Read Ebook: Science and the Infinite; or Through a Window in the Blank Wall by Klein Sydney T Sydney Turner

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I have referred above to the sense of touch; it is, I think, clear that the first impression a child can have of sight must take the form of feeling the image on its retina, as though the object were actually inside the head, and it could have no idea that it was outside until, by touching with the hand, it would gradually learn by experience that the tangible outside object corresponded with the image located in the head; this is fully borne out by the testimony of men who, born blind, have, by an operation, received their sight late in life; in each case their first experience of seeing gave the impression that the object was touching the eye, and they were quite unable to recognise by sight an object such as a cup or plate or a round ball which they had commonly handled and knew perfectly well by touch; in fact, the idea of an object formed by the sense of touch is so absolutely different to that formed by the sense of sight that it would be impossible without past experience to conclude that the two sensations referred to one and the same object. The image formed on the retina has nothing in common with the sense of hardness, coldness, and weight experienced by touch, the only impression on the retina being that of colour or shade, and an outline; it is, however, hardly conceivable that even the outline of form would be recognised by the eye until touch had proved that form comprised also solidity and that the two ideas had certain motions in common both in duration in Time and extension in Space.

Again, our senses of sight and hearing are alike based on the appreciation of frequencies of different rapidity; brightness and colour in light are equivalent to loudness and pitch in sound, but in sound we have no equivalent to perception of form or situation in space; it gives us no knowledge of the existence of objects when situated at great distances, nor can movements be followed even at short distances without having material contact, by means of the air, with the object; sight indeed appears to have to do with Space- and sound with Time-perception. In examining Nature by means of our senses we find we are so hemmed in by what we have always taken for granted and so bound down by modes of reasoning derived from what we have seen, heard, or felt in our daily life, that we are sadly hampered in our search after the truth. It is difficult to sweep the erroneous concepts aside and make a fresh start. In fact the great difficulty in studying the Reality underlying Nature is analogous to our inability to isolate and study the different sounds themselves which fall upon the ear, if our own language is being uttered, without being forced to consider the meaning we have always attached to those sounds.

Let us now go back to the contention that it is not we who are looking out upon Nature but that our senses are being bombarded from without; we are living in a world of continuous and multitudinous changes, and as our senses require change or motion for their excitation, without those changes we could have no cognisance of our surroundings, we should have no consciousness of living; but if we base our thought entirely on sense perception, taking for granted that Time and Space have reality instead of recognising that they are only modes or limits under which those senses act, the Wall will ever remain opaque to us. Let us try and make this clearer. If we analyse the impression we receive from Motion, we find it is made up of the product of our two limitations, it is the time that an object takes to go over a certain space. We must come therefore to the conclusion also that Motion itself has no existence in reality apart from our senses. The result of not being able to appreciate this, is that the finiteness of our sense, caused by its dependence on Motion for excitation, surrounds us with illusions; one of these illusions is what we call solidity or continuity of sensation. If you hold a cannon-ball in your hand, perception by the sense of touch tells you that it is continuous, or what is called solid and hard; but it is not so in reality except as a concept limited by our finite senses. A fair analogy would be to liken it to a swarm of bees, for we know that it is composed of an immense number of independent atoms or molecules which are darting about, and circling round each other at an enormous speed but never touching; they are also pulsating at a definite enormous rate; we can at will increase their motion by heat or reduce by cold; if our touch perception were sensitive enough we should feel those motions and should not have the sensation of a solid. We have a similar case of limitation in our other senses, which we shall grasp better in another View through our Window. We can hear beats only up to fifteen in a second, beyond that number they give the sensation of a musical or continuous sound. In our sense of sight we can see pulsations or intermittent flashes up to only six in a second, beyond that number they give the sensation of a continuous light; a gas jet, if extinguished and relit six times in a second, can be seen to flicker, but beyond that rate is to our sense of sight a steady flame. The effect may also be shown by making the top of a match red-hot; when stationary or moving slowly, it is a point of light, but, moved quickly, it becomes a continuous line of light.

Even apart from our senses we find Motion giving the characteristics of solidity: a wheel with only a few spokes, if rotated quickly enough, becomes quite impermeable to any substance, however small, thrown at it; a thin jet of water only half an inch in diameter, if discharged at great pressure equivalent to a column of water of 500 metres, cannot be cut even with an axe, it resists as though it were made of the hardest steel; a thin cord, hanging from a vertical axis, and being revolved very quickly, becomes rigid, and if struck with a hammer it resists and resounds like a rod of wood; a thin chain and even a loop of string, if revolved at great speed over a vertical pulley, becomes rigid and, if allowed to escape from the pulley, will run along the ground as a hoop.

If, on the other hand, our perception were decreased below six times per second, all motion would be accelerated, until with perception reduced to one unit in twenty-four hours the sun would appear only as a band across the sky, and we could not follow its motion any more than, as we have seen, we could follow the point of a red-hot match. If perception were reduced far enough, plants and trees would grow up visibly before our eyes. But we must leave this subject now, as this and the Time Microscope will be treated in a later View.

If at this moment we and all our surroundings were reduced to half their size and everything were moving twice as quickly, we should absolutely have no cognisance of any change, neither could we possibly note any difference if everything were reduced to a hundredth part of the original size and were going a hundred times quicker; and even when reduced a thousand or a million times, or to such minuteness that the whole of our solar system with its revolving planets became no larger than one of those atoms in the needle point, and the whole of the starry universe therefore reduced to the size of the needle point, its millions of suns coinciding with the millions of planetary systems in that steel particle--our earth would still revolve round the sun, though no larger than one of those minute planetary particles and travelling at the rate of light, but we should still have no knowledge of any change, in fact, our life would go on as usual, though it was difficult a few minutes ago to think it conceivable that so small a globe could be inhabited by sentient beings.

It is from this store of knowledge that our Physical Ego is ever trying to win fresh forms of thought, and, in response to our persistent endeavours, that Inner-self, from time to time, buds out a new thought; the Physical Ego has already prepared the clothing with which that bud must be clad before it can come into conscious thought, because, as Max M?ller has shown us, we have to form words before we can think; so does the Physical Ego clothe that ethereal thought in physical language, and by means of its organ of speech it sends that thought forth into the air in the form of hundreds of thousands of vibrations of different shapes and sizes, some large, some small, some quick, some slow, travelling in all directions and filling the surrounding space; there is nothing in those vibrations but physical movement, but each separate movement is an integral part or thread of that clothing. Another Physical Ego receives these multitudinous vibrations by means of its sense organ, weaves them together into the same physical garment, and actually becomes possessed of that ethereal thought--an unexplained marvel, and probably the most wonderful occurrence in our daily existence, especially as it often enables the second Physical Ego to gain fresh knowledge from its own Real Personality. Now, in connection with this, consider the fact, already emphasized, that it is not we who are looking out upon Nature, but that it is the Reality which is ever trying to make itself known to us by bombarding our sense organs with the particular physical impulses to which those organs can respond, and, if we aspire to gain a knowledge of what is behind the physical, it is clear that all our endeavours must be towards weaving these impulses into garments and then learning from them the sublime Truths which the Reality is ever trying to divulge to us.

