Bygone Beliefs (Redgrove, H. Stanley)

VIP免费

2024-12-18 0 0 214.19KB 78 页 5.9玖币

Bygone Beliefs

H. Stanley Redgrove

Table of Contents

Bygone Beliefs......................................................................................................................................................1

H. Stanley Redgrove................................................................................................................................1

PREFACE................................................................................................................................................1

I. SOME CHARACTERISTICS OF MEDAEVAL THOUGHT............................................................2

II. PYTHAGORAS AND HIS PHILOSOPHY......................................................................................4

III. MEDICINE AND MAGIC..............................................................................................................11

IV. SUPERSTITIONS CONCERNING BIRDS...................................................................................14

V. THE POWDER OF SYMPATHY: A CURIOUS MEDICAL SUPERSTITION...........................19

VI. THE BELIEF IN TALISMANS......................................................................................................22

VII. CEREMONIAL MAGIC IN THEORY AND PRACTICE...........................................................33

VIII. ARCHITECTURAL SYMBOLISM.............................................................................................42

IX. THE QUEST OF THE PHILOSOPHER'S STONE........................................................................46

X. THE PHALLIC ELEMENT IN ALCHEMICAL DOCTRINE........................................................56

XI. ROGER BACON: AN APPRECIATION......................................................................................68

XII. THE CAMBRIDGE PLATONISTS..............................................................................................72

Bygone Beliefs

H. Stanley Redgrove

http://www.blackmask.com

PREFACE• I. SOME CHARACTERISTICS OF MEDAEVAL THOUGHT• II. PYTHAGORAS AND HIS PHILOSOPHY• III. MEDICINE AND MAGIC• IV. SUPERSTITIONS CONCERNING BIRDS• V. THE POWDER OF SYMPATHY: A CURIOUS MEDICAL SUPERSTITION• VI. THE BELIEF IN TALISMANS• VII. CEREMONIAL MAGIC IN THEORY AND PRACTICE• VIII. ARCHITECTURAL SYMBOLISM• IX. THE QUEST OF THE PHILOSOPHER'S STONE• X. THE PHALLIC ELEMENT IN ALCHEMICAL DOCTRINE• XI. ROGER BACON: AN APPRECIATION• XII. THE CAMBRIDGE PLATONISTS•

BYGONE BELIEFS

BEING A SERIES OF

EXCURSIONS IN THE BYWAYS

OF THOUGHT

H. STANLEY REDGROVE

_Alle Erfahrung ist Magic, und nur magisch erklarbar_.

NOVALIS (Friedrich von Hardenberg).

Everything possible to be believ'd is an image of truth.

WILLIAM BLAKE.

MY WIFE

PREFACE

THESE Excursions in the Byways of Thought were undertaken at different times and on different occasions;

consequently, the reader may be able to detect in them inequalities of treatment. He may feel that I have

lingered too long in some byways and hurried too rapidly through others, taking, as it were, but a general

view of the road in the latter case, whilst examining everything that could be seen in the former with,

perhaps, undue care. As a matter of fact, how ever, all these excursions have been undertaken with one and

the same object in view, that, namely, of understanding aright and appreciating at their true worth some of the

more curious byways along which human thought has travelled. It is easy for the superficial thinker to

dismiss much of the thought of the past (and, indeed, of the present) as _mere_ superstition, not worth the

trouble of investigation: but it is not scientific. There is a reason for every belief, even the most fantastic, and

Bygone Beliefs 1

it should be our object to discover this reason. How far, if at all, the reason in any case justifies us in holding

a similar belief is, of course, another question. Some of the beliefs I have dealt with I have treated at greater

length than others, because it seems to me that the truths of which they are the images−− vague and distorted

in many cases though they be−−are truths which we have either forgotten nowadays, or are in danger of

forgetting. We moderns may, indeed, learn something from the thought of the past, even in its most fantastic

aspects. In one excursion at least, namely, the essay on "The Cambridge Platonists," I have ventured to deal

with a higher phase−−perhaps I should say the highest phase−− of the thought of a bygone age, to which the

modern world may be completely debtor.

