If you go expecting to find chaps with small round heads and bulging
glasses spouting formulae, then you are in for a surprise. The roadshow
contains all the delights of an activity park. Hands-on displays, toys,
games and puzzles from around the world, knots, stamps, mathematical videos
and books are just some of the novelties.

The Joint Mathematical Council and the Royal Society were responsible
for setting the wheels of the show in motion in Leeds in November. Their
aim was to dispel the unattractive image mathematics has of being a dull,
elitist subject. The roadshow, which will be touring the country into the
late 1990s (see below for venues), is an opportunity for anyone and everyone
to experience some of the unexpected delights of the subject.

As the roadshow travels around its emphasis is likely to shift. It is
up to the local organisers to select the range of material they will display.
I visited the show in Bedford. Here, the Bedfordshire Mathematics Centre
have aimed it at school children.

The exhibition was set up in a school gym with Mathematical Horizons,
a group of interactive exhibits from France, commanding the central position.
I quickly became engrossed in puzzling out how Euler could have crossed
over the bridges in his city without needing to retrace his steps at any
point; a novel introduction to the value of graphical representation.

Johnny Ball’s contribution, Games of the World, caught my attention
next. And I was unwilling to move on before I had worked out a strategy
for outwitting my opponent at Awa ree, one of the Mancala counting games
from Africa.

In Bedford there has been a constant stream of school children through
the show and the organisers rated it a great success. One young girl told
me, ‘I like everything except for the boring stuff,’ then added, ‘and I
don’t think there is any boring stuff here.’ Undaunted by the more baffling
exhibits, she gave me an illuminating description of the German Frontiers
in Chaos display: ‘really weird patterns to make your eyes go funny’.

I came away from the show sharing some of her enthusiasm, but I was
also disappointed. The impact of many of the exhibits was lost through sheer
lack of space. For example, the arrestingly beautiful chaos pictures were
cluttered up on screens at the side of the room. I almost overlooked a fascinating
display on knots.

As the roadshow tours some of these weaknesses will, no doubt, be ironed
out. At which point, even the least numerate person going along will discover
that maths is enjoyable and is an integral part of our culture.

16 January to 9 February: Institute of Education, London. Tel: Sue Burns
01-636 1500. 13 to 28 February: University of Southampton. Tel: Dr Frank
Rhodes 0703 595000. 7 to 16 March: St Andrew’s College of Education, Glasgow.
Tel: Gerry McKaig 041 943 1424. 20 to 29 March: Elgin Academy, Elgin. Tel:
Bill Richardson 0343 543485. 1 to 17 April: University of Edinburgh. Tel:
Dr David Monk 031 667 1081, ext 2827.

Sarah Law is a science writer.

For some time, astronomers have suspected that the light source at the
heartof violent, or ‘active’, galaxies doesnot radiate evenly in all directions.
Now,two different groups – an international collaboration of scientists
calling themselves the Lovers of Active Galaxies (LAG), and a team at the
European Southern Observatory (ESO) in Munich – have made observations which
confirm that a fraction of this light is ‘beamed’ in two opposite directions.

According to Michael Penston, a British member of LAG, the appearance
of an active galaxy depends on the direction we observe it from because
some of the light may be beamed. He and his colleagues used the Isaac Newton
Telescope in the Canary Islands to study the beaming of light in the nearby
Seyfert galaxy, NGC 4151. A Seyfert galaxy has a point source of light in
its core, which astronomers have traditionally regarded as a weaker version
of a brilliant quasar.

Penston says that ‘somebody sitting in the beam and looking at the centre
of NGC 4151 would see a source 16 times brighter than we do when we look
at the galaxy’. This would make the galaxy’s centre look like a quasar.
The two beams of NGC 4151 point in directions almost perpendicular to the
line joining us to the galaxy.

According to Penston, intense ultraviolet radiation is beamed from the
centre of the galaxy, then scattered by the surrounding gas. ‘The beam produces
an extended optical structure,’ he says, ‘just like the trail produced when
a searchlight is shone on a misty night.’ The gas acts as a fluorescent
screen.

The ‘searchlight’ in NGC 4151 is quite weak and is visible only to a
distance of about 3000 light years from the centre of the galaxy. However,
the group at ESO has observed optical beams in distant radio galaxies, and
these extend up to about 35 000 light years (Nature, vol 341, p 307).

The ESO team has measured the colour and polarisation of the light from
two distant radio galaxies, 3C₂77.2 and 3C₃68. Clive
Tadhunter, a member of the group, says that the results indicate that ultraviolet
light is being beamed in these galaxies. Tadhunter points out that the daylight
sky is polarised and appears blue because light from the Sun is scattered
by the Earth’s atmosphere. ‘For the same reason’, he says, ‘the light from
the extended structures in these galaxies is very blue and highly polarised.’

