MASONIC GEOMETRY
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 thematically-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.
"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. 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".
To understand how geometry
"demonstrates the more important truths of morality," it is essential to
comprehend just what this science 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 a measurement of time or space, of atom or electron, of
event of process, but measurement it certainly 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.
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.
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
the 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 of that
which is universally observed, and universally constant. It 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, Yet we are learning that what seems "true"
when bounded by earthly conditions, is not necessarily "true" when considered
from a greater and more distant viewpoint. Belief in Deity is not the result
of the process of the intellect, but of the heart and soul.
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 the " Supreme Being," the immortality of the
Soul. Geometry demonstrates the more important truths of morality
and the human mind is so constituted that it cannot conceive of a plan without some
intelligence to make the plan. 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 these measurements is concluded that the orbit
of a certain planet, "Venus" for example, 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, one reduces these facts to exact data. From
these one predicts that on a certain day, at a certain hour, minute and second,
Venus will appear against the sun- will transit. In other words
; 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.
The previous statement is here repeated;
there can be no plan without a planner.
It is inescapably true that, 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.
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 the Deity to be less perfect than His creatures.
3...All His
creatures exhibit love, tenderness, devotion, for their children.
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 known 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, lines.,
angles., measurements., axioms., theorems., 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, exists.,
moves., evolves., lives., according to definite laws, or plans. Knowing that
plans cannot create themselves, we are logically compelled to believe in the
planner. In the nature of things, as we know them. 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 process of the
mind can prove the certainty of thesoul.
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