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Robot Mathematician Solves Nine Simultaneous Equations
In this age of electronics,
pocket-sized computers such
as the iPhone make math
easy and portable.
A ONE-TON machine that in a single
action can solve nine simultaneous
equations with nine unknowns so
complicated in form they might well
require days of laborious computa-
tion by trained mathematicians has
been developed at the Massachusetts
Institute of Technology. Known as the
simultaneous calculator, the machine
is the product of three years’ research
by Dr. John B. Wilbur of the depart-
ment of civil engineering. Cooperat-
ing with him has been Dr. Vannevar
Bush, vice-president of technology
and dean of engineering, who under
the Institute’s program to eliminate
delay and complications in engi-
neering and research, has previously
made important contributions to the
mechanical solution of mathemati-
cal problems, including the famous
differential analyzer. The simultane-
ous linear algebraic equations solved
by the new machine occur constantly
over a wide range of engineering and
scientific analyses. Thus although the
calculator was originally designed
for the solution of problems in civil
engineering, such as those involved
in the construction of skyscrapers, it
is expected to prove equally useful in
such diverse fields as nuclear phys-
ics, geodetic surveying, genetics and
psychology. The mathematician will
be able to use it for the evaluation of
determinants especially and in sev-
eral other fields, since the machine
under some circumstances can solve
for even more than nine unknowns.
The machine weighs approximately
2,000 pounds and has more than
13,000 separate parts, including 600
feet of flexible steel tape and almost
1000 ballbearing pulleys.
‘Robot Einstein’ outdone by today’s cell phones
Now, though, a 2,000-pound machine with 1,000 ball-
bearing pulleys like the one that Wilbur developed is far
from necessary. Computers rely on electronics rather than
mechanics, and those electronics improve every year. An app
available for the iPhone today can solve a system of 200 lin-
ear equations with 200 variables in 0.15 seconds. And it fits
in your pocket.
One generation’s most impressive inventions can over time
become another’s oddities — rendered obsolete and even
cumbersome by more advanced technologies. Such was the
case with a mechanical calculator developed by John Wilbur
of MIT in the 1930s.
By tilting a series of plates and then making a single movement of the mechanism, Wilbur could solve a system of
nine linear equations with nine variables in just a few seconds. Solving such sets of algebraic equations had — and still
has — cross-disciplinary appeal, because the technique allows
scientists to study complex systems in which many variables
depend on each other. At the time, solving for nine variables in
this way could take days with a paper-and-pencil approach.
As for Wilbur’s car-sized machine, it seems to have vanished along with its usefulness. For many years the machine,
dubbed “Robot Einstein,” sat in a hallway of Building 1 at MIT,
home to the department of civil engineering. But the machine
was last seen in the late 1950s, and (though a replica has
turned up in Tokyo) no one has been able to track down the
original’s whereabouts. — Elizabeth Quill
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