Simpleton

“ But simplicity is, after all, but an expression of human appreciation. Furthermore, even if this view were contested, there would seem to be no reason to suppose that nature should prefer simplicity to complexity in the first place. As a matter of fact, what little we know of nature proves that the reverse is true when we cease to view phenomena in an approximate macroscopic way and adopt a more microscopic standpoint. To illustrate: There is no more simple law in physics than that of perfect gases ”

“ It is clear that in a complex fact a thousand circumstances are united by chance, and that only a chance still much less probable could reunite them anew. But are there any simple facts? And if there are, how recognize them? What assurance is there that a thing we think simple does not hide a dreadful complexity? All we can say is that we ought to prefer the facts which seem simple to those where our crude eye discerns unlike elements. And then one of two things: either this simplicity is real, or else the elements are so intimately mingled as not to be distinguishable. ”

“ This is a perfection; it is being: to deny the quality of accident is to remove a negation. To say that a being is a substance is to deny that it is an accident: these two ideas are contradictory and cannot be attributed to the same subject at the same time.
126. Simplicity is affirmed of God. This attribute denies nothing; to be convinced of this we need only recollect what simplicity is. The simple is one; the composite is a union of beings. If the parts are real, as they must be if there is a true composition, the resultant is a collection of beings subordinated to a certain law of unity. ”

“ If this axiom had any clear grounds of truth, it would not apply to proximate laws; for even when the ultimate law is simple the results may be infinitely diverse, as in the various elliptic, hyperbolic, parabolic, or circular orbits of the heavenly bodies. Simplicity is naturally agreeable to a mind of limited powers, but to an infinite mind all things are simple. ”

“ And though complexity does not appear to embarrass the operations of the laws of nature, and is admitted, without scruple, when there is reason for it, simplicity is the usual character of such laws, and appears to have been a ground of selection in the formation of the universe, as it is a mark of beauty to us in our contemplation of it. ”

“ Simplicity is a negative property. When we say that any thing is simple, we deny that it has parts, but we affirm none of its properties; we say what it is not, not what it is. Therefore, in maintaining that sensitive faculties are not repugnant to a pure spirit, we ought to restrict the proposition; we should express our meaning more exactly, if instead of saying "sensitive faculties are not repugnant to a pure spirit," we should say, "sensitive faculties are not repugnant to the simplicity of a pure spirit." ”

“ In the examples discussed, we have limited ourselves to problems of extreme simplicity; but even in these simple problems we have seen that different descriptions, though equivalent in theory, were far from equivalent in practice. When we come to consider problems of greater complexity, such as those with which modern science deals, the uniqueness of one particular type of description stands out with increased definiteness, and it is this particular simple continuous description where everything is harmonious and connected that is deemed to constitute the real description. ”

“ The desire for simplicity is impatience at superfluity, and the impatience arises from a sense of hindrance.
The first obligation of Simplicity is that of using the simplest means to secure the fullest effect. But although the mind instinctlvely rejects all needless complexity, we shall greatly err if we fail to recognise the fact, that what the mind recoils from is not the complexity, but the needlessness. ”

“ Simplicity is a necessary law of every being: a composite being ought to be called a union of beings, rather than a being.
20. We have said that simple substances are not objects of our intuition, which has none worthy to be called simple excepting the acts of our mind. The reason of this is, that the principal medium of our intuition is sensibility, which is founded upon representations, themselves based upon extension. There can be no doubt that the acts of our mind, given us by intuition, in the inward sense are perfectly simple ”

“ We are now ready to consider the second respect in which nature may be simple, namely, because the material of which it is built may reduce to a few sorts of elements. In this discussion it will be convenient to consider also at the same time the more inclusive simplicity arising from simple laws acting on simple elements. The immediate question for us here is one of fact: does nature seem to be getting intrinsically simpler as we get toward small scale phenomena? ”

“ Of these hypotheses, perhaps the most important is that of the simplicity of nature, because of its wide spread diffusion and the effect it has had on physical thought. The hypothesis of simplicity assumes several forms; some physicists are convinced that the laws which govern nature are simple, others that the ultimate stuff of which nature is composed is simple (perhaps protons and electrons and energy) , or there may be a combination of both views into the belief that ultimately we shall find simple ultimate elements behaving according to simple laws. ”

“ An earth that rotates and revolves is simpler to conceive of than is a stationary earth with a rigid composition of stars, swinging around it, stars kept apart by some unknown substance, or inter-repulsion. But all those who think that simplification is a standard to judge by are referred to Herbert Spencer’s compilations of data indicating that advancing knowledge complicates, making, then, complexity, and not simplicity, the standard by which to judge the more advanced. ”

“ If a perpetual talk about one's own robustness leads to being less robust, it is even more true that a perpetual talking about one's own simplicity leads to being less simple. One great complaint, I think, must stand against the modern upholders of the simple life--the simple life in all its varied forms, from vegetarianism to the honourable consistency of the Doukhobors. This complaint against them stands, that they would make us simple in the unimportant things, but complex in the important things. ”

“ As for the criterion of simplicity, which enables us to select one co-ordination rather than another, it appears to be linked with our valuing of the expenditure of effort. Thus, even a dog finds it simpler to enter a house by the front door rather than clamber in through the back window. At any rate, inasmuch as, with small variations, all human beings agree unanimously on those co-ordinations which are to be regarded as the simplest, we may assume the urge towards simplicity to be fundamental. ”

