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SCIENCE AND THE INFINITE
“THE MYSTERY OF THE APEX”        VIEW NO. 3
SCIENCE AND THE INFINITE                   ORTHROUGH A WINDOW IN THE     BLANK WALL                   BY          SYDNEY T...
First published November 1912           Reprinted September 1917.This electronic edition issued by Celephaïs Press,      s...
TO    THE RIGHT HON.ARTHUR JAMES BALFOUR
PREFACEIN venturing to prepare this little volume forthe eyes of the reading public, I am fullyaware of the difficulties o...
Science and the Infinitemade mountains out of mole-hills, whereas ifwe treated them at their true value we shouldlook at t...
Prefaceseemed to calm anxieties connected with thefear of death and to render the impenetrableVeil more transparent, which...
Science and the InfiniteReality; and yet we know that Motion is butthe product of Time and Space, and these areonly the tw...
Prefaceupon physical life as a mode of frequency, akinto Light, Electricity, Magnetism, ChemicalAction, the Vibration of a...
Science and the Infinitethese suggestions succeeded in augmentingthe number of those who have already startedon the true “...
CONTENTS                    VIEW ONE                     PAGECLEARING THE APPROACH .          .   .   .   .     1         ...
SCIENCE AND THE INFINITE                   VIEW ONE      CLEARING THE APPROACHTHE proof that the Human Race is still in it...
Science and the Infiniterecent years that we have been able to realisethat it is the Invisible which is the Real, thatthe ...
Clearing the Approachattained to its clear perception, will be able tocontinue the study by themselves and thus getfurther...
Science and the Infiniteonly the absence of light, so the negative ofGoodness, i.e. Evil, may in reality be lookedupon as ...
Clearing the Approachfall upon the eye at different angles, con-stituting form, and with different frequenciesgiving colou...
Science and the Infinitethat star to make itself known to us but todeclare to us its distance, its size, and con-ditions o...
Clearing the Approachcommonly handled and knew perfectly wellby touch; in fact, the idea of an object formedby the sense o...
Science and the Infiniteby means of our senses we find we are sohemmed in by what we have always takenfor granted and so b...
Clearing the Approachreceive from Motion, we find it is made upof the product of our two limitations, it isthe time that a...
Science and the Infinitesensation of a musical or continuous sound.In our sense of sight we can see pulsationsor intermitt...
Clearing the Approach    Now with regard to this limit of timeperception, which gives us the phenomenonof Solidity, I have...
Science and the Infinitevibrating at that enormous rate.        I havemade several experiments in this direction,and some ...
Clearing the Approachor even arresting its visible motion for pur-poses of investigation without interferingwith the natur...
Science and the Infinitethe very end of the point of the finest needle,we get so minute a particle of steel that it ishard...
Clearing the Approachfollow me down another path leading to theelucidation of the same subject.   If at this moment we and...
Science and the Infiniteeach of the atoms in the steel point becameas large as our solar system and the steelpoint as larg...
Clearing the Approachreality apart from our physical senses, thatthey are only the modes under which we re-ceive impressio...
Science and the Infinitetravelling in all directions and filling the sur-rounding space; there is nothing in thosevibratio...
VIEW TWO               THE VISION“THY Will be done on Earth as it is in Heaven,”is in true consonance with the old philoso...
Science and the Infiniteplane. Although we have no words to express,nor indeed minds to grasp, the wonders andglories of t...
The Visioncient, whereas the latter, being subservient toTime and Space, can only think in finite words,requires successio...
Science and the Infinitenow aware of something higher and more per-fect than himself, he found that he was able toform ide...
The VisionPersonality is akin to that Great Reality,that we cannot search out and know thatPersonality; it is not an idea,...
Science and the Infinitenear the bank, gather to itself so large avolume of water, that, when it reaches thesea, it has be...
The Visionthis competition for influence over our actionsprovides the basis for the exercise of man’sFree-will—the choice ...
Science and the Infiniteform a direct concept of that power, although Ifeel that it comprises all that is good and real in...
The Visionit all limitations of Time and Space. I awake asfrom a dream to find my true heritage in theSpiritual Universe.”...
Science and the Infinitewhat might be called a kind of ecstasy, I hadan overpowering sense of longing for unionwith the Re...
The Visionincentive on earth, and is implanted in ournatures for the good and furtherance of therace; it is, in fact, the ...
Science and the Infiniteof symbolic forms, and I want to make itquite clear that the description I am attempt-ing must nec...
The Visionfact that the whole of that visible scene isactually depicted on the surface of your retinaand has no other exis...
Science and the Infiniteshuttered; it has necessarily been only anoblique view and clothed in symbolic phrase-ology, but t...
The Visionthe portal 0f Symbolic Thought. the Raptureof Music can only be truly understood by onewho has already experienc...
Science and the InfiniteCreation is an instantaneous Thought of theReality;—that it is only by the process ofanalysing in ...
The Visionat those times, and the very joy of their re-membrance seems to be giving us a prescienceof that which we shall ...
VIEW THREE  MYSTICISM AND SYMBOLISM“WHO can doubt that the Mystics know morethan the Theologians, and that the Poets knowm...
Mysticism and Symbolismam trying to storm the Sanctuary of the Un-thinkable, the Infinite, by means of a Ladderwhich canno...
Science and the Infinitethe Absolute find me out and possess me andthus make me feel that that which is withinme is akin t...
Mysticism and SymbolismSoul; but that is missed by those who arealways asking questions, and arguing, aboutwhat that knowl...
Science and the Infinitedomain of “Intellectualism,” but does nottake us far towards the goal of our aspira-tions. I shall...
Mysticism and Symbolismenchantment with the concept as a whole, apartfrom specialising any particular character orevent in...
Science and the Infinitecould best permanently record and teach theiraspirations to the masses. Every beautifulthought fou...
Mysticism and SymbolismI have given the whole subject, in extenso,under the title “Magister Mathesios.”   To understand th...
Science and the Infinitestone of all Knowledge, because, among allother channels of thought, it alone was theexponent of a...
Mysticism and Symbolismsquares, because in every Right-Angled Tri-angle, as expounded by the PythagoreanTheorem, the squar...
Science and the Infinitetriangle, upon which its property is based, isthe Right Angle. The Greeks gave to thisRight Angle ...
Mysticism and Symbolism    Now let us come to the closing years ofthe tenth century. What a strange conditionof the buildi...
Science and the Infinitebeauty to Architectural design? We mustgo to the Monasteries and Religious Housesto find the expla...
Mysticism and Symbolismcentury, when Simon Grynæus, the greatestGreek scholar on the Continent, and com-panion of Melancth...
Science and the Infinitecome down to us from that time invariablystate that “at the head of all the Sciencesstands Geometr...
Mysticism and Symbolismat the beginning of our Era, to represent thePast and Future Eternities generating theLogos; but th...
Science and the InfiniteHoly Spirit, representing this new birth. Toshow the extraordinary reverence and highvalue attache...
Mysticism and Symbolismmore rarely, the Blessed Virgin are repre-sented, has no reference, except in name, toa fish, but r...
Science and the Infinite   Let us now return to the Vesica Piscis.In the paintings and sculptures of the MiddleAges, we fi...
Mysticism and Symbolismimportant documents began with an Invoca-tion of the Tres Personæ, or were garnishedwith symbolic i...
Science and the InfiniteGeometry was synonymous with Masonry, andthe very foundation of the Science of Geo-metry, as expou...
Mysticism and Symbolismtwo former used circles and squares on theirtracing- boards, as units for their proportions,in draw...
Science and the InfiniteCathedrals are measurable in this manner,and their choirs may be so measured almostwithout excepti...
Mysticism and Symbolismbasis found exactly applicable to the workof the fifteenth century, since which timemathematical pr...
Science and the Infinitefinitely without making any change in form.However often the operation is performed,the parts rema...
Mysticism and Symbolismhands the means of trisecting the RightAngle.   Now, the three great problems of antiquitywhich eng...
Science and the Infinitecentre of base is a true Plumb line, formingat its foot the perfect right angle, so importantin th...
Mysticism and SymbolismTriangle, forming the three Vesicæ, by meansof which the Pentagon is drawn, and fromwhich also we g...
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
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Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
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Science and the infinite or through a window in the blank wall by sydney t klein
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Science and the infinite or through a window in the blank wall by sydney t klein
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Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
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Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
Science and the infinite or through a window in the blank wall by sydney t klein
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Science and the infinite or through a window in the blank wall by sydney t klein

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SCIENCE AND THE INFINITE OR THROUGH A WINDOW IN THE BLANK WALL BY SYDNEY T KLEIN

Some ideas are a bit outdated due to newer scientific perspectives and discoveries, (the book was written in the early 20th century) but many fit well with contemporary thought and were therefore well ahead of their time including many confirmed by current scientce. Especially intriguing is his commentary on our limited, 3-dimensional observable shadow of the ultimate reality, the nature of our true selves, and the all inclusive relative aspects of time. Enjoy a journey of surprising and expansive visions of reality.

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  1. 1. SCIENCE AND THE INFINITE
  2. 2. “THE MYSTERY OF THE APEX” VIEW NO. 3
  3. 3. SCIENCE AND THE INFINITE ORTHROUGH A WINDOW IN THE BLANK WALL BY SYDNEY T. KLEIN SECOND IMPRESSION LONDON WILLIAM RIDER & SON, LIMITEDCATHEDRAL HOUSE, PATERNOSTER ROW, E.C. 1917
  4. 4. First published November 1912 Reprinted September 1917.This electronic edition issued by Celephaïs Press, somewhere beyond the Tanarian Hills (Leeds, Yorkshire, England) November 2003.
  5. 5. TO THE RIGHT HON.ARTHUR JAMES BALFOUR
  6. 6. PREFACEIN venturing to prepare this little volume forthe eyes of the reading public, I am fullyaware of the difficulties of the subject andthe inadequacy of the expressions I have beenable to employ, but I have made the attempt atthe request of those who have found con-solation in some of the thoughts hereinembodied; and the messages left by othersbefore they passed away, embolden me tohope that many others may find in thisvolume some points of interest which willhelp them to appreciate better the “joys” whichthis life has for those who know howto look for them, and that perhaps others mayeven gain a clearer conception of that whichawaits us beyond the Veil. Many of us allow ourselves to be over-whelmed by the small worries and vexations ofeveryday life, clothing them with a realityquite disproportionate to their importance;we are too apt to look at them, as it were,through a powerful microscope, piling powerupon power of magnification, until we have ix
  7. 7. Science and the Infinitemade mountains out of mole-hills, whereas ifwe treated them at their true value we shouldlook at them through a telescope, in the re-verse direction, when they would appear notonly trivial, but would be seen to be tooremote to have any material effect on ourlives. The sub-title of this volume, and indeed itsinception, arose from my lately coming in con-tact with one of those establishments which aredoing for humanity what a mothers armsdo for the child who is “sick unto death”—a beautiful home with cheerful rooms andcheerful nurses, where patients are tenderlycared for after severe operations, carriedthrough by our most ferrous surgeons, somecases, alas, almost hopeless from the first. Atthe head of this establishment was one of thosekindly self-abnegating personalities, whoseloving sympathy and encouragement havecomforted the dying and smoothed the pathfor many a weary pilgrim passing form thislife to the next. With immense responsi-bilities on her shoulders, and after a day full ofstrenuous work, the head of this establish-ment would often sit through the night forhours by the couch of those whose lives couldnot possibly be prolonged for more than a fewdays. It was a few simple answers elicitedby the questions brought to me form thosepoor sufferers, and the way such answers x
  8. 8. Prefaceseemed to calm anxieties connected with thefear of death and to render the impenetrableVeil more transparent, which suggested thetitle, “Through a Window in the Blank Wall”I do not wish to lay claim to having madeany startling discovery; similar thoughts,especially those concerning the non-reality ofTime and Space, have no doubt occurred toothers, but the whole problem “What is theReality?” has been insistently pressing on meever since I can remember, and I have triedto give here in simple colloquial language,without any attempt at rhetoric, the conclu-sions I have personally come to as to what isthe Truth. The study of ancient and modern philo-sophic theories is useful as showing how im-possible it is, for even the greatest thinkersof any age, to grasp the Absolute with ourunderstanding or to measure the Infinitewith our finite units. The propounders of allthese theories seem to me to be, withoutexception, looking in the wrong direction forthe “Reality of Being”; they are all arguingfrom the standpoint of “Intellectualism” in asimilar manner to that of the “Theologians”referred to in View Three. Our latest ex-positor of this, M. Henri Bergson, bases histheory upon “Life” being the Reality; thishe postulates is a “flowing” in Time, andMovement therefore becomes for him the xi
  9. 9. Science and the InfiniteReality; and yet we know that Motion is butthe product of Time and Space, and these areonly the two modes or limitations under whichour senses act and upon which our veryconsciousness of living depends. Surely theAbsolute cannot be localised, must be Omni-present, and therefore independent of Space—cannot have a beginning or end, must beOmniscient, and therefore independent ofTime; these two unrealities can therefore haveno existence in “Reality of Being.” If,then, there is any truth in “Intuition,” wehave, in this theory, the Reality, “Life,” notonly limited by the unreal but actually depen-dent for its very existence upon those limita-tions! In these Views I have attempted, on thecontrary, to show that Time and Space have noexistence apart from our Physical Senses;they are the modes only under which weappreciate motion, or what we call physicalphenomena, and as our conceptional know-ledge is based upon our perceptional know-ledge, our very consciousness of living islimited by Time and Space, and we mustsurely therefore look behind consciousnessitself, beyond the conditioning in Time andSpace for the Reality of Being, otherwisephysical motion, the product of these twolimitations, would become the Reality ofBeing. I have also suggested reasons for looking xii
  10. 10. Prefaceupon physical life as a mode of frequency, akinto Light, Electricity, Magnetism, ChemicalAction, the Vibration of a Tuning Fork, or theSwing of a Pendulum, and therefore atransient phenomenon having to do onlywith the Race; Life can under these condi-tions only be looked upon as a reality in thesame sense in which all other forms of energyor matter appear real to our finite senses—namely, as the shadows or manifestations of theAbsolute on our limited plane of Con-sciousness. However strongly I may be convinced—as Iam—of the truth of my arguments, and how-ever sure I may be that many others will notonly agree with my conclusions, but will seethat in “Introspection” rather than in “Intel-lectualism " lies the key to the Mystery, I donot wish to appear dogmatic in any of thesuggestions contained in this volume; I amstating my own convictions, but at the sametime I fully recognise that the presentationof the Absolute, with its infinite variety ofaspects, must necessarily be different to everyindividual; we are all of the same genus, buteach individual Ego is, as it were, a differentspecies, and I do not therefore expect that myattempt to solve the Riddle of the Universewill appeal to all alike. It is, however, a truesaying that “there is something to be learntfrom every human being,” and if I have by xiii
  11. 11. Science and the Infinitethese suggestions succeeded in augmentingthe number of those who have already startedon the true “Quest,” and have helped, how-ever imperfectly, to enrich some lives withthe “joy” of knowing their oneness with theAll-loving, my aim has indeed been attained. SYDNEY T. KLEIN.“HATHERLOW,” REIGATE, 1st June 1912. xiv
  12. 12. CONTENTS VIEW ONE PAGECLEARING THE APPROACH . . . . . 1 VIEW TWOT HE VISION . . . . . . . . 19 VIEW THREEMYSTICISM AND SYMBOLISM . . . . 36 VIEW FOURLOVE IN ACTION . . . . . . . 71 VIEW FIVETHE PHYSICAL FILM . . . . . . 100 VIEW SIXSPACE . . . . . . . . . . 122 VIEW SEVENTIME . . . . . . . . . . 141 VIEW EIGHTCREATION . . . . . . . . . 165 xv
  13. 13. SCIENCE AND THE INFINITE VIEW ONE CLEARING THE APPROACHTHE proof that the Human Race is still in itsinfancy may be seen in the fact that we stillrequire Symbolism to help us to maintain andcarry forward abstract thought to higherlevels, even as children require picture booksfor that purpose. The Glamour of Symbolism,Rapture of Music, and Ideal of Art, which cometo us in later years, had their beginnings whento the child every blade of grass was a fairytale and a grass plot a marvellous fairy forest.The great aspiration of the Human Race is togain a knowledge of the Reality, the Noumenonbehind the phenomenon; but the fact that frominfancy we have been accustomed to confineour attention wholly to the objective, believingthat to be the reality, has surrounded us with aconcrete boundary wall through which wecan only at times, with difficulty, get transientglimpses of that which is beyond. It is only in 1
  14. 14. Science and the Infiniterecent years that we have been able to realisethat it is the Invisible which is the Real, thatthe visible is only its shadow or its manifesta-tion in the Physical Universe, and that Timeand Space have no existence apart from ourphysical senses, in short, that they are onlythe modes or limits under which those sensesact or receive their impressions and by whichthey are necessarily rendered finite. The difficulty is that our physical sensesonly perceive the surface of our surroundings,and that we have hitherto been looking at theWoof of Nature as though it were the glassof a window covered with patterns, smudges,flies, &c., comprising all that we call physicalphenomena and which, when analysed in termsof Time and Space, produce the appearance ofsuccession and motion. It requires a keenerperception, unbounded by these limitations, tolook through the glass at the Reality whichis beyond. I propose then in a series of shortviews, through a window not hitherto un-shuttered and in a direction which I believehas not before been attempted, to lead thoseof my readers who have the necessary aspira-tion, patience, and, above all, strenuous per-sistence, to a watch-tower, situated well abovethe mists and illusions of our ordinary every-day thoughts, whence they will find it possibleto get a glimpse of a strange new country,and where those who have by practice once 2
  15. 15. Clearing the Approachattained to its clear perception, will be able tocontinue the study by themselves and thus getfurther insight into that wonderful region ofThought which I have called “True Occult-ism”—the knowledge of the Invisible which isthe Real in place of the Visible which isonly its shadow. Let us first try and understand the condi-tions under which phenomena are presented tous. In our perception of sight, we find thegreater the light, the greater the shadow; alight placed over a table throws a shadow onthe floor, though not sufficient to prevent ourseeing the pattern of the carpet; increase thelight and the shadow appears now so darkthat no pattern or carpet can be seen; not thatthere is now less light under the table hut thelight above has to our sense of sight createdor made manifest a greater darkness. Thus,throughout the Universe, as interpreted by ourPhysical Ego, we find phenomena rang-ing themselves under the form of positive andnegative, the apparently Real and the UnrealThe Good making manifest its negative Evil.The Beautiful ,, ,, ,, Ugly.The True ,, ,, ,, False.Knowledge ,, ,, ,, Ignorance.Light ,, ,, ,, Darkness.Heat ,, ,, ,, Cold.But the negatives have no real existence. Asin the case of light we see that the shadow is 3
  16. 16. Science and the Infiniteonly the absence of light, so the negative ofGoodness, i.e. Evil, may in reality be lookedupon as folly or wasting of opportunity forexercising the Good. Owing to their limita-tions our thoughts are based upon relativity,and it is hardly thinkable that we could, underlour present conditions, have any cognisanceof the positive without its negative; we shallin fact see later on that it is by examining thePhysical, the negative or shadow, that wecan best gain a knowledge of the Spiritual,the positive or real. The first step to a clear understanding ofthis, is to recognise that it is not we who arelooking out upon Nature but that it is theReality which is ever trying to enter andcome into touch with us through our senses,and is persistently trying to waken within usa knowledge of the sublimest truths. It isdifficult to realise this, as from infancy wehave been accustomed to confine our atten-tion wholly to the objective, believing that tobe the reality, Let us try and grasp this fact. If we analyseour sense of sight, we find that the onlyimpression made on our bodies by ex-ternal objects is the image formed upon theretina; we have no cognisance of the separateelectro-magnetic rills forming that image,which, reflected from all parts of an object, 4
  17. 17. Clearing the Approachfall upon the eye at different angles, con-stituting form, and with different frequenciesgiving colour to that image; that image isonly formed when we turn our eyes in the rightdirection to allow those rills to enter; and,whereas those rills are incessantly beat-ing on the outside of our sense organ whenthe eyelid is closed, they can make no im-pression unless we allow them to enter byraising that shutter. It is not then anyvolition from within that goes out to seizeupon and grasp the truths from Nature, butthe phenomena are as it were forcing theirway into our consciousness. This is moredifficult to realise when the object is near tous, as we are apt to confound it with oursense of touch, which requires us to stretchout our hand to the object, but it is clearerwhen we take an object far away. In ourtelescopes we catch the rills of light whichstarted from a star a thousand years ago andthe image is still formed on the retina nowalthough those rills are in fact a thousandyears old and, invisible to our unaided eye,have been falling upon mankind from thebeginning of life on this globe, trying to getan entrance to consciousness. It was, how-ever, only when, by evolution of thought, theknowledge of optics had produced the tele-scope that it became possible not only for 5
