"the Omnific Word
Took the golden compasses, prepared
in God's eternal store, to circumscribe,
This universe, and all created things.
One foot he centred, and the other turned
Round through the vast profundity obscure,
And said: "Thus far extend, these far thy bounds,
This by thy just circumstance, O world."

(Milton: "Paradise Lost")

In my previous Paper entitled "The Lodge Man," I attempted to show you how the Lodge and its Officers might be correlated to the ideal Man and his component parts. I now propose to carry this concept a stage father, and for htis purpose I have selected a title expressing in three words the basis of the ideas which I wish to place before you. These three words should be interpreted as follows:-

(1) Masonic:
Indicating Freemasonry defined as "an art founded on the principles of Geometry."

(2) Anthropometric:
The Geometry of the Lodge is concerned with the measurements of the perfect Man; hence the term Antropometric - "man measuring."

(3) Cosmogenesis:
Geometry (literally "earth-measurement") is synonymous with "self-knowledge;" hence Cosmogenesis i.e. "the birth of a cosmos."

The ancient Geometers have exercised a profound influence upon the doctrine concealed within the architectural phraseology of modern Freemasonry, and it is therefore a matter for enduring regret that so little is known to us concerning PYTHAGORAS. What little we do know, however, serves but to enhance for us the interest of the Teacher and his philosophy; and basing our estimate on the extent of his influence on the thought of succeding ages, we recognize in him one of the world's master-minds. The interest of Pythagoras in Geometry began when in his youth he came into contact with THALES the reputed Father of Geometry, and then found the right ground for its development in Egypt, which country he visited while still young. Egypt is generally regarded as the birth place of Geometry, and one geometrical fact knwon to the Egyptians was that if a triangle is constructed having its sides 3, 4, and 5 units long respectively, then the angle opposite the longest side is exactly a right angle. The Greek mind, however, was not satisified with this bald statement of mere facts - it cared little for practical applications, but sought above all for the underlying "reason" of everything. In our modern day we are beginning to realize the value of the results achieved by this type of mind, and to appreciate that the general laws formulated by its endeavours, are frequently of immense practical importance - of far more importance than the mere rules-of-thumb beyond which so-called practical minds never advance. No better example of the triumph of the theoretical or speculative over the practical mind can be adduced than that affored by Pythagoras. Given the Egyptain rule for constructing a right angle, the mind of Pythagoras, searching for its full significance, made the gigantic geometrical discovery which is to this day known as the Theorem of Pythagoras - the law that in every right-angled triangle the square on the side opposite the right angle is equal in area to the sum of the squares on the other two sides. The importance of this discovery can hardly be overestimated. It is of fundamental importance in most branches, and the basis of the whole of trigonometry - the special branch of geometry that deals with the practical mensuration of triangles. EUCLID devoted the whole of the first book of his "Elements of Geometry" to establishing the truth of this theorem; how Pythagoras demonstrated it we unfortunately do not know. Now, Pythagoras was by no means a mere geometer; at heart he was both philosopher and moralist. Without and within himslef he search below the surface, and his view of the world directed his geometrical research. As Mr. W.B. Frankland says in his book, "The story of Euclid;" The Ionanian teacherss had reduced the worl in thought, till it rested upon a few broad principles. With the assumption of four elements, they were prepared to buuild up the fabric of NAture, for the world, according to their view, was composed only of Fire, Earth, Air and Water in various mixtures." This specualtion does not find acceptance in scientific cirlces today, when th enumber of elements is generally recknoned to be far greater than four; but the old idea that these elements were built up of atoms has servived in fact, been carried further, for the most accurate results yet attained in the computation of atomic weights have been reached by the actual counting up of the number of ultimate physical atoms of each element. According to the Greek thinkers, these four kinds of atoms, namely the fiery, the earthen, the aerial, and the watery, were of distinct shapes, but all in their way perfectly regular and symmetrical. Sooner or later, it was found that there were five such shapes that a symmetrical solid might take viz. the TETRAHEDRON, the CUBE, the OCTAHEDRON, the ICOSAHEDRON, and the DODECAHEDRON, and these symmetrical solids were regarded by Pythagoras, and by the Greek thinkers after him, as of the greatest importance. It should be noted that in order to be perfectly symmetrical and regular, a solid must have an equal number of faces meeting at each of its angles, and these faces must be regular polygons, i.e., figures whose sides and angles are all equal. The construction of the "regular solids" is as follows:-

TETRAHEDRON: having four equilateral triangles as faces

CUBE: having six squares as faces.