From our viewpoint, we do not see a bright point in the centre of these
galaxies, but the new observations suggest that someone seeing the galaxy
along one of the beams would see a central brilliant source that looks like
a quasar.

Optical beaming might also explain recent observations made by two Israeli
astronomers, Hagai Netzer and Dan Maoz. They measured a rapid variation
in the brightness of both the centres and the surrounding gas of nearby
Seyfert galaxies. They had expected to observe a time delay between the
variations in the brightness of the gas and central source because of the
time taken for the light from the centre to reach this gas, believed to
lie several light months away. They were astonished by how rapidly the brightness
of the scattered light changed, mimicking the central source. However, if
the scattered light is coming from a beam that points almost towards us,
this could explain the time lag between the signals.

‘The big challenge now,’ says Penston, ‘is to explain the origin of
this beaming.’ One idea that is popular with astronomers is that the intense
ultraviolet radiation is beamed by a jet of relativistic electrons. Another
possibility is that part of the central source is being shadowed, perhaps
by the accretion disc – a ring of dense material believed to surround the
centre of active galaxies. Penston believes that it is unlikely that a single
beaming mechanism is responsible in all the different active galaxies.

One thing is certain, there are not as many different types of galaxies
out there as previously supposed. Sarah Law

ÐÓ°ÉÔ­´´s have known since the 1970s that they can attract and trap
small particles with the aid of an intense laser beam. The initial discovery
was made by Arthur Ashkin at Bell Laboratories in New Jersey, who found
that he was able to use a beam to trap small bacteria. At the Rowland Institute,
Burns and his colleagues decided to study Ashkin’s trapping mechanism in
the laboratory. They realised that a similar ‘optical force’ might arise
between particles if they were exposed to laser light, and that the force
might be capable of holding the particles in a fixed arrangement.

To investigate the optical force, the scientists shone a laser beam
with a wavelength of 0.387 micrometres on two plastic spheres, each only
1.43 micrometres in diameter. They found that when the spheres were separated
by a distance equal to an integer multiple of the laser’s wavelength, the
spheres formed stable ‘molecules’. The spheres were more tightly bound when
they were closer together and exposed to a stronger laser beam. As soon
as the researchers turned off the laser beam, the forces between the spheres
disappeared, and random thermal motion took over.

According to Burns, the spheres form stable ‘molecules’ because each
sphere scatters a small fraction of the laser light in the form of spherical
waves. These create a pattern of ripples in space, rather like those produced
by a stone dropped into water. The ‘light ripples’ from the two spheres
combine with the incident laser light to produce what physicists refer to
as an interference pattern; that is, in some parts of space, the waves reinforce
each other, while in others they cancel each other out. It is this interference
pattern, or ‘field of force’ that is responsible for the optical forces
that hold the spheres together.

The pattern of ripples changes with the distance between the two spheres.
When the spheres are separated by integer multiples of the beam’s wavelength,
the ripples reinforce each other. Each sphere then finds itself in the vicinity
of a series of peaks and troughs which become deeper towards the centre
of the pattern. The troughs, which physicists call ‘potential wells’, are
positions of low energy in which the spheres can sit – provided, that is,
that the well is sufficiently deep to prevent their thermal energy from
jiggling them out of it.

When both spheres are in nearby troughs in the interference pattern,
the ‘molecule’ is stable. As the distance between the spheres changes, the
fields destroy each other. The spheres then encounter forces that move them
together until they reach the next stable configuration.

According to Burns, optical molecules are only the first stage in his
team’s investigation. He and his colleagues hopeto create one- and even
two-dimensional ‘crystals’ using the laser beam. Because the optical forces
have a long range, it may be possible for spheres to arrange themselves
in a regular pattern so that all the scattered fields reinforce one another.
In such a situation, the potential wells will get deeper and the structure
more stable as each new sphere is added to the pattern. This is precisely
the criterion for growing a crystal structure.

The scientists say that it is still too early to think of definite applications
of their work. ‘At the moment,’ says Burns, ‘we are just having a lot of
´Ú³Ü²Ô.’

Colin Walker and his colleagues have been studying partridges in the
laboratory (Pesticide Biochemistry and Physiology, vol 34, 1989). They believe
that by using partridges as a model they may be able to predict how certain
types of pesticide interact with each other inside birds.

‘If these studies are confirmed in the field,’ says Walker, ‘it may
be necessary to rethink the way farmers apply their pesticides in the future.’
Safety limits on pesticides, which are set by the government’s Agricultural
Development and Advisory Service, are set for each pesticide in isolation.