"Some Characteristics of Mediaeval Thought," and the two essays on Alchemy, have appeared in _The

Journal of the Alchemical Society_. In others I have utilised material I have contributed to _The Occult

Review_, to the editor of which journal my thanks are due for permission so to do. I have also to express my

gratitude to the Rev. A. H. COLLINS, and others to be referred to in due course, for permission here to

reproduce illustrations of which they are the copyright holders. I have further to offer my hearty thanks to Mr

B. R. ROWBOTTOM and my wife for valuable assistance in reading the proofs. H. S. R.

BLETCHLEY, BUCKS, _December_ 1919.

I. SOME CHARACTERISTICS OF MEDAEVAL THOUGHT

IN the earliest days of his upward evolution man was satisfied with a very crude explanation of natural

phenomena−−that to which the name "animism" has been given. In this stage of mental development all the

various forces of Nature are personified: the rushing torrent, the devastating fire, the wind rustling the forest

leaves−−in the mind of the animistic savage all these are personalities, spirits, like himself, but animated by

motives more or less antagonistic to him.

I suppose that no possible exception could be taken to the statement that modern science renders animism

impossible. But let us inquire in exactly what sense this is true. It is not true that science robs natural

phenomena of their spiritual significance. The mistake is often made of supposing that science explains, or

endeavours to explain, phenomena. But that is the business of philosophy. The task science attempts is the

simpler one of the correlation of natural phenomena, and in this effort leaves the ultimate problems of

metaphysics untouched. A universe, however, whose phenomena are not only capable of some degree of

correlation, but present the extraordinary degree of harmony and unity which science makes manifest in

Nature, cannot be, as in animism, the product of a vast number of inco−ordinated and antagonistic wills, but

must either be the product of one Will, or not the product of will at all.

The latter alternative means that the Cosmos is inexplicable, which not only man's growing experience, but

the fact that man and the universe form essentially a unity, forbid us to believe. The term "anthropomorphic"

is too easily applied to philosophical systems, as if it constituted a criticism of their validity. For if it be true,

as all must admit, that the unknown can only be explained in terms of the known, then the universe must

either be explained in terms of man−−_i.e_. in terms of will or desire−− or remain incomprehensible. That is

to say, a philosophy must either be anthropomorphic, or no philosophy at all.

Thus a metaphysical scrutiny of the results of modern science leads us to a belief in God. But man felt the

need of unity, and crude animism, though a step in the right direction, failed to satisfy his thought, long

before the days of modern science. The spirits of animism, however, were not discarded, but were modified,

co−ordinated, and worked into a system as servants of the Most High. Polytheism may mark a stage in this

process; or, perhaps, it was a result of mental degeneracy.

What I may term systematised as distinguished from crude animism persisted throughout the Middle Ages.

The work of systematisation had already been accomplished, to a large extent, by the Neo−Platonists and

Bygone Beliefs

I. SOME CHARACTERISTICS OF MEDAEVAL THOUGHT 2

whoever were responsible for the Kabala. It is true that these main sources of magical or animistic philosophy

remained hidden during the greater part of the Middle Ages; but at about their close the youthful and

enthusiastic CORNELIUS AGRIPPA (1486−1535)[1] slaked his thirst thereat and produced his own attempt

at the systematisation of magical belief in the famous _Three Books of Occult Philosophy_. But the waters of

magical philosophy reached the mediaeval mind through various devious channels, traditional on the one

hand and literary on the other. And of the latter, the works of pseudo−DIONYSIUS,[2] whose immense

influence upon mediaeval thought has sometimes been neglected, must certainly be noted.

[1] The story of his life has been admirably told by HENRY MORLEY (2 vols., 1856).

[2] These writings were first heard of in the early part of the sixth century, and were probably the work of a

Syrian monk of that date, who fathered them on to DIONYSIUS the Areopagite as a pious fraud. See Dean

INGE'S _Christian Mysticism_ (1899), pp. 104−−122, and VAUGHAN'S _Hours with the Mystics_ (7th ed.,

1895), vol. i. pp. 111−124. The books have been translated into English by the Rev. JOHN PARKER (2 vols.

1897−1899), who believes in the genuineness of their alleged authorship.

The most obvious example of a mediaeval animistic belief is that in "elementals"−−the spirits which

personify the primordial forces of Nature, and are symbolised by the four elements, immanent in which they

were supposed to exist, and through which they were held to manifest their powers. And astrology, it must be

remembered, is essentially a systematised animism. The stars, to the ancients, were not material bodies like

the earth, but spiritual beings. PLATO (427−347 B.C.) speaks of them as "gods". Mediaeval thought did not

regard them in quite this way. But for those who believed in astrology, and few, I think, did not, the stars

were still symbols of spiritual forces operative on man. Evidences of the wide extent of astrological belief in

those days are abundant, many instances of which we shall doubtless encounter in our excursions.

