Letters: Singular mistake
Feedback’s comment on BR’s singular Passenger’s Charter (4 April) is
pertinent when read in conjunction with the letter from John Mee in the
same issue referring to the principle of someone called Archimede.
Do not worry however, it is not just us scientists; I recently attended
a performance of Orpheus in the Underworld where one of the characters was
given in the programme as Glady’s.
John Dowding Witham, Essex
Letters: Arthritis gene
Your report that a gene has been ‘discovered’ linking salmonella infection
with arthritis (This Week, 21 March), although quite interesting, is not
exactly a recent observation.
The first report that HLA-B 27 is linked to salmonella arthritis was
made by the Danish workers Friis and Svejgaard some 18 years ago. Furthermore
the link between HLA-B 27 and Reiter’s disease was made even earlier by
Brewerton and co-workers from London. Actually, this topic was discussed
in the pages of New 杏吧原创 some 14 years ago by one of us (‘The link
between genes and disease’ by Alan Ebringer, 21 September 1978).
It is clear that HLA-B 27 is an interesting gene linking infection with
arthritis and it would appear that this has been known for some time.
K. Ahmadi, C. Wilson, A. Ebringer King’s College London
Letters: Anti-pop
On reading about the anti-noise technology to quieten cars (Technology,
28 March) a thought occurred to me.
Would it be possible to supply pop records with their corresponding
anti-noise versions so that those of us who are afflicted with ghetto-blasting
neighbours could get a bit of peace?
Izzy Hanson University of Liverpool
Letters: Flying upside down
There is no mystery as to how an aeroplane can fly upside down (Letters,
4 April). The amount of lift generated (and the direction in which it acts)
depends primarily on the direction from which the air approaches the wing,
as well as on its cross-sectional shape and other matters. When flying inverted,
the pilot holds the nose of the aircraft much further from the ground than
the tail (by pushing forward on the control column). Significant lift is
then generated, but at the cost of very much more drag than in normal flight.
If the plane has a powerful enough engine which will keep running, inverted
flight may be maintained, otherwise the plane will slow down until some
recovery action has to be taken. I know it works, I’ve done it.
Michael Webber Portishead, Bristol
Letters: Battery bashing
I don’t know the answer to Jonathan Wallace’s question (Letters, 28
March) as to whether nickel-cadmium batteries should be run down fully or
only part way, but either way I know what to do about it.
If you drop a ‘tired’ battery about a foot onto a concrete floor a few
times it renews the battery wonderfully. The theory (folklore?) is that
a layer of crystals builds up around the electrodes and dropping the battery
breaks the crystals.
Whatever the truth of the theory, it certainly works.
Michael Bell Hitchin, Hertfordshire
* * *
Editor’s note: We have heard that in some cases this does work. But
be careful – you may cause the battery to leak, which could damage your
equipment. As to Wallace’s question, the advice we received from battery
experts is that Ni-Cd batteries should be completely discharged before charging,
but lead-acid batteries should be regularly topped up with charge.
Letters: Uncomputable?
I found in Paul Davies’s otherwise enjoyable article one error of logical
reasoning concerning the proof of uncomputable numbers (‘Is Nature Mathematical?’
21 March).
Quote: ‘Imagine a list of all computable numbers written out as decimal
expansions. (The list will be infinitely long, but the basic form of the
proof is identical . . . ) Now change one digit in each number, and make
up a new number. This number cannot have been present on the original list.
But the list contains all computable numbers. Hence the new number must
be uncomputable.’
In fact, the process describes the method of computing a new number
not in the list. How can one say that it is uncomputable? Instead, the above
paragraph is rather a proof to the fact that one cannot (even in principle)
create an exhaustive list of uncomputable numbers.
Lassi Hyvarinen Le Vesinet, France
* * *
Paul Davies writes: My description of Turing’s proof was a little too
brief, and has caused confusion. It is correct that the ‘diagonal’ construction
provides a means to compare a number that is not on the original list. Yet
that list is supposed to contain all computable numbers. Hence there is
a contradiction. It is from this very contradiction that we can conclude
that there cannot exist a machine to generate all computable numbers. Hence
there exist uncomputable numbers.
An excellent detailed discussion of this can be found in The Emperor’s
New Mind by Roger Penrose.
Letters: Uncomputable?
There is more to the ‘incompleteness’ of mathematics than Paul Davies
suggests. As Morris Kline writes in his book Mathematics: The loss of certainty:
‘The research by Leopold Lowenheim and simplified and completed by Thoralf
Skolem in a series of papers from 1922 to 1933, disclosed new flaws in the
structure of mathematics . . . Whereas Godel’s incompleteness theorem tells
us that a set of axioms is not adequate to prove all the theorems belonging
to the branch of mathematics that the axioms intended to cover, the Lowenheim-Skolem
theorem tells us that a set of axioms permits many more essentially different
interpretations than the one intended. The axioms do not limit the interpretations
or models. Hence mathematical reality cannot be unambiguously incorporated
in axiomatic systems.’