  18. 18. Science and the Infinitethat star to make itself known to us but todeclare to us its distance, its size, and con-ditions of existence, and even the differentelemental substances of which it was com-posed a thousand years ago. Yet, when wenow allow its image to form on the retina,our consciousness insists on fixing its attentionupon that star as an outside object, refusingto allow that it is only an image inside the eyeand making it difficult to realise that that starmay have disappeared and had no exist-ence for the past 999 years, although in ordi-nary parlance we are looking at and seeingit there now. I have referred above to the sense of touch;it is, I think, clear that the :first impression achild can have of sight must take the formof feeling the image on its retina, as though theobject were actually inside the head, andit could have no idea that it was outsideuntil, by touching with the hand, it wouldgradually learn by experience that the tangibleoutside object corresponded with the imagelocated in the head; this is fully borne out bythe testimony of men who, born blind, have,by an operation, received their sight late inlife; in each case their first experience ofseeing gave the impression that the object wastouching the eye, and they were quiteunable to recognise by sight an object such as acup or plate or a round ball which they had 6
  19. 19. Clearing the Approachcommonly handled and knew perfectly wellby touch; in fact, the idea of an object formedby the sense of touch is so absolutely differentto that formed by the sense of sight that itwould be impossible without past experienceto conclude that the two sensations referredto one and the same object. The image formedon the retina has nothing in common withthe sense of hardness, coldness, and weightexperienced by touch, the only impression onthe retina being that of colour or shade, andan outline; it is, however, hardly conceivablethat even the outline of form. would be re-cognised by the eye until touch had provedthat form. comprised also solidity and thatthe two ideas had certain motions in commonboth in duration in Time and extension inSpace. Again, our senses of sight and hearing arealike based on the appreciation of frequenciesof different rapidity; brightness and colour inlight are equivalent to loudness and pitch insound, but in sound we have no equivalent toperception of form. or situation in space; itgives us no knowledge of the existence ofobjects when situated at great distances, norcan movements be followed even at short dis-tances without having material contact, bymeans of the air, with the object; sight indeedappears to have to do with Space- and soundwith Time-perception. In examining Nature 7
  20. 20. Science and the Infiniteby means of our senses we find we are sohemmed in by what we have always takenfor granted and so bound down by modesof reasoning derived from what we have seen,heard, or felt in our daily life, that we aresadly hampered in our search after the truth.It is difficult to sweep the erroneous conceptsaside and make a fresh start. In fact thegreat difficulty in studying the Reality under-lying Nature is analogous to our inability toisolate and study the different sounds them-selves which fall upon the ear, if our ownlanguage is being uttered, without beingforced to consider the meaning we havealways attached to those sounds. Let us now go back to the contention that itis not we who are looking out upon Naturebut that our senses are being bombarded fromwithout; we are living in a world of con-tinuous and multitudinous changes, and as oursenses require change or motion for theirexcitation, without those changes we couldhave no cognisance of our surroundings, weshould have no consciousness of living; but ifwe base our thought entirely on sense per-ception, taking for granted that Time andSpace have reality instead of recognising thatthey are only modes or limits under whichthose senses act, the Wall will ever remainopaque to us. Let us try and make thisclearer. If we analyse the impression we 8
  21. 21. Clearing the Approachreceive from Motion, we find it is made upof the product of our two limitations, it isthe time that an object takes to go over a certainspace. We must come therefore to theconclusion also that Motion itself has no ex-istence in reality apart from our senses. Theresult of not being able to appreciate this, isthat the finiteness of our sense, caused by itsdependence on Motion for excitation, surroundsus with illusions ; one of these illusions is whatwe call solidity or continuity of sensation. Ifyou hold a cannon-ball in your hand, percep-tion by the sense of touch tells you that it iscontinuous, or what is called solid and hard;but it is not so in reality except as a conceptlimited by our finite senses. A fair analogywould be to liken it to a swarm of bees, for weknow that it is composed of an immensenumber of independent atoms or moleculeswhich are darting about, and circling roundeach other at an enormous speed but nevertouching; they are also pulsating at a definiteenormous rate; we can at will increase theirmotion by heat or reduce by cold; if our touchperception were sensitive enough we shouldfeel those motions and should not have thesensation of a solid. We have a similar Case oflimitation in our other senses, which we shallgrasp better in another View through ourWindow. We can hear beats only up to fifteenin a second, beyond that number they give the 9
  22. 22. Science and the Infinitesensation of a musical or continuous sound.In our sense of sight we can see pulsationsor intermittent flashes up to only six in asecond, beyond that number they give thesensation of a continuous light; a gas jet,if extinguished and relit six times in a second,can be seen to flicker, but beyond that rateis to our sense of sight a steady flame. Theeffect may also be shown by making thetop of a match red-hot; when stationary ormoving slowly, it is a point of light, but,moved quickly, it becomes a continuous lineof light. Even apart from our senses we find Motiongiving the characteristics of solidity: a wheelwith only a few spokes, if rotated quicklyenough, becomes quite impermeable to anysubstance, however small, thrown at it; a thinjet of water only half an inch in diameter, ifdischarged at great pressure equivalent to acolumn of water of 500 metres, cannot becut even with an axe, it resists as though itwere made of the hardest steel; a thin cord,hanging from a vertical axis, and being re-volved very quickly, becomes rigid, and ifstruck with a hammer it resists and resoundslike a rod of wood; a thin chain and even aloop of string, if revolved at great speedover a vertical pulley, becomes rigid and, ifallowed to escape from the pulley, will runalong the ground as a hoop. 10
  23. 23. Clearing the Approach Now with regard to this limit of timeperception, which gives us the phenomenonof Solidity, I have lately been able to devisean arrangement which, acting as a micro-scope for Time, gives the sensation of anincrease in sight perception up to severalthousand units per second; it is based onthe fact that though the eye can only seesix times per second it can see for the one-millionth part of a second. An example ofthis is the well-known experiment of seeing abullet in its flight; the bullet makes elec-trical connection resulting in a spark whichilluminates the bullet when opposite the eye.The electrical spark exists only for the mil-lionth of a second, and as the bullet in thattime has no perceptible movement it. is seenstanding absolutely still with all marks upon itquite visible to the eye. When Sight per-ception is increased up to the rate at whichtime may be said to flow for any particularobject we apparently get into the reality, thepermanent now where motion ceases to existas a sensation. A tuning-fork, kept vibrat-ing, by means of an electro-magnet, at 2000times per second, may to our sense of sightbe gradually slowed down and, optically,brought absolutely to a standstill, for as long asdesired, and the smallest irregularity ofits surface may be minutely examined,though it continues to be heard and felt 11
  24. 24. Science and the Infinitevibrating at that enormous rate. I havemade several experiments in this direction,and some very curious facts connected withthe sensation of Motion are brought tolight by means of this increase in perceptivepower. If the sense of sight is increased to125 units per second, motion at the rate of oneinch per second is barely visible; takingthe common house-fly, whose wings vibrateabout 400 times per second, its units of per-ception would appear to be about two-thirdsof those beats, as I found it had no cogni-sance of Motion below two inches per second ;you can put your finger on any fly providedyou do not approach it faster than the aboverate, it turns its head up to look at yourfinger but can see no motion in it; if youapproach at over three inches per second itwill always fly away before you are within afoot. I found that a dragon-fly, whose wingsvibrate about 200 times per second, had onlyhalf the number of unit perceptions of the flyand could apparently see motion at about oneinch per second but not under. In the con-verse of the above we have then the principleof a Microscope for Time, somewhat similarto the Microscope for Space of our labora-tories. If our perception were increasedsufficiently we could slow down any motionfor examination, however rapid; there wouldbe no difficulty in following a lightning flash 12
  25. 25. Clearing the Approachor even arresting its visible motion for pur-poses of investigation without interferingwith the natural sequence of cause andeffect. If, on the other hand, our perception weredecreased below six times per second, allmotion would be accelerated, until with per-ception reduced to one unit in twenty-fourhours the sun would appear only as a bandacross the sky, and we could not follow itsmotion any more than, as we have seen, wecould follow the point of a red-hot match. Ifperception were reduced far enough, plants andtrees would grow up visibly before our eyes.But we must leave this subject now, as thisand the Time Microscope will be treated in alater View. Let us try and appreciate the fact that,under our present conditions, our conceptionsof the immense and minute—namely, exten-sion in Space, and that of quick and slow orduration in Time—are purely relative, andthat from this arise those pseudo-conceptionswhich we call the infinitely extended and theinfinitely lasting. Under our present limita-tions it is impossible for us to grasp the wholeof any Truth, if we could do that, there wouldbe no such mystery of Infinity to puzzle us;we could, as it were, see all around it, butthat is again looking through another window.We are now considering relativity. If we cut off 13
  26. 26. Science and the Infinitethe very end of the point of the finest needle,we get so minute a particle of steel that it ishardly visible to the naked eye, and yet weknow that that small speck contains not onlymillions but millions of millions of what arecalled atoms, all in intense motion and nevertouching each other. Try and conceive howsmall each of these atoms must be, and thentry and grasp the fact, only lately proved bythe discovery of Radio-activity, that each ofthese atoms is a great family made up ofbodies analogous to the planets of our solarsystem and whose rate of motion is compar-able only to that of Light. This is not theory,it is fact clearly demonstrated to us by thestudy of Radio-activity. Curiously enough,we know more about these bodies than we doof the atom itself ; we actually know their sizeand weight and the speed with which theymove. We do not yet know what is at thecentre of this system, but we do know thateach of these bodies is as far away from thecentre as our planet is from the sun (93,000,000miles), and as far from its neighbours as ourplanet is, relatively to its size. And now, for thepurpose of grasping this subject of relativity, Iwant you to ask yourself whether it is con-ceivable that a world, so small as those bodies Iare, could possibly be inhabited by sentientbeings. Leaving you to form your own con-clusion upon this point, I will ask you to 14