It has been said that the theological and philosophical atmosphere of the Middle Ages was "scholastic," not

mystical. No doubt "mysticism," as a mode of life aiming at the realisation of the presence of God, is as

distinct from scholasticism as empiricism is from rationalism, or "tough−minded" philosophy (to use JAMES'

happy phrase) is from "tender−minded". But no philosophy can be absolutely and purely deductive. It must

start from certain empirically determined facts. A man might be an extreme empiricist in religion (_i.e_. a

mystic), and yet might attempt to deduce all other forms of knowledge from the results of his religious

experiences, never caring to gather experience in any other realm. Hence the breach between mysticism and

scholasticism is not really so wide as may appear at first sight. Indeed, scholasticism officially recognised

three branches of theology, of which the MYSTICAL was one. I think that mysticism and scholasticism both

had a profound influence on the mediaeval mind, sometimes acting as opposing forces, sometimes operating

harmoniously with one another. As Professor WINDELBAND puts it: "We no longer onesidedly characterise

the philosophy of the middle ages as scholasticism, but rather place mysticism beside it as of equal rank, and

even as being the more fruitful and promising movement."[1]

[1] Professor WILHELM WINDELBAND, Ph.D.: "Present−Day Mysticism," _The Quest_, vol. iv. (1913),

P. 205.

Alchemy, with its four Aristotelian or scholastic elements and its three mystical principles−−sulphur,

mercury, salt,−− must be cited as the outstanding product of the combined influence of mysticism and

scholasticism: of mysticism, which postulated the unity of the Cosmos, and hence taught that everything

natural is the expressive image and type of some supernatural reality; of scholasticism, which taught men to

rely upon deduction and to restrict experimentation to the smallest possible limits.

The mind naturally proceeds from the known, or from what is supposed to be known, to the unknown.

Indeed, as I have already indicated, it must so proceed if truth is to be gained. Now what did the men of the

Middle Ages regard as falling into the category of the known? Why, surely, the truths of revealed religion,

Bygone Beliefs

I. SOME CHARACTERISTICS OF MEDAEVAL THOUGHT 3

whether accepted upon authority or upon the evidence of their own experience. The realm of spiritual and

moral reality: there, they felt, they were on firm ground. Nature was a realm unknown; but they had analogy

to guide, or, rather, misguide them. Nevertheless if, as we know, it misguided, this was not, I think, because

the mystical doctrine of the correspondence between the spiritual and the natural is unsound, but because

these ancient seekers into Nature's secrets knew so little, and so frequently misapplied what they did know.

So alchemical philosophy arose and became systematised, with its wonderful endeavour to perfect the base

metals by the Philosopher's Stone−−the concentrated Essence of Nature,−− as man's soul is perfected through

the life−giving power of JESUS CHRIST.

I want, in conclusion to these brief introductory remarks, to say a few words concerning phallicism in

connection with my topic. For some "tender−minded"[1] and, to my thought, obscure, reason the subject is

tabooed. Even the British Museum does not include works on phallicism in its catalogue, and special

permission has to be obtained to consult them. Yet the subject is of vast importance as concerns the origin

and development of religion and philosophy, and the extent of phallic worship may be gathered from the

widespread occurrence of obelisks and similar objects amongst ancient relics. Our own maypole dances may

be instanced as one survival of the ancient worship of the male generative principle.

[1] I here use the term with the extended meaning Mr H. G. WELLS has given to it. See _The New

Machiavelli_.

What could be more easy to understand than that, when man first questioned as to the creation of the earth, he

should suppose it to have been generated by some process analogous to that which he saw held in the case of

man? How else could he account for its origin, if knowledge must proceed from the known to the unknown?

No one questions at all that the worship of the human generative organs as symbols of the dual generative

principle of Nature degenerated into orgies of the most frightful character, but the view of Nature which thus

degenerated is not, I think, an altogether unsound one, and very interesting remnants of it are to be found in

mediaeval philosophy.

