Homogeneity

“ Spencer invented the notion of a primordial homogeneity, from which it is impossible to conceive how any heterogeneity could originate. Well now, this entropia is a kind of ultimate homogeneity, a state of perfect equilibrium. For a soul avid of life, it is the most like nothingness that the mind can conceive. ”

“ No demurrer to the conclusions drawn, can be based on the ground that perfect homogeneity nowhere exists; since, whether that state with which we commence be or be not one of perfect homogeneity, the process must equally be towards a relative heterogeneity. ”

“ And that ‘homogeneity’ is the very condition laid down for the beginning, from which mechanical evolution is to educe the universe. In the Spencerian formula there is no qualification of the term homogeneous. It postulates ‘an indefinite, incoherent homogeneity,’ that is, an indefinite cloud, with balanced motion in all its atoms which neither attracts nor repels, and is in itself infinitely incapable of change. ”

“ Thus it became apparent that this transformation of on indefinite, incoherent homogeneity into a definite coherent heterogeneity, which goes on everywhere, until it brings about a reverse transformation, is consequent on certain simple laws of force. Given those universal modes of action which are from moment to moment illustrated in the commonest changes around us, and it follows that there cannot but result the observed metamorphosis of an indeterminate uniformity into a determinate multiformity. ”

“ To-day the last word of science, or rather of scientific philosophy, appears to be that, by virtue of the degradation of energy, of the predominance of irreversible phenomena, the material, sensible world is travelling towards a condition of ultimate levelness, a kind of final homogeneity. And this brings to our mind the hypothesis, not only so much used but abused by Spencer, of a primordial homogeneity, and his fantastic theory of the instability of the homogeneous. ”

“ Professor Ward quotes from me the sentence—“The absolutely homogeneous must lose its equilibrium; and the relatively homogeneous must lapse into the relatively less homogeneous.”—First Principles, p. 429. Then presently he writes:—
“In truth, however, homogeneity is not necessarily instability. ”

“ The other way in which physical environment affects homogeneity is by determining similarity or difference of occupations and, through them, similarities or differences of practical interests and of acquired qualities. So long as such differences are determined in many small areas, the result is merely a greater differentiation of the parts, without danger to the unity of the whole nation. ”

“ Every member of the aggregate presents itself in a more or less peculiar way towards the light, towards the air, and towards its point of support; and according to the relative homogeneity or heterogeneity in the incidence of the agencies thus brought to bear on it, will be the relative homogeneity or heterogeneity of its shape. ”

“ In the individual we see the first phase of existence characterized by a state of homogeneity wherein nothing is distinct, and we follow step by step the gradations of its transition to a greater complexity, and to states characterized by increasing distinction of parts, as their dissimilarity becomes greater. ”

“ The instability of the homogeneous is thus deducible from that primordial truth which underlies our intelligence. One stable homogeneity only, is hypothetically possible. If centres of force, absolutely uniform in their powers, were diffused with absolute uniformity through unlimited space, they would remain in equilibrium. This however, though a verbally intelligible supposition, is one that cannot be represented in thought; since unlimited space is inconceivable. But all finite forms of the homogeneous—all forms of it which we can know or conceive, must inevitably lapse into heterogeneity. ”

“ Now here is an obvious difficulty, for since homogeneity consists in being without qualities, it is difficult to see how one homogeneity can be distinguished from another. This difficulty is usually avoided by the assertion that homogeneity takes two forms, one in which its contents co-exist, and another in which they follow one another. Space, then, we say, is that homogeneous medium in which we are aware of side-by-sideness, Time—that homogeneous medium in which we are aware of an element of succession. ”

“ That the state of homogeneity is an unstable state we have found to be a universal truth. Each species must pass from the uniform into the more or less multiform, unless the incidence of external forces is exactly the same for all its members, which it never can be. Through the process of differentiation and integration, which of necessity brings together, or keeps together, like individuals, and separates unlike ones from them, there must nevertheless be maintained a tolerably uniform species, so long as there continues a tolerably uniform set of conditions in which it may exist. ”

“ Were the other view of an original universal homogeneity correct, how conies it that we have still co-existent every stage of advance from the lowest to the highest, and that there is not a greater equality?—a difficulty which does not exist if we suppose things to have been on the whole, as they are now, from the very first. ”

“ Every differentiation of structure being a result of some difference in the relations of the parts to the agencies acting on them, it follows that the more multiplied and more unlike the agencies, the more varied must be the differentiations wrought. Hence the change from a state of homogeneity to a state of heterogeneity, will be marked in proportion as the environing actions to which the organism is supposes it is only are complex. ”

“ The tendency of modern thought is to recur to the archaic idea of a homogeneous basis for apparently widely different things—heterogeneity developed from homogeneity. Biologists are now searching for their homogeneous protoplasm and Chemists for their protyle, while Science is looking for the force of which electricity, magnetism, heat, and so forth, are the differentiations. ”

“ The process of integration, acting locally as well as generally, combines with the process of differentiation to render this change not simply from homogeneity to heterogeneity, but from an indefinite homogeneity to a definite heterogeneity; and this trait of increasing definiteness, which accompanies the trait of increasing heterogeneity, is, like it, exhibited in the totality of things and in all its divisions and subdivisions down to the minutest. ”

“ In the series of organisms we should thus find a succession of states like those which constitute the history of the individual, with this difference, that in the individual we can make out the link which connects the primitive homogeneity with the final heterogeneity, while in the series of organisms all we can do is to connect, with a considerable degree of probability, the hypothetical starting-point with the positive goal. ”

“ It is therefore, thanks to the approximate homogeneity of the matter studied by physicists, that mathematical physics came into existence. In the natural sciences the following conditions are no longer to be found:—homogeneity, relative independence of remote parts, simplicity of the elementary fact; and that is why the student of natural science is compelled to have recourse to other modes of generalisation. ”

“ Hence the general truth that development is a change from incoherent, indefinite homogeneity, to coherent, definite heterogeneity, becomes a self-evident one when observation has shown us the state in which organisms begin and the state in which they end. ”

“ General Principle of the Homogeneity of the Complex and its Components.—The assimilation of brute bodies to living bodies, and of the inorganic kingdom to the organic, was, in the mind of these philosophers, the natural consequence of positing a priori the principles of continuity and evolution. ”

“ The universe is really homogeneous. Heterogeneity is only in appearance. There seen to be different substances, different powers, etc. throughout nature. But take two different substances, say a piece of glass and a piece of wood, grind them up together fine enough, reduce them till there is nothing more to reduce, and the substance remaining appears homogeneous. All substances in the last analysis are one. Homogeneity is the substance, the reality; heterogeneity is the appearance of many things as though they were many substances. ”

“ If, from late stages in the Earth's history, we run back, and find the lines of chemical evolution continually converging, until they bring us to bodies which we cannot decompose, may we not suspect that, could we run back these lines still further, we should come to still decreasing heterogeneity in the number and nature of the substances, until we reached something like homogeneity? ”

“ Along with this redistribution of the matter composing any evolving aggregate there goes on a redistribution of the retained motion of its components in relation to one another; this also becomes, step by step, more definitely heterogeneous.
"'8. In the absence of a homogeneity that is infinite and absolute, that redistribution, of which evolution is one phase, is inevitable. ”

“ What reason is there for assuming primordial homogeneity, since every backward step would show us, together with the unravelling of what is now in process of weaving, a counter-balancing weaving of what is now in process of disintegration? Were this earth all, we might dream of universal advance by shutting our eyes to a great many incompatible facts ”

“ But this surely we are not entitled to maintain, for we are then distinguishing two supposed homogeneities by asserting a difference of quality in them. To do so is to take away homogeneity. We must think again and seek a way out of this difficulty. ”

“ The most general reply is, of course, that since the state of homogeneity is by necessity unstable, time inevitably brings about inequality of positions among those whose positions were at first equal. ”

“ A second general theorem on the relation of the concrete to the abstract is that which is ordinarily designated under the name of Principle of Homogeneity. It is undoubtedly much less important in its applications than the preceding, but it particularly merits our attention as having, by its nature, a still greater extent, since it is applicable to all phenomena without distinction, and because of the real utility which it often possesses for the verification of their analytical laws. ”

“ In this necessity for adaptation we recognize a consequence of our first principles. The state of homogeneity must give way to a state of heterogeneity: a species must be ever growing more and more varied in its forms; old species must be ever breaking up into new. If at one time a species consisted of individuals alike in all respects, the action of the various forces of the environment would soon put an end to this uniformity ”

“ The primordial cell in differentiating out of homogeneity into heterogeneity developed different qualities in different beings, and of the organs integrated from the heterogeneous elements each has its use and many are essential to life. ”

“ To say, as above, that complete molecular homogeneity existing among the members of a species, must render impossible that mutual molecular disturbance which constitutes fertilization, is but another way of saying that the actions and re-actions of each organism, being in perfect balance with the actions and re-actions of the environment upon it, there remains in each organism no force by which it differs from any other—no force which any other does not meet with an equal force—no force which can set up a new evolution among the units of any other. ”

“ When in attempting the solution of great problems we have recourse to such simplifications; when, in order to elude difficulties of calculation, we depart so widely from natural and physical conditions, the results relate to an ideal world, they are in reality nothing more than flights of the imagination.
In order to apply mathematical analysis usefully to the determination of the figure of the earth it was necessary to abandon all idea of homogeneity, all constrained resemblance between the forms of the superposed and unequally dense strata ”

“ This loss of homogeneity which the special instability of organic aggregates fits them to display more promptly and variously than any other aggregates, must be shown in more numerous ways in proportion as the incident forces are more numerous. ”

“ Our own expression is that all things are acting to advance to the homogeneous, or are trying to localize Homogeneousness. Homogeneousness is an aspect of the Universal, wherein it is a state that does not merge away into something else. We regard homogeneousness as an aspect of positiveness, but it is our acceptance that infinite frustrations of attempts to positivize manifest themselves in infinite heterogeneity: so that though things try to localize homogeneousness they end up in heterogeneity so great that it amounts to infinite dispersion or indistinguishability. ”

“ Indeed, if we may take the principle of evolution to be the differentiation of the homogeneous, we may go further and say that the whole theory of evolution, and not merely a particular historic science, such as the science of religion, {24} postulates differentiation and the principle of difference, and does not explain it,—evolution cannot start, the homogeneous cannot be other than homogeneous, until the principle of difference and the power of differentiation is assumed. ”

“ The higher the fruits, the more senseless the destruction. What set the homogeneous moving in the first instance and made it become the heterogeneous? This would be the question which we should have to ask if the law were tendered as a physical explanation of the origin of the world. Why, we might also ask, is the coherent to be called the heterogeneous, and the incoherent the homogeneous? ”