Move to the music
Question: When I walk along Oxford Street in central London, I often see
people selling little figurines that appear to dance to music that is being
played from a cassette recorder close to them. How do they work? From a few
metres away they seem to just be pieces of card with string for arms and
legs.
Answer: The cardboard figures are suspended above the ground on a fine
thread. One end of the thread is attached to the aerial of a cassette player and
the other end is attached to a heavy object such as a bag. The sound from the
speakers causes the aerial to vibrate. This vibration is transferred along the
thread to the figures, making them dance.
Laurence Watson (aged 10)
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Pembridge, Herefordshire
Answer: The ensemble is made of strings, elastic bands and card. The setting
is usually close to a wall so you can鈥檛 see the back of it. A salesperson is by
the side of a cassette player, and a little farther away along the wall the
puppet is dancing. If you look away from the salesperson and the puppet, you鈥檒l
find an inconspicuous-looking person a couple of yards away, usually with a
jacket hanging from their shoulder facing the setting. Look closely at their
hand or foot and you should see it moving rhythmically. They are holding the
other end of a piece of invisible nylon string that鈥檚 attached to the cassette
player. The puppet is simply attached to that string by a clip on its back and
is dancing to the movements of the hand of the accomplice. Simple, effective,
cheap and puzzling enough to make people want to buy.
Laurence Bosc
Leeds, West Yorkshire
Reports of this scam came in from readers in London, New York, Blackpool,
Sydney, Kansas City, Tokyo, Rome, Milan, Venice, Dublin, Athens, Paris, Chicago,
Kyoto and Sicily. Is there an international federation of street con-artists? Or
do such tricks just spread naturally around the world? Interestingly, it has now
virtually vanished from London, presumably because there is a limit to how long
it is possible to gull the public. However, it appears this is not the first
time around for this trick鈥擡d
Answer: The effect is an old magic trick that has been updated with modern
technology. Unknown to the average passer-by, a seemingly disinterested
bystander is the controller of this illusion. Everyone pays attention to the
salesman, which allows the assistant to manipulate an 鈥渋nvisible鈥� horizontal
nylon thread (the original was done with thread or long lengths of hair). The
assistant usually has a garment draped over their arm to hide the simple back
and forth motion of their hand. More details are in Magic and
Perception by Bob Friedhoffer (Franklin Watts, 1996).
Bob Friedhoffer
New York
Roman division
Question: How did the Romans express fractions?
Answer: In scientific work, which was always written in Greek, the Romans
used sexagesimal fractions, like those used for angles and time, expressed by
Greek literal numbers and positional notation.
For everyday uses, common fractions were always used, often spelled out, such
as tribus duas partes (with thirds two parts) for 鈪�. The solidus (the
line in a fraction between the two numerals), or any implied division, was never
used. However, abbreviations were often used if necessary. The most common were
S or SK (semisque, or 鈥渁nd a half鈥�) for 陆, and T or TK for 鈪�; 1陆
could be written ISK. A symbol for the sestertius (a unit of money
worth 2陆 bronze asses), was IIS, later written HS. F, Z or FZ was used for 鈪�
while 录 was represented by the usual modern division symbol 梅, or :- -, or G,
or a backward C, the scilicus. An overhead horizontal bar meant either
1/12 or 1/16, and could be combined with dots and other symbols. Common
fractions were often expressed as sums of simpler fractions, for example 9/16 =
1/2 + 1/16, written S鈥� 鈥�.
A good place to see such fractions is Book X of Vitruvius鈥檚 De
Architectura, where they鈥檙e used in connection with the construction of
military machines. However, ignorant medieval (and modern) copyists have
corrupted many fractions in existing texts because they did not understand the
unfamiliar symbols. There are also a few examples of fractions in inscriptions
but evidence is scanty and, as classical scholars usually pay little attention
to numbers, science or mathematics, the usual reference works provide no
enlightenment.
Roman practical calculations were done on the abacus, which used a decimal
notation for whole numbers, but not for fractions (which were usually monetary
fractions), and these had special columns of beads.
Incidentally, the notation for large numbers was different from that used in
today鈥檚 Roman numerals, and more convenient. Except for I, V and X, Roman
numerals were not the usual alphabetical letters we see today, but symbols
derived from Etruscan and other sources. L, C, D and M evolved from these, but
many of the more unusual symbols remained for fractions. Even Greek letters are
sometimes found. X was also used for ⅙.
So, except for the simpler fractions, there was little standardisation. Roman
engineers relied more on analogue and graphical methods of calculation than we
do today, and numerical calculations were avoided as far as possible.
Jim Calvert
Exeter, Devon
Answer: The Egyptians used fractions and evidence survives in a few papyri,
notably the Rhind papyrus, bought in Luxor in 1858 by Henry Rhind鈥攏ow in
the British Museum. It dates from 1650 BC and was probably copied from a text
written two centuries earlier. It shows methods of calculation, problems,
exercises and puzzles involving fractions. There was an Egyptian symbol denoting
fractions and the numerator was always 1, except for 鈪� and 戮. Even these
could be derived by subtracting 鈪� and 录 from the whole. Intermediate values
could be expressed as the sum of unit fractions, for example ⅗ = 鈪� + ⅕ +
1/15.
Abstract fractions, as we know them today, were probably invented by Hindu
mathematicians in about AD 500, and the horizontal bar (the solidus) was
introduced by the Arabs around 1200.
John Richmond
Worcester Park, Surrey