22 January 2022 | New Scientist | 55Tom Gauld
for New Scientist
Answers
Quick quiz #135
Answers1 Gyrification2 The Atacama desert
in South America3 Plantigrade4 A red dwarf, or M dwarf5 Prime numbersQuick crossword
#99 AnswersACROSS 1 Calcium, 5 Colitis,
9 Americium, 10 Nonyl,
11 Gallium, 12 Lamella,
13 Sebum, 15 Resonance,
17 Seventeen, 19 Toxic,
21 Mollusc, 23 Cannula,
25 Teeth, 26 Anomalies,
27 Ceresin, 28 MalleusDOWN 1 Coal gas, 2 Lyell,
3 Iridium, 4 Mail merge, 5 Camel,
6 Lensman, 7 TinyLinux,
8 Solvate, 14 Bevel gear,
16 Sonic boom, 17 Somatic,
18 Noughts, 19 Tyndall,
20 Chassis, 22 Chain, 24 Urine#150 A jigsaw puzzle
SolutionConventional jigsaws are
rectangular, and multiplying
together the number of pieces
along the short and long edges
gives the total number of pieces.
This jigsaw has 468 pieces. The
prime factors of 468 are 2, 2, 3,
3 and 13, so possible dimensions
of the jigsaw are 26 x 18 or 36 x
13 or 39 x 12, and so on. But
conventional jigsaws aren’t long
and thin, so 26 x 18 is the only
jigsaw-shaped rectangle. This
would have 2 x 26 plus 2 x 16
(not 18, to avoid counting the
corner pieces twice) = 84 edge
pieces, including corners.Tom Gauld
for New Scientist
a long time to recover that.
It took me many months to
realise exactly what I found so
disturbing about the moon: it, too,
was upside down. Once I grasped
this, I could “see” the man in the
moon for the first time in my life.
Changing tune
Will composers run out of new
combinations of musical notes
to create original melodies? Or
are there infinite combinations?
(continued)
Richard Widdess
Department of Music, SOAS
University of London
The question cannot be answered
because it is under-specified.
If it is just a question of new
combinations of notes, then it
is obvious that we can always
add another note to an existing
sequence, just as we can add 1 to
any other number and generate
a new number. If there is a limit
on the length of a melody, or
a minimal difference between
melodies that is greater than
one note, or there are rules
of combination that must be
followed, then the number of
possible melodies may be finite.
In language, linguist
Noam Chomsky has argued that
recursive syntax can, in principle,
generate an infinite number of
grammatical sentences. It is
an intriguing question, as yet
unresolved, whether the same
could be true of melody.Kaye Butler
Highworth, Queensland, Australia
A previous answer to this question
(4 December) cites a musical piece
by John Cage with the title 4’ 33”
(4 minutes and 33 seconds of
silence, i.e. absolute zero sound).
For the uninitiated, 4’33’’ isn’t
a random number but is
273 seconds. Geddit?Natalie Roberts
Watford, Hertfordshire, UK
John Cage’s silent composition
4’33” may be considered a baseline
for any variation of tune, just
as long as the duration and/or
sounds are altered. This appears
reasonable, theoretically speaking,
but reminded me of something
I read that illustrates a flaw in
this approach.
The estate of Cage supposedly
threatened to sue another artist,
Mike Batt, for plagiarism. Batt had
launched an album with his band,
The Planets, that included a piece
composed of 1 minute of total
silence. Cage’s lawyers apparently
argued that this new silent
composition was plagiarised
(the lawsuit turned ou to be a
publicity stunt).
So although the variety
of “tunes” may be infinite,
too little variation will lead to
accusations of plagiarism. By
the way, Batt pointed out that
his piece was better anyway, as
he could “say in one minute what
Cage could only say in 4 minutes
and 33 seconds”. ❚“ It took me many
months to realise
exactly what I found
so disturbing about
the moon: it, too,
was upside down”