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Foretelling Eclipses

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                Foretelling Eclipses
     Becoming a Prophet Is Easier than You Think

                  William H. Calvin


      If you are in a tight spot, you may find yourself wishing for a
solar eclipse to turn day into night, as in _A Connecticut Yankee in
King Arthur's Court_.  If you knew the eclipse was going to happen
(but others didn't), you could pretend to "command the heavens.
While Mark Twain's solar eclipse was an invention, his inspiration
was probably a real-life incident involving Christopher Columbus in
1504, where the explorer "stole the moon" to get himself out of a
similarly sticky situation in Jamaica.
      I doubt that Columbus was the first to pretend to manipulate
the heavens (and since lunar eclipses are seen far more frequently
than solar eclipses, they were probably the typical target).  One
imagines that eclipse prediction was a standard tool of the prehistoric
priesthoods, back in the days before it was commonly understood
that the clockwork orbits of earth and moon were all that eclipses
involved (and that neither seems to be modified by prayers and
offerings).  A shaman who could appear to move the heavens might
have been able to dominate neighboring tribes as well -- and oft-
fulfilled prophesies might convert a shaman into a full-fledged
prophet, lending authority to what the shaman had to say on other
subjects.
      Columbus probably had a nautical almanac that listed
upcoming eclipses -- but remember that 1504 was long before
Galileo or Newton, well before those orbits were understood.  The
astronomical lore of the times probably used a list of magic numbers,
rather like that of the Mayan astronomers who wrote the Dresden
Codex (no, it's not written on porcelain -- that's just the German
museum where the bark now resides, one of the few pieces of
"pagan" writing to have escaped the Inquisition-haunted Spanish
priests, who zealously destroyed what they couldn't understand).
      Back before record-keeping, however, there were likely some
simple methods for eclipse prediction.  Knowledge of them seems to
have been lost to modern astronomers, who might be unable to
impress the natives if shipwrecked on some island without their
computers and reference books.  How to make stone tools was also
forgotten when metal tools became popular; only recently have
archaeologists such as Nick Toth rediscovered how to make an
Acheulean hand ax or a Clovis-style spear point.  Similarly I have
been trying to recover prehistoric methods of eclipse prediction,
methods far simpler than those orbital calculations or lists of magic
numbers.  Having discovered a dozen methods so far, I have
concluded that warning of imminent eclipses is far easier than it first
appears.  Here I will just give a short course in how to do it,
emphasizing how success can be improved by using crystals,
necklaces, and suitably-placed windows.  In _How the Shaman Stole
the Moon_ (Bantam, 1991 hardcover, 1992 softcover), I explain why
the methods work, relate them to archaeoastronomy sites such as
Stonehenge and those in the American Southwest, and discuss the
origins of protoscience.

The Holy Leaf
      Total _solar_ eclipses are impressive but rare.  A partial solar
eclipse is hard to see, even if you know when it is going to happen;
the only one I've ever seen via naked eye happened to occur just
before sunset, as the sun and moon set together over the Olympic
Mountains as viewed from Seattle.  You can sometimes study the
sun's shape just before sunset, as its brightness is filtered enough by
the long path through the atmosphere so as to permit brief glimpses.=20
And that evening as the sun neared the horizon, it obviously had the
moon just in front of it, obscuring its lower left; the three-
dimensionality was quite striking.  But most solar eclipses don't
occur so conveniently close to the horizon.
      Any fan of eclipses has heard of pinhole cameras, producing
an inverted image of the eclipsing sun on a screen.  Pinhole images
are far easier than you might think; this isn't a matter of needing a
darkened tent with a hole in the roof.  Pinhole images occur in
nature, as you can discover lounging in the shade of a tree whose
leaves have been perforated by insects.  Likely someone remembered
those little round spots of light that had inexplicably turned into
crescents before the world darkened.  Odd-shaped spots, all facing
the same way, is certainly striking; you feel as if "something is
happening."  Warped reality.
      Just hold a perforated leaf at arm's length toward the sun, the
way that a child instinctively does to backlight an autumn leaf.  But
you look down at your chest at the leaf's shadow -- and see the little
crescent of light in the midst of the shadow.  As you move the leaf
farther away, the light spot changes from the shape of the insect's
hole to the shape of the eclipsing sun.  The smaller the hole, the
sharper the image.  If leafless, merely cross your fingers (for good
luck?) to produce a small opening and inspect your hand's shadow
for a little crescent.