These remnants are very marked in alchemy. The metals, as I have suggested, are there regarded as types of

man; hence they are produced from seed, through the combination of male and female principles−−mercury

and sulphur, which on the spiritual plane are intelligence and love. The same is true of that Stone which is

perfect Man. As BERNARD of TREVISAN (1406−1490) wrote in the fifteenth century: "This Stone then is

compounded of a Body and Spirit, or of a volatile and fixed Substance, and that is therefore done, because

nothing in the World can be generated and brought to light without these two Substances, to wit, a Male and

Female: From whence it appeareth, that although these two Substances are not of one and the same species,

yet one Stone cloth thence arise, and although they appear and are said to be two Substances, yet in truth it is

but one, to wit, _Argent−vive_."[1] No doubt this sounds fantastic; but with all their seeming intellectual

follies these old thinkers were no fools. The fact of sex is the most fundamental fact of the universe, and is a

spiritual and physical as well as a physiological fact. I shall deal with the subject as concerns the speculations

of the alchemists in some detail in a later excursion.

[1] BERNARD, Earl of TREVISAN: _A Treatise of the Philosopher's Stone_, 1683. (See _Collectanea

Chymica: A Collection of Ten Several Treatises in Chemistry_, 1684, p. 91.)

II. PYTHAGORAS AND HIS PHILOSOPHY

IT is a matter for enduring regret that so little is known to us concerning PYTHAGORAS. What little we do

know serves but to enhance for us the interest of the man and his philosophy, to make him, in many ways, the

most attractive of Greek thinkers; and, basing our estimate on the extent of his influence on the thought of

succeeding ages, we recognise in him one of the world's master−minds.

Bygone Beliefs

II. PYTHAGORAS AND HIS PHILOSOPHY 4

PYTHAGORAS was born about 582 B.C. at Samos, one of the Grecian isles. In his youth he came in contact

with THALES−−the Father of Geometry, as he is well called,−−and though he did not become a member of

THALES' school, his contact with the latter no doubt helped to turn his mind towards the study of geometry.

This interest found the right ground for its development in Egypt, which he visited when still young. Egypt is

generally regarded as the birthplace of geometry, the subject having, it is supposed, been forced on the minds

of the Egyptians by the necessity of fixing the boundaries of lands against the annual overflowing of the Nile.

But the Egyptians were what is called an essentially practical people, and their geometrical knowledge did

not extend beyond a few empirical rules useful for fixing these boundaries and in constructing their temples.

Striking evidence of this fact is supplied by the AHMES papyrus, compiled some little time before 1700 B.C.

from an older work dating from about 3400 B.C.,[1] a papyrus which almost certainly represents the highest

mathematical knowledge reached by the Egyptians of that day. Geometry is treated very superficially and as

of subsidiary interest to arithmetic; there is no ordered series of reasoned geometrical propositions

given−−nothing, indeed, beyond isolated rules, and of these some are wanting in accuracy.

[1] See AUGUST EISENLOHR: _Ein mathematisches Handbuch der alten Aegypter_ (1877); J. Gow: _A

Short History of Greek Mathematics_ (1884); and V. E. JOHNSON: _Egyptian Science from the Monuments

and Ancient Books_ (1891).

One geometrical fact known to the Egyptians was that if a triangle be constructed having its sides 3, 4, and 5

units long respectively, then the angle opposite the longest side is exactly a right angle; and the Egyptian

builders used this rule for constructing walls perpendicular to each other, employing a cord graduated in the

required manner. The Greek mind was not, however, satisfied with the bald statement of mere facts−−it cared

little for practical applications, but sought above all for the underlying REASON of everything. Nowadays

we are beginning to realise that the results achieved by this type of mind, the general laws of Nature's

behaviour formulated by its endeavours, are frequently of immense practical importance−− of far more

importance than the mere rules−of−thumb beyond which so−called practical minds never advance. The

classic example of the utility of seemingly useless knowledge is afforded by Sir WILLIAM HAMILTON'S

discovery, or, rather, invention of Quarternions, but no better example of the utilitarian triumph of the

theoretical over the so−called practical mind can be adduced than that afforded by PYTHAGORAS. Given

this rule for constructing a right angle, about whose reason the Egyptian who used it never bothered himself,

and the mind of PYTHAGORAS, searching for its full significance, made that gigantic geometrical discovery

which is to this day known as the Theorem of PYTHAGORAS−−the law that in every right−angled triangle

the square on the side opposite the right angle is equal in area to the sum of the squares on the other two

sides.[1] The importance of this discovery can hardly be overestimated. It is of fundamental importance in

most branches of geometry, and the basis of the whole of trigonometry−−the special branch of geometry that

deals with the practical mensuration of triangles. EUCLID devoted the whole of the first book of his

_Elements of Geometry_ to establishing the truth of this theorem; how PYTHAGORAS demonstrated it we

unfortunately do not know.