  27. 27. Clearing the Approachfollow me down another path leading to theelucidation of the same subject. If at this moment we and all our surround-ings were reduced to half their size and every-thing were moving twice as quickly, we shouldabsolutely have no cognisance of any change,neither could we possibly note any differenceif everything were reduced to a hundredthpart of the original size and were going ahundred times quicker; and even when reduceda thousand or a million times, or to suchminuteness that the whole of our solar systemwith its revolving planets became no largerthan one of those atoms in the needle point,and the whole of the starry universe thereforereduced to the size of the needle point, itsmillions of suns coinciding with the millionsof planetary systems in that steel particle—our earth would still revolve round the sun,though no larger than one of those minuteplanetary particles and travelling at the rateof light, but we should still have no know-ledge of any change, in fact, our life would goon as usual, though it was difficult a fewminutes ago to think it conceivable that sosmall a globe could be inhabited by sentientbeings. Once more let us consider that the changeis made in the direction of expansion in spaceand slowing down of Time; let all our sur-roundings be so enormously increased that 15
  28. 28. Science and the Infiniteeach of the atoms in the steel point becameas large as our solar system and the steelpoint as large as the visible universe, eachatom therefore taking the place of a star, andmotion being reduced in proportion; it is stillabsolutely inconceivable that we could knowof any change having taken place, though thelength of our needle, which was at first, say,one inch, would now be so great that light,travelling 186,000 miles per second, would take500,000 years to traverse its length, and thestature of each one of us would be so greatthat light would require over 36,000,000 yearsto travel from head to foot, and that 36,000,000years would have to be multiplied 163,000,000times, making 5860 millions of millions ofyears to represent the time that an ordinarysneeze would take under such conditions. Andyet we have only gone towards the infinitelygreat exactly as far as we at first went to-wards the infinitely small, and it is still abso-lutely inconceivable that we could be consciousof any change, our everyday life would go onas usual, we should be quite oblivious to thefact that every second of time, with all itsincidents and thoughts, had been lengthenedto 5860 millions of millions of years. Do wenot now begin to grasp the fact that immen-sity and minuteness in extension, and motionin duration, are figments only of our finiteminds, that Time and Space have no objective 16
  29. 29. Clearing the Approachreality apart from our physical senses, thatthey are only the modes under which we re-ceive impressions of our surroundings? Withperfect perception we should know that theonly Reality is the Spiritual, the Here com-prising all Space and the Now all Time. One more look through the window beforewe part, and we may see what I consider thegreatest miracle in our everyday life: TheInner-self of each one of us, being part of theReality or Spiritual, is independent of Spacelimitations and must therefore be Omnipre-sent, is independent of Time and thereforeOmniscient. This inevitable deduction will beexplained more fully in another View. It is from this store of knowledge thatour Physical Ego is ever trying to win freshforms of thought, and, in response to ourpersistent endeavours, that Inner-self, fromtime to time, buds out a new thought; thePhysical Ego has already prepared the cloth-ing with which that bud must be clad beforeit can come into conscious thought, because, asMax Miiller has shown us, we have to formwords before we can think; so does thePhysical Ego clothe that ethereal thought inphysical language, and by means of its organof speech it sends that thought forth into theair in the form of hundreds of thousands ofvibrations of different shapes and sizes, somelarge, some small, some quick, some slow, 17
  30. 30. Science and the Infinitetravelling in all directions and filling the sur-rounding space; there is nothing in thosevibrations but physical movement, but eachseparate movement is an integral part orthread of that clothing. Another PhysicalEgo receives these multitudinous vibrationsby means of its sense organ, weaves themtogether into the same physical garment, andactually becomes possessed of that etherealthought—an unexplained marvel, and prob-ably the most wonderful occurrence in ourdaily existence, especially as it often enablesthe second Physical Ego to gain fresh know-ledge from its own Real Personality. Now,in connection with this, consider the fact,already emphasized, that it is not we who arelooking out upon Nature, but that it is theReality which is ever trying to make itselfknown to us by bombarding our sense organswith the particular physical impulses to whichthose organs can respond, and, if we aspireto gain a knowledge of what is. behind thephysical, it is clear that all our endeavoursmust be towards weaving these impulses intogarments and then learning from them thesublime Truths which the Reality is evertrying to divulge to us. 18
  31. 31. VIEW TWO THE VISION“THY Will be done on Earth as it is in Heaven,”is in true consonance with the old philosophicdictum that “Everything in heaven must haveits counterpart on earth”; in other words, theReality has all Its multitudinous manifesta-tions, every noumenon its phenomenon, inthe physical universe. If we now examinethose traits of our surroundings which affectus most, and best help us to reach the highestlevel of abstract thought of which our natureis capable, we find that it is the recognition ofthe Beauty (comprising also the Good andthe True) in everything, which constitutes thepower held over our minds by what we maycall the Glamour of Symbolism, the Raptureof Music, and the Ideal of Art. But this in-fluence is still only sensuous, it does not carryus beyond the extension of that Wondermentand Enchantment which had their birth withour first visit to Fairyland. This is, I think,evident, as Beauty is not the Reality; it isonly what may be called the sensuous expres-sion of the Reality or Spiritual on the physical 19
  32. 32. Science and the Infiniteplane. Although we have no words to express,nor indeed minds to grasp, the wonders andglories of that which is behind the Veil, it ispossible for some of us to get a glimpse of itthrough our Window, and to those the fol-lowing pages may be helpful, but to othersthe Wall will remain blank; and, here at thecommencement, I should like to warn thosewho have not been through a certain experi-ence, to which I shall refer, that no wordsof mine will open the Window for them;at the same time it is probable that manyof my readers, who think at this stage thatthey have no knowledge of the subject ofthis View, will, as we proceed, recognise inthe view through the Window something theyhave experienced more than once in theirlifetime, and to these I address myself. Let us first try to understand what weknow concerning ourselves. The longer onelives and the more one studies the mysteryof “Being,” the more one is forced to theconclusion that in every Human Being thereare two Personalities, call them what youlike—“the Real and its Image,” “the Spiritualand its Material Shadow,” or “the Transcen-dental and its Physical Ego.” The former ineach of these duads is, as referred to in our firstView, not conditioned in Time and Space, isindependent of Extension and Duration, andmust therefore be Omnipresent and Omnis- 20
  33. 33. The Visioncient, whereas the latter, being subservient toTime and Space, can only think in finite words,requires succession of ideas to accumu-late knowledge, is dependent on perception ofmovements for forming concepts of itssurroundings, and, without this perception, itwould have no knowledge of existence. Let us go back into the far distant past,before the frame and brain of what we nowcall the genus Homo was fully developed: hewas then an animal pure and simple, consciousof living but knowing neither good nor evil;there was nothing in his thoughts more per-fect than himself; it was the golden age of in-nocency; he was a being enjoying himself in aperfect state of nature with absolute freedomfrom responsibility of action. But, as agesrolled on, under the great law of evolution, hisbrain was enlarging and gradually being pre-pared for a great and wonderful event, whichwas to make an enormous change in his modeof living and his outlook on the future. Asseeds may fall continually for thousands ofyears upon hard rock without being able togerminate, until gradually, by the disintegra-tion of the rock, soil is formed, enabling theseed at last to take root; so for countless ageswas the mind of that noble animal beingprepared until, in the fulfilment of time, theSpiritual took root and he became a livingsoul. The change was marvellous; he was 21
  34. 34. Science and the Infinitenow aware of something higher and more per-fect than himself, he found that he was able toform ideals above his ability to attain to,resulting in a sense 0f inferiority, akin to a”Fall”; he was conscious of the difference ofRight and Wrong, and felt happy and blessedwhen he followed the Good, but ashamed andaccursed when he chose the Evil; he becameupright in stature, and able to communicatehis thoughts and wishes to his fellows bymeans of language; and by feeling his free-dom to choose between the Good, Beautiful,and True on one hand, and the Evil, Ugly,and False on the other, he became awarethat he was responsible and answerable toa mysterious higher Being for his actions.This at once raised him far above otheranimals, and he gradually began to feel thepresence within him of a wonderful power,the nucleus of that Transcendental Self whichhad taken root, and which, from that age tothis, has urged Man ever forward first toform, and then struggle to attain, higherIdeals of Perfection. As a mountaineer who,with stern persistence, struggles upward fromheight to height, gaining at each step a clearerand broader view, so do we, as we progressin our struggle upwards, toward the under-standing of Perfection, ever see more and moreclearly that the Invisible is the Real, that thevisible is only its shadow, that our Spiritual 22
  35. 35. The VisionPersonality is akin to that Great Reality,that we cannot search out and know thatPersonality; it is not an idea, it cannot beperceived by our senses, any more than wecan see a sound by our sense of sight ormeasure an Infinity by our finite units; allwe can so far do is to feel and mark itseffect in guiding our Physical Ego to choosethe real from the shadow, the plus fromthe minus, receiving back in some marvel-lous mode of reflex action the power to drawfurther nourishment from the Infinite. Asthat Inner Personality becomes more andmore firmly established, higher ideals andknowledge of the Reality bud out, and, asthese require the clothing 0f finite expres-sions before they can become part of ourconsciousness, so are they clothed by ourPhysical Ego and become forms of thought;and, although the Physical Ego is only theshadow or image, projected on the physicalscreen, of the Real Personality, we are able,by examining these emanations and mark-ing their affinity to the Good, the Beautiful,and the True, to attain at times to more thantransient glimpses of the loveliness of thatwhich is behind the veil. As in a river flow-ing down to the sea, a small eddy, howeversmall, once started with power to increase,may, if it continues in midstream, instead ofgetting entangled with the weeds and pebbles 23
  36. 36. Science and the Infinitenear the bank, gather to itself so large avolume of water, that, when it reaches thesea, it has become a great independent force;so is each of us endowed, as we come into thislife, with a spark of the Great Reality, withpotential force to draw from the Infinite inproportion to our conscientious endeavours tokeep ourselves free from the deadening effectsof mundane frivolities and enticements, turn-ing our faces ever towards the light ratherthan to the shadow, until our personalitybecomes a permanent entity, commanding anindividual existence when the physical cloth-ing of this life is worn out, and for us allshadows disappear. If man became a conscious being on somesuch analogous lines as indicated, it is clearthat he is, as it were, the offspring of twodistinct natures, and subject to two widelyseparated influences; the Spiritual ever urginghim towards improvement in the directionof the Real or Perfect, and the Physical orAnimal instincts inviting him in the oppositedirection. These latter instincts are not wrongin themselves, in a purely animal nature, butare made manifest as urging him in the direc-tion of the shadow or Imperfect when theycome in contact, and therefore in competition,with the Spiritual. Neither the Spiritual northe Physical can be said to possess Free-will;they must work in opposite directions, but 24
