Fellowcrafts receive several admonitions and exhortations regarding
the sciences of geometry and astronomy, and many an initiate has
wondered just how far his duty should carry him in undertaking anew
the study of branches of mathematics which are associated in his
mind with much troubled effort in school days.
While some mathematically-minded men may find the same joy in the
study of lines, angles, surfaces, spheres and measurements, which
the musician obtains from his notes, the painter from his
perspective and colors and the poet from his meter and rhymes,
comparatively few brethren rejoice in the study of the
mathematically abstruse.
This must have been as well known to Preston, when he wrote those
portions of our Fellowcraft Degree which we owe to his genius, as to
any modern. So it seems fair to conclude that it was less the
literal study of geometry, with a design to become an expert, than a
figurative appreciation of its implications which the great Master
of Masonry had in mind. Indeed a careful and critical examination of
the ritual which speaks of geometry, and its child, astronomy, will
demonstrate this.
Fellowcraft ritual, in this country, with very few exceptions trace
back to Thomas Smith Webb. Because of the variations which ritual
committees, Grand Lecturers and others have introduced, so that few
Jurisdictions are exactly at one as to what is the proper form, our
examination here will be based on Webb. His several paragraphs, here
quoted in succession although separated in his "Monitor," read as
follows:
"Geometry treats of the powers and properties of magnitudes in
general, where length, breath, and thickness, are considered, from a
point to a line, from a line to a superficies and from a superficies
to a solid".
"By this science, the architect is enabled to construct his plans,
and execute his designs; the general to arrange his soldiers; the
engineer to mark out ground for encampments; the geographer to give
us the dimensions of the World, and all things therein contained, to
delineate the extent of seas, and specify the divisions of empires,
kingdoms and provinces; by it, also, the astronomer is enabled to
make his observations, and to fix the duration of times and seasons,
years and cycles. In fine, geometry is the foundation of
architecture, and the root of mathematics".
"Astronomy is that divine art, by which we are taught to read the
wisdom, strength, and beauty of the Almighty Creator, in those
sacred pages of the celestial hemisphere. Assisted by astronomy, we
can observe the motions, measure the distances, comprehend the
magnitudes, and calculate the periods and eclipses, of the heavenly
bodies. By it, we learn the use of the globes, the system of the
world and the preliminary law of nature. While we are employed in
the study of this science, we must perceive unparalleled instances
of wisdom and goodness, and through the whole creation, trace the
Glorious Author by his words".
"Geometry, the first and noblest of sciences, is the basis on which
the superstructure of Masonry is erected. By geometry we may
curiously trace nature, through her various windings, to her most
concealed recesses. By it, we discover the power, the wisdom, and
the goodness of the Grand Artificer of the Universe, and view with
delight the proportions which connect this vast machine. By it, we
discover how the planets move in their different orbits, and
demonstrate their various revolutions. By it, we account for the
return of seasons and the variety of scenes which each season
displays to the discerning eye. Numberless worlds are around us, all
framed by the same Divine Artist, which roll through the vast
expanse, and are all conducted by the same unerring laws of nature".
"The study of the liberal arts, that valuable branch of education,
which tends so effectively to polish and adorn the mind, is
earnestly recommended to your consideration; especially the science
of Geometry, which is established as the basis of our art. Geometry,
or Masonry, originally synonymous terms, being of a divine and moral
nature, is enriched with the most useful knowledge; while it proves
the wonderful properties of nature, it demonstrates the more
important truths of morality."
The interested Mason will find here far less of admonition to make
himself a geometer than an attempt to make him appreciate what the
science of geometry means to Masonry, as a demonstration of the
"glorious works of creation," the majesty and awe-inspiring
magnitude of the universe, and thus, the "perfections of our divine
creator.
To understand how geometry "demonstrates the more important truths
of morality," it is essential to comprehend just what thisscience
really is.
Geometry is that deductive science which deals with the properties
of space, and masses which occupy space.
Science is exact and classified knowledge. In the last analysis all
science is measurement. It may be measurement of time or space, of
atom or electron, of event of process, but measurement it is. Hence
Geometry, which is based on measurements of areas, masses, angles,
spaces and the relations between them, is fundamental to all
science.
