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Calculus is a powerful mathematical
toolbox for dealing with phenomena in a
state of flux, from the flow of water to the
expansion of the cosmos. As such, a
better name for it would be ‘fluxions’ – a
term coined by Isaac Newton, one of the
two 17th Century mathematicians
regarded as its inventors, the other being
the German Gottfried Leibniz. Not that
Newton saw it that way. Having invented
it in secret in the 1660s, he was horrified
when Leibniz went public with similar
methods, having independently
discovered them about 10 years later.
Newton launched an unjustified
campaign of character assassination
against Leibniz, yet could not stop the
adoption of his rival’s name for the
technique (from the Latin for ‘counting
stone’). It’s now known that some basic
ideas in calculus had been explored
much earlier. For example, Archimedes
showed how to work out the area
enclosed by curves by dividing it up into
tiny strips. This is a trick exploited in
integral calculus to work out the total
effect of a series of tiny changes.
However, none of Leibniz and Newton’s
predecessors realised the full power of
what they were working on.
WHO REALLY DISCOVERED?
NO EASY ANSWER
CALCULUS
Isaac Newton Gottfried Leibniz
We most definitely will! New elements are
created by smashing known ones together
at super-fast speeds. Ununoctium (first
identified in 2002, but only recently
recognised and due to get a proper name
soon) is the heaviest known element and
was made by firing about 40 quintillion
calcium nuclei (travelling at almost the
speed of light) into californium (which is
itself man-made)! This made just three
ununoctium atoms that hung around for
about one millisecond before radioactively
decaying. The laboratories that found
ununoctium (and other elements) are
already busy smashing more atoms
together in the search for elements to start
a new row of the periodic table. MLWill we discover any
more elements?
Could
Neanderthals
speak?
Forty years ago, the consensus
was that they could not.
Neanderthals didn’t make cave
paintings, or flint arrowheads, and
their larynx wasn’t positioned low
enough to allow them to make
the full range of human vocal
sounds. But more recent
discoveries have shown that
Neanderthals had a hyoid
bone, tongue nerves and
hearing range that was very
similar to modern humans, and
quite different to other primates.
Neanderthals also shared the
FOXP2 gene with us, which is
thought to be involved in
speech and language. Prof
Steven Mithen of Reading
University has suggested
that Neanderthals may
have had a ‘proto-
language’ that was
halfway between speech
and music. LV