[1] Fig. 3 affords an interesting practical demonstration of the truth of this theorem. If the reader will copy

this figure, cut out the squares on the two shorter sides of the triangle and divide them along the lines AD,

BE, EF, he will find that the five pieces so obtained can be made exactly to fit the square on the longest side

as shown by the dotted lines. The size and shape of the triangle ABC, so long as it has a right angle at C, is

immaterial. The lines AD, BE are obtained by continuing the sides of the square on the side AB, _i.e_. the

side opposite the right angle, and EF is drawn at right angles to BE.

After absorbing what knowledge was to be gained in Egypt, PYTHAGORAS journeyed to Babylon, where he

probably came into contact with even greater traditions and more potent influences and sources of knowledge

than in Egypt, for there is reason for believing that the ancient Chaldeans were the builders of the Pyramids

and in many ways the intellectual superiors of the Egyptians.

Bygone Beliefs

II. PYTHAGORAS AND HIS PHILOSOPHY 5

At last, after having travelled still further East, probably as far as India, PYTHAGORAS returned to his

birthplace to teach the men of his native land the knowledge he had gained. But CROESUS was tyrant over

Samos, and so oppressive was his rule that none had leisure in which to learn. Not a student came to

PYTHAGORAS, until, in despair, so the story runs, he offered to pay an artisan if he would but learn

geometry. The man accepted, and later, when PYTHAGORAS pretended inability any longer to continue the

payments, he offered, so fascinating did he find the subject, to pay his teacher instead if the lessons might

only be continued. PYTHAGORAS no doubt was much gratified at this; and the motto he adopted for his

great Brotherhood, of which we shall make the acquaintance in a moment, was in all likelihood based on this

event. It ran, "Honour a figure and a step before a figure and a tribolus"; or, as a freer translation renders it:−−

"A figure and a step onward Not a figure and a florin."

"At all events, as Mr FRANKLAND remarks, "the motto is a lasting witness to a very singular devotion to

knowledge for its own sake."[1]

[1] W. B. FRANKLAND, M.A.: _The Story of Euclid_ (1902), p. 33

But PYTHAGORAS needed a greater audience than one man, however enthusiastic a pupil he might be, and

he left Samos for Southern Italy, the rich inhabitants of whose cities had both the leisure and inclination to

study. Delphi, far−famed for its Oracles, was visited _en route_, and PYTHAGORAS, after a sojourn at

Tarentum, settled at Croton, where he gathered about him a great band of pupils, mainly young people of the

aristocratic class. By consent of the Senate of Croton, he formed out of these a great philosophical

brotherhood, whose members lived apart from the ordinary people, forming, as it were, a separate

community. They were bound to PYTHAGORAS by the closest ties of admiration and reverence, and, for

years after his death, discoveries made by Pythagoreans were invariably attributed to the Master, a fact which

makes it very difficult exactly to gauge the extent of PYTHAGORAS' own knowledge and achievements.

The regime of the Brotherhood, or Pythagorean Order, was a strict one, entailing "high thinking and low

living" at all times. A restricted diet, the exact nature of which is in dispute, was observed by all members,

and long periods of silence, as conducive to deep thinking, were imposed on novices. Women were admitted

to the Order, and PYTHAGORAS' asceticism did not prohibit romance, for we read that one of his fair pupils

won her way to his heart, and, declaring her affection for him, found it reciprocated and became his wife.

SCHURE writes: "By his marriage with Theano, Pythagoras affixed _the seal of realization_ to his work. The

union and fusion of the two lives was complete. One day when the master's wife was asked what length of

time elapsed before a woman could become pure after intercourse with a man, she replied: `If it is with her

husband, she is pure all the time; if with another man, she is never pure.' " "Many women," adds the writer,

"would smilingly remark that to give such a reply one must be the wife of Pythagoras, and love him as

Theano did. And they would be in the right, for it is not marriage that sanctifies love, it is love which justifies

marriage."[1]

[1] EDOUARD SCHURE: _Pythagoras and the Delphic Mysteries_, trans. by F. ROTHWELL, B.A. (1906),

pp. 164 and 165.