  37. 37. The Visionthis competition for influence over our actionsprovides the basis for the exercise of man’sFree-will—the choice between progression andstagnation. The Spiritual influence must con-quer in the long run, as every step under thatinfluence is a step towards the Real and cannever be lost; the apparent steps in the otherdirection are only negative or retarding, andcan have no real existence, except as a dragon the wheel which is always moving in thedirection of Perfection, thus hindering theprocess of growth of the Personality. The stages in development of the PhysicalEgo and its final absorption in the Transcen-dental may perhaps be stated as follows— The Physical Ego loquitur: “ I become aware of being surrounded byphenomena, I will to see—I perceive andwonder what is the meaning of everything—I begin to think—I reflect by combiningformer experiences—I am conscious that Iam, and that I am free to choose betweenRight and Wrong, but that I am responsiblefor my actions to a Higher Power; that whatI call ‘I am’ is itself only the shadow, orin some incomprehensible sense the breath-ing organ, of a wonderful divine Afflatus orPower which is growing up within, or inintimate connection with me, and which itselfis akin to the Reality. Owing to my sensesbeing finite I cannot with my utmost thought 25
  38. 38. Science and the Infiniteform a direct concept of that power, although Ifeel that it comprises all that is good and real inme, and is in fact my true personality; I amconscious of it ever urging me forward towardsthe Good, Beautiful, and True, and that eachstep I take in that direction (especially whentaken in opposition to the dictates of physicalinstincts) results in a further growth of thatTranscendental Self. With that growth Irecognise that it is steadily gaining powerover my thoughts and aspirations. I learnthat the whole physical Universe is a mani-festation of the Will of the Spiritual, thatevery phenomenon is as it were a sublimethought, that it should be my greatest indi-vidual aspiration to try to interpret thosethoughts, or when, as it seems at present, ourstage in the evolution of thought is not farenough advanced, I should during my shortterm of life do my best to help forward theknowledge of the Good, Beautiful, and Truefor those who come after. As I grow old theReal 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 independentof earthly desires and aspirations, and, whenthe term of my temporary sojourn here drawsto a close, I feel myself slackening my holdof the physical until at last I leave go entirely,and my physical clothing, having fulfilled itsuse, drops off and passes away, carrying with 26
  39. 39. The Visionit all limitations of Time and Space. I awake asfrom a dream to find my true heritage in theSpiritual Universe.” If we try to form a conception of the stagesof growth of the Transcendental Self it would, Ithink, be somewhat as follows:The first conscious- entity would be . .As it became nour- } ness of the Spiritual I know that Love is the Summum Bonum. ished it would be } I love. I love with my wholeThen . . . . . { being. I know that I am partThen . . . . . { of God and God is Love. I am perfected in Lov-And lastly . . . . { ing and Knowing.And the above is the best description I havebeen able to formulate of the developmentof the Mystical Sense by means of which wecan get a view of the Reality throughour Window. I will try to give my ownexperience of this, which will, I know, wakean echo in other hearts, as I have metthose who have felt the same. From achild I always had an intense feeling thatLove was the one thing above all worthhaving in life, and, as I grew older and be-came aware that my real self was akin to theGreat Spirit, at certain times of elation or 27
  40. 40. Science and the Infinitewhat might be called a kind of ecstasy, I hadan overpowering sense of longing for unionwith the Reality, an intense love and cravingto become one with the Al1-Ioving. Whenanalysed later in life this was recognised assimilar 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 gentlesplash of a mountain stream, makes onealways want to open ones arms wide to em-brace and hold fast the beautiful in Nature, asthough ones Physical Ego, wooed by theBeautiful which is the sensuous (not sensual)expression of the Spiritual, longed to becomeone with the Physical, as the Personality orTranscendental Ego craves to become onewith the Reality. It is the same intense feel-ing which makes a lover, looking into the eyesof his beloved, long to become united in theperfection of loving and knowing, to be onewith that being in whom he has discovered alikeness akin to the highest ideal of which hehimself is capable of forming a conception. As in heaven, so on earth the Physical Ego,though only a shadow, has in its sphere thesame fundamental characteristic craving asthe Transcendental Personality has for thatwhich is akin to it, and it is this wonderfullove that, as the old adage says, makesthe world go round. It is the most powerful 28
  41. 41. The Visionincentive on earth, and is implanted in ournatures for the good and furtherance of therace; it is, in fact, the manifestation on thematerial plane of that craving of the Innerself for union with, and being perfected inloving and knowing, that Infinite Love ofwhich it is itself the likeness. If we canrealise that everything on the physical planeis a shadow, symbol, or manifestation of thatwhich is in the Transcendental, the Mystica1Sense, through contemplating these as sym-bols, enables us at certain times, alas! tooseldom and fleeting in character, to get be-yond the Physical; but those of my readerswho have been there will know how impos-sible it is to describe, in direct words, whichwould carry any meaning, either the pathby which the experience is gained or a trueaccount of the experience itself. I will try,however, and I think I may be able to leadmy readers, by indirect inductive sugges-tion, to a view of even these difficult sub-jects, by using the knowledge we havealready gained in our first view throughthis Window. If an artist were required todraw a representation of the OmniscientTranscendental Self, budding out new forms ofthought in response to the conscientiousefforts of, and the providing of suitable cloth-ing by, the Physical Ego, as referred to inView No. I, he would be obliged to make use 29
  42. 42. Science and the Infiniteof symbolic forms, and I want to make itquite clear that the description I am attempt-ing must necessarily be clothed in symboliclanguage and reasoning, and must not betaken as in any way the key by which thedoor of “the sanctuary” may be opened; it isonly possible by it to help the mind to grasp thefact that there is a Window through whichsuch things may be seen, the rest dependsupon the personality of the seer. Now bear in mind that it is not we who arelooking out upon Nature, but that it is theReality, which, by means of the physical, is per-sistently striving to enter into our conscious-ness, to tell us what? QeÕj ¨gaph Ÿstin (God isLove). As in Thompsons suggestive poem,“The Hound of Heaven”—the Hidden whichdesires to be found—the Reality is ever hunt-ing us, and will never leave us till He hastaught us to know and therefore to love Him,and, as seen in our first view, the first step is totry to see through the woof of nature to theReality beyond. To this may also be addedthe attempt to hear the “silence” beyond theaudible. Try now to look upon the whole“visible” as a background comprising land-scape, sea, and sky—we shall get help in thisdirection in a later View—and then bring thatbackground nearer and nearer to your con-sciousness. It requires practice, but it can bedone; it may help you if you remember the 30
  43. 43. The Visionfact that the whole of that visible scene isactually depicted on the surface of your retinaand has no other existence for you. The neareryou can get the background to approach, themore clearly you can see that the wholephysical world of our senses is but a thin veil, amere soap film, which at death is pricked andparts asunder, leaving us in the presence of theReality underlying all phenomena. The samemay be accomplished with the “audible,”which is indeed part of the same physicalfilm, though this is not at :first easy to recog-nise. As pointed out in View No.1, there islittle in common between our sense of sightand hearing; but the chirp of birds, the humof bees, the rustle of wind in the leaves,the ripple of a stream, the distant sound ofsheep bells, and lowing of cattle form a back-ground of sound which may be coaxed toapproach you; the only knowledge you haveof such sounds is their impression or image onthe flat tympanum of your ear; they have noother existence for you; and again you mayrecognise that the physical is but a thin tran-sient film. With the approach of the physicalfilm all material sensation becomes as it wereblurred, as near objects become when the eyelooks at the horizon, and gradually escapesfrom consciousness. I have tried in the foregoing to suggest amethod by which our Window may be un- 31
  44. 44. Science and the Infiniteshuttered; it has necessarily been only anoblique view and clothed in symbolic phrase-ology, but those who have been able to graspits meaning will now have attained to whatmay be called a state of self-forgetting, thesilencing or quieting down of the Physical Ego;sight and sound perceptions have been put inthe background of consciousness, and itbecomes possible to worship or love the veryessence of beauty without the distraction ofsense analysis and synthesis or temptation toform intellectual conceptions. We are now prepared to attempt the lastaspect of our view—namely, the descriptionof what is experienced when the physicalmists have been evaporated by the MysticalSense. Again we find that no direct de-scription is possible, language is absolutelyinadequate to describe the unspeakable, com-munications have to be physically transmittedin words to which finite physical meaningshave been allocated. The still small voicewhich may at times of Rapture be moment-arily experienced in Music, is something muchmore wonderful than can be formed by sounds,and this perhaps comes nearest to the ex-pression necessary for depicting the vision ofthe soul; but it cannot be held or described, it isquickly drowned by the physical sense ofaudition. As the Glamour of Symbolism canonly be transmitted to one who has passed 32
  45. 45. The Visionthe portal 0f Symbolic Thought. the Raptureof Music can only be truly understood by onewho has already experienced it, and the Ideal 0fArt requires a true artistic temperament tocomprehend it, so it is, I believe, impossibleto describe, with any chance of success, thiswonderful experience to any but those whomMr. A. C. Benson, in his Secret of the Threadof Gold, very aptly describes as having alreadyentered “the Shrine.” Those who have beenthere will know that it is not at all equivalentto a vision, it is not anything which can be seenor heard or felt by touch; it is entirelyindependent 0f the physical senses; it is notGiving or Receiving, it is not even a receivingof some new knowledge from the Reality; ithas nothing to do with thought or intellectualgymnastics; all such are seen to be but mist.The nearest description I can formulate is :—Awondrous feeling of perfect peace;—absoluterest from physical interference;—perfect con-tentment;—the sense of Being-one-with-the-Reality, carrying with it a knowledge thatthe Reality or Spiritual is nearer to us andhas much more to do with us than thePhysical has, if we could only see the truthand recognise its presence;—that there is noreal death;—no finiteness and yet no Infinity;—that the Great Spirit cannot be localised orsaid to be anywhere, but that everywhere isGod;—that the whole of what we call 33