It may come as a shock to some minds to know that there is not,
strictly speaking, any really "exact" science. One of the greatest
truths man has learned, in all his centuries of study, is that there
is no absolute to be known; all truths, including the mathematical,
are relative. There is no absolute rock on which any Geometry,
either the familiar Euclidian Geometry of our school days or the
non-Euclidian Geometry of the mathematician, can be based.
For all Geometries are founded upon some assumptions. The axioms of
geometry are so called self-evident truths which not only need no
proof, but which cannot be proved. These self-evident truths are
those which we instinctively know by experience; truths which no
counter experience questions. And right here we meet with one of the
great and pregnant meanings of geometry from the Masonic standpoint.
The whole of the system of Freemasonry, the essence of all its
teachings, the content of all its philosophy, the soul of all its
morality, rest upon an axiom, an assumption which can never be
proved, as either mathematical or legal world understands the word
proof...the existence of Deity.
Deity can neither be proved nor disproved, using the word in the
scientific sense. Proof is a process of the mind, a matter of logic,
a satisfaction of the intellect, and in the end rests upon the
assumption that which is universally observed, and universally
constant, has always been so and always will be so. It is
unthinkable to our minds that two plus two could ever be other than
four, though we performed the addition in the farthest star. Yet we
are learning that what seems "true" when bounded by earthly
conditions, is not necessarily "true" when considered from a vaster
and more distant viewpoint.
Belief in Deity is not the result of the process of the intellect,
but of the heart and soul.
Man is now, has always been, and presumably will always be,
Universal in his belief in, and longing for, a Great Architect of
the Universe. Masons accept the belief without question. It is a
part of our lives; we could have no Masonry without it. Lacking it
we could not live, as we understand life. But from the scientific
standpoint it is as impossible to prove as are any of Euclid's
axioms, without which there could be no geometry.
And those very statements are as near a "proof" as we can come.
Surely if it is a fair assumption that the geometry on which rests
all science, and which rests all hope and happiness in life, but
which is not scientifically provable, a true belief.
We are taught that geometry "demonstrates the more important truths
of morality."
What are the "more important truths of morality?"
"Morality" can hardly here mean any code of human conduct, such as
the observance of the ten commandments, the "live and let live" idea
on which modern civilization is founded, observance of manmade laws,
etc. Such indeed, is morality in the strict sense, but here morality
must mean something much greater and quite different. The "more
important truths of morality" which geometry teaches must be those
fundamental beliefs on which all life is founded: the existence of
Deity, the immortality of the Soul, the reality of the love of God
for his Children.
The intelligent reader will have noted that here Preston says
"demonstrate" and not "prove", as he does a phrase before. Geometry
may "prove the wonderful properties of nature" but "demonstrate" is
as much as we can claim for the "more important truths of morality."
Imagine yourself in the middle of the Sahara desert. You are alone,
many miles form any human being. You have no knowledge whatever that
any one has passed this way before. Suddenly you come upon a watch,
lying in the sand. It is running, and it agrees with your watch. On
tests you find that the watch will run but thirty-six hours without
winding.
You are absolutely certain, and no one could convince you to the
contrary, that (1) some human being was here within thirty-six hours
or (2) that the watch was tied to some animal, and fell off that
animal at the spot where you found it, or (3) that it was tied to
some bird, and fell from the bird, or (4) that it was dropped from
an airplane or balloon.
The one inescapable fact is that the watch is running; it had been
wound with-in thirty-six hours.
Geometry "demonstrates the more important truths of morality" very
much as the watch demonstrated to you that some one has been where
you found it, before you. A running watch "proves" a maker and a
winder...the human mind is so constituted that it cannot conceive of
a plan without some intelligence to make the plan. No power or
argument could convince you that the watch made itself; or rolled or
flew to the spot where you found it. It is a watch-therefore it was
made by hands. IT runs-therefore it was would. It is where no watch
can be, ordinarily speaking-therefore it was brought to that spot by
something living.