OCTAHEDRON: having eight equilateral triangles as faces

ICOSAHEDRON: having twenty equilateral triangles as faces.

DODECAHEDRON: having twelve regular pentagons (or five-sided figures) as faces.

As I have already intimated, the Greeks visualized the world as being composed of the four elements - Earth, Air, Fire, Water - and to the Greek mind the conclusion was inevitable that the shapes of the particles of the elements were those of the regualr solids. Thus Earth-aprticles were cubical, the cube being the regular solid possessed of greatest stablility; Fire-particles were tetrahedral, the tetrahedron being the simplest and, hence, lightest solid. Water particles were icosahedral for exactly the reverse reason, whilst air particles, as intermediate between the two latter, were octahedral. The Dodacahedron was, to these anceint mathematicians, th emost mysterious of the solids; it was by far the most difficult to construct, the accurate drawing of the regular pentagon necessitating a rather elaborate application of the great Theorem of Pythagoras. Hence, the conclusion, as Plato puts it, that "this (the regular dodecahedron) the Deity employed in tracing the plan of the Universe" - (Plato: "The Timaeus"). In further reference to this geometrical conception, Mr. W.B. Frankland, in his "The Story of Euclid," remarks: "In those early days the innermost secrets of nature lay in the lap of geometry, and the extraordinary inference follows that Euclid's "Elements," which are devoted to the investigation of the regular solids, are therefore in reality and at bottom an attempt to "solve the universe;" Euclid, in fact, made this goal of the Pythagoreans the aim of his Elements." This is undoubtedly the case, and the Pythagorean theorem (Euc. i. 47) marks the first stage on the journey towards the construction of the regualr solids. This Theorem of the Squares is a geometrical truth of unique beauty and extreme significance, and I would here remind you that the well known 47th. Proposition, has come (although few Freemasons could explain why) to be inscribed upon the official Jewel worn by a Past MAster in our Speculative Lodges today. The geometrical conception is also plainly alluded to in the Royal Arch Degree instruction, where the five regualr solids are introduced and described as "the four elements and the sphere of the universe."

My purpose in drawing your attention to these speculations of the ancient Geomters is to emphasize our Masonic system of philosophical thought which upholds the unity of the Cosmos, asserting that God (T.G.G.O.T.U.) and the spiritual may be perceived immanent in the things of this world, becuase all things natural are symbols and emblems of spiritual verities. To quote from one of the "Golden Verses" attributed to Pythagoras: "The Nature of this Universe is in all things alike;" commenting upon which, Hierocles, writting in the fifth or sixth century, remarks that "Nature, in forming this Universe after the Divine Measure and Proportion, made it in all things conformable and like to itself, analogically in different manners. Of all the different species, diffused throughout the whole, it made, as it were, an Image of the Divine Beauty, imparting variously to the copy of the perfections of the Original" - ("Commentary of Hierocles on the Golden Verses of Pythagoras"). In the lecture on the First Degree tracing board Freemasonry is spoken of as "an art founded on the principles of Geometry," but we must be careful how we interpret this term. To the ordinary man Geometry means nothing more than the branch of mathematics associated with the problems of Euclid, and is regarded as a subject having no relation to Masonic ceremonial and ideals. To the ancient philosphers, however, Geometry was one of the "seven liberal arts and sciences," an echo of which is still heard in the Fellowcraft Degree of our modern system. The word Geometry means literally the science of earth-measurement, but again the "earth" of the ancients did not mean, as it does to us, this physical planet. With the philosophers "earth" signified primoridial substance, otherwise spoken of as "undifferentiated soul-stuff," although we must also be careful not to confuse this with the physical matter of which our mortal bodies are composed. That is but corruptible impermanet stuff which merely forms a temporary encasement of the imperishable true "earth" or substance of our suls, and enables them to enter into sense-relations with the physical world. The distinction here must be clearly grasped and held in mind, for Freemasonry has to deal not so much with the trnasient outward body as with the eternal inward being of man, notwithstanding the fact that the outward body is temporarily invovled with the latter. It is the immortal soul of man which is the ruined temple and needs to be rebuilt upon the principles of spiritual science. The mortal body of it, with its unruly wills and affections, stands in the way of that achievement; it is the rubble which has to be cleared before the new foundations can be set and the new structure reared. Yet even rubble can be made to serve useful purposes and be rearranged and worked into the new erection, and accordingly man's outer temporal nature can be disciplined and utilised in the reconstruction of himself. But in order to effect this reconstruction he must first have a full understanding of the material he has to work with and to work upon, and for this purpose he must be made acquainted with what we know Masonically as "the form of the Lodge."