VIEW TWO

THE VISION

Let us go back into the far distant past, before the frame and brain of what we now call the genus Homo was fully developed: he was then an animal pure and simple, conscious of living but knowing neither good nor evil; there was nothing in his thoughts more perfect than himself; it was the golden age of innocency; he was a being enjoying himself in a perfect state of nature with absolute freedom from responsibility of action. But, as ages rolled on, under the great law of evolution, his brain was enlarging and gradually being prepared for a great and wonderful event, which was to make an enormous change in his mode of living and his outlook on the future. As seeds may fall continually for thousands of years upon hard rock without being able to germinate, until gradually, by the disintegration of the rock, soil is formed, enabling the seed at last to take root; so for countless ages was the mind of that noble animal being prepared until, in the fulfilment of time, the Spiritual took root and he became a living soul. The change was marvellous; he was now aware of something higher and more perfect than himself, he found that he was able to form ideals above his ability to attain to, resulting in a sense of inferiority, akin to a "Fall"; he was conscious of the difference of Right and Wrong, and felt happy and blessed when he followed the Good, but ashamed and accursed when he chose the Evil; he became upright in stature, and able to communicate his thoughts and wishes to his fellows by means of language; and by feeling his freedom to choose between the Good, Beautiful, and True on one hand, and the Evil, Ugly, and False on the other, he became aware that he was responsible and answerable to a mysterious higher Being for his actions. This at once raised him far above other animals, and he gradually began to feel the presence within him of a wonderful power, the nucleus of that Transcendental Self which had taken root, and which, from that age to this, has urged Man ever forward first to form, and then struggle to attain, higher Ideals of Perfection. As a mountaineer who, with stern persistence, struggles upward from height to height, gaining at each step a clearer and broader view, so do we, as we progress in our struggle upwards, toward the understanding of Perfection, ever see more and more clearly that the Invisible is the Real, that the visible is only its shadow, that our Spiritual Personality is akin to that Great Reality, that we cannot search out and know that Personality; it is not an idea, it cannot be perceived by our senses, any more than we can see a sound by our sense of sight or measure an Infinity by our finite units; all we can so far do is to feel and mark its effect in guiding our Physical Ego to choose the real from the shadow, the plus from the minus, receiving back in some marvellous mode of reflex action the power to draw further nourishment from the Infinite. As that Inner Personality becomes more and more firmly established, higher ideals and knowledge of the Reality bud out, and, as these require the clothing of finite expressions before they can become part of our consciousness, so are they clothed by our Physical Ego and become forms of thought; and, although the Physical Ego is only the shadow or image, projected on the physical screen, of the Real Personality, we are able, by examining these emanations and marking their affinity to the Good, the Beautiful, and the True, to attain at times to more than transient glimpses of the loveliness of that which is behind the veil. As in a river flowing down to the sea, a small eddy, however small, once started with power to increase, may, if it continues in midstream, instead of getting entangled with the weeds and pebbles near the bank, gather to itself so large a volume of water, that, when it reaches the sea, it has become a great independent force; so is each of us endowed, as we come into this life, with a spark of the Great Reality, with potential force to draw from the Infinite in proportion to our conscientious endeavours to keep ourselves free from the deadening effects of mundane frivolities and enticements, turning our faces ever towards the light rather than to the shadow, until our personality becomes a permanent entity, commanding an individual existence when the physical clothing of this life is worn out, and for us all shadows disappear.

If man became a conscious being on some such analogous lines as indicated, it is clear that he is, as it were, the offspring of two distinct natures, and subject to two widely separated influences; the Spiritual ever urging him towards improvement in the direction of the Real or Perfect, and the Physical or Animal instincts inviting him in the opposite direction. These latter instincts are not wrong in themselves, in a purely animal nature, but are made manifest as urging him in the direction of the shadow or Imperfect when they come in contact, and therefore in competition, with the Spiritual. Neither the Spiritual nor the Physical can be said to possess Free-will; they must work in opposite directions, but this competition for influence over our actions provides the basis for the exercise of man's Free-will--the choice between progression and stagnation. The Spiritual influence must conquer in the long run, as every step under that influence is a step towards the Real and can never be lost; the apparent steps in the other direction are only negative or retarding, and can have no real existence, except as a drag on the wheel which is always moving in the direction of Perfection, thus hindering the process of growth of the Personality.

The stages in development of the Physical Ego and its final absorption in the Transcendental may perhaps be stated as follows--

The Physical Ego loquitur:

"I become aware of being surrounded by phenomena, I will to see--I perceive and wonder what is the meaning of everything--I begin to think--I reflect by combining former experiences--I am conscious that I am, and that I am free to choose between Right and Wrong, but that I am responsible for my actions to a Higher Power; that what I call 'I am' is itself only the shadow, or in some incomprehensible sense the breathing organ, of a wonderful divine Afflatus or Power which is growing up within, or in intimate connection with me, and which itself is akin to the Reality. Owing to my senses being finite I cannot with my utmost thought form a direct concept of that power, although I feel that it comprises all that is good and real in me, and is in fact my true personality; I am conscious of it ever urging me forward towards the Good, Beautiful, and True, and that each step I take in that direction results in a further growth of that Transcendental Self. With that growth I recognise that it is steadily gaining power over my thoughts and aspirations. I learn that the whole physical Universe is a manifestation of the Will of the Spiritual, that every phenomenon is as it were a sublime thought, that it should be my greatest individual aspiration to try to interpret those thoughts, or when, as it seems at present, our stage in the evolution of thought is not far enough advanced, I should during my short term of life do my best to help forward the knowledge of the Good, Beautiful, and True for those who come after. As I grow old the Real Ego in me seems to be taking my place, the central activity of my life is being shifted, as I feel I am growing in some way independent of earthly desires and aspirations, and, when the term of my temporary sojourn here draws to a close, I feel myself slackening my hold of the physical until at last I leave go entirely, and my physical clothing, having fulfilled its use, drops off and passes away, carrying with it all limitations of Time and Space. I awake as from a dream to find my true heritage in the Spiritual Universe."