  46. 46. Science and the InfiniteCreation is an instantaneous Thought of theReality;—that it is only by the process ofanalysing in Time and Space that we imaginethere is such a thing as succession of events;—that the only Reality is the Spiritual, theHere embracing all Space and the Now em-bracing all Time. How few of us who are now drawingtowards the end of our sojourn here, havenot, at certain times during our lives, ex-perienced something akin to what I havetried to put before you in the above! Doesnot a particular scent, a beautiful countryscene, a phrase in music, the beauty or pathosin a picture, symbolic sculpture in a grandcathedral, or even a chance word spoken inour hearing, every now and then waken inour innermost consciousness an enchantingmemory of some wonderful happy momentof the past when the sun seemed to have beenshining more brightly, the birds singing moremerrily, when everything in nature seemedmore alive, and our very beings seemedwrapped up in an intense love of our sur-roundings? On those occasions we were notfar from seeing behind the veil, though wedid not recognise it at the time; but when wenow look back, with experience gained byadvancing years, and consider those visionsof the past, we cannot help seeing that thephysical film was to our eyes more transparent 34
  47. 47. The Visionat those times, and the very joy of their re-membrance seems to be giving us a prescienceof that which we shall experience, when foreach one of us the physical film is pricked andpasses away like a scroll. 35
  48. 48. VIEW THREE MYSTICISM AND SYMBOLISM“WHO can doubt that the Mystics know morethan the Theologians, and that the Poets knowmore than the Scientists? for this inner appre-hension is surely the highest and truest kindof Knowledge.” Such were the words writtento me lately by a clergyman of great learn-ing and of unimpeachable orthodoxy, whosemature knowledge of the Higher Mysterieshas been gained by a life-long study of theDivine. In View No.1 we saw that the firststep towards opening our Window, was tograsp the fact that it is not we who are look-ing out upon Nature, but that it is the Realitywhich is ever trying to enter and to come intotouch with us, through our senses, and is per-sistently trying to wake within us a know-ledge of the sublimest truths: but this hasnot yet been appreciated by the Theologian;he is looking outwards instead of inwards,and asks the question, based on intellectualconception, in the form “Can I find out theAbsolute so that I may possess Him ?” andthe answer ever comes back, “No, because I 36
  49. 49. Mysticism and Symbolismam trying to storm the Sanctuary of the Un-thinkable, the Infinite, by means of a Ladderwhich cannot reach beyond our finite con-ceptions, and can deal therefore only with theshadows, cast by the outlying ramparts, uponour physical plane." An example of this issurely seen in the lecture lately delivered bythe Bishop of Oxford (Dr. Gore) to the Uni-versity of Oxford (13th February 1912, re-ported in the Guardian of 16th February),when he made the statement that the greatestdifficulty we have is to recognise that theAbsolute is a God of Love. His exact wordswere: “I believe that there are a great manyof us who know, perhaps from bitter experi-ence, that whatever difficulties there are aboutreligious belief are difficulties about believingin a God of Love; whatever is our experience,and however sunny is our disposition. anysteady thinking will make it apparent thatthought, apart from the Christian revelation,presumed and accepted, or reflected uncon-sciously, has never got at it, and even after ithas been in the world, thought is continuallyfinding it hard to retain the idea of God theCreator, or the truth that God is Love, partlyowing to the limitations of human thinking,partly, and even more, owing to the experienceof man and of nature.” On the other hand the Mystic, with intro-spection, asks the question in the form “Can 37
  50. 50. Science and the Infinitethe Absolute find me out and possess me andthus make me feel that that which is withinme is akin to, is, in fact, a part of Him andthat I am possessed thereby?” and the answerever comes back from those who are on thetrue Quest:—“Yes; because the Unthink-able, the Hidden which desires to be found, isever trying to come into our Consciousness towaken the knowledge that His Sanctuary, orwhat is called the Kingdom of Heaven, iswithin us, that we are not an external but aninternal creation of the All-loving.” Such arealisation is, as pointed out in “The Vision,”far above Analysis and Synthesis or Intel-lectual gymnastics, which can deal only withthe finite and are seen to be but Mist. Howmany valuable thoughts are wrecked and lostfrom our inability to formulate and describethem intellectually, even in our own conscious-ness. We are too apt to lay the blame upon,and to doubt, the Truth of those conceptions,because we are unable to find words to expressthem; the very act of attempting to analysesuch thoughts in Time and Space destroys ourpower of carrying them to higher levels.Those who have once realised that the know-ledge of the Absolute is the true Divine Lifewithin us, can, as we have seen, at certaintimes and under certain conditions, experi-ence that wonderful joy of perception bymeans of what I have called the Eye of the 38
  51. 51. Mysticism and SymbolismSoul; but that is missed by those who arealways asking questions, and arguing, aboutwhat that knowledge consists in; the command“Seek and ye shall find, knock and it shall beopened unto you, ask and it shall be givenyou,” was not meant for the intellect but for theHeart, not for logical controversy but forinward discernment, not for physical enjoy-ment but for the nourishment of the Trans-cendental Ego. All things may be possibleto him that believeth, but how much more isthis true of him who, as referred to in ViewNo. 2, is perfected in “Loving and Knowing.”The nearer we get to that consciousness ofBeing - one - with - the - Reality, the more wesee and can meditate upon the wonderful“joy” which permeates all creation; butwithout that consciousness it is invisible, andthe world is dark and evil and unloving, and tomany, alas! appears more the handiworkof a Devil than of a God of Love. Mysticism is not, as the man in the streetgenerally thinks, the study of the “Myste-rious,” but is the attempt to gain a knowledgeof the Reality, the ultimate Truth in every-thing, especially the perception of that wonder-ful Transcendental Power which is growingup within, or in close connection with, eachone of us. The study of the Physical Sciences,as also of the various forms of Religionaround us, is useful and fascinating in the 39
  52. 52. Science and the Infinitedomain of “Intellectualism,” but does nottake us far towards the goal of our aspira-tions. I shall, however, attempt to show, in mynext View, that by examining the pheno-mena of Nature and realising that they aresymbols only of the Noumenon, the Reality,which is behind them, it is possible to reach apoint where we may even feel that we arethinking, or having divulged to us, what maybe called the very thoughts of the Absolute.We shall see that this can only be accomplishedby first recognising that the Invisible is theReal, that the visible is only its shadow, that allour surroundings are but the images, oroutlines, of the Reality cast on the Physicalplane of our Senses; to accomplish this, wehave to understand the use of SymbolicThought for sustaining and carrying con-ceptions to a higher level; because, asalready explained, we can only express and,indeed, think of the Invisible or Infiniteunder terms of the Visible or Finite. Let megive you a glimpse at what may be calledthe “Glamour of Symbolism " ; it is difficult toexplain to those who have not yet thought ofor felt it, but the following may be helpful : Think of the loveliest story or poem youhave ever read, the most entrancing music youhave ever heard, or the most beautiful paint-ings you have ever seen, and think how, at theend, you experienced a wonderful glow of 40
  53. 53. Mysticism and Symbolismenchantment with the concept as a whole, apartfrom specialising any particular character orevent in the story, phrase in the music, or sub-ject in the pictures; then do the same with oneof those wonderful cathedrals of the twelfth tofourteenth centuries, the epoch of that beau-tiful Gothic style which I shall show wasfounded upon the highest mystical form ofSymbolism possible to those who lived at thethen zenith of Mystical Thought in the historyof the world. The number of cathedrals builtduring those three centuries was so prodigiousthat, without the documentary evidence whichwe have, it would be absolutely incredible.Every part of those buildings, even to thesmallest decorations, was, as shown by any ofthe old writers on Religious Symbolism, such asDurandus, planned to symbolise some beauti-ful thought, aspiration, tradition, or religiousbelief. The highest Thinkers, Artists, Poets,Philosophers, and Mystics in those centuriesbecame Architects, and, in pure contemplationof and love for the Divine, helped to beautifydesign by giving up their lives and energiesto the work without reward. It was, in fact, atthat period the surest means by which theycould record their ideals and aspirations.Before the advent of the printing press, with itsfacilities for spreading knowledge broad- cast,they appreciated that Tectonic Art andIconography were the means by which they 41
  54. 54. Science and the Infinitecould best permanently record and teach theiraspirations to the masses. Every beautifulthought found its expression in some symbol ofartistic design. Each Cathedral was, in fact,a beautiful complete story, and, when this hasbeen fully grasped, the enchantment of thewhole, the thread of gold running throughthe whole of that wonderful pile, is what maybe called the Glamour of Symbolism. For the last 400 years, Archæologists, Archi -tects, and others interested in the history ofTectonic art, have been trying without availto discover what is called “the lost secret ofGothic Architecture”; even Sir ChristopherWren had a try and expressed his opinionthat it was lost for ever. They were all look-ing in the wrong direction, confining them-selves to the mists of physical intellectualperception, and could not get beyond thatlimited range of thought. I propose now, inillustration of this View, to show what thissecret was. It has the making of a fascinatingRomance; it is the most wonderful exampleof what I will call “the Evolution of Thought asdepicted by Human strivings after theTranscendental in Mediæval Mysticism.” Ishall give it in a brief form, touching only onthose essential points which require a veryslight knowledge of Geometry, but thoseinterested in the subject may refer to ArsQuatuor Coronatorum (vol. xxiii., 1910), where 42
  55. 55. Mysticism and SymbolismI have given the whole subject, in extenso,under the title “Magister Mathesios.” To understand the subject it is necessary .torecognise fully the place Geometry held, notonly among Mediæval Builders, but also inClassical times; it was recognised in thoseearly 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 timewhen the “Greek Age of Reason” was at itszenith, and Plato, the greatest of the philo-sophers, was teaching at Athens, workingthus, let it be known to his honour, solelyfor the love he bore to science, for he alwaystaught gratuitously. What qualification wasrequired of those who attended his Academy?Look up over the porch, and you will see writ-ten in large capitals these words : MHDEIS AGEWMETRHTOS EISITW MOU THN STEGHN. “Let no one who is ignorant of Geometryenter my doors.” At the root of Socratic teaching was theidea that wisdom is the attribute of the God-head, and Plato, for twenty years the com-panion and most favoured pupil of Socrates,was imbued with that doctrine, and, havingarrived at the conclusion that the impulse tofind out TRUTH was the necessity of in-tellectual man, he saw in Geometry the key- 43
  56. 56. Science and the Infinitestone of all Knowledge, because, among allother channels of thought, it alone was theexponent of absolute and undeniable truth.He tells us that “Geometry rightly treatedis the Knowledge of the Eternal”; andPlutarch gives us yet another instance ofPlato’s teaching concerning this subject, inwhich he looks upon God as the Great Archi-tect, when he says, “Plato says that God isalways geometrising.” Holding, therefore, asPlato did, that God was a great Geometer,and that the aim of philosophy was the ac-quisition of a knowledge of the Eternal, itis natural that he should make a knowledgeof Geometry imperative on those wishing tostudy philosophy. This was continued alsoby those philosophers who succeeded Platoin the management of the Academy, as weare told that Zenocrates turned away anapplicant for admission, who knew no geo-metry, with the words : poeÚou, lab¦j g¦r oÙk œceij tÁj filosof…aj. “Depart, for thou hast not the grip ofphilosophy." In connection with the idea that God wasa Geometer, must be taken the contentionheld by the Egyptians, and after them theGreeks and Arabs, that the Right-AngledTriangle symbolised the nature of the Uni-verse; it was called the law of the three 44