The Instruction Lectures of our Craft describe the form of the Lodge as "a parallelopipedon;" that is, a figure whose sides are parallelograms and whose opposite faces are parallel. This is symbolised by the "double cube," a pair of cubes which can be considered in three relationships; separate, conjoined and combined. Separated they are represented in the Lodge by the "rough" and "perfect" ashlars. Conjoined they are the limiting cubes of a Tesseract (the four-dimensional extension of the Cube), lying in relation to each other in four dimensions, as do the opposite square surfaces limiting a cube in three dimensions. Combined they form a single cube, being (according to the solution of the Delian problem) increased in each direction in the ratio of the cube root of two. I am aware that these definitions are not calculated to give much satisfaction to the modern Craftsman, and the real difficulty in grasping the fundamental geomtery of the Lodge is, that like the real man, it cannot be contacted in full in a three-dimensional space continium such as we are normally accustomed to work in. In its simplest form it may be expressed as a four-dimensional concept, to be contacted by the senses only in sections, one layer, as it were, at a time. We are therefore supplied with the appropriate symbols, and it must be acknowledged that the compilers of our system evinced exceptional insight in providing them for us. A hint is given here, and a hint there, each insignificant in itself, yet in the aggregate giving the measure and the stature of the Cosmic Man, whom it is the intention of our Ritual to present to our view. You will find a fuller presentation of this aspect of the subject in my Paper, "The Masonic Trinity and the Way of the Cross," which I recommend you to study in conjunction with this and the other Papers in ther series. I would, however, in this place call to your minds the "methods of advance" and the "regular steps" appropriate to the Three Degrees of the Craft, for these demonstrate a progression thropugh stages of increasing dimensionality, culminating in the beautiful four-dimensional symbolism of the M.M.'s advance. The advacne in the Third Degree, of course, illustrates perfectly the axiom of spiritual science that the perfect cube must of necessity pass through the metamorphosis of the Cross, and I am prepared to affirm that any Order formed with the aim of studying the composition and nature of the manifested Universe, must inevitably incorporate the symbolism of the Cross. We know that the symbol of the Cross is the Key-note of the New Testament of the V. of the S.L. It is also the Quaternary in Nature, the four letters of the Holy Name, I.H.V.H., the Tetragrammaton, which with the addition of the letter of the Holy Spirit, Shin, becomes Yeheshuah, the Name of the Messiah. In Alchemy, whether Spiritual or physical, we are told that the ultimate secret is to find the centre of the Cross. A true understanding of the four-lettered Name, containing as it does the powers of the four elements of nature, Air, Water, Fire, and Earth, from their lowest degree to their highest aspect, would imply a knowledge and power of creation as well as that of death and destruction. The Ancient Wisdom implied that this Name might only be pronounced by the Initiate who has attained the Supreme Initiation, that is to say, "He who has learnt to be One with the FIRST MOVER and be His Will." I will leave you to reflect upon the full import of the symbolism of the Universal Cross as this is illustrated in our Craft system of Initiation.

I have mentioned the symbolism of the "double cube," and I now wish to discuss briefly the possibility of correlating this with the Greek conception of the "regular dodecahedron." I freely admit that the mathematical correlation is not easily grasped by those brethren whos emode of thought is not naturally along pictorial and geomtrical lines, but it can be made so, to some extent, by means of models. By th euse of models it can be demonstrated that if cubic block is divided in a certain manner, and then turned inside out, the resultant figure is a dodecahedron which exactly contains within itself a cube of the same dimensions as the original cube. The remainder of the volume of the dodecahedron is not equal to that of the cube, but it might perhaps be called a close approximation, and it is quite feasible that the old Geometers put forward this solution of the famous Delian problem as a mask to cover the real object of their research. In any case, and however we may be incliend to contest the specualtions of the Greek thinkers regarding the duplication of the cube, we must not overlook the fact that it has often been pointed out by mathematicians in our day that the reproduction of a solid as its mirror image is only possible by turning it over, or folding it, in the fourth dimension, in the same manner that a plane figure (i.e. a two dimensional figure) can only be reversed by pulling it through itself in its own plane; in other words, by pullling it through the third dimension. This, indeed, is one of the arguments advanced in support of the theory that animate bodies are actually constructed to contain, or act as channels for, four-dimensional beings. Moreover, when viewed in this way, the double cube is seen as a wonderful symbol of the perfected man, providing that we bear in mined that the real man, the Overself, dwells in what to us is the non-existant space in the plane of cleavage between the two cubes. Admittedly, it is very difficult for some types of mind to grasp this conception, but, once grasped, it will be found to shed a great deal of light upon man considered as a geometrical being, in himself representing the geometrical conception or genesis of a Cosmos; Man made in the imag eof God - the Microcosm manifesting as the model of the Macrocosm. There are several Masonic lay-outs which illustrate different geometrical designs of the symbolism of the Lodge, but as these are found on examination to be nearly all based upon the 3, 4, 5 triangle of Euclid 1 -47, this aspect of the subject forms a complete study by itself and we must leave it until a more favourable opportunity presents itself.

