Complexion

“ She is a young married lady, about four or five and twenty, middle sized, finely modeled, a Grecian outline of face, a complexion sallow yet healthful, raven black hair, eyes dark, large, and beaming, softened by long eyelashes, lips full and rosy red, yet finely chiseled, and teeth of dazzling whiteness. ”

“ When I entered my room, I was surprised to see Annabella Wilmot standing before my toilet-table, composedly surveying her features in the glass, with one hand flirting her gold-mounted whip, and the other holding up her long habit.
"She certainly is a magnificent creature!" thought I, as I beheld that tall, finely developed figure, and the reflection of the handsome face in the mirror before me, with the glossy dark hair, slightly and not ungracefully disordered by the breezy ride, the rich brown complexion glowing with exercise, and the black eyes sparkling with unwonted brilliance. ”

“ “Souls have complexions too: what will suit one will not suit another.” ”

“ 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. ”

“ None the less it would be hasty to conclude that colours or any given sensations are simple. We are often struck by the likeness of complex wholes—two faces, say—long before we can discern the exact points of resemblance. Still, so long as there is no perceptible complexity in the individual presentations there can be no analysis of them, and, therefore, neither abstraction nor comparison based upon it. Can we find elsewhere the complexity that generalization and comparison invariably imply? ”

“ That is, is the sense in which a human brain is more complex than an ant brain the same sense in which a Mozart concerto is more complex than a folk tune? One way or another, what’s the significance of the answer to that question—if there’s an analogous sense of complexity behind all these cases (and I shall argue that there is, at least in most cases) , what does that mean for the practice of science? What can we learn by looking at disparate examples of complex systems? ”

“ Going further into the matter, we must break up the conception into two parts, and distinguish between the actual production of complexity and the mere transformation of complexity from a condition invisible to us into complexity visible to our senses. ”

“ The laws, then, of the formation of character being the principal object of scientific inquiry into human nature, it remains to determine the method of investigation best fitted for ascertaining them. And the logical principles according to which this question is to be decided, must be those which preside over every other attempt to investigate the laws of very complex phenomena. For it is evident that both the character of any human being, and the aggregate of the circumstances by which that character has been formed, are facts of a high order of complexity. ”

“ Does not the infinitude of division refer to the utterness of individuality? Does not the entireness of the complex hint at the perfection of the simple? It is not that the atoms, as we see them, are divided or that they are complex in their relations—but that they are inconceivably divided and unutterably complex:—it is the extremeness of the conditions to which I now allude, rather than to the conditions themselves. ”

“ If we analyse a judgment, every word in which it is expressed, whether it is a noun or a verb or a preposition or a conjunction, conveys a distinct meaning, indicates a term or a relation, each of which can be made a distinct object to the mind, and all of which are combined in the single meaning the judgment expresses. It is in this complexity that the possibility of error lies, and the possibility increases as the complexity increases. ”

“ But unless some element of balance were there (although not present to introspection) each complex filling, when up for judgment, would have been pushed to the same limit. It, therefore, does seem, in cases where the complex fillings occupied a larger space than the horizontals, that the subject, not trying consciously to secure a balance of interests, was influenced more purely by the factor of complexity, and that his judgments lend support to our theory.
Subject H was the only subject who consistently preferred [556] to have all complex fillings occupy the larger space. ”

“ 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. ”

“ Too often apparent complexities are only the result of an abstruse contemplation of abstract possibilities. Give honest, fearless, practical treatment to each concrete case as it arises, indulge more in inductive reasoning which predicates laws upon facts, not facts upon laws, and complexity gives way to common sense. ”

“ When our problem has been selected, and the necessary mental discipline has been acquired, the method to be pursued is fairly uniform. The big problems which provoke philosophical inquiry are found, on examination, to be complex, and to depend upon a number of component problems, usually more abstract than those of which they are the components. It will generally be found that all our initial data, all the facts that we seem to know to begin with, suffer from vagueness, confusion, and complexity. ”

“ Nor is it in the least objectionable by reason of the infinite complexity of its conceived structure. For, as the Supplementary Essay showed us, the real world is certainly infinitely complex in structure, and there is no contradiction in conceiving an infinitely complex object as real. But, from our point of view, the world of a Self, whatever continuity of internal structure it may in some aspects possess, is in its principal form of expression embodied in a discrete series of acts, of individual expressions, of stages of self-representation and of self-revelation. ”

“ But what the ordinary psychologies call 'ideas' are nothing but parts of the total object of representation. All that is before the mind at once, no matter how complex a system of things and relations it may be, is one object for the thought. Thus, 'A-and-B-and-their-mutual-incompatibility-and-the-fact-that-only-one-can-be-true-or-can-become-real-notwithstanding-the-probability-or-desirability-of-both' may be such a complex object ”