If we try to form a conception of the stages of growth of the Transcendental Self it would, I think, be somewhat as follows:

The first consciousness} of the Spiritual } I know that Love is the Summum Bonum. entity would be.... }

As it became nourished } I love. it would be.... }

Then.... I love with my whole being.

Then.... I know that I am part of God and God is Love.

And lastly.... I am perfected in Loving and Knowing.

And the above is the best description I have been able to formulate of the development of the Mystical Sense by means of which we can get a view of the Reality through our Window. I will try to give my own experience of this, which will, I know, wake an echo in other hearts, as I have met those who have felt the same. From a child I always had an intense feeling that Love was the one thing above all worth having in life, and, as I grew older and became aware that my real self was akin to the Great Spirit, at certain times of elation or what might be called a kind of ecstasy, I had an overpowering sense of longing for union with the Reality, an intense love and craving to become one with the All-loving. When analysed later in life this was recognised as similar in kind, though different in degree, to the feeling which, when in the country, surrounded by charming scenery, wild flowers, the depths of a forest glade, or even the gentle splash of a mountain stream, makes one always want to open one's arms wide to embrace and hold fast the beautiful in Nature, as though one's Physical Ego, wooed by the Beautiful which is the sensuous expression of the Spiritual, longed to become one with the Physical, as the Personality or Transcendental Ego craves to become one with the Reality. It is the same intense feeling which makes a lover, looking into the eyes of his beloved, long to become united in the perfection of loving and knowing, to be one with that being in whom he has discovered a likeness akin to the highest ideal of which he himself is capable of forming a conception.

How few of us who are now drawing towards the end of our sojourn here, have not, at certain times during our lives, experienced something akin to what I have tried to put before you in the above! Does not a particular scent, a beautiful country scene, a phrase in music, the beauty or pathos in a picture, symbolic sculpture in a grand cathedral, or even a chance word spoken in our hearing, every now and then waken in our innermost consciousness an enchanting memory of some wonderful happy moment of the past when the sun seemed to have been shining more brightly, the birds singing more merrily, when everything in nature seemed more alive, and our very beings seemed wrapped up in an intense love of our surroundings? On those occasions we were not far from seeing behind the veil, though we did not recognise it at the time; but when we now look back, with experience gained by advancing years, and consider those visions of the past, we cannot help seeing that the physical film was to our eyes more transparent at those times, and the very joy of their remembrance seems to be giving us a prescience of that which we shall experience, when for each one of us the physical film is pricked and passes away like a scroll.

VIEW THREE

MYSTICISM AND SYMBOLISM

To understand the subject it is necessary to recognise fully the place Geometry held, not only among Mediaeval Builders, but also in Classical times; it was recognised in those early times as the head of all the Sciences, and was the A, B, C of Hellenic Philosophy. Come back with me 2300 years, to the time when the "Greek Age of Reason" was at its zenith, and Plato, the greatest of the philosophers, was teaching at Athens, working thus, let it be known to his honour, solely for the love he bore to science, for he always taught gratuitously. What qualification was required of those who attended his Academy? Look up over the porch, and you will see written in large capitals these words:

"Let no one who is ignorant of Geometry enter my doors."

At the root of Socratic teaching was the idea that wisdom is the attribute of the Godhead, and Plato, for twenty years the companion and most favoured pupil of Socrates, was imbued with that doctrine, and, having arrived at the conclusion that the impulse to find out TRUTH was the necessity of intellectual man, he saw in Geometry the keystone of all Knowledge, because, among all other channels of thought, it alone was the exponent of absolute and undeniable truth. He tells us that "Geometry rightly treated is the Knowledge of the Eternal"; and Plutarch gives us yet another instance of Plato's teaching concerning this subject, in which he looks upon God as the Great Architect, when he says, "Plato says that God is always geometrising." Holding, therefore, as Plato did, that God was a great Geometer, and that the aim of philosophy was the acquisition of a knowledge of the Eternal, it is natural that he should make a knowledge of Geometry imperative on those wishing to study philosophy. This was continued also by those philosophers who succeeded Plato in the management of the Academy, as we are told that Zenocrates turned away an applicant for admission, who knew no geometry, with the words:

The Secret handed down in the Craft, from Architect to Architect, was how to form a perfect right angle, or, as it was called, the "Square," without possibility of Error, and this I have called "the Knowledge of the Square." Vitruvius, who, at the beginning of our Era, wrote his thesis on Tectonic art, which is still the text-book of Architecture for Ancient buildings, says Pythagoras taught his followers to form a gnomon, or square, as follows: "Take three rods, of three lengths, four lengths, and five lengths long; with these form a triangle, and, if each rod be squared, you have 9, 16, and 25, and the areas of the two former will be equal to the latter."

