to the nothing
of the zero of mathematics
zero's progress through the ages, is a process beset with obstacles
both theological and practical. in the end it was the practical
applications that won the day, for zero was the crux of that
great medieval invention, double entry bookkeeping. all the
priests' arguments were finally no match for the emerging
power of the modern capitalist machine. all those zeros at the
bottoms of merchants' ledgers--each signifying a perfect balance
of credits and debits--served to impart to zero the status of
a true number; a status that was further enhanced by the introduction
of negative numbers, which also arose naturally in the new system,
as when debts exceeded earnings. slowly, zero came to be seen
as one point along a continuous spectrum, the fulcrum of a line
stretching indefinitely to the left with the negative numbers
and indefinitely to the right with the positives.
in modern mathematics, zero has taken on a life of its own.
no longer simply a number, zero has become one of the pivotal
concepts in many mathematical systems. in calculus and analytic
geometry, it manifests as the maxima and minima of functions
; in set theory, it becomes the null or empty set , and as it
is "infinity's twin. dividing by zero always equals infinity;
the two numbers are thereby conjoined in a strange symbiosis
being, "equal and opposite and equally destructive."
perhaps nothing has surprised mathematicians so much as the
fact that all the numbers can be generated from the nothingness
of the empty set, a feat elegantly demonstrated by John von
Neumann, the great architect of the modern electronic computer.
on first encounter, many people find von Neumann's prestidigitation
unsettling frankly likening this mathematical hat trick to setting
a host of angels "dancing on the head of a pin." that the entire
spectrum of the numbers can be created ex nihilo, as it were,
remains one of the more enigmatic features of modern mathematics.
- based on a text by Margaret Wertheim
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