The numerical expression of a scientific statement has traditionally been
the m anner by which scientists have verified a theo retical description of the phy sical world. During this
century there has been a revolution in both the nature and extent to which this num erical comparison can be
made. Indeed, it seem s likely that when the history of this century is definitively written, it will be the
developm ent of the computer, which will be regarded as its greatest technological achievem ent - not nuclear
power. While it is true that the origins of the digital com puter can be traced through the work of Isaac
Babbitt, Herm ann Hollerith, and others in the nineteenth century, the real advance came after the Second
World War when machines were developed that were ab le to carry out an extended sequence of instructions
at a rate that was very much greater than a hum an could m anage. We call such machines program mable.
The electronic digital computer of the sort developed by John von Neumann and ot hers in the 1950s really
ushered in the present com puter revolution. While it is still to soon to delineate the form and consequences
of this revolution, it is already clear that it has fo rever changed the way in wh ich science and engineering
will be done. The entire approach to numerical analy sis has changed in the past two decades and that change
will most certainly continue rapidly into the future. Prio r to the advent of the electronic digital computer, the
emphasis in com puting was on short cuts and methods of verification which insured that com putational
errors could be caught before they propagated through the solution. Little attention was paid to "round off
error" since the "hum an com puter" could easily control such problem s when th ey were encountered. Now
the reliability of electronic machines has nearly elim in ated concerns of random error, but round off error can
be a persistent problem.
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