Now let us come to the closing years of the tenth century. What a strange condition of the building craft was to be seen all over Europe; not a church was being built, nor had been built, for the last twenty years; the thousand years after Christ was drawing to its close, everybody was waiting for, and expecting, the world to come to an end; no new undertakings were begun. How much money went into the hands of the Monasteries and other Religious Houses, as peace offerings for the future welfare of the givers, nobody can say; it was probably enormous. When, however, the eleventh century was well started and the crisis was over, churches were built on a large scale, as shown by the numerous remains we have of Norman buildings of the last half eleventh century, and building was probably at its height about A.D. 1140 to 1150; but at this period an extraordinary thing happened. Hitherto the arches in the Norman style were round-headed and their columns enormously thick to carry them; but suddenly the style changed into the beautiful Gothic all over Europe. No single country can claim precedence, it was almost simultaneous; churches half finished in the round style were not only completed in the pointed, but had parts already built altered to the new style. What, then, determined this sudden change, resulting in a wonderful accession of beauty to Architectural design? We must go to the Monasteries and Religious Houses to find the explanation. These Houses had become the Patrons of Masonry, the providers of the funds for building Cathedrals, &c.; it naturally followed that, growing up alongside the Operative Science, there was a Religious symbolism being gradually formed which attached itself specially to the tools used by Masons, and thus formed the basis of Moral teaching--"to act on the Square," "to keep within the bounds of the Compasses," "to be Level in all your dealings," &c., &c. A wonderful, new, and Mystical form of Symbolism was opened to them with the advent of Geometry. The text-book of Geometry was unknown throughout the whole of Europe, omitting Spain, from the sixth to the beginning of the twelfth century; it was, as I have pointed out, well known in Greece before our Era, and continued to be so up to about the sixth century A.D. In the fourth century lived the Greek, Theon of Alexandria, so well known for his edition of Euclid's Elements, with notes, from which all Greek MSS. which first came to light in the sixteenth century were taken, being entitled , "from Theon's Lectures," and which he probably used as a text-book in his classes; but these MSS. had all been lost before the seventh century, and were not recovered again until the sixteenth century, when Simon Grynaeus, the greatest Greek scholar on the Continent, and companion of Melancthon and Luther, discovered a copy in Constantinople. Meanwhile, Theon's edition had been translated into Arabic, and thus preserved by the Mohammedans, and it was only at the beginning of the twelfth century that Athelard of Bath, who had been travelling in the East, came to study at Cordova, in Spain, and there found the Arabic MSS. of Euclid; these he translated into Latin, and this translation must have come into the hands of the patrons of the building craft at the very time when the Gothic style had its origin; it was the only Latin translation known in Europe, and was, some centuries later, the text-book of the first printed edition of Euclid.

One can well understand the object which led the learned Rabbi Maimonides, the greatest savant of the Middle Ages, when addressing his pupils in the twelfth century, to command his hearers: "When you have discovered the meaning thereof, do not divulge it, because the people cannot philosophise nor understand that to the Infinite there is no such thing as Sex;" but later on the noted writer on Symbolism, Durandus, in the introduction to his book, is more explicit, and gives the real meaning as follows: "The Mystical Vesica Piscis ... wherein the Divinity and, more rarely, the Blessed Virgin are represented, has no reference, except in name, to a fish, but represents the Almond, the symbol of Virginity and self-production."

The Vesica Piscis, and its name, is intimately connected with the discovery, by Augustus Caesar in the century preceding our Era, as narrated by Baronius, of a prophecy in one of the Sibylline books, foretelling "a great event coming to pass in the birth of One who should prove to be the true 'King of Kings,' and Augustus Caesar therefore dedicated an altar in his palace to this unknown God." Eusebius and St. Augustine inform us that the first letter of each line of the verses from the Erythrean Sibyl containing this prophecy, formed the word , and were taken as representing the sentence: . Based upon this discovery arose that extraordinary enthusiasm, during the second, third, and fourth centuries, for hunting up further prophecies in Pagan sources, resulting in a great number of Sibylline verses being invented, giving the minutest details in the Life of our Lord. These fabrications seem to have been at that time generally accepted by the masses as true prophecies, though we know now that they were written some centuries after the events they were supposed to foretell.