The Crystal Warning
      Crystals, at least those with many small-but-flat reflecting
surfaces, also ought to be useful for viewing eclipses; a small facet
serves to combine the pinhole with a mirror.  Just pull the shades
except for a small opening, lay your crystal or jewel on the window
sill in the sunlight, and walk up to inspect the crescent spots
reflected onto the walls.  And watch them slowly change.  Spangles
embedded in a plaster wall can produce the same effect, if small
enough (a square millimeter is about right).
      Once you've learned one of the pinhole methods, you can
give an hour's warning of a solar eclipse, know it's happening long
before anyone else notices that the sun is dimming.  Still, you can't
spend all your time watching pinholes for solar eclipses, on the off
chance one might happen.  We now know that solar eclipses can
happen only at the new moon, and a superstitious wariness about
new moons probably developed into an important bit of astronomical
lore for the prehistoric shaman.  When the crescent moon can no
longer be seen before dawn, watch out for the next several days.=20
When the crescent moon can again be seen above the sunset (a day
especially important in religions such as Islam), you can relax your
vigil.

The Clinched Fist Prediction
      Similarly, lunar eclipses only happen at the full moon.  But
the moon looks full for several nights:  Which one is it?  Back
before orbits were understood, "full moon" was likely defined as the
night that the moon rose just before sunset, looking especially large
and rosy (that's the night when there's a chance of a lunar eclipse; it
is often the night _before_ your calendar indicates a full moon).
      There are ways to narrow down solar eclipse danger zones
even further by paying attention to the more common lunar eclipses.=20
Following a lunar eclipse, there's no chance of another for the next
five full moons, but then there is a 56 percent chance of another
eclipse on the sixth full moon.  If one doesn't occur then, there is
still an 11 percent chance of a lunar eclipse on the twelfth full moon.=20
If you raise the alarm every sixth and twelfth full moon following an
observed eclipse, you've got two chances out of three of acquiring a
reputation for foreknowledge.
      You can imagine how this might have been discovered, back
before careful records were kept.  Surely a second lunar eclipse
within a year of another would be cause for some observers to
discuss when the previous one occurred, counting backward to
discover that it had been either six or twelve full moons ago.  And
so the sixth and the twelfth full moon after an eclipse could readily
get the reputation of being particular danger periods.  _One counts to
six, and then counts to six again_.
      Too bad we only have five fingers, you say?  Contrary to the
usual decimal notions, one can readily count to six and twelve on the
fingers.  On the sixth full moon, you close down those five extended
fingers and clench your fist.  On the seventh, you pick up the count
on the other hand, extending one finger -- and so on to two clenched
fists upon the twelfth full moon.  That makes the full moons
coinciding with a clenched fist the "dangerous ones," threatening to
disappear.  After a year with no eclipses, the danger zones expand to
include the full moon preceding a multiple of six, i.e., 17 _and_ 18,
23 _and_ 24, 29 _and_ 30, etc.
      Solar eclipses, I discovered from studying the reference books
on eclipses in history, also occur on the same six-month spacing as
the lunar eclipses.  They're at the new moon which precedes or
follows the full moon eclipse alert.  Thus you need not get started on
_solar_ eclipse prediction by observing one solar eclipse and
counting new moons thereafter:  You get synchronized by observing
even a partial _lunar_ eclipse, counting by sixes, and watching out
for the new moons that precede and follow the lunar eclipse alerts.
      So lunar eclipse prediction is potentially quite easy, so long
as you can be wrong a certain amount of the time.  The method is
crude, compared to modern scientific theories, but it could have been
quite successful for an interesting reason.