PYTHAGORAS was not merely a mathematician. he was first and foremost a philosopher, whose philosophy

found in number the basis of all things, because number, for him, alone possessed stability of relationship. As

I have remarked on a former occasion, "The theory that the Cosmos has its origin and explanation in Number

. . . is one for which it is not difficult to account if we take into consideration the nature of the times in which

it was formulated. The Greek of the period, looking upon Nature, beheld no picture of harmony, uniformity

and fundamental unity. The outer world appeared to him rather as a discordant chaos, the mere sport and

plaything of the gods. The theory of the uniformity of Nature−−that Nature is ever like to herself−−the very

essence of the modern scientific spirit, had yet to be born of years of unwearied labour and unceasing delving

Bygone Beliefs

II. PYTHAGORAS AND HIS PHILOSOPHY 6

into Nature's innermost secrets. Only in Mathematics−− in the properties of geometrical figures, and of

numbers−− was the reign of law, the principle of harmony, perceivable. Even at this present day when the

marvellous has become commonplace, that property of right−angled triangles . . . already discussed . . .

comes to the mind as a remarkable and notable fact: it must have seemed a stupendous marvel to its

discoverer, to whom, it appears, the regular alternation of the odd and even numbers, a fact so obvious to us

that we are inclined to attach no importance to it, seemed, itself, to be something wonderful. Here in

Geometry and Arithmetic, here was order and harmony unsurpassed and unsurpassable. What wonder then

that Pythagoras concluded that the solution of the mighty riddle of the Universe was contained in the

mysteries of Geometry? What wonder that he read mystic meanings into the laws of Arithmetic, and believed

Number to be the explanation and origin of all that is?"[1]

[1] _A Mathematical Theory of Spirit_ (1912), pp. 64−65.

No doubt the Pythagorean theory suffers from a defect similar to that of the Kabalistic doctrine, which,

starting from the fact that all words are composed of letters, representing the primary sounds of language,

maintained that all the things represented by these words were created by God by means of the twenty−two

letters of the Hebrew alphabet. But at the same time the Pythagorean theory certainly embodies a

considerable element of truth. Modern science demonstrates nothing more clearly than the importance of

numerical relationships. Indeed, "the history of science shows us the gradual transformation of crude facts of

experience into increasingly exact generalisations by the application to them of mathematics. The enormous

advances that have been made in recent years in physics and chemistry are very largely due to mathematical

methods of interpreting and co−ordinating facts experimentally revealed, whereby further experiments have

been suggested, the results of which have themselves been mathematically interpreted. Both physics and

chemistry, especially the former, are now highly mathematical. In the biological sciences and especially in

psychology it is true that mathematical methods are, as yet, not so largely employed. But these sciences are

far less highly developed, far less exact and systematic, that is to say, far less scientific, at present, than is

either physics or chemistry. However, the application of statistical methods promises good results, and there

are not wanting generalisations already arrived at which are expressible mathematically; Weber's Law in

psychology, and the law concerning the arrangement of the leaves about the stems of plants in biology, may

be instanced as cases in point."[1]

[1] Quoted from a lecture by the present writer on "The Law of Correspondences Mathematically

Considered," delivered before The Theological and Philosophical Society on 26th April 1912, and published

in _Morning Light_, vol. xxxv (1912), p. 434 _et seq_.

The Pythagorean doctrine of the Cosmos, in its most reasonable form, however, is confronted with one great

difficulty which it seems incapable of overcoming, namely, that of continuity. Modern science, with its

atomic theories of matter and electricity, does, indeed, show us that the apparent continuity of material things

is spurious, that all material things consist of discrete particles, and are hence measurable in numerical terms.

But modern science is also obliged to postulate an ether behind these atoms, an ether which is wholly

continuous, and hence transcends the domain of number.[1] It is true that, in quite recent times, a certain

school of thought has argued that the ether is also atomic in constitution−− that all things, indeed, have a

grained structure, even forces being made up of a large number of quantums or indivisible units of force. But

this view has not gained general acceptance, and it seems to necessitate the postulation of an ether beyond the

ether, filling the interspaces between its atoms, to obviate the difficulty of conceiving of action at a distance.

[1] Cf. chap. iii., "On Nature as the Embodiment of Number," of my _A Mathematical Theory of Spirit_, to

which reference has already been made.