“ What, then, is the relationship between effective complexity and dynamical complexity? Moreover, if effective complexity is the right way to formalize the intuitions behind complexity, why is this the case? ”

“ This chapter has consisted in a sustained description of the concept, and an argument for its role as a marker for the kind of complexity we’re after when we’re doing science. The insight at the heart of dynamical complexity is that complexity, at least as it concerns science, is a feature of active, changing, evolving systems. Previous attempts to define complexity have overlooked this fact to one degree or another, and have tried to account for complexity primarily in terms of facts about the static state of a system. ”

“ Analysis, then, in the Science of Mind, you will perceive, is founded wholly on the feeling of relation which one state of mind seems to us to bear to other states of mind, as comprehensive of them; but, while this seeming complexity is felt, it is the same thing to our analysis, as if the complexity, instead of being virtual and relative only, were absolute and real. ”

“ If all systems are complicated, then, what makes one system a complex system, and another a simple system? This is not an easy question to answer, and an entirely new academic field—complex systems theory—has grown up around attempts to do so. Despite the centrality of the concept, there’s no agreed-upon definition of complexity in the complex systems theory literature. ”

“ 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. ”

“ But the complexity with which alone we are concerned is not absolute but relative,—a seeming complexity, which is involved in the very feeling of relation of every sort. That we are thus impressed with certain feelings of relation of conceptions to conceptions, no one can doubt who knows, that all science has its origin in these very feelings ”

“ One simple measure tends to occur to almost everyone when confronted with this problem for the first time: perhaps complexity is a measure of the number of independent parts that a system has—a value that we might call “mereological size.” This accords rather well with complexity in the ordinary sense of the word: an intricate piece of clockwork is complex largely in virtue of having a massive number of interlocking parts—gears, cogs, wheels, springs, and so on—that account for its functioning. ”

“ While there is no single value for effective complexity, we can perfectly coherently talk about summing all the useful ways given our goals and values. The value of this sum will change as we make new scientific discoveries—as we discover new patterns in the world that are worth paying attention to—but this again just serves to emphasize the point from Chapter One: the world is messy, and science is hard. Complexity theory is part of the scientific project, and so inherits all the difficulties and messiness from the rest of the project. ”

“ Such laws, which hold good, not for phenomena in their entirety, but for certain isolated groups of facts under narrowed conditions, are called laws of the factors of phenomena. And since the complexity of phenomena is such that it is [62] difficult for the human mind to grasp all the interlacing threads of causation at a single glance, men of science have endeavoured to isolate their several strands, and, applying the principle of analysis, without which reasoning is impossible, to separate out the factors and determine their laws. ”

“ In such systems, the whole is more than the sum of the parts, not in an ultimate, metaphysical sense, but in the important pragmatic sense that, given the properties of the parts and the laws of their inter-action, it is not a trivial matter to infer the properties of the whole. In the face of complexity, an in-principle reductionist may be at the same time a pragmatic holist... ”

“ With the experimental proof that variation consists largely in the unpacking and repacking of an original complexity, it is not so certain as we might like to think that the order of these events is not pre-determined. ”

“ Hence, a certain degree of complexity in an object is necessary to sustain our interest in it, if we exclude, as we must of course in these experiments, extraneous grounds of interest. Doubtless there are limits to the degree of complexity which we find interesting and which compels attention. A mere confused or disorderly complex, wanting altogether in unity, could hardly be expected to secure attention, if there is any truth in the principle, already recognized, that the definite has in ideation a distinct advantage over the vague. ”

“ It is undeniable that the visual field, for example, is complex; and so far as I can see, there is always self-contradiction in the theories which, while admitting this complexity, attempt to deny that it results from a combination of mutually external units. ”

“ When we reflect upon the multitude, the variety, and the complexity of the facts to be explained, and the scantiness of our information regarding them, we shall be ready to acknowledge that a full and satisfactory solution of so profound a problem is hardly to be hoped for, and that the most we can do in the present state of our knowledge is to hazard a more or less plausible conjecture. ”

“ I believe that the realization of the complexity of a material unit, and its analysis into constituents analogous to sensations, is of the utmost importance to philosophy, and vital for any understanding of the relations between mind and matter, between our perceptions and the world which they perceive. ”

“ For evidently in describing an actual occasion α, we are nearer to the total concrete fact when we describe α by predicating of it some member of its associated hierarchy, which is of a high grade of complexity. We have then said more about α. Thus, with a high grade of complexity we gain in approach to the full concreteness of α, and with a low grade we lose in this approach. Accordingly the simple eternal objects represent the extreme of abstraction from an actual occasion; whereas simple eternal objects represent the minimum of abstraction from the realm of possibility. ”

“ If formulæ of any degree of complexity, however great, are admitted, it would seem that any system, whose state at a given moment is a function of certain measurable quantities, must be a deterministic system. ”