When the Shaman is Half Right
      The psychology of intermittent reinforcement suggests that
being wrong occasionally wasn't a problem:  it was an advantage (at
least, to the shaman).  What would you do if you feared eclipses, but
were solemnly told that one was coming -- and by someone who was
right last time?  Trying to prevent eclipses through fervent prayer,
before and during an eclipse, surely must have _seemed_ to work
most of the time.  After all,
      =09 many of the predicted eclipses didn't happen (the methods
           were crude and so there were a lot of what are now
           called "false positives"); this could have led a lot of
           people to believe that their prayers had prevented the
           eclipse; and
      =09 many of the predicted eclipses that nonetheless happened
           were _partial,_ allowing someone to conclude that the
           prayers had reversed the moon in its tracks, preventing
           a total eclipse.
And so prayer was powerfully reinforced -- it seemed to work.  If
the priestly predictions were nearly always wrong, of course, the
announcements would have soon lost their credibility.  If the
predictions were always right, eclipses lose their fascination for many
people.  Being right just enough of the time is what makes some
situations so attractive, as gambling illustrates.
      I can see how large groups of people would have been
psychologically trapped, that _predicted_ eclipses would have made
them believe in the power of wishful thinking.  A control
experiment, that would have omitted prayers after half of the eclipse
warnings, would have shown them that the eclipse occurrence or
duration was independent of their prayers.  Again, priestly credibility
would have suffered.  But the control experiment is a recent
scientific innovation, invented after scientists discovered that they
were fooled too often by mere coincidence.
      I'm not surprised that people were fooled by _post hoc ergo
propter hoc_ -- the classical fallacy of "_after_ this, therefore
_because_ of this," a fallacy that fools us every day even when we're
alert to it.  Despite its unreliability, one thing following another is a
powerful way in which we learn our way around our environment,
especially when dealing with the unfamiliar, such as a rare event.
      Partial eclipses might have gotten prayer started back before
prediction was discovered, wishful thinking during the initial phases
being credited with the avoidance of a total eclipse.  And given
something (the shaman's warning) to trigger the prayers a few hours
or days ahead of time, the belief in the power of prayer to move the
heavens was sure to emerge -- and, of course, prediction itself would
have become valued by the leadership, a powerful incentive to more
and better science.
      Frequently-successful eclipse prediction would have helped
the shaman with everyday matters as well.  Forget for a moment the
literary depiction of the shaman as some sort of psychedelic guru and
consider what the anthropologists say about the shaman's range of
skills.  Besides predicting weather, the shaman of most known
hunter-gatherer tribes is supposed to be able to cure illness and bring
down illness upon enemies (or at least _appear_ to do so!).  Given
the strength of the placebo effect (for pain, it is now estimated that
one of every two sufferers gets some temporary relief just from the
power of suggestion), one can easily imagine that a shaman who had
just manipulated the moon or sun would have even more success
than usual at relieving pain.
      Even if the leadership was blind to the Columbus-style
possibilities for manipulation, even if the healers didn't know about
eclipses, the prediction aspect itself would still have been handy to a
fortune-teller -- and we humans seem to have an inordinate appetite
for predictions about what the future might bring.  While eclipses
might be unrelated to "You will meet a dark stranger" and other such
staples of the repertoire, a fortune-teller's ability to occasionally
predict eclipses would be a powerful validation of her or his abilities.=20
(If she's right about the moon disappearing for an hour, then surely
she has a powerful pipeline to the spirits -- and maybe we'd better
make her a nice gift).

When Your Shadow Points at the Rising Moon
      "Reach out and touch the moon" if you can (but usually you
can't).  The only times when the full moon rises in your sunset
shadow are, however, spectacular -- they tend to be followed by
lunar eclipses in the next several hours.  Like the leaves and crystals
that give an hour's warning of a solar eclipse in progress, the shadow
directions are capable of being used for a few hours warning of a
lunar eclipse.
      It's all because the earth's shadow, narrowing like a cone,
stretches out into space; you can't see it, but it is just to the _left_ of
the rising moon (should your sunset shadow point to the _right_ of
the moon, you can be sure that no eclipse will happen, as the moon
moves left during the night in its orbit).
      You need not understand that to invent a simple rule, to
watch out for those full moons when the sunset shadows point at the
rising moon.  If your sunset shadow points at the moon when it is
already a half-dozen diameters above the horizon, that doesn't count.=20
If the moon rises after sunset (assuming that you haven't some hills
in the way, elevating the horizons), you're safe too.  It is when the
full moon is no more than a few diameters off the eastern horizon at
sunset that an eclipse is possible -- provided the Pointing Shadow is
somewhat to the left of the moonrise.
      But what about all of those hazy sunsets over the Pacific,
where the shadows are pretty hard to see?  You can solve such
problems (and those associated with the fuzzy edges of shadows) by
looking directly at the setting sun, getting your line of sight from an
edge of the sun itself rather than from a shadow.  And how can you
do that, if you also have to look at the rising moon?  Yes, I know
that you can turn around -- but how do you know that you've turned
exactly half a circle, short of using a modern surveying instrument?