According to BERGSON, life−−the reality that can only be lived, not understood−−is absolutely continuous

(_i.e_. not amenable to numerical treatment). It is because life is absolutely continuous that we cannot, he

Bygone Beliefs

II. PYTHAGORAS AND HIS PHILOSOPHY 7

says, understand it; for reason acts discontinuously, grasping only, so to speak, a cinematographic view of

life, made up of an immense number of instantaneous glimpses. All that passes between the glimpses is lost,

and so the true whole, reason can never synthesise from that which it possesses. On the other hand, one might

also argue−−extending, in a way, the teaching of the physical sciences of the period between the postulation

of DALTON'S atomic theory and the discovery of the significance of the ether of space−−that reality is

essentially discontinuous, our idea that it is continuous being a mere illusion arising from the coarseness of

our senses. That might provide a complete vindication of the Pythagorean view; but a better vindication, if

not of that theory, at any rate of PYTHAGORAS' philosophical attitude, is forthcoming, I think, in the fact

that modern mathematics has transcended the shackles of number, and has enlarged her kingdom, so as to

include quantities other than numerical. PYTHAGORAS, had he been born in these latter centuries, would

surely have rejoiced in this, enlargement, whereby the continuous as well as the discontinuous is brought, if

not under the rule of number, under the rule of mathematics indeed.

PYTHAGORAS' foremost achievement in mathematics I have already mentioned. Another notable piece of

work in the same department was the discovery of a method of constructing a parallelogram having a side

equal to a given line, an angle equal to a given angle, and its area equal to that of a given triangle.

PYTHAGORAS is said to have celebrated this discovery by the sacrifice of a whole ox. The problem appears

in the first book of EUCLID'S _Elements of Geometry_ as proposition 44. In fact, many of the propositions

of EUCLID'S first, second, fourth, and sixth books were worked out by PYTHAGORAS and the

Pythagoreans; but, curiously enough, they seem greatly to have neglected the geometry of the circle.

The symmetrical solids were regarded by PYTHAGORAS, and by the Greek thinkers after him, as of the

greatest importance. To be perfectly symmetrical or regular, a solid must have an equal number of faces

meeting at each of its angles, and these faces must be equal regular polygons, _i.e_. figures whose sides and

angles are all equal. PYTHAGORAS, perhaps, may be credited with the great discovery that there are only

five such solids. These are as follows:−−

The Tetrahedron, having four equilateral triangles as faces.

The Cube, having six squares as faces.

The Octahedron, having eight equilateral triangles as faces.

The Dodecahedron, having twelve regular pentagons (or five−sided figures) as faces.

The Icosahedron, having twenty equilateral triangles as faces.[1]

[1] If the reader will copy figs. 4 to 8 on cardboard or stiff paper, bend each along the dotted lines so as to

form a solid, fastening together the free edges with gummed paper, he will be in possession of models of the

five solids in question.

Now, the Greeks believed the world to be composed of four elements−−earth, air, fire, water,−−and to the

Greek mind the conclusion was inevitable[2a] that the shapes of the particles of the elements were those of

the regular solids. Earth−particles were cubical, the cube being the regular solid possessed of greatest

stability; fire−particles were tetrahedral, the tetrahedron being the simplest and, hence, lightest solid.

Water−particles were icosahedral for exactly the reverse reason, whilst air−particles, as intermediate between

the two latter, were octahedral. The dodecahedron was, to these ancient mathematicians, the most mysterious

of the solids: it was by far the most difficult to construct, the accurate drawing of the regular pentagon

necessitating a rather elaborate application of PYTHAGORAS' great theorem.[1] Hence the conclusion, as

PLATO put it, that "this [the regular dodecahedron] the Deity employed in tracing the plan of the

Universe."[2b] Hence also the high esteem in which the pentagon was held by the Pythagoreans. By

Bygone Beliefs

II. PYTHAGORAS AND HIS PHILOSOPHY 8

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

5.9 玖币 0人已下载

立即下载 VIP免费下载

摘要：

BygoneBeliefsH.StanleyRedgroveTableofContentsBygoneBeliefs......................................................................................................................................................1H.StanleyRedgrove.............................................................................

展开>> 收起<<

Bygone Beliefs (Redgrove, H. Stanley).pdf

共78页,预览16页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Bygone Beliefs (Redgrove, H. Stanley)

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: