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Considered From Mathematical, Geometrical, Metaphysical, and Cosmogonical Standpoints; Irrefutable r n o p . r . 6. MORROW. S PACE is considered by the majority of modern minds to be illimitable or infinite; it is held that the great room ofthe universe, the great openness, is absolutely boundless, and that in any direction, one might go on an imaginary journey in a straight line without ever reaching a limit. The question is often asked, Can you think of space as having bounds? The usual conclu- sion is that if we try to suppose an end or bound to space in any direction we will perceive that nothing could ever be a barrier; that any supposed end or bound would but mark a place from which, think as we like, there would still be a space beyond, for it is unthink- able otherwise. Therefore, if we strain our imagination and stretch it to the utmost, it is claimed that we can never conceive of the vastness of infinite direction.
If we were to illustrate even the greatest span of in- finite space which can be reached abstractly by any mental process, it would not suffice to form an adequate conception of endlessness. Suppose a vast globe one decillion miles in diameter filled with atoms of matter; take the atoms, one by one, and place them in a line, so that each one shall be a decillion miles from the other, until every atom is removed from the globe and arranged in the line. The vast extent of the line thus formed would be but an infinitesimal part of infinity !
The idea of illimitable space has grown out of falla- cious astronomical concepts, licensed by the Euclidean system of geometry, in which it is held as fundamentals that two straight lines cannot enclose finite space, and that parallels can neither meet nor diverge in space, no matter if extended eternally.
In astronomy, the size of the universe has been constantly increasing since the days of Copernicus, and its space has corre- spondingly enlarged. The telescope has never enabled man to see the barrier; perpendiculars from a convex earth have never reached imaginable bounds. On and on, the bounds of the universe have been extended until they are removed altogether; and the idea is prevailing that infinite space is filled with worlds, and that the stellar universe reaching beyond the Milky Way, is as a mere atom of existence compared with the vast field of constantly whirling orbs and systems,—worlds without end in a limitless, formless universe!
Euclidean Geometry Rejected by Modern Mathe- maticians.
Strange as it may seem to many minds drifting with the current of popular thought, and enamored with the idea of the infallibility of abstract space spec- ulation, there are many able men in the world wdio deny that space is illimitable. It is a well-known fact that ^all of the able mathematicians of the present century reject the geometry of Euclid as untenable and defective; the fundamental axioms of the old Grecian
Proofs of the Limitation of Form.
system were assumed,—a conclusion now generally con- ceded in mathematical circles. The old theory of par- allels has been declared to be fallacious by such men as Gauss, Bolyai, Reimann, Helmholtz,and others. The modern geometries, which have supplanted the Euclid- ean, known as the non-Euclidean, reject the postulates of Euclid as being untrue, and hold that parallels may meet and diverge, and that properties of space may be regarded as limited.
The old geometry considered only the "space of ex- perience," founded upon fixed planes; in the non-Euclid- ean systems it is held that the space of experience does not extend in absolutely straight lines, but differing slightly from the zero of a. plane surface so that a point which should move forward in a Euclidean straight line shall ultimately arrive at the same point, having trav- ersed a circumference.
In the great. Reimannian system of geometry it is maintained that there is no necessity, from a geometrical basis, for considering space as infinite; that space itself has such a curvature that what seems to us to be a straight line returns to itself, something after the manner of the surface of a sphere, containing only a, finite number of square miles.
Astronomer Newcomb says that the idea of the flni- tude of space, although transcending his conceptions, does not contradict them; and the Standard Dictionary concludes that it is possible that some of the non-Euclid- ean systems of geometry may represent space more nearly than the old system, if we conclude that the difference is so slight as to be incapable of detection by any means in our power. Thus the greatest geometers of the nine- teenth century deny the infinity of space; they hold from geometrical principles which have supplanted the postulates of Euclid, that there is no such thing as con- tinuous and infinite direction in fact, and that therefore space is limited.
Following the idea of the limitation of space, there is a growing opinion among able astronomers that the universe is limited; for it would be inconsistent to hold that finite space could contain an infinite universe.
Newcomb has reached the conclu- sion, which is shared by others, that the modern tele- scope has reached the confines of universal dimension; and now the question may be asked of the Copernican as well as the Koreshan astronomers, What is on the outside, if the universe and its space are limited ?
Metaphysical Proofs of Space Limitation. Idealists, ignorant of the relations of mind and mat- ter, have held that space is purely ideal, having no ob- jective reality, it being merely a subjective condition.
We are willing to grant that "infinite space" isa sub- jective condition only, admitting that absurd and im- possible things may be conceived through application of the principles of fallacy, in which the thought is per-
verted and the mind made to conceive the exact oppo- site of that which really exists.
And as long as truth is not possessed by the mind, various conceptions will be entertained concerning the properties of space.
Real space, the space with which we are acquainted, is extension or room, the three dimensions of which are length, breadth, and thickness.
