A little fun from one of my favorite writers on science, life and attitudes.
REH
Questioning the calendar
A skeptic confronts the millennium
By Stephen Jay Gould
Feb. 26 — We have a false impression, buttressed by some
famously exaggerated testimony, that the universe runs with
the regularity of an ideal clock, and that God must therefore
be a consummate mathematician.
GALILEO DESCRIBED THE COSMOS as “a grand book written
in the language of mathematics, and its characters are triangles,
circles and other geometric figures.” The Scottish biologist D’arcy
Thompson, one of my earliest intellectual heroes and author of the
incomparably well-written Growth and Form, (first published in 1917
and still vigorously in print, the latest edition with a preface by
yours truly) stated that “the harmony of the world is made manifest
in Form and Number, and the heart and soul and all the poetry of
Natural Philosophy are embodied in the concept of mathematical
beauty.”
THE DIVINE MATHEMATICIAN
Many scientists have invoked this mathematical regularity to
argue, speaking metaphorically at least, that any creating God must
be a mathematician of the Pythagorean school.
For example, the celebrated physicist James Jeans wrote: “From
the intrinsic evidence of his creation, the Great Architect of the
Universe now begins to appear as a pure mathematician.” This
impression has also seeped into popular thought and artistic
proclamation. In a lecture delivered in 1930, James Joyce defined the
universe as “pure thought, the thought of what, for want of a better
term, we must describe as a mathematical thinker.”
MYSTERIES OF THE CALENDAR
Why do we base calendars on cycles at all? Why do we recognize a
thousand-year interval with no tie to any natural cycle?
If these paeans and effusions were invariably true, I could
compose my own lyrical version of the consensus. For I have
arrived at the last great domain for millennial questions —
calendrics. I need to ask why calendrical issues have so fascinated
people throughout the ages, and why so many scholars and
mathematicians have spent so much time devising calendars and
engaging in endless debates about proper versus improper,
elegantly simple versus overly elaborate, natural versus contrived
systems for counting seconds, minutes, hours days, weeks,
months, lunation, years, decades, centuries and millennia, tuns and
baktuns, thirish and karanas, ides and nones.
SIGNIFICANCE OF 1,000
Our culturally contingent decision to recognize millennia and to
impose divisions by 1,000 upon a solar system that includes no
such natural cycle, adds an important ingredient to this maelstrom
of calendrical debate.
If God were Pythagoras in Galileo’s universe, calendrics would
never have become an intellectual subject at all. The relevant cycles
for natural timekeeping would all be nice, crisp easy multiples of
each other — and any fool could simply count. We might have a
year (earth around sun) with exactly ten months (moon around
earth) and with precisely one hundred days (earth around itself) to
the umpteenth and ultimate decimal point of conceivable rigor in
measurement.
But God, thank goodness, includes both Loki and Odin, the
comedian and the scholar, the jester and the saint. God did not
fashion a very regular universe after all. And we poor sods of his
image are therefore condemned to struggle with calendrical
questions till the cows come home, and Christ comes round again
to inaugurate the millennium.
NATURE’S SYMMETRY
Oh, I don’t deny that some corners of truly stunning
mathematical regularity grace the cosmos in domains both large and
small. The cells of a honeybee’s hive, the basalt pillars of the
Giant’s Causeway in Northern Ireland make pretty fair and regular
hexagons. Many “laws” of nature can be written in an
astonishingly simple and elegant mathematical form. Who would
have thought that E=mc2 could describe the unleashing of the
prodigious energy in an atom?
But we have been oversold on nature’s mathematical regularity
— and my opening quotations in this essay stand among the worst
offenders. If anything, nature is infinitely diverse and constantly
surprising — in J.B.S. Haldane’s famous words, “not only queerer
than we suppose, but queerer than we can suppose.”
BLOODY-MINDED NATURE
I call this “bloody-minded nature” because I wish to specify the
two opposite domains of nature’s abject refusal to be
mathematically simple for meaningful reasons. The second domain
forces every complex society — as all have independently done,
from Egypt to China to Mesoamerica — to struggle with
calendar-making as a difficult and confusing subject, not a simple
matter of counting.
Many questions about the millennium — Why do we base
calendars on cycles at all? Why do we recognize a thousand-year
interval with no tie to any natural cycle? — arise directly from these
imposed complexities. Any adequate account of our current
millennial madness therefore requires that we understand why
calendrics has been such a troubling and fascinating subject for all
complex human societies.
SUN AND MOON
In the first domain, apparent regularities turn out to be
accidental — and the joke is on us. In the most prominent example,
consider the significance and importance that traditional culture
invested in the equal size of sun and moon in the sky — a major
source of richness for our myths and sagas, and a primary
ingredient in our recipe for meaningful order in the heavens: “And
God made two great lights: the greater light to rule the day, and the
lesser light to rule the night” (Genesis 1:16).
Our intrinsic mental
need to seek numerical
regularity as one way of
ordering a confusing
world drives us to keep
track of the three great
natural cycles: the days
of the earth’s rotation,
the lunations of the
moon’s revolution, and
the years of the earth’s
revolution.
But the equality in observed size is entirely fortuitous, and not
a consequence of any mathematical regularity or law of nature. The
sun’s diameter is about 400 times larger than the moon’s, but the
sun is also about 400 times more distant — so the two discs appear
nearly identical in size to any observer on earth.
A SEARCH FOR SYMMETRY
In the second and opposite domain, deeply useful and
earnestly sought regularities simply do not exist — and we must
resort to inconvenient approximations and irreducible unevenness.
The complexities of calendrics arise almost entirely within this
domain — and I shall illustrate this essential point with two primary
examples that have dogged humanity ever since Og the Caveperson
first recognized that his full-moon symbols , all neatly and carefully
inscribed on his mammoth-shoulderblade scratching board, did not
line up evenly with the day symbols carved into the row just below.
So Og scratched his head, decided that he must have made a
mistake, kept his records ever more carefully, and always got the
same uneven result.
(Og either went mad, became a crashing bore to his fellows and
ended up in exile, or went with the empirical flow and became the
first architect of a complex and approximate calendar.)
The two primary examples that have plagued all complex
cultures — the fractional number of days and lunations in the solar
year — arise from the same source: nature’s stubborn refusal to
work by simple numerical relations in the very domain where such
regularity would be most useful to us. Nature, apparently, can make
a gorgeous hexagon, but she cannot (or did not deign to) make a
year with a nice even number of days or lunations.
NATURE’S WAY
Artificial constructs like
weeks and millennia do
not map astronomical
events, and arise for
more complex and
contingent reasons of
human history.
What a bummer. Both our practical requirements (to know the
seasons for hunting or agriculture and the tides for fishing or
navigation, not to mention that great bugaboo of Christian history,
the calculation of Easter) and our intrinsic mental need to seek
numerical regularity as one way of ordering a confusing world,
drives us to keep track of the three great natural cycles — the days
of the earth’s rotation, the lunations of the moon’s revolution, and
the years of the earth’s revolution. (Our other major cycles, from
weeks to millennia, do not map astronomical events, and arise for
more complex and contingent reasons of human history.)
If any of these three natural cycles worked as an even multiple
of any other, we could have such a nice, easy and recurrent
calendar — making life ever so much more convenient. Nature,
however, gives us nothing but fractionality to innumerable and
non-ending decimal places.
Stephen Jay Gould is a distinguished professor of zoology and
geology at Harvard University and is curator for invertebrate
paleontology at Harvard’s Museum of Comparative Zoology. He is
the author of books, including “Full House” and “Dinosaur in a
Haystack.” This excerpt from his “Questioning the Millennium”
was reprinted with the permission of Harmony Books, c. 1997,
Stephen Jay Gould.