Paul Davies has forgotten the fact that in physics it is not only a
question of computability/solvability of topological problems of four-dimensional
space-time but also of irreversibility. No computer can ever be made large
enough to track an irreversible system.
I feel Paul Davies did not pose a right question when he asks: ‘Just
why is the world structured in such a way that we can describe its basic
principles using ‘do-able’ mathematics?’
The visualisable interpretation of mathematical formulae which gives
them meaning is an expression of the ‘soul’ of the civilization which has
created them. In this way, our scientific world picture is only of relative
validity. Its fundamental concepts, such as infinite space, force, energy
and motion, are an expression of our occidental type of mind, and do not
hold for the world picture of other civilizations.
It may well be that quite different forms of science, of mathematics
in the sense of hypothetico-deductive systems, are possible for beings
who don’t carry our biological and linguistic constraints – mathematical
‘physics’ that are much more fit than ours to deal with such aspects of
reality.
Igor Fodor Munich, Germany
Letters: Uncomputable?
The basic supposition that science requires ‘an ordered universe subject
to precise mathematical laws’ is clearly questionable.
Precise mathematics works only on finite systems. Either infinite extension
in space-time or infinitely deep complexity vitiates completeness of any
set of mathematical laws – as corresponds nicely to Godel’s theorem.
The whole idea that mathematical laws have some independent existence,
rather than being useful descriptions of physical reality, constructed by
humans, leads to uncomputability conundrums like those explained by Paul
Davies.
Max Wallis University of Wales, Cardiff
Letters: Simple science
I was intrigued by the recent press coverage of the discovery of drugs
concealed inside lead ingots.
No one questioned the commercial sense in shipping a low-value metal
from South America to the UK, ostensibly for refining, when it could just
as easily have been refined in South America and where the lead price is
probably higher.
There was much discussion as to why X-rays could not be used to detect
the cavities and that ultrasonics was the only suitable method. What about
measuring volume – they were nice regular solids – and weighing them? Voids
sufficient to conceal significant quantities of drugs would have been immediately
obvious.
David Pullman Morpeth, Northumberland
Letters: Trading pain
David Morton’s and Judith Hampson’s excellent pieces on animal experimentation
(‘A fair press for animals’ and ‘The secret world of animal experiments’,
11 April) highlight the novel and interesting requirement of the 1986 act
that the Home Secretary make a cost-benefit analysis before permitting a
project to proceed. He is required to weigh ‘the likely adverse effects’
on the animals against ‘the benefit likely to accrue’. This is asking a
lot of a Home Secretary (in practice, his officials) and raises some fundamental
philosophical questions as well as the practical ones raised by Hampson.
First, is he to measure benefits and costs entirely in terms of suffering?
Secondly, does he give equal weight to all species, human and nonhuman?
Thirdly, to what extent does he aggregate costs and benefits across individuals?
Let us assume, for the sake of brevity, that the answers to the first
two questions are in the affirmative: he measures costs and benefits in
terms of suffering and avoids speciesism by giving no more weight to the
pains or pleasures of humans and dogs, for instance, than he does to those
of rats and reptiles.
This leaves the question of trading off the pains and pleasures of some
against those of others. This utilitarian approach would allow, for example,
in circumstances outside the laboratory, a group of sadists to justify torturing
a child on the grounds that their aggregated pleasures outweigh the pain
and distress of their victim. Against this is a traditional rights position
which would argue that each individual patient has a right not to be (painfully)
experimented upon regardless of benefit to others. Clearly the Act tends
to take the former view but in doing so must raise further questions – best
answered, perhaps, by informed public opinion rather than Whitehall mandarins.
Richard Ryder Haytor, Devon
Letters: Teach the teachers
As a recent graduate I share Jim Baggott’s misgivings about a move towards
a two-tier (teaching versus research) system for Britain’s universities
(Forum, 4 April). However, one benefit of such a change would be a much
needed re-examination of teaching methods in higher education.
It seems that only then will there be widespread realisation within
the academic community that the ability to teach well is not, for most people,
an innate skill but instead is the product of good training.
Considering that they are such an essential part of undergraduate courses,
lectures are often presented in a remarkably poor manner, as any student
who has dozed through an hour of barely audible monotone in a stuffy lecture
theatre will testify.
It is surely an anomaly that university teachers, unlike their counterparts
in schools, are not required to attain some standard level of proficiency
before they are set loose on students.
At present, teaching is an undervalued skill in our universities and
until some formal training is introduced it will be our students, not teachers,
who suffer. Training should begin at postgraduate or postdoctoral level
and need not be restricted to those who intend only to teach. Oral presentations
are a vital, but often neglected, part of research as well, whether it is
a paper to fellow scientists at a conference or a proposal to potential
sponsors in a boardroom.
Bob Ward University of Manchester