The Sun Priest and the Moon Priest
      The low-tech solution is to get a friend to help:  use _two_
observers, standing some distance apart from one another.  Observer
_A_ stands still while Observer _B_ moves around until the rising
moon is located just behind _A. _ Then _B_ remains standing there,
and Observer _A_ (continuing to stand still) sights past him toward
the setting sun.  If the setting sun is indeed behind _B,_ then the
observers must be on the line from sun to moon.
      Now it seems unlikely that prescientific peoples would have
formulated the rule as a "straight line" relationship.  They'd have
personified things, if folk culture is any clue.  They might have
called Observer _A_ the "Sun Priest" because he watched the sunset,
called Observer _B_ the "Moon Priest" (or some such).  They would
have watched for those occasions when the sun "touched" the Moon
Priest in the same manner as the rising moon had "touched" the Sun
Priest.  Symmetry, no less.  How close is close?  For lunar eclipses
in the evening, several diameters (the sun and moon are both about
half a degree); for eclipses after midnight, warnings will be pretty
unreliable (but maybe few will notice, being asleep!).
      You can also use the Two Priests method to determine the
day of the equinox; this will be left as an exercise for the reader's
ingenuity.

What Good is Half a View?
      The Pointing Shadow and Two Priests methods require that
you get the hills out of the way.  >From an island or peninsula, you
can usually find a beach with a view, giving a flat horizon to both
east and west (my favorite is that promontory southeast of Athens,
where the Temple of Poseidon is).  Most people, living in most
places, don't have such nice viewpoints with their opposite views.=20
Their shaman would search for methods that would allow successful
warnings from observations involving only half a horizon:  northeast-
to-southeast, for example, without any need for a view to the west.
      I have a variety of solutions to that problem; they're not
entry-level in quite the manner of the others, but they are far simpler
than the intermediate-level magic numbers and the high-level orbital
calculations.  These low-level methods all involve using a familiar
viewpoint and knowing a reference direction or two.
      Lacking the proper sunset view, you have to make do with
the sunrise view that morning.  Fortunately (to use an example from
autumn or winter), sunrise is as far south of due east as the sunset
will be south of due west.  Therefore the earth's shadow cone that
evening at sunset will be equally north of due east.  A moonrise
which is as far north of due east as the sunrise was south of due east
is an eclipse warning.
      All fine and good, provided that you've already discovered
how to determine due east from the equinox (one of the outcomes of
that reader's exercise).  But there is an easier way:  just use the
extreme position of sunrise in the southeast (which occurs on the
winter solstice) and the other extreme sunrise position in the
northeast (from the summer solstice).  They're both the same
distance from due east.  Thus, all you need do is to note the position
of today's sunrise relative to the nearest extreme (winter solstice
sunrise in this example); if moonrise tonight is equally far from the
other extreme, you have an eclipse warning.