  57. 57. Mysticism and Symbolismsquares, because in every Right-Angled Tri-angle, as expounded by the PythagoreanTheorem, the squares, formed on the twosides containing the Right Angle, must to-gether be exactly equal to the square onthe third side, whatever the shape of thetriangle may be. The Right Angle at anearly date gave its name to the odd num-bers, which were called, by the Greeks, gno-monic numbers, as personifying the male sex,and the Right-Angled Triangle was also calledthe Nuptial Figure, or Marriage, thePythagorean Theorem receiving the name, tÕqeèrhma t¾j nÚmfej (the Theorem of the Bride).Plutarch, in his Osiris and Isis, tells us inexplanation of this, “The Egyptians imaginedthe nature of the Universe like this mostbeautiful triangle, as Plato also seems tohave done in his work on the State, whenhe sketches the picture of Matrimony underthe form of a Right-Angled Triangle. Thattriangle contains one of the perpendicularsof three, the base of four, and the hypotenuseof five parts, the square of which is equal to thesquares of those sides containing the rightangle. The perpendicular (three) is the Male,Osiris, the originating principle (¢rc») ; the base(four) is the Female, Isis, the receptive prin-ciple (Øpdoc») ; and the Hypotenuse (five) is theoffspring of both, Horus, the product(¢potšlesma).” The central feature of this 45
  58. 58. Science and the Infinitetriangle, upon which its property is based, isthe Right Angle. The Greeks gave to thisRight Angle the name of Gnomon (meaningKnowledge), and it has ever since been, underthe form of a carpenters ..square," the emblemor symbol of an Architect, the Master Mason,as personifying the Great Architect of theUniverse—namely, He who has the know-ledge of Geometry; and, as the Right-AngledTriangle represented the Universe, it wasupon the perfection of this Gnomon, or know-ledge, that the very existence of the Uni-verse depended, because the law of the threesquares only holds good when that angle isperfect. The Secret handed down in the Craft,from Architect to Architect, was how toform a perfect right angle, or, as it wascalled, the “Square,” without possibility ofError, and this I have called “the Know-ledge of the Square.” Vitruvius, who, at thebeginning of our Era, wrote his thesis onTectonic art, which is still the text-book ofArchitecture for Ancient buildings, says Pytha-goras taught his followers to form a gnomon, orsquare, as follows: “Take three rods, ofthree lengths, four lengths, and five lengthslong; with these form a triangle, and, if eachrod be squared, you have 9, 16, and 25, andthe areas of the two former will be equal tothe latter.” 46
  59. 59. Mysticism and Symbolism Now let us come to the closing years ofthe tenth century. What a strange conditionof the building craft was to be seen all overEurope; not a church was being built, norhad been built, for the last twenty years; thethousand years after Christ was drawing toits close, everybody was waiting for, and ex-pecting, the world to come to an end; no newundertakings were begun. How much moneywent into the hands of the Monasteries andother Religious Houses, as peace offerings forthe future welfare of the givers, nobody cansay; it was probably enormous. When, how-ever, the eleventh century was well startedand the crisis was over, churches were built ona large scale, as shown by the numerousremains we have of Norman buildings of thelast half eleventh century, and building wasprobably at its height about A.D. 1140 to 1150;but at this period an extraordinary thinghappened. Hitherto the arches in the Normanstyle were round-headed and their columnsenormously thick to carry them; but sud-denly the style changed into the beautifulGothic all over Europe. No single countrycan claim precedence, it was almost simul-taneous; churches half finished in the roundstyle were not only completed in the pointed,but had parts already built altered to the newstyle. What, then, determined this suddenchange, resulting in a wonderful accession of 47
  60. 60. Science and the Infinitebeauty to Architectural design? We mustgo to the Monasteries and Religious Housesto find the explanation. These Houses hadbecome the Patrons of Masonry, the providersof the funds for building Cathedrals, &c.; itnaturally followed that, growing up along-side the Operative Science, there was a Reli-gious symbolism being gradually formed whichattached itself specially to the tools used byMasons, and thus formed the basis of Moralteaching—“to act on the Square,” “to keepwithin the bounds of the Compasses,” “to beLevel in all your dealings,” &c., &c. Awonderful, new, and Mystical form of Sym-bolism was opened to them with the advent ofGeometry. The text-book of Geometry wasunknown throughout the whole of Europe,omitting Spain, from the sixth to the begin-ning of the twelfth century; it was, as I havepointed out, well known in Greece before ourEra, and continued to be so up to about thesixth century A.D. In the fourth century livedthe Greek, Theon of Alexandria, so well knownfor his edition of Euclid’s Elements, with notes,from which all Greek MSS. which first cameto light in the sixteenth century were taken,being entitled ™k tîn qeènoj sunousiîn, “fromTheons Lectures,” and which he probably usedas 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 48
  61. 61. Mysticism and Symbolismcentury, when Simon Grynæus, the greatestGreek scholar on the Continent, and com-panion of Melancthon and Luther, discovereda copy in Constantinople. Meanwhile, Theon’sedition had been translated into Arabic, andthus preserved by the Mohammedans, and itwas only at the beginning of the twelfth cen-tury that Athelard of Bath, who had beentravelling in the East, came to study at Cor-dova, in Spain, and there found the ArabicMSS. of Euclid ; these he translated in to Latin,and this translation must have come into thehands of the patrons of the building craft atthe very time when the Gothic style had itsorigin; it was the only Latin translation knownin Europe, and was, some centuries later, thetext-book of the first printed edition of Euclid. The Operative Masons had always formedtheir Right-Angled Triangles by means ofmundane measures of 3, 4, and 5 units to eachside respectively, as was done by the Harpe-donaptæ of Egypt 5000 years ago, and 2500years later by Pythagoras, and this samemethod continues to be used to this day; but tothose of a religious turn of mind, who hadonly lately become conversant with Euclid,and looked upon Geometry not only as theheight of all learning, but, as they progressedin the knowledge of its bearing on the Scienceof. building, actually made it synonymouswith Tectonic Art (the old MSS. which have 49
  62. 62. Science and the Infinitecome down to us from that time invariablystate that “at the head of all the Sciencesstands Geometry which is Masonry”), theremust have come a wave of wonderful en-thusiasm when they first discovered thatthe Geometrical way of creating a RightAngle, as given in Euclid I. ii., was by meansof an Equilateral Triangle, by joining theApex with the centre of the base. ThisEquilateral Triangle was the earliest symbolwe know of the Divine Logos in connectionwith that wonderful figure the Vesica Piscis;and as the Bible declared that the Universewas created by the Logos (the Word), so theSquare which represented the Universe wasnaturally created by means of the Equi-lateral Triangle. A great mystery this musthave appeared to those who, like the Hellenicphilosophers, postulated that everything onEarth has its counterpart in Heaven, and who,in their religious mysticism, were alwayslooking for signs of the transcendental in theirtemporal surroundings. But in what awe and reverence must theyhave held Geometry, when they further foundthat the Equilateral Triangle, representingthe Logos, was itself generated, as shownin the first Problem of Euclid, upon whichthe whole Science of Geometry was there-fore based, by the intersection of two Circles!These two Circles were held by the Greeks, 50
  63. 63. Mysticism and Symbolismat the beginning of our Era, to represent thePast and Future Eternities generating theLogos; but the whole figure (Euclid I. i.) wasat the time we are now dealing with lookedupon by Mediæval Architects as representingthe Three Divine personæ, and that part, orcavity, of the figure which is bounded by theArcs of the two circles, and which takes toitself one-third of each of the two generatingcircles (making its perifera exactly equal withthat remaining to each of the two circles, allthree therefore being co-equal), and in whichthe Equilateral Triangle is formed (vide frontis-piece), was naturally held by the MediævalArchitects, and indeed from earliest times, asthe most sacred Christian Emblem—namely,that of Regeneration or " New Birth." The Cavity is evidently referred to in theMystical Gospel of St. John (iii. 16), in thequestion by and answer to Nicodemus, and itwas the eye of the needle referred to in St.Mark x. 25, in answer to the question in verse17, and again in St. Luke xviii. 25. In laterages this symbol was extensively used by theChristian Church to surround the “Soul ofa Saint" after death (illustrated in MagisterMathesios). The date of the birth of a Saintwas always given as the date on which he orshe died and had been born again in theSpiritual Life, and the Saint was depicted ina Vesica Piscis, the vulva of the Ruach or 51
  64. 64. Science and the InfiniteHoly Spirit, representing this new birth. Toshow the extraordinary reverence and highvalue attached to this symbol, it is only neces-sary to remember that, from the fourth cen-tury, when Theon of Alexandria lectured onGeometry, and onwards, all Seals of Colleges,Abbeys, Monasteries, and other religious com-munities, as well as of ecclesiastical persons,have been made invariably of this form, andthey continue to be made so to this day. Itwas also in allusion to this most sacred ancientemblem that Tertullian, and other earlyFathers, spoke of Christians as “Pisciculi.” Itwas called the “Vesica Piscis” (Fish’sBladder), and named, no doubt, by the Greeksat the beginning of our Era, for the purposeof misleading the ignorant from the truemeaning of the Figure. One can well understand the object whichled the learned Rabbi Maimonides, the great-est savant of the Middle Ages, when address-ing his pupils in the twelfth century, tocommand his hearers: “When you have dis-covered the meaning thereof, do not divulge it,because the people cannot philosophise norunderstand that to the Infinite there is nosuch thing as Sex;” but later on the notedwriter on Symbolism, Durandus, in the intro-duction to his book, is more explicit, and givesthe real meaning as follows: “The MysticalVesica Piscis . . . wherein the Divinity and, 52
  65. 65. Mysticism and Symbolismmore rarely, the Blessed Virgin are repre-sented, has no reference, except in name, toa fish, but represents the Almond, the symbolof Virginity and self-production.” The Vesica Piscis, and its name, isintimately connected with the discovery, byAugustus Cæsar in the century preceding ourEra, as narrated by Baronius, of a prophecy inone of the Sibylline books, foretelling “a greatevent coming to pass in the birth of One whoshould prove to be the true ‘King of Kings,’and Augustus Cæsar therefore dedicated analtar in his palace to this unknown God.”Eusebius and St. Augustine inform us that thefirst letter of each line of the verses from theErythrean Sibyl containing this prophecy,formed the word ICQUS: (a fish), and weretaken as representing the sentence: IhsoujCristÕj Qeoà UiÕj Swt»r (“Jesus Christ, theSon of God, the Saviour”). Based upon thisdiscovery arose that extraordinary enthu-siasm, during the second, third, and fourthcenturies, for hunting up further prophe-cies in Pagan sources, resulting in a greatnumber of Sibylline verses being invented,giving the minutest details in the Life ofour Lord. These fabrications seem to havebeen at that time generally accepted by themasses as true prophecies, though we know.now that they were written some centuriesafter the events they were supposed to foretell. 53
  66. 66. Science and the Infinite Let us now return to the Vesica Piscis.In the paintings and sculptures of the MiddleAges, we find it constantly used to circum-scribe the figure of the Saviour, especiallywhenever He is represented as judging theworld and in His glorified state. Many beauti-ful examples of this in Anglo-Saxon work ofthe tenth century may be seen in King Edgar’sBook of Grants to Winchester Cathedral andthe famous Breviary of St. Ethelwolfe. Numer-ous illustrations of these and other pictures ofthe Middle Ages, as also diagrams of theproperties of the Vesica Piscis, can be seen inthe volume I have already referred to deal-ing fully with this subject. The building fraternity was a purely Chris-tian community; the First Crusade raised agreat enthusiasm for building ChristianChurches, and brought in large gifts of moneyfor that purpose. Up to 1140 Norman Archi.tecture held sway, having the “Square” for itsunit, its greatest symbol being the Gnomon,representing knowledge; but about that time, aswe have seen, arose from the study of Geo-metry, the head of all learning, a Mysticalform having the mysterious figure of theVesica Piscis, the true Gothic Arch, withthe Equilateral triangle enclosed as its unit,and symbolising the Trinity in Unity. Therecognition of the import of the Trinity wasparamount throughout those early days; all 54
  67. 67. Mysticism and Symbolismimportant documents began with an Invoca-tion of the Tres Personæ, or were garnishedwith symbolic illustrations thereof; all theold MSS., already referred to, which havecome down to us from that period, invari-ably commence with “In the name of theFather and of the Son and of the HolyGhost.” It can therefore be readily understoodwhat determined the sudden change between1140-1150, resulting in that wonderful ac-cession of beauty to architectural designwhich we find in the Gothic. The incen-tive had to be a strong one, and of an emi-nently religious character, to accomplish theradical change of throwing over so absolutelythe Norman, and commencing to build en-tirely on what are called Gothic lines. Acareful examination of the proportions ofthe structures themselves, and the characterof the decorations found in the finest ex-amples of buildings representing that style. atonce shows us that the incentive was thesymbolism attached to the mysterious figurecalled the Vesica Piscis, which appears tobe not only the principal feature upon whichthe whole style rests, but is also employed. as asymbol of the Divine, wherever we haveGothic Architecture, either in painted windowsor mural decorations. Every Cathedral has itsVesica Piscis, often of enormous dimensions. 55
  68. 68. Science and the InfiniteGeometry was synonymous with Masonry, andthe very foundation of the Science of Geo-metry, as expounded by Euclid, was his firstproposition. Every single problem in the wholeof his books necessitates for its constructionthe use of this one foundation—namely, “howto form an Equilateral Triangle,” and this is theMystical form of “the Knowledge of theSquare.” This triangle, symbolising the Logos,is therefore not only the beginning of theScience of Geometry, and therefore of Masonry,the Head of all the Sciences, but it is by thattriangle that all Geometrical forms, and there-fore forms of knowledge, are made, and itbecame the most mysterious and secret symbolof the Logos, for is it not written by St. Johnthat “In the beginning was the Logos, andby it were all things made”; so the VesicaPiscis, the cradle of the Logos, became thegreat secret of Masonry, the foundation aswe find it upon which Gothic Architecturewas evolved, the means by which its won-derful plans were laid down, and the mostreverenced figure in Religious Symbolism, asshown by its use in seals, engravings, sculp-tures, pictures, &c.. throughout the MiddleAges. Let me make this clearer. The more oneexamines the typical points in the Saxon,Norman, and Gothic styles of Architecture, themore clearly one sees that the Architects of the 56
  69. 69. Mysticism and Symbolismtwo former used circles and squares on theirtracing- boards, as units for their proportions,in drawing up both ground plans and eleva-tions, with here and there suggestions onlyof the Equilateral Triangle having been madeuse of in some of the smaller details; whereasthe Gothic Architects seem to have used theVesica Piscis almost entirely. This explainsthe reason why true Gothic buildings havealways been said to be built mainly on thebasis of the Equilateral Triangle; this natu-rally follows, because the use of the Vesicacreates, and therefore necessitates, the appear-ance of the Equilateral Triangle in every con-ceivable situation. The following quotationis typical of the leading essay writers on thissubject: “The Equilateral Triangle enterslargely into, if it does not entirely control,all mediæval proportions, particularly in theground plans. In Chartres Cathedral theapices of two Equilateral Triangles (videfrontispiece to these Views), whose commonbase is the internal length of the transept.measured through the two western piers ofthe intersection, will give the interior length,one apex extending to the east end of thechevet within the aisles, the other to theoriginal termination of the Nave westward,and the present extent of the side aisles inthat direction. With slight deviation, most,if not all, the ground plans of the French 57
  70. 70. Science and the InfiniteCathedrals are measurable in this manner,and their choirs may be so measured almostwithout exception. Troyes Cathedral is inexact proportion with that of Chartres, andthe choirs of Rheims, Beauvais, St. Ouen atRouen, and others are equally so. BourgesCathedral, which has no transept, is exactlythree Equilateral Triangles in length inside,from the East end of the outer aisle to theEastern columns supporting the West Towers.Most English Cathedrals appear to have beenconstructed in their original plans upon simi-lar rules.” White’s Classical Essay on Archi-tecture compares the Norman with the Gothic,where he says: “In what is usually called theNorman period, the general proportions andoutlines of the Churches are reducible to cer-tain rules of setting out by the plain Square.As Architecture progressed the Square gradu-ally disappeared, and the proportion of generaloutline, as well as of detail, fell in more andmore with applications of the EquilateralTriangle, till the art, having arrived at itsculminating point, or that which is generallyacknowledged to be its period of greatestbeauty and perfection. in the thirteenth and thebeginning of the fourteenth centuries, againbegan to decline. With this decline theEquilateral Triangle was almost lost sight of,and then a mode of setting out work bydiagonal squares was taken up, for such is the 58
  71. 71. Mysticism and Symbolismbasis found exactly applicable to the workof the fifteenth century, since which timemathematical proportions have been gener-ally employed.” And after referring to numer-ous scale drawings of Churches, windows,doors, and arches, he points out that everystudent of Church architecture must pro-nounce those of the untraceried and traceriedfirst point to be the most beautiful of all, thoseof the Norman to be a degree less so, and thoseof the perpendicular and debased to be farinferior to either, and in that analysis we findthat the Equilateral Triangle was used almostexclusively for determining one order (theGothic), the Square for another (the Norman),and the Square diagonally divided for the other(the debased). Now let me try to describe the wonderfulproperties of the Vesica Piscis, so that youmay understand the mystery which shroudedit in the minds of those Mediæval builders.The rectangle formed by the length andbreadth of this figure, in the simplest form,has several extraordinary properties; it maybe cut into three equal parts by straightlines parallel to the shorter side, and these partswill all be precisely and geometricallysimilar to each other and to the whole figure,—strangely applicable to the symbolism attachedat that time to the Trinity in Unity,—andthe subdivision may be proceeded with inde- 59
  72. 72. Science and the Infinitefinitely without making any change in form.However often the operation is performed,the parts remain identical with the originalfigure, having all its extraordinary proper-ties, the Equilateral Triangle appearing every-where, whereas no other rectangle can havethis curious property. It may also be cut into four equal partsby straight lines parallel to its sides, andagain each of these parts will be trueVesicas, exactly similar to each other, and tothe whole. and of course the EquilateralTriangle is again everywhere. . Again, if two out of the tri-subdivisionsmentioned above be taken, the form of these to-gether is exactly similar, geometrically, to halfthe original figure, and again the EquilateralTriangle is ubiquitous on every base line. Again, the diagonal of the rectangle isexactly double the length of its shorter side,which characteristic is absolutely unique,and greatly increases its usefulness for plot-ting out designs; and this property of courseholds good for all the rectangles formed bythe original figure and for the other speciesof subdivision. But perhaps its most mys-terious property (though not of any practicaluse) to those who had studied Geometry, andto whom this figure was the symbol of theDivine Trinity in Unity, so dear to them,was the fact that it actually put into their 60
  73. 73. Mysticism and Symbolismhands the means of trisecting the RightAngle. Now, the three great problems of antiquitywhich engaged the attention and wonder-ment of geometricians throughout the MiddleAges, were “the Squaring of the Circle,”“the Duplication of the Cube,” and lastly,”the Trisection of an Angle,” even Euclidbeing unable to show how to do it; and yetit will be seen that the diagonal of one of thesubsidiary figures in the tri-subdivision,together with the diagonal of the wholefigure, actually trisect the angle at thecorner of the rectangle. It is true that itonly showed them how to trisect one kind ofangle, but it was that particular angle whichwas so dear to them as symbolising theircraft, and which was created by the Equila-teral Triangle. All these unique properties placethe figure far above that of a squarefor practical work, because even when thediagonal of a square is given, it is impossibleto find the exact length of any of its sides orvice versa; whereas in the Vesica rectanglethe diagonal is exactly double its shorterside, and upon any length of line which maybe taken on the tracing-board as a base forelevation, an Equilateral Triangle will befound whose sides are of course all equaland therefore known, as they are equal tothe base, and whose line joining apex to 61
  74. 74. Science and the Infinitecentre of base is a true Plumb line, formingat its foot the perfect right angle, so importantin the laying of every stone of a building. In the volume referred to I have given askeleton plan upon such a scale of subdivisionthat a tracing-board, of 5 feet by 8 feet, wouldbe divided up into over one million parts, and,as all these subdivisions are perfect representa-tions of the original Vesica figure with all itsproperties, the design of the largest building,with the minutest detail, could be draftedwith absolute accuracy. There are manyother curious properties of this Figure, butthey are difficult to explain without diagrams. Iwill, however, give one more example of itscreative power. The problem of describing aPentagon must have puzzled architects con-siderably in those early times, but this wasagain easily accomplished by means of theVesica. Albrecht Dürer, the great designerand engraver, who lived at the end of thefifteenth century, refers to the Vesica in hisworks (Dureri Institutune Geometricarum, lib.ii. p. 56) in a way which shows that it was ascommonly known in his time as the Circle,Square, and Triangle. His instructions forforming a Pentagon are: “Designa circinoinvariato tres piscium vesicas” (describe withunchanged compasses three vesicæ piscium).Three similar circles are described withcentres at the angles of an Equilateral 62
  75. 75. Mysticism and SymbolismTriangle, forming the three Vesicæ, by meansof which the Pentagon is drawn, and fromwhich also we get a beautiful form of archvery common in the thirteenth century(vide illustrations in Magister Mathesios).This is also the method used in that oldmanuscript of the fifteenth century named“Geometria deutsch.” In this old MS. it isalso shown that the easiest method for findingthe centre of a circle, however large, or anysegment of a circle, is by means of the VesicaPiscis. And just as we see so many Cathedralsof the Middle Ages are stated by antiquariansto have been planned on the EquilateralTriangle, so do we find the Pentagon appear-ing as the basis of Architectural designs ofbuildings of a later date, such as LiverpoolCastle, Chester Castle, and other similarstructures; but the true means by whicheach were laid down, as in the case of theEquilateral Triangle, was again the VesicaPiscis. A beautiful example of decoration,on the basis of the Vesica, is seen in thetomb of Edward the Confessor in West-minster Abbey. I will conclude this subject by quoting fromthe summing up by Prof. Kerrich (PrincipalLibrarian to the University of Cambridge in1820), in his masterly Essay on Architecture,where he gives the different forms of whathe calls the “Mysterious Figure,” used in the 63

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