The Geometer measures the "number-less worlds around us, which roll
through the vast expanse and are all conducted by the same unerring
laws of nature." From his measurements he concludes that the orbit
of a certain planet-say Venus-is such and thus, and its time of
travel from here to there is so-and-so days. By careful computation,
aided by numberless observations, he reduces these facts to exact
data. From these he predicts that on a certain day, at a certain
hour, minute and second, Venus will appear against the sun- will
transit, in other words.
It, then, Venus does cross the face of the sun, beginning at the
time predicted, and taking just the interval prophesied to do so,
the geometer knows, as well as it is possible for the human mind to
know, that his calculations are correct.
In other words, Venus revolved in her orbit and the sun swung in
his, according to plan.
The astronomer repeats the feat for a thousand heavenly happenings.
Eclipses of the sun and moon, the tides, occultation of countless
stars, the beginning and ending of "times and seasons" he predicts
in advance with such accuracy and certainty, that no brother
scientist questions the verity of his predictions. All are agreed
that the numberless worlds about us "roll through the vast expanse"
according to a plan.
The previous statement is here repeated; there can be no plan
without a planner.
In this way, then does geometry demonstrate the most important
possible truth of "morality'-the definite existence of Some One who
planned; planned with such exactitude that even poor witless
ignorant humans are able to prophesy the future results of the
working of that plan.
Some "stupid atheists" counter such an argument by saying "You do
not need a plan- the planets revolve according to natural law." Very
well, Who made the natural law? If the skeptic says "Eclipses are
but the nature of things" Who created the nature of things? Question
can be added to question, and each push the answer further back in
space and time and consciousness, but inevitably, at the end, we
come to the WHO? That is geometry's "demonstration" of the most
important truth.
Our minds are wholly sense bound. We can obtain no information
regarding the universe except through our five senses, and the use
our intelligences make of the information thus secured. A man
without sight, hearing, smell, taste and feeling, might still think,
but he could not communicate, nor be communicated to.
A man so born could never learn anything, since he would have no
channels through which even the simplest information could run. It
is inescapably true that is in our universe are facts which cannot
be learned by our senses, mortals can never learn them. In other
words, there is a limit to human knowledge. Therefore must there be
a limit beyond which no human science, such as geometry, can
demonstrate great truths. But with these are not concerned, since
those truths, physical or moral of which we know and of which we
teach that a geometrical demonstration is possible, are sufficiently
beyond common understanding without asking for others still less
comprehensible
If the "more important truths of morality" are, as stated:
1...Existence of Deity:
2...Immortality;
3...Love of God for his children:
then geometry can be said to demonstrate them all in demonstrating
the first, thus:
1...There is no plan without a planner-geometry
proves that the universe runs according to a
plan, which follows laws so exact that
predictions successfully can be make from them.
2...It is impossible for Deity to be less
perfect than His creatures.
3...All His creatures exhibit love, tenderness,
devotion, for their children. No human parent
but would give indefinite life to his child if
he could.
4...Therefore, Deity, infinitely more perfect
than the most perfect of His children, has, in
His infinite love, provided infinite life for
His children.
The attempt to prove that which is know of the soul in terms known
only of the mind is more or less fruitless. But it is only by some
such process of reasoning that we can follow out the admonitions of
the Fellowcraft Degree. We are to study geometry, not so much in
books and lines and angles and measurements and axioms and theorems
and propositions and problems, as in a demonstration of the
"wonderful properties of nature." From these we deduce that the
universe in general, and the world in particular, exist, move,
evolve, live, according to definite laws, or plans. Knowing that
plans cannot create themselves, any more than the watch in the
desert could create and wind itself, we are logically compelled to
believe in the planner. In the nature of things, as we know the,,.
He who plans must be more perfect than we who were planned. Our
virtues, then, must be but pale reflections of His. If we would not
deny immortality to those dependent upon us whom we love, then the
love of the Great Architect, and His provision of immortality, are
as much proved to us as any processes of the mind can prove the
certainty of thesoul.
So considered, the study of geometry. so magnificently set forth in
the Fellowcraft Degree, becomes not an admonition to "do examples"
or "learn from a book" but a clarion call to understand that "the
heavens declare the glory of God, and the firmament sheweth His
Handiwork."
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