Short Talk Bulletin - Vol. 12, May 1934, No.5
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
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
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
wecould 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
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
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 witness 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:
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 the soul.
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 she with His Handiwork."