Walker and his colleagues first studied a class of fungicides, which
farmers use on cereals, to see how they altered a bird’s tolerance to organophosphate-based
insecticides. They expected a potentiation because certain organophosphates,
which farmers apply in an inactive form, become harmful to birds if they
are activated.

The group of enzymes which are responsible for activating the insecticides
are known as cytochrome P450s. They are present naturally at low levels
in birds, but these fungicides are known to cause an increase in the levels
of these enzymes within certain birds.

Walker and his colleagues showed that the level of the P450s increased
greatly when the partridges were given the fungicide prochloraz orally at
doses of 180 milligrams per kilogram. Gail Johnston, a colleague of Walker,
believes that birds may well be exposed to such a dose in the field. Farmers
are using prochloraz as a seed dressing at 200 to 500 mg/kg. In a day a
bird weighing 500 grams might eat 50 grams of seed and so take in 20 to
50 mg/kg by this method alone.

The scientists next confirmed that this increased level of enzymes did
make the organophosphate more poisonous to the partridges. After treating
the birds with prochloraz, they injected malathion at very low doses, between
5.6 and 11 mg/kg. These doses proved lethal. In control birds which were
not given an initial prochloraz dose, the malathion had no effect.

When the researchers gave the same doses of malathion orally, the birds
did not die. However, the activity of a group of enzymes known as esterases,
which are present in the birds’ blood, decreased. This is the first stage
of organophosphate poisoning. Johnston described the results as ‘highly
significant’. Earlier fieldwork, sponsored by the Ministry of Agriculture,
showed that birds could be exposed to levels of organophosphates which were
sufficient to produce similar effects in the blood.

Johnston and Walker have obtained similar results from a range of other
related fungicides and organophosphates. They have also carried out in vitro
studies which confirm that there is a change in the level of P450s which
interferes with the metabolism of organophosphates.

Johnston is now looking at the possibility of a second mechanism by
which pesticides applied together could be more harmful to birds. Early
results suggest that there is a potentiation of the group of insecticides
known as carbamates by organo- phosphates.

In this case, she explained, the organophosphates reduce the activity
of a group of enyzmes in the bird which are responsible for rendering the
carbamates harmless.

Walker emphasised that ‘field tests were all important to assess whether
birds could acquire doses of pesticide sufficient to produce these dramatic
toxic effects.’ Nick Sotherton of the Game Conservancy at Fordingbridge
was impressed by the Reading study and hoped to collaborate with the Reading
group in future field studies.

Astronomers need such a map of the sky in order to guide the Hubble
Space Telescope when NASA launches it next year. The listing, known as the
Guide Star Catalogue, will also provide a valuable resource for astronomers
in general.

Harvey MacGillivray of the Royal Observatory in Edinburgh described
one use for the catalogue that could save valuable observation time on telescopes.
Many of the unusual objects that astronomers want to observe, such as brown
dwarfs, are very faint, he explained. The catalogue will provide an accurate
reference grid which will make it much easier for astronomers to obtain
coordinates for these objects.

The American institute’s project involved processing 1477 photographic
plates of the sky that were taken in the late 1970s by the Schmidt Telescope
on Mount Palomar in California and the UK Schmidt Telescope in Australia.
It has taken eight years of intensive effort to complete the work. The scientists
have so far catalogued objects down to only the 15th magnitude (4000 times
as faint as the limit that the naked eye can detect). They have also stored
the images of objects down to the 21st magnitude (250 times fainter still)
on optical disc.

Astronomers at the institute plan to use the complete data to search
for objects that they have identified by recording radio waves, infrared
radiation and X-rays. The map will be particularly useful in the automated
search for X-ray sources identified by Rosat, the X-ray satellite operated
jointly by NASA and West Germany, which is scheduled for launch in 1990.

A further aim of the project is to search for new sources that change
over time, such as variable quasars and erupting dwarf novae. The map makes
this possible because there is a high degree of overlap between the 1477
plates collected by the Schmidt telescopes; almost two-thirds of the sky
appears on at least two plates. Since adjoining plates may have been exposed
days or even months apart, a variable star will appear at different magnitudes
on each plate, making it easier to detect.

Unfortunately, the Guide Star Catalogue contains no information about
the movements of the stars. The catalogue will become increasingly inaccurate
throughout the lifetime of the Hubble Space Telescope. The scientists estimate
that, five years after its launch, 10 per cent of the stars catalogued will
have drifted sufficiently far to make them useless for guiding the craft.

ÐÓ°ÉÔ­´´s at the institute are currently studying surveys of the sky
that were made in the 1950s. They aim to compare these maps with their catalogue.
The comparison will allow them to calculate the speeds at which the guide
stars are moving and eventually to include this essential information in
the catalogue. Sarah Law