FRESNO - As twilight falls each evening in the Westerly sky above the City this week, look south for the Moon. From the 1st through the 8th it makes its way past a long diagonal line of planets.
On the 1st the thin waxing crescent stood above and to the right of Mercury, which was almost down on the horizon (try binoculars). On the 2nd and 3rd the Moon passed faint Mars and brilliant Venus. By the 4th the Moon, was a thick crescent, is off to the right of bright Jupiter. Four nights later, by the 8th, the now-gibbous Moon will be very near Saturn. Also in the line, but too faint to see without binoculars or a telescope, are Uranus and Neptune
This month, all nine planets cluster together in one small swath of
the sky. My new friend's neighbor has a cat with the same name as mine.
My stepdaughter in New Jersey and a psychologist friend in L.A. are
expecting a baby on the same day.
Are these portentous cosmic occurrences? Or merely curious
coincidences?
It's not an idle question. Much of science involves trying to
determine which events are connected by common causes, and which are
linked only by the luck of the draw.
'In mathematics, in science, and in life, we constantly face the
delicate, tricky task of separating design from happenstance,' writes
Ivars Peterson in his latest book, 'The Jungles of Randomness: A
Mathematical Safari.'
Is a cluster of cancer cases in McFarland, CA the result of toxic
residues, or a normal blip in the distribution of disease? Are those
black spots in the photograph evidence that house-sized snowballs are
raining on Earth, or random noise in the detector?
Mathematics can help sort out these scenarios. Indeed, a little
mathematical know-how may be the only known antidote to a pervasive
frailty of the human mind: the perception of causes and connections
behind purely chance events.
As Peterson, the mathematics and physics editor for Science News,
points out, human beings are programmed to perceive patterns in chaotic
events - the better to make sense of an often confusing visual world. They
see forms in cracks on the ceiling, faces on the moon, woolly sheep in
clouds. They group clusters of adjacent stars into images of warriors and
serpents and dippers in the sky.
'Humans are predisposed to seeing order and meaning in a world that
too often presents random choices and chaotic evidence' he writes.
Indeed, most amazing coincidences are created in the mind - like the constellations in the sky - from the human tendency to find plausible
links between objects and events.
Consider two strangers sitting in adjoining seats on airplane. What
are the chances that they will have something in common?
Given the vast number of possibilities - from shared favorite authors
to hometowns, past lovers and current jobs, schools and acquaintances - it
can be shown that in 99 times out of 100 the two passengers will be
linked in some way by less than two intermediaries, according to
mathematician John Allen Paulos.
The number of things the two people don't share will vastly outweigh
the number of things they do. But only the shared links will be
remembered as amazing coincidences.
The same is true, Paulos says, of prophetic dreams. Often, people will
dream about, say, an earthquake or a plane crash, only to read in the
paper the next day that it actually happened. But given the fact that
roughly 250 million people in the U.S. spend several hours in dreamland
each night, 'we should expect as much. In reality, the most
astonishingly incredible coincidence imaginable would be the complete
absence of coincidence' he said.
Sometimes, coincidences do point to deep truths. Einstein, for
example, was bothered by the well-known fact that gravity and inertia
balance out exactly in our universe. That is why a bowling ball and a
golf ball dropped from a high shelf hit the ground at the same
time--because while gravity pulls harder on the bowling ball, inertia
endows the bowling ball with a greater resistance to being pulled.
Einstein thought this uncanny equivalence had to be more than a funny
coincidence - and came up with the idea that both gravity and inertia are
aspects of a bigger picture - the curvature of space-time.
In the same way, there is a lot more than coincidence behind the fact
that more smokers than nonsmokers get lung cancer. Sometimes coincidence
does point to a cause.
How can one tell the difference between coincidences based on cause
and those based on chance? Statisticians use all kinds of filters to
determine which is which, but even the mathematically immune can use some
easy tricks to keep from getting fooled.
For example, they can remember that large numbers of anything are
bound to create coincidences. For example, it is certain that at least
250 of the 250 million people living in the United States will experience
a one-in-a-million coincidence every day - purely by chance.
And while the odds that any one person will win the lottery twice in
the same year is astronomical, the percentage that any of the millions of
previous lottery winners will win another lottery in their lifetime is
pretty good.
The fact is, events that people normally think of as highly unlikely
are often very likely. If someone flips a coin a hundred times, the
chances of coming up with a long string of heads or tails are more likely
than not. It's not an amazing coincidence. It's the natural order of the universe.
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