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All the world's a test, as well as a
stage, and those with high scores can bow like triumphant
actors before walking away with the prize, which, in the
case of IQ tests, goes to those who know the most
bypasses. Consider three trivial examples: |
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● I before E
except after C or when sounded like A |
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● HOMES |
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● Thirty days have
September, April, June and November |
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The grade-school student who knows the
first will score higher on a spelling test than fellow
classmates who attempt to memorize the spelling of
individual words. The
pupil who learns the second can effortlessly rattle off
the names of the Great Lakes. Knowing the third insures that
overnight homework assigned on April 30 will never have
points shaved off because it is dated April 31. Those of
us who learned these mnemonics—these
bypasses—at an early
age scored higher on tests and were regarded by our
teachers as being more intelligent than our peers,
although bypasses are much more than a schoolchild's bag of
mnemonics.
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Bypasses: A scientifically proven problem-solving
technique |
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Bypasses have been defined with mathematical precision
(Melzak, 3-16) and applied to
areas as diverse as telecommunications, nuclear-magnetic
cooling, and Special Relativity; but Melzak's rough definition
suits our purposes: "a bypass [is something]
which promotes a transport or a passage or the solution of
a problem in a three-stage reduction process whose first
and last stages are each other's inverses." Bypasses are
easier than Melzak makes them sound. In fact, a bypass
is simply a middle step that replaces a harder problem
with an easier one.
Here's an example far removed from youthful mental
calisthenics. Consider an elderly man taking a senility
test. The tester asks him to count down, aloud, from 100
by 7. A surprisingly large number of people get tangled up
because the task is harder than it first appears—try
it and see for yourself. A clever person would
simply replace the relatively "hard" problem of repeatedly
subtracting 7 with the "easy" problem of repeatedly
subtracting 10 and adding 3.
Is this a bypass? Let's see if it meets the
requirements. Step 1 is counting down from 100 by 7. Step
2 is replacing "subtract 7" with the equivalent "subtract
10 and add 3" and using this to solve the problem. Step 3
is returning to the first step, now substituting 93 for
100. This is a classic bypass: Start at the first step,
move to an easier solution domain at the second and work
out the answer there, then make the round trip back to the
first. Another example can be seen in the famous WW2 adventure movie The Great Escape. Hundreds of
Allied POWs are confined in a German camp surrounded
by an electrified fence and fortified towers manned by Nazis
with machine guns and search lights. The prisoners escape
by digging a tunnel
under the fence—there's
the bypass—to a location safely past German
scrutiny. That is
right-brain thinking at its best: a creative, clever solution to a thorny puzzle. |
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| Newton and
Einstein: Two Geniuses, One Idea |
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Bypasses revolutionized Complexity Theory when Dr.
Melzak introduced them around twenty years ago, although the basic idea
of solving a difficult problem by
replacing it with an easier one goes back at least as far
as Sir Isaac Newton's invention of differential
calculus to solve hard problems that he subsequently restated in geometric terms for publication
in the Principia. Albert Einstein developed much of
Special Relativity, and all of General Relativity, with
bypasses proposed by Hermann Minkowski, his former
mathematics professor at the ETH in Zurich.
Please don't misunderstand.
Nothing approaching that degree of difficulty will be found here. In fact, some of
the bypasses you'll encounter on the next page are so
simple they fall into the category of tips, tricks, and
secrets—but consider
this
classic observation: What is a trick the first
time one meets it is a device the second time and a method
the third (LeVeque,
7). |
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References and Authorities |
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| W. J. LeVeque. Fundamentals of Number
Theory. Reading, Massachusetts: Addison-Wesley, 1977. |
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| Z. A. Melzak. Bypasses: A Simple
Approach to Complexity. New York: Wiley, 1983. |
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