Let me make this clearer. The more one examines the typical points in the Saxon, Norman, and Gothic styles of Architecture, the more clearly one sees that the Architects of the two former used circles and squares on their tracing-boards, as units for their proportions, in drawing up both ground plans and elevations, with here and there suggestions only of the Equilateral Triangle having been made use of in some of the smaller details; whereas the Gothic Architects seem to have used the Vesica Piscis almost entirely. This explains the reason why true Gothic buildings have always been said to be built mainly on the basis of the Equilateral Triangle; this naturally follows, because the use of the Vesica creates, and therefore necessitates, the appearance of the Equilateral Triangle in every conceivable situation. The following quotation is typical of the leading essay writers on this subject: "The Equilateral Triangle enters largely into, if it does not entirely control, all mediaeval proportions, particularly in the ground plans. In Chartres Cathedral the apices of two Equilateral Triangles , whose common base is the internal length of the transept, measured through the two western piers of the intersection, will give the interior length, one apex extending to the east end of the chevet within the aisles, the other to the original termination of the Nave westward, and the present extent of the side aisles in that direction. With slight deviation, most, if not all, the ground plans of the French Cathedrals are measurable in this manner, and their choirs may be so measured almost without exception. Troyes Cathedral is in exact proportion with that of Chartres, and the choirs of Rheims, Beauvais, St. Ouen at Rouen, and others are equally so. Bourges Cathedral, which has no transept, is exactly three Equilateral Triangles in length inside, from the East end of the outer aisle to the Eastern columns supporting the West Towers. Most English Cathedrals appear to have been constructed in their original plans upon similar rules." White's Classical Essay on Architecture compares the Norman with the Gothic, where he says: "In what is usually called the Norman period, the general proportions and outlines of the Churches are reducible to certain rules of setting out by the plain Square. As Architecture progressed the Square gradually disappeared, and the proportion of general outline, as well as of detail, fell in more and more with applications of the Equilateral Triangle, till the art, having arrived at its culminating point, or that which is generally acknowledged to be its period of greatest beauty and perfection in the thirteenth and the beginning of the fourteenth centuries, again began to decline. With this decline the Equilateral Triangle was almost lost sight of, and then a mode of setting out work by diagonal squares was taken up, for such is the basis found exactly applicable to the work of the fifteenth century, since which time mathematical proportions have been generally employed." And after referring to numerous scale drawings of Churches, windows, doors, and arches, he points out that every student of Church architecture must pronounce those of the untraceried and traceried first point to be the most beautiful of all, those of the Norman to be a degree less so, and those of the perpendicular and debased to be far inferior to either, and in that analysis we find that the Equilateral Triangle was used almost exclusively for determining one order , the Square for another , and the Square diagonally divided for the other .

Now let me try to describe the wonderful properties of the Vesica Piscis, so that you may understand the mystery which shrouded it in the minds of those Mediaeval builders. The rectangle formed by the length and breadth of this figure, in the simplest form, has several extraordinary properties; it may be cut into three equal parts by straight lines parallel to the shorter side, and these parts will all be precisely and geometrically similar to each other and to the whole figure,--strangely applicable to the symbolism attached at that time to the Trinity in Unity,--and the subdivision may be proceeded with indefinitely without making any change in form. However often the operation is performed, the parts remain identical with the original figure, having all its extraordinary properties, the Equilateral Triangle appearing everywhere, whereas no other rectangle can have this curious property.

It may also be cut into four equal parts by straight lines parallel to its sides, and again each of these parts will be true Vesicas, exactly similar to each other, and to the whole, and of course the Equilateral Triangle is again everywhere.

Again, if two out of the tri-subdivisions mentioned above be taken, the form of these together is exactly similar, geometrically, to half the original figure, and again the Equilateral Triangle is ubiquitous on every base line.

In the volume referred to I have given a skeleton plan upon such a scale of subdivision that a tracing-board, of 5 feet by 8 feet, would be divided up into over one million parts, and, as all these subdivisions are perfect representations of the original Vesica figure with all its properties, the design of the largest building, with the minutest detail, could be drafted with absolute accuracy. There are many other curious properties of this Figure, but they are difficult to explain without diagrams. I will, however, give one more example of its creative power. The problem of describing a Pentagon must have puzzled architects considerably in those early times, but this was again easily accomplished by means of the Vesica. Albrecht D?rer, the great designer and engraver, who lived at the end of the fifteenth century, refers to the Vesica in his works in a way which shows that it was as commonly known in his time as the Circle, Square, and Triangle. His instructions for forming a Pentagon are: "Designa circino invariato tres piscium vesicas" . Three similar circles are described with centres at the angles of an Equilateral Triangle, forming the three Vesicae, by means of which the Pentagon is drawn, and from which also we get a beautiful form of arch very common in the thirteenth century . This is also the method used in that old manuscript of the fifteenth century named "Geometria deutsch." In this old MS. it is also shown that the easiest method for finding the centre of a circle, however large, or any segment of a circle, is by means of the Vesica Piscis. And just as we see so many Cathedrals of the Middle Ages are stated by antiquarians to have been planned on the Equilateral Triangle, so do we find the Pentagon appearing as the basis of Architectural designs of buildings of a later date, such as Liverpool Castle, Chester Castle, and other similar structures; but the true means by which each were laid down, as in the case of the Equilateral Triangle, was again the Vesica Piscis. A beautiful example of decoration, on the basis of the Vesica, is seen in the tomb of Edward the Confessor in Westminster Abbey.

I will conclude this subject by quoting from the summing up by Prof. Kerrich , in his masterly Essay on Architecture, where he gives the different forms of what he calls the "Mysterious Figure," used in the most noted Gothic buildings: he says, "I would in nowise indulge in conjectures as to the reference these figures might possibly have to the most sacred mysteries of religion; independently of any such allusion, their properties are of themselves sufficiently extraordinary to have struck all who have observed them."

One more glance through the Window at what I will call--

"The Mystery of the Apex."

Radio-active substances then are really forges for forming new structures of matter or forms of energy, rather than quarries from which they are cut, and we seem to get a glimpse of the origin of life, perhaps itself the cause of "retrogression" in the material, coming through from the Reality, the Infinite beyond the physical Universe.

VIEW FOUR

LOVE IN ACTION

A great forest tree forms each year a multitude of separate buds; each of these buds is an independent plant which has only a temporary existence and has no present knowledge of the other buds, but it is by means of all these buds and the leaves they develop, that the tree is nourished and increases from year to year. Still more wonderful is the fact that it is these temporary existences which, in accordance with the general law of life-production, form special "ovules," which we call seeds, each of which has the potentiality for growing up into a great forest tree, which, in its turn, is capable of pushing forth temporary existences in countless directions. We have, in the above process of creating a forest tree, a likeness on the Physical Plane to what I would suggest is the process not only of the creation of the Race, but, on the Transcendental Plane, the multiplication of permanent personalities by means of, or in connection with, the temporary and Space-limited Human Physical Ego.

Again, as the human mind forms a thought, clothes it in physical language, and sends it forth in such a form as not only affects our material sense of hearing, but conveys to the hearer the very thought itself, so the whole Physical Universe is a temporary and Space-limited representation of the Reality which is behind, is in fact the materialisation of the Will or Thought of the Great Spirit. The "taking root" or advent of the Spiritual to the genus homo, made it possible for man to interpret the Good, Beautiful, and True in the phenomena of nature, and, as we, by studying these materialisations, gain knowledge of the Reality, and our personalities become real powers, so may we at length approach the point where we may feel that we are thinking, or having divulged to us, the very thoughts of God; and, though it may never be possible in this life to form a full conception of the Reality, we may, I think, even with our present state of knowledge, aspire to understand the messages conveyed to us in some of the multitudinous forms, under which these thoughts are presented to us, and I propose giving an example of this later on in this View.

Once more, in the case of a picture, it is possible, by examining and comparing a number of certain short lines in perspective, to discover not only the position occupied by the Artist, but also the point to which all those lines converge; so by examining and combining certain lines of Thought on the Physical Plane, and following them as far as we can with our present knowledge towards the point where our Ideals of the Good, Beautiful, and True intersect, we may reach the position from which we may be able to form, although through a glass darkly, even a conception of the Great Reality, and therefore of Its Offspring the Transcendental Ego, and its connection with the Universe.

As the whole of Nature is the temporary and Space-limited manifestation of the Reality, so the individual Physical Ego is the manifestation in Time and Space of the Transcendental Ego or true Personality. The Physical Ego is its transient expression and has no other use beyond this life. Each Physical Ego helps, or should help forward, the general improvement of the Race towards perfection. Each generation should come into being a step nearer to the Spiritual, until it can be pictured that at the final consummation, there will be nothing imperfect, no shadow left; the full complement of Spiritual Personalities being complete in the Great All-Father.

Do we not then see clearly that the Physical Ego, comprised in what we call "I am," "I perceive," "I think," "I conceive," "I remember," is transient, and has only to do with the progress of the Race? It is the Shadow or Image in the Physical Universe of that Personality which Transcends Time and Space. Take away a small portion of the Brain, the organ of the Mind, and Memory is wiped out, remove the greater part of it and the manifestation of the Physical Ego is destroyed; though the body is as much alive as before, there is apparently nothing left but the physical life, which it has in common with all animals, plants, and probably, as strongly suggested by late discoveries in Radio-activity, even with what is called inorganic matter. The Brain, and therefore the Ego, is not a necessity for Physical life; this is clearly seen in the lower forms of life--it would be difficult to point out the brain of a Cabbage or an Oak Tree.

In the last forty years we have entered upon a new era of religion and philosophy; we hear no more of the old belief that the study of scientific facts leads to atheism or irreligion; we begin to see that Religion and Science must go hand in hand towards elucidating the Riddle of the Universe, and such a change enables us even to aspire to show, as I now propose to do, that it is possible, by examining certain phenomena in Nature, to reach that point where we may feel that we are listening to and understanding, though through a glass darkly, what may be called the very Thoughts of the Great Reality. I will take for examination the subject most intimately connected with the title of this View--namely, the nature of the growth of the Transcendental Personality, upon what that growth depends, and how we may understand that the attainment to Everlasting Life is dependent upon that growth.

I have already pointed out in View Two that the Transcendental Personality, being Spiritual, and therefore akin to the Great Reality, may be said to have no free-will of itself. Its will or influence must always be working towards perfection in the form "Let Thy Will, which is also my will, be done"; the efficacy of its influence with the Great Reality depends on its growth or nourishment by the knowledge of the Good, Beautiful, and True ever bringing it more and more nearly into perfect touch or sympathy with the All-loving. The power of prayer therefore depends upon two conditions; it must be in the form of "Let thy Will be done," and that which prays must be capable of making its petition felt, by having already gained a knowledge of what that Will is. I am, of course, not referring to that form of prayer which, alas with so many, seems to be the attempt to get as much out of the Absolute as is possible, with the least amount of trouble.

If now we carefully examine the Phenomena around us, we make the extraordinary discovery that this power to influence is the very basis of survival and of progress throughout the universe. In the organic world all Nature seems to be praying in one form or another, and only those that pray with efficacy, based upon the above two conditions, survive in the struggle for existence. The economy of Nature is founded upon that inexorable law the "Survival of the Fittest"; every organism that is not in sympathy with its environment, and cannot therefore derive help and nourishment from its surroundings, perishes. Darwin tells us that the colours of flowering plants have been developed by the necessity of attracting the bees, on whose visits depends the power of plants to reproduce their species; those families of plants which do not as it were pray to the bees with efficacy, fail to attract, are not therefore fertilised, and disappear without leaving successors. Flowers may also be said to be praying to us by their beauty, or usefulness, and in some cases, as with orchids, by their marvellous shapes. We answer their prayer by building hot houses and tending them with care, because they please us, and therefore we help them to live; while, on the contrary, those plants that have not developed these qualities are not only neglected, but, in some cases, as with weeds, we take special trouble to exterminate them, because their existence is distasteful to us.

Charles Darwin also tells us that Heredity and Environment are the prime influences under which the whole Organic World is sustained; in other words, every organism has implanted in it by heredity the principle of life, but the conditions under which it will be possible for that life to expand and come to perfection, rest entirely upon its power to bring itself into harmony with its environment. This principle of life does not come naked into the world, it is fortified by heredity, with power gained by its parents in their struggle for existence, and in their persistence to get into sympathy with their environment. The knowledge they gained, by this struggle, they have handed down to their offspring, and given it thereby the possibility of also gaining for itself that knowledge of, and power to get into sympathy with, its environment, upon which its future existence will depend. So may we not see that in the Spiritual World, these two conditions dominate, and that it is only by the clear comprehension of their reality that we can understand how all-important it is for the soul to bring itself nearer and nearer into harmony with its environment, the Spiritual, and how the efficacy of prayer depends upon the Knowledge of what is the Will of God?

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