Measuring the Horizon with a Necklace
      How do you compare those angles or arcs (as we post-
Euclidian types would say)?  The nicest way I know is to hold a
string of beads at arm's length, say an unfastened necklace with a
little slack so that beads can slide a ways (to start, force all the beads
over to the right end).  Hold it up to the sunrise with the necklace's
right end at the well-known winter solstice sunrise direction, which
you have memorized (or because you have erected a marker, though
it need not be as elaborate as those megaliths at Stonehenge).  Slide
your left hand over until reaching the rising sun and take a hold on
the bead under the sun.  Let the other beads slide down the slack.
      Maintain that separation between the two sets of beads (tie a
knot or something) until evening, when you observe the moonrise.=20
Hold the end of the necklace to line up with the summer solstice
sightline and see if the moon rises over the last bead in the tightly
packed group from the morning's observation.  If it comes close,
there's your eclipse warning.  _Solstice directions are actually useful
for eclipses_.  My guess is that's why the architects of sites such as
Stonehenge were so fond of immortalizing sightlines to the winter
and summer solstice sunrises.  Their use as anchors for a calendar
has always seemed illogical because the sunrise position on the
horizon changes so slowly from day to day (they're not called the
"standstills" for nothing); you can miss the reversal day by a week,
especially when it's cloudy in winter, and that's no way to run a
calendar.
      A necklace, of course, isn't required; you can use any old
stick, breaking it to the right length to preserve the data until
moonrise.  Note that you only have to make a very simple
comparison -- it's not really measurement, doesn't really require a
knowledge of geometric concepts such as angle.  But you can see
how the fancier concepts might have followed, once a shaman
discovered how useful such a technique was.  In particular, the
necklace beads (pi=A4on nuts are favored by the Indians as they have a
soft core that can be punched out after grinding off the two ends,
handy for stringing onto long hair) would make a good calibrated
ruler, a nice way into inventing the counting and record-keeping
needed for intermediate-level magic number schemes.
      We've solved the lunar eclipse warning problem for those
folk living on a eastern coastline, having a sea horizon but only to
the east.  What about those poor folks inland, with a nice even
horizon that is, alas, elevated several degrees?  _The method will still
work_, surprisingly enough.  There are problems with the Two
Priests and Pointing Shadow methods where horizons are elevated:=20
since the sun rises at an angle to the vertical, so a sunrise delayed by
a hill is also a bit to the south of where it would have been if you
had removed the hill.  Elevated horizons can change a straight line
into a dogleg, because a delayed sunrise appears slightly to the south
and a premature sunset is also shifted south.  If both horizons are
equally elevated, the error doubles.
      But such problems are minor when dealing with only an
eastern horizon.  Both sunrise and moonrise are shifted around
toward the south, but since you're always taking differences with the
solstice directions (also shifted), the errors cancel.  The horizon just
needs to be _uniformly_ elevated.

The Ditch and Bank
      One way to smooth out a bumpy horizon is to build a level
bank nearby, preferably in an arc around the observer's traditional
viewing position.  Thus both summer and winter sunrises are equally
delayed, as are moonrises.  An enigmatic feature of the megalithic
monuments in the British Isles (seen most impressively at Avebury, a
hour's drive to the north of Stonehenge) is a circular ditch and bank,
the former likely the source of the latter.  For the elevated horizon
scheme to work, only a fraction of a circle is actually needed, from
northeast to southeast.
      An easy way to level such a bank is after the winter rains fill
the ditches:  use the high-water mark, making the top of the bank
some fixed height above it.  This should have been easy at
Stonehenge and Avebury, as they dug through the thin soil and well
into the underlying chalk; a floating scum of chalk powder leaves
behind an excellent bathtub ring.  The do-it-yourselfer might prefer
to utilize the top of a fence.

Sunrise atop a Pinnacle
      Before anyone digs a ditch or builds a fence, let me point out
a far simpler method:  just pivot around a pinnacle (such as a tall
fence post), keeping the rising sun hidden behind it (move back until
just a little of the left and the right side of the sun peek out on each
side).  You will have to keep moving north as the sun rises, to
maintain the two-point view.  The sun finally crests the post,
showing three pinpoints of sun:  left, right and over the post.  The
sun then becomes too bright to look at, so you look at your feet and
mark the final viewing position for the day.
      >From one day to the next, the observer's final position will
change, eventually reaching a northerly extreme at winter solstice,
then reversing.  The southern end of the path traced by the diligent
observer will mark the summer solstice viewing position.=20
Maintaining the two-point view will cause you to create a circular
arc centered on your pivot (you have, after all, created a light lever,
seesawing with the seasons); the curved observer path will be about
as long as the distance to the pivot.
      After sunrise, lay a long stick along the ground (or rope, or
lengthy necklace) from your final viewing position to the nearest
turnaround.  Then take it over to the other extreme, laying it out
along the observer's path.  Observe the full moon that evening,
marking the observer position when the moon begins to crest the
pinnacle.  If it is in the predicted place marked by the end of the
stick, solemnly pronounce your eclipse warning.  You can do the
same thing, holding a forked stick against the nearest solstice marker.
      Instead of a standard observer watching the sunrise move
every day along the horizon, one has a moving observer obtaining a
standard view of sunrise every day.  The observer's position becomes
the measurement.  Best of all, the pinnacle pivot saves you leveling
the horizon:  the top of the pinnacle is the standard elevation at
which both sunrise and moonrise are observed.  Like the fence, the
lower the better:  pinnacles little higher than the tallest bump on the
horizon are to be preferred.  The observer's arc needs to be fairly
level; shorelines and old lake beds are ideal (and many a parking lot
will do).  A pier piling off an east-facing shoreline would make a
good pivot.