“ Not only do we discover new phenomena, but those we think we know are revealed in unlooked-for aspects. In the free ether the laws preserve their majestic simplicity, but matter properly so called seems more and more complex; all we can say of it is but approximate, and our formulæ are constantly requiring new terms.
But the ranks are unbroken, the relations that we have discovered between objects we thought simple still hold good between the same objects when their complexity is recognised, and that alone is the important thing. ”

“ No doubt, if our means of investigation became more and more penetrating, we should discover the simple beneath the complex, and then the complex from the simple, and then again the simple beneath the complex, and so on, without ever being able to predict what the last term will be. We must stop somewhere, and for science to be possible we must stop where we have found simplicity. ”

“ The only virtue their theoretic conception need have is simplicity, and a simple conception is an equivalent for the world only so far as the world is simple,—the world meanwhile, whatever simplicity it may harbor, being also a mightily complex affair. Enough simplicity remains, however, and enough urgency in our craving to reach it, to make the theoretic function one of the most invincible of human impulses. The quest of the fewest elements of things is an ideal that some will follow, as long as there are men to think at all. ”

“ This mistaken notion of simplicity has been the general fault of all system-makers, who are so taken up with some favourite hypothesis or principle, that they make it the sole hinge on which every thing else turns, and forget that there is any other power really at work in the universe; all other causes being either set aside as false and nugatory, or else resolved into that one. There is another principle which has a deep foundation in nature that has also served to strengthen the same feeling ”

“ If we study the history of science we see produced two phenomena which are, so to speak, each the inverse of the other. Sometimes it is simplicity which is hidden under what is apparently complex; sometimes, on the contrary, it is simplicity which is apparent, and which conceals extremely complex realities. What is there more complicated than the disturbed motions of the planets, and what more simple than Newton's law? ”

“ Take, too, that simplification of the facts, which I have mentioned as one of the essentials to modern success. Up to a certain point, and if the aim sought is worth while, it is admirable. The world is altogether too ‘full of a number of things’ not to demand their simplification for the attainment of a single purpose. Some of them must be lopped off. But the larger your majority, the more primitive the simplicity it demands, and the more drastic the pruning. It cuts off living branches along with the dead. ”

“ It has this merit in common with the opposite theory of no inspiration. Both are simple, precise, and very easy of application. But simplicity is not always a sign of truth. The facts of nature and life are more apt to be complex than simple. Theories distinguished by their simplicity most commonly ignore or omit a part of the facts. Simplistic theories are generally one-sided and partial. Materialism, Atheism, Idealism, Fatalism, are all very simple theories, and explain all difficulties with a marvellous rapidity. ”

“ Then again, nature must be simple, or at least simple to a first approximation. Theoretically, simplicity cannot exist in nature, since the whole influences the part and the part influences the whole. ”

“ They may, for example, get the notion that my proposition involves a denial of the rigidity of the laws of association: it would be quite on a par with much that is current. I do not mean that logical simplicity is a consideration of no value at all, but only that its value is badly secondary to that of simplicity in the other sense. ”

“ Indeed even a very "complicated" addition may promote unity of the resultant whole. "Simplicity" does not refer to the properties of individual parts ; simplicity is a property of wholes. Finally, the addition must be viewed also in terms of such characteristic "whole properties" as closure, equilibrium, and symmetry. [4]
From an inspection of Figs. 20-22 we are led to the discovery of still another principle: The Factor of Closure. If A, B, C, D are given and AB/CD constitute two self-enclosed units, then this arrangement rather than AC/BD will be apprehended. ”

“ If, then, we may assume that the criterion of simplicity presents no further difficulty, the problem reduces to determining whether or not the theoretical physicist introduces presuppositions and assumptions uncritically. We are here concerned solely with the physicist and theoretical physicist, not with the pure mathematician, whose procedure is entirely different. ”

“ Simplicity is not ugliness, nor poverty, nor barrenness, nor necessarily plainness. What is simplicity for another may not be for you, for your condition, your tastes, especially for your wants. It is a personal question. You go beyond simplicity when you attempt to appropriate more than your wants, your aspirations, whatever they are, demand—that is, to appropriate for show, for ostentation, more than your life can assimilate, can make thoroughly yours. There is no limit to what you may have, if it is necessary for you, if it is not a superfluity to you. ”

“ Now, if it is asked why the one party assigns a higher reality to the fact and the other to the law, it will be found that mechanism and dynamism take the word simplicity in two very different senses. For the first, any principle is simple of which the effects can be foreseen and even calculated: thus, by the very definition, the notion of inertia becomes simpler than that of freedom, the homogeneous simpler than the heterogeneous, the abstract simpler than the concrete. ”

“ She is unaware of the complexity of the problem.”
“You think that Malcolm, too, was so simple?”
“I do. Not so simple as Miss Latimer; but simpler than you, and you know it; and far simpler than I am; and you know that, too, my dear.”
She sought no dispute. Almost with a hard patience she went on. “Wasn’t their definiteness intuition rather than illusion? Isn’t intuition easier for the simple than for the complex?”
“Intuition isn’t definiteness; that’s just what it isn’t. As for it’s being easier; everything is easier, of course, to simple people.” ”