You will no doubt recall that when we discussed the study of evolutionary Symbolism, I pointed out that the symbolism of the two triangles was intended to illustrate diagramatically the psyxhological classification of the Personality and the Individuality. According to the symbolism, these were shown to gradually appraoch and merge with, a central point representing the Mind, thus giving rise to many of our best known Masonic symbols. There is one symbol, however, belonging to a Degree now lying outside the range of the Craft system which I ought to mention here as it is implied in the Three Degrees, and is essential to a proper understanding of our present study. This symbol is known as the four-pointed Star, and it takes the form of the familiar interlaced triangles, and if we view the central square as representing the MInd, then the points of the triangels will symbolise the remaining principles alloted to the Personality and Individuality, and the whole symbol will be seen to show forth the six fold man functioning through his vehicles by the perfecting of the mental instrument. Now, there is a Masonic tradition which declares that the Headstone of the Corner should itself be a perfect replica of the completed building, and this conforms with the maxim of our science that teh Microcosm must come forth as a minature Macrocosm, and give the key by which the knowledge of the Macrocosm can be attained. The geometrical figure of the four-pointed star may therefore be taken as representing the Lodge, with the W. Master as the central point - four square - Wisdom linking the manifold man into one composite whole, and drawing into himself all the other offices. Further, when the points representing the Officers (psychological principles) are shown as folded inwards towards the centre, their juxtaposition brings into being a perfect example of one of the most important of buildings from the Masonic point of view - the PYRAMID - The LIght. Moreover, this, with its mirror image, gives the central figure round which the cubic stone is built, and by joining up the centres of the sides of the cube we see that it is built round, and contains the OCTAHEDRON. All the five regualr solids are based upon one, the simplest of them, the TETRAHEDRON, and two of htese interlaced symmetrically show in their points and intersections, the points of the CUBE and of the OCTAHEDRON, while five similarly interlaced give the points of the ICOSAHEDRON and the DODECAHEDRON. I would again emphasise that this is a difficult subject to treat of briefly. Indeed, I would stress that its fuller study must of necessity be left to individuals for search and, where possible, to personal tuition, for we are here intimately concerned with that work about which a Master-Mason is presumed to be able to give private instruction to Brethren in the inferior degrees.

And now we must leave our brief attempt to sketch the gemotrical process of measuring the stature of the Lodge Man by means of Masonic Anthropometry. There are many difficulties to be overcome befroe progress is apparent, but the aspirant for Masonic advancement must steadily and conscientiously perserve along the path to that which he seeks, just as each candidate engages himself to so in repsect of its ceremonial portrayal; and every Brother may be assured of receiving his exact dues for the labour he expends. Remember, that our Masonic labour involves the making of our whole being perfect, and that we are expressly instructed that it is intended to render the circle complete. We as we know ourselves at present, are not a circle, but a square, which is but the fourth part of a circle, and it follows that until we know the other three-fourths, we can never make the circle of our being complete, neither can we truly know ourselves. In former times, as I have intimated, these deeper problems of being were the subject of geometrical exppression, and echoes of the science remain to us in the Craft today in our references to squares, triangles, and circles. Did I not agree with thee for a penny?, says the Great Master in the V.of the S.L.,for the round disc of the coin is an emblem of the completeness which is denoted by the Circle, and it is this same wholeness which every Freemason is enjoined to effect in himself. Let us, then, supplicate the G.G.O.T.U. that the rays of heaven may shed their benign influence to enlighten us in the paths of virtue and science.