Complexity

“ 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. ”

“ 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. ”

“ The complexity of the individual thing which we call a tree or a flower or an animal, or, if you please, a social state (and indeed those more or less abstruse things which we know as arts and sciences) , are but a further evolution of the complexity of the world machine, and life has brought them about and apparently saved them to the world, possibly for the purpose of partial self-expression. ”

“ The farther I pursue this quite negative direction of relaxation, the more extension and complexity I shall create; and the more the complexity in its turn increases, the more admirable will seem to be the order which continues to reign, undisturbed, among the elements. ”

“ 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. ”

“ 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? ”

“ 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? ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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 ”

“ 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. Current philosophical ideas share these defects; it is therefore necessary to create an apparatus of precise conceptions as general and as free from complexity as possible, before the data can be analysed into the kind of premisses which philosophy aims at discovering. In this process of analysis, the source of difficulty is tracked further and further back, growing at each stage more abstract, more refined, more difficult to apprehend. ”

“ 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? ”

“ As the highest generalization comprises the fewest attributes, the concrete expression of this idea will present the simplest possible physical form and the least complexity of organization, and thus will present the lowest types of life; and as the individual comprises the greatest number of attributes, its concrete expression will present the greatest complexity, and consequently the highest type of life. [Pg 31] We have seen that the logical process begins with the general and ends with the individual ”

“ While showing the general principles which prevail in the variation of living creatures, it only points out the infinite complexity of the causes and circumstances which have led to the present state of things. ”

“ A second class of objector is prepared to admit that there has been an increase of complexity, an increase in the degree of organization during evolution, but refuses to allow that increase of complexity has any value in itself, whether biological or philosophical, and accordingly refuses to dignify this trend towards greater complexity by the name of progress. ”

“ In dