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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 the soul.
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Carmel
Lodge No. 680 F.&A.M.