A Calendar without Counting
      The longer the distance to the obscuring pinnacle, the more
the daily position jumps.  With a lever arm of several miles, you can
create an excellent calendar without any need for counting days,
since there will be a unique observer position for each day of the
half-year (you can even see the little movements during the
standstills).  If it isn't cloudy, you'll always know what day it is
from your marks on the observer path, which will also need to be
several miles long.
      Actually, pinnacles aren't essential for either calendar or
eclipse uses:  any cliff profile or building edge will suffice (you keep
_one_ edge of the sun or moon in sight until it crests).  Nor is a
circular path essential for eclipse warning:  a straight-line path that is
approximately north-south will do (and for calendar-only use, even
that requirement can be relaxed).
      You can also use levered sunset views for a calendar, though
not for eclipses.  Creating a good calendar is even easier than
predicting eclipses, thanks to the "mechanical advantage" of light
levers.

Sun Daggers on the Wall
      The most familiar levered sightline is, of course, the shadow.=20
The sun rises in the east and, as it gets higher in the sky, it is also
moving south.  And so, given a window on an eastern wall, the patch
of sunlight on your western wall starts high on the wall and moves
down -- but also north.  It is as if the corner of the window frame
was the fulcrum of a lever.
      For simplicity, imagine a window that is merely a thin
vertical slit (as when a thin sliver of light sneaks in past the window
shade to prematurely awaken you in the morning).  First a "sun
dagger" appears high on your wall, slowly moving down and to the
right.  When it reaches the floor, mark the spot.  Tomorrow the spot
will be different, as the sun's path through the sky changes with each
passing day.  The solstice sunrises will mark two extreme positions
on the floor.  Lay out a belt (or stick) from the spot reached by
today's sunrise and move it over to the other extreme position, to
predict a position for the full moon's rise tonight.  Watch the "moon
dagger" move down the wall to the right, and see if it reaches the
floor at the same spot on the belt.
      Simplicity.  If the bottom of the window is high above the
floor, you'll want to build a level shelf halfway up the wall, so that
measurements are made when both sun and moon are still low in the
sky but higher than the tallest obstruction.  For ordinary windows
that produce rather wide daggers, use where the lower right corner
hits the floor (or shelf) as your criterion.  Any north-south wall
opposite an eastern window will do; it can even be rounded, like that
of the Navajo hogan (with its east-facing doorway), just so long as it
is symmetrical around an east-west line.
      Ultimately, such shadow schemes cannot be very accurate in
comparison to the other eclipse techniques that directly observe an
edge of the sun (and even they are likely to fail one time in three);
long levers, as in the great kivas of the Anasazi at Chaco Canyon,
tend to be defeated by the shadow edges becoming fuzzy.  Small
sundials aren't very accurate at telling time either, but people often
decorate their homes with them, imitating the big ones.  A lot of the
rock art in southwestern caves that is illuminated by "sun daggers" or
shadow edges may be similarly decorative, with the shaman making
the serious eclipse and seasonal determinations elsewhere.

Dispersing the Moonbeams
      I'd recommend doing something to improve those sometimes-
faint moon daggers.  You can always position your head along the
floor, and look to see where the moon first appears.  But that's
awkward.
      Fortunately, you can reflect the moonbeams (and sunbeams)
around the room.  You just line up a series of crystals along the
floor, watching to see which is the first to glow.  Making a necklace
out of crystals is even better.  Lay out the necklace from the extreme
nearest the sunrise in the morning, marking the first one illuminated
(just slide the extras away from it).  Then move it over to the other
extreme and come back at moonrise, see which crystal catches the
moonbeam first.  Rhinestone belts might serve the purpose, if you're
not up to drilling holes in crystals.

Toward a Mental Archaeology
      Shamanistic protoscience should not be confused with the
_modern_ versions of astrology, crystal power, numerology, fortune-
telling, faith healing, and the like.  Eclipse methods do indeed touch
upon some practices for which a fascination still persists in many
societies; it makes one curious about why humans are so much more
intrigued than are the apes with predicting the future, collecting shiny
jewels, and watching the heavens.  There is an occupational niche
created by this fascination; it is presently exploited by the purveyors
of a variety of rather tiresome fringe enterprises, many with
pseudoscientific pretensions.
      Their purveyors as a group are now different than back in the
days when those subjects were part of the more general intellectual
mainstream, before things split apart into philosophy, religion,
medicine, science, and fringe.  The intellectual giants used to
participate in the now-fringe discussions (Isaac Newton is a classic
example from three centuries ago), back before so many were
recognized as illusory dead ends.  Improvements in eclipse prediction
by Newton, for example, might have taken some of the fascination
out of crystals (to the extent that they had been useful for warning of
solar and lunar eclipses) and out of numerology (to the extent that
some numerology was validated by those lists of magic numbers
used by the Maya and the authors of Columbus's nautical almanac).
      Selling an illusory shortcut to power seems to be the modern
motivation of the purveyors, not the advance of knowledge -- though
one must acknowledge that the fringe would be considerably less
popular (and its purveyors considerably poorer) if scientists did a
better job of making their subject accessible to the 94 percent of the
U.S. population who cannot pass a simple test of "scientific literacy.
While there is now an educated subpopulation that is relatively
immune to their claims of power, their purveyors have media
assistance in propagandizing the less experienced (and besides all
their paid advertising, try comparing the column-inches that your
local newspaper devotes weekly to astrology and to basic science).
      To predict something without understanding why the
prediction works may seem more like magic than science -- at least
in the turn-the-rational-crank view of science.  Textbooks
emphasizing the rational over the creative aspect of science are one
reason why many people imagine "doing science" as about as much
fun as balancing their checkbook.  It should be emphasized that, on
the frontiers of research, one is often investigating some creative
scheme that _seems_ to work, though you don't yet know why.  We
tend to find out why (or forget about the scheme) within decades, but
that's on the modern time scale of scientific advance; in
protoscience, they surely persisted for many generations without any
advance in understanding, tantalizing but entangled with the
irrelevant, passed along as tradition.
      Whether any of the present eclipse methods are, indeed,
_re_inventions of a prehistoric method remains for an archaeological
analysis to evaluate.  The fact that there are so many eclipse methods
suggests that there are many potential routes to this kind of
knowledge base.  Not only could predictive physical science have
developed before the mathematics and geometry of the ancient
Greeks and Chinese, but it could have flourished long before
organized record-keeping -- even back in hunter-gatherer times,
during the long haul of the ice ages when the hominid brain was still
enlarging and reorganizing.

                         ###
copyright 1990 by William H. Calvin

      Though he has a side interest in how protoscience
      bootstrapped itself, the author is better known as a
      neurophysiologist, author of _The River that Flows
      Uphill:  A Journey from the Big Bang to the Big
      Brain_ (Sierra Club Books 1987), _The Cerebral
      Symphony:  Seashore Reflections on the Structure of
      Consciousness_ (Bantam 1989), and _The Ascent of
      Mind:  Ice Age Climates and the Evolution of
      Intelligence_ (Bantam 1990).  This article is adapted
      from _How the Shaman Stole the Moon:  In Search of
      Ancient Prophet-Scientists from Stonehenge to the
      Grand Canyon_ (Bantam 1991).
           E-mail:  [email protected]_ or
           [email protected]_