These dimensions are properties of form, as well as properties of space, a dem- onstration of the fact that space is the extension or room of form.
Dimension is a general property of form, and limitation is a specific characteristic of dimension. Space therefore, is the property of extension of existing things, the room which they occupy, and is not to be considered apart from form; for if space is a property of extension of form, only form can oceup3T space, and space cannot be conceived of except in relation to form.
Size is determined by the three appreciable dimen- sions of space. The mind has faculties of conception of form and size; if these are qualities of the mind, and are also properties of natural things, they demonstrate the correlation of mind and matter, and consequently the relations of form and formation through the continual descent and mutation of spirit to matter, resulting in the complete expression, with all of the qualities of the mind, in variety of forms and relations of the physical cosmos. The mind can appreciate the properties of form, the dimensions and limitation of form and its con- comitant space; therefore, the limitation of form and space is thinkable; illimitability is not thinkable, and in consideration of the laws of the relations of the meta- physical to the physical, the relations of mind and mat- ter, the conclusion is inevitable that t h a t which is un- thinkable has no existence.
From a metaphysical standpoint then, it is demonstrable t h a t illimitability is neither a property of matter nor space, and does not belong to them, and therefore space, which is the prop- erty of extension of form, and which comprises dimen- sions of form, is limited.
Mathematical Roots and Evolutions, and the Geometry of Cosmic E g g .
Mathematics demonstrates the unity and the har- mony of the universe, its completeness, its limitation and variety of relations, and the immutability of its laws; its principles inhere in the very laws of being, and are expressed in all the forms of existence.
Mathemat- ics is the exact and infallible language of cause, and its terms are susceptible of translation, with equal abso- luteness and infallibility, into every realm of the uni- verse.
It involves the laws and principles of logic, syn- thesis, and analysis, the laws of analogy, symbolism, correspondence, and correlation; its definitions are exact, and its conclusions are absolute and unvarying; it is finite,complete,and perfect.
The applied principles of mathematics translate qualities of thought to cor- relate forms and motions, and qualities of life t o human language; and correlate physics and metaphys- ics, mind and matter, cause and effect, man and cosmos.
Mathematics is the infallible lo&'ic of relations.
Mathematical roots aud evolutions, equations and progressions, are manifest in all domains in the uni- verse.
Their principles are the fundamentals of life and existence, the principles of the relations and qualities of existence.
Cause is complete, hence finite: its functions are mathematically correlated, and its possibilities are equal to, and no greater than, the measure of its poten- tial energy.
The ultimate evolutions of all roots rep- resent perfect numbers, therefore are limited in number. The universe, the analogue of man, as the ultimate ex- pression and evloutionof its inherent life is mathematic- ally perfect, complete, and limited ; and its concomitant space, possessing definite mathematical relations and geometrical qualities of extense, is therefore limited.
The very fundamentals of mathematics are thus re- solved into an irresistible protest against the popular unthinkable misconception of space, an infallible refuta- tion of the idea of an infinite universe; for if the uni- verse were infinite, and if its space were infinite, there could be no mathematics !
Geometry is the mathematics of form; it treats of space and its relations. The etymology of the word de- fines the greatest form to which it is applicable; it is from yeu/ierpia, from ye, earth, and perpoe, to measure; it is the mathematics of earth-measurement.
Ge or gava in Hebrew means body, the human form as the micro- cosm, and its correspondential and analogous earth- body.
Geometry is the mathematics of thehumanform and of the earth or macrocosm, demonstrating the Ko- reshan conclusion that the earth is the form or body of the universe.
Geometry is the mathematics of existing forms aud their actual relations; it is founded upon the laws of the universal, structured cell. The principles of geometry are applicable only to form and its properties of space, dimension, and limitation; and as geometry cannot possibly be applied to infinity, the conclusion is inevitable that neither the universe nor space is illimit- able.
Geometry infallibly demonstrates t h a t the uni- verse and its room are limited. The great room of the universe is cellular; the great cell occupies its own space, all the space there is. It is a structure of form, a structure of limitation.
The earth is the material boundary of exterior space. We can thus conceive of the limitations of universal form, the limited boundary, beyond which there is no space.
In nature there are no flat planes of any considerable di- mensions; and any system of geometry founded on • planes is defective and fallacious.
The positive surfaces in the natural universe, on which parallels enclose finite space, are concave, convex, cylindrical, and conical.
Natural parallels in the universe are curves, embracing space which returns to itself, the largest dimension of which is the 25,000-mile circumference of the earth.
In the demonstrations of the Koreshan Cosmogony, the old geometrical system of Euclid is overthrown, with the resultant unthinkable and impossible propositions of the infinitude of space, and the equally absurd sys- tems of astronomy which have endeavored to fill the space which fallacy, in its ignorance of the true geome- try of form, has presumed and failed to create!
The Flaming Sword · Vol. 13, No. 21 · Apr 7, 1899 · PDF pp. 6-7