MASONRY AND THE ANCIENT SCIENCES
This Short Talk Bulletin is the work of
Brother Robert N. Crawford, Clearwater Lodge
No. 127, Clearwater, Florida, who has given
it as a lecture to enthusiastic groups of
Masons in his vicinity.
Masonry and the physical sciences, especially
astronomy and geometry, are so closely allied
that to speak of one is to imply the other.
One marvels at the scientific knowledge the
ancient builders displayed in their designs
of structures, in handling and shaping
materials, and in construction.
Astronomy is probably the most ancient of the
physical sciences, for primitive man paid
attention to the sky and stars while tending
his flocks by night. Josephus, the famous
Jewish historian, followed closely the Bible
story of creation. Speaking of the fourth
descendant of Noah and his son Terah,
Abraham's father, he wrote, "God afforded
them a longer life on account of their
virtues and the good use they made of it in
astronomical and geometrical discoveries." In
writing of Abraham's sojourn in Egypt, he
also noted, "Abraham communicated to them
arithmetic and delivered to them the science
of astronomy. They were unacquainted with
these parts of learning, for these sciences
came from the Chaldeans to Egypt and from there to the Greeks."
Astronomers today can accurately predict an
eclipse of the sun or moon within two or
three seconds; astronomers four thousand
years ago could and did predict with an
accuracy of one day. Thales of Miletus,
probably the greatest of all Ionian Greeks,
calculated and predicted the eclipse of the
sun on May 28, 585 B.C. It was Thales who saw
the moon not as a rabbit, a piece of cheese,
or other childish fancy, but as a dark
spherical object circling the earth at a
fixed distance, visible because the sun shone
upon it, and eclipsing the sun at regular
intervals. Thales was the first astronomer to
show that the phases of the moon were due to
natural causes because of the relative
positions of the sun, moon, and earth. Thales
taught his pupils how to determine the height
of a mountain by measuring the length of its
shadow when the length of their own shadows
equalled their height.
Democritus in 430 B.C. taught that the Milky
Way was not the product of the cow, but a
vast number of stars too feeble to be seen
individually. Two thousand years later it was
conceded that Democritus was not a romancer
telling stories to amuse his children. Two
Greeks in Alexandria, Eratosthenes and
Apollonius, calculated the mean diameter of
the earth to an accuracy of ten per cent.
Hipparchus not only calculated the precession
of the equinoxes with remarkable accuracy,
but also discovered that the old Chaldean
calendar of 365 - 1/5 days was eleven minutes
too long. Hipparchus was also the first
astronomer to record the observation of a new
star. The ancient Chaldeans, Babylonians,
Egyptians, Hindus, and Mayas were all
excellent astronomers.
Geometry is one of the most ancient of the
physical sciences, long called the Queen of
Mathematics. Geometry is the basis on which
the superstructure of Freemasonry is erected.
The word is derived from two Greek words
meaning "to measure the earth" and was so
named because it was first used by the
Egyptians as early as 5,000 B.C. for
establishing boundaries which were
obliterated annually by the Nile floods.
The University of Alexandria was the first
great seat of learning in the ancient world.
Euclid, the father of geometry, founded a
school of mathematics there in 300 B.C.
Euclid was said to be a mild-mannered man who
was kind to all sincere students of
mathematics. It is related that one student
complained that geometry brought no money,
whereupon Euclid gave the student three coins
from his own purse. When Ptolemy, Pharaoh of
Egypt, risked if there was not an easier way
to learn geometry than to study Euclid's
methods, Euclid gave the response for which
he is famous, "There is no royal road to
geometry". The Elements of Euclid is a book
on geometry written in Greek, later
translated into Arabic, and then into Latin.
No book, except perhaps the Bible, has had
more editions printed than this mathematical
treatise. The logic of presentation is
perfect. It could be used today because it is
much better than some and equally as good as
most books on geometry.
Perhaps the most important proposition in his
book is the Forty-seventh Problem with which
all Masons are familiar: "The square on the
hypothenuse of any right-angled triangle is
equal to the sum of the squares on the other
two sides." This fundamental truth was known
to the early Hindus and Egyptians; Pythagoras
in 550 B.C. gave the proof which associates
his name with the theorem. Freemasons regard
it as a symbol of the truths that the arts
and sciences reveal to the intelligent man.
There are many right-angled triangles having
sides expressed by integral numbers, the
simplest having sides of 3, 4, and 5. The
Egyptians were quite familiar with this
triangle and used it for the design of the
pyramid of Khefren at Gizeh, built about
2,500 B.C. By doubling the sides of this
triangle we get a triangle having sides of 6,
8, and 10, which constituted the earliest
surveyor's chain. It was used for centuries
for laying out a line at right angles to any
other line.
The pyramids of Egypt illustrate the
fundamental principles of geometry. It is
truly remarkable that these ancient
structures, like almost all ancient buildings
having religious significance, are oriented
exactly on the cardinal points of the
compass. The accuracy of orientation, east
and west, of the larger pyramids is
represented by an error of less than six
minutes of one degree as determined by the
use of our most modern instruments. The
methods used by the ancients for achieving
such accuracy have long been studied by
archaeologists and mathematicians, with only
general agreement as to the probable method
used. It is now believed such accuracy could
have been attained only with the aid of one
or more of the fixed stars, since the compass
was unknown to the ancients. Which of the
fixed stars cannot be determined with
certainty, but obviously it was necessary to
fix only one cardinal point exactly, and the
remaining three could easily have been
determined by the use of the simple
instruments available to the builders.
True north was probably determined by
sighting on a star in the northern heavens
and bisecting the angle formed by its rising
and setting positions. To achieve accuracy it
would have been necessary either to observe
the true horizon at the points where the star
rose and set, or to create an artificial
horizon at a uniform height above these two
points. This would have been fairly simple
for the ancient Egyptians to do, by
constructing a level wall to represent the
horizon.
Neither astronomy, geometry, nor mathematics
could have been developed without a system of
numbers. Thus the early origin of numbers
could be assumed if no evidence of their
antiquity were available. Signs or symbols of
numbers have existed ever since two primitive
men described how many fish they caught, how
many animals they killed, how many days until
the next hunt, or how many wives and children
each had.
Primitive man used his ten fingers for
counting, so we call this method of counting
"digital" because "digit" means finger. To
denote 1, primitive man held up one finger;
for 2, he held up two fingers; for 3, he held
up three fingers, and so on; but when he got
to 10, he was at a loss to denote a higher
number. He probably waved his arms sidewise
in sweeping fashion meaning "very many" as
being more than 10. For "none" or "nothing"
he probably shook his head from side to side
or held out his hands palms up and shrugged
his shoulders. We often see this gesture
today to express the same idea.
In, addition to digitals for visual
indication of numerals, primitive man could
record numbers by scratching in sand with a
stick, or on stone with another stone, by
making one vertical stroke for 1, two
vertical strokes for 2, three strokes for 3,
and so on. Now he could count beyond 10 by
simply adding strokes in a line. Soon,
however, he discovered he could lessen his
effort in writing large numbers by making a
diagonal line across four vertical strokes,
the group denoting 5. Then he could write
large numbers and count them in groups of
5's, a method still in use today.
The Egyptians adopted a somewhat similar
system of writing numbers by using vertical
strokes up to 10 which they represented by an
inverted letter U, thus simplifying the
writing of large numbers. 11 was written U1,
12 was U11, 13 was U111, and so on up to 20,
which was two inverted U's. 21 was UU1, 22
was UU11, and so on. 30 UUU; 40 was UUUU and
so on up to 100, which was denoted by another
sign. It is believed that the early Hindus
actually invented and used such symbols for
numbers, taught them to the Arabs, who passed
them to the Egyptians, who in turn gave them
to the Greeks and thus to Europe.
The early Greeks used an awkward system of
numbers. The first nine letters of their
alphabet denoted the numerals 1 to 9. Alpha
was 1, Beta was 2, Gamma was 3, and so on up
to 9. The next nine letters of their alphabet
were used to denote 10, 20, 30, and so on up
to 90. Then the remaining letters of their
alphabet denoted 100, 200, 300, and so on;
but since the Greek alphabet contained only
twenty-four letters, they had to invent other
signs for 600 and higher. Obviously, such a
system was very cumbersome and complicated
for use in solving even the most simple
problems in arithmetic. Note that so far no
sign or symbol for zero, or 0, has been
mentioned.
The Romans also developed an extremely
cumbersome system of numerals with which we
are familiar. Imagine a Roman banker writing
the figure denoting the annual budget. He
would require the side of a house.
During the twelfth century the Arabs
perfected the old Hindu numeral system and
for the first time there appeared a sign for
zero. By 1400 A.D. the Arabian numeral system
was widely used and generally understood
except in Italy, where the Roman system
persisted until the middle of the sixteenth
century. The zero was in general use.
However, Victor von Hagen, an authority on
the Mayas who settled thousands of years ago
in Yucatan, Mexico, believes that the Mayas
had invented and used the zero many centuries
before the Hindus and employed it extensively
in remarkable astronomical calculations in
developing their calendar.
Numbers are far older than arithmetic. In
fact, arithmetic is a comparatively modern
science. "Arithmos" means "number" in Greek.
Pythagoras and other ancient Greeks
contributed greatly to the evaluation of
number concepts, but Pythagoras was more of a
numerologist than a mathematician. In fact,
he was "crazy about numbers". He made them
the basis of an esoteric cult which practiced
secret rites and ceremonies. For instance, 4
was the perfect number because there are four
sides to a square, four seasons in the year,
four elements (fire, water, cold, and heat),
and four letters in God's name (DEUS).
In Hebrew mysticism, 40 was another "loaded"
number: forty days' and nights' rain to make
the Deluge, forty days and nights for Moses'
visit with Jehovah on Mount Sinai, forty
years' wandering in the wilderness, and forty
stripes, kine, cubits, or sockets of silver.
The number 3 was particularly sacred to the
ancients: 3 symbolized the three sides of an
equilateral triangle, man's earliest sign for
God, because the triangle is the first
possible closed and endless figure. The
ancient Egyptians venerated most highly the
trinity of Osiris, Isis, and Horus. Masons
also regard three as a special symbol; three
degrees, three principal officers, three
Great Lights, etc.
In many respects the number 7 was a most
excellent number: the walls of Jericho fell
because of seven priests blasting on seven
trumpets for seven days and encompassing the
city seven times. There are seven deadly
sins, seven virtues, seven spirits of God,
seven liberal arts and sciences, seven colors
in the rainbow, seven golden candlesticks,
seven years to build King Solomon's Temple,
and seven edges on our Masonic apron (four
on. the square and three on the triangle).
Seven, of course, wins on the first pass with
dice.
Some ancient structures and the origin of
units of measurements are also very
interesting to the speculative Builder. The
Ark of the Covenant built by the Israelites
in the wilderness under the direction of
Moses, who received his instructions from
Jehovah, measured five feet long, three feet
wide, and three feet high. While this may not
be considered a large wooden box today to
serve as a base for an overlay of pure gold,
inside and out, we must consider the fact
that it was made from shittim wood, now known
as acacia, which grows with a very gnarled
structure similar to the apple tree, seldom
produces a trunk greater than seven inches in
diameter, and with a woody part having such a
high density that it will barely float on
water. It is similar to lignum vitae, or
ironwood. This wood is so hard that ordinary
woodworking tools dull rapidly in shaping it
and steel working tools are required to shape
it easily. Judging from these properties, we
can realize that the Israelites were required
to build the Ark from innumerable small
pieces of shittim wood and to dowel or
mortice the individual pieces together.
Consider also the Tabernacle of Moses, a
"knock-down" structure of shittim boards
twenty feet long by three feet wide, which
had to be fabricated from many small pieces.
Similar problems had to be solved for the
Altar of Incense, four feet square and two
feet high, and for the Table of Shew-bread,
four by three by two feet. These furnishings
for the Holy of Holies were made from shittim
wood and overlaid with pure gold.
King Solomon's Temple and Citadel were other
ancient structures built with extreme
precision. All Masons are familiar with the
Temple. Some of the measurements given in the
description of that edifice and its
furnishings must be approximate, however. For
example, the Molten Sea's dimensions are
given in the Bible as ten cubits in diameter
and thirty cubits in circumference. We know
that the relationship between the diameter
and circumference is not 1 to 3, but 1 to
3.1416 (or pi).
In those early days the lack of a "yardstick"
was not as serious a drawback as might be
imagined. While far removed from the rules
and tapes we are familiar with, their methods
of measurement were good enough for their
purposes. So long as only one man did the
measuring, it didn't make any difference how
accurate their "yardstick" was, or even how
long it was. In fact even now it doesn't make
any difference how long an inch, a foot, or a
yard is; what really is important is that
everyone means the same thing when an inch, a
foot, or a yard is used. In other words, any
unit of measurement must be standardized so
that it means the same thing to everyone. The
cubit of ancient times was the length of a
man's forearm from his elbow to the tip of
his middle finger. In many respects this was
a handy measuring stick. It was always
available; it couldn't be mislaid, so nobody
wasted time trying to find it. It was
convenient because everybody had one.
However, the cubit was not a fixed dimension
because it was not standardized; its length
varied according to the size of the man doing
the measuring. If Noah had been a small man,
his ark might have been only 400 feet long.
If Noah had been a very large man, his ark
might have been 500 feet long!
We no longer use the cubit as a unit of
length, but we have other units of measure
which originated in much the same way. A foot
started out as the length of a man's foot; in
early times the foot varied from eleven to
fifteen inches. When early man began to use
his arms and feet for measuring lengths, it
was only natural that he thought of using
legs, hands, and fingers. Horses' heights are
still measured by "hands", the breadth of a
man's hand, or approximately four inches.
What we call an inch originally was the width
of a man's thumb and also the length of his
forefinger from the first joint. In 1324 King
Edward of England standardized the inch as
"three barley-corns, round and dry, laid end
to end". Twelve times this inch became the
foot. Three times the length of a foot was
the distance from the average man's nose to
the tip of his outstretched arm, which
distance became the yard. Two yards became
the fathom, which several centuries ago was
the distance across a man's outstretched
arms. One half a yard became a cubit and half
a cubit became the span, which was also the
distance between a man's little finger and
his thumb when his hand was stretched as far
as possible. A hand was half a span and was
also the width across a man's hand at the
base of the fingers.
For many centuries mankind used these
convenient units for measuring short
distances. Today the international base
standard is the wave length of light, because
it is the only known invariable unit of
length.
One is forced to conclude that the ancients
were not stupid or lacking in knowledge and
resourcefulness. In fact, the ancient
scientists and builders were excellent
engineers, astronomers, geometers, and
mathematicians. They would "stack up" with
the best of ours today. They were the
original founders and patrons of the
philosophic and speculative orders which
represented the Freemasonry of a bygone era.
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