programme to deal with this backlog, this will
have left a whole cohort of teenagers unprotected from tuberculosis. Last year
there were several outbreaks in Britain.
Either the government is serious about the benefits of inoculation, or it is
insisting on MMR as the only option since it fears that the NHS would be
incapable of offering separate jabs for measles in infancy and mumps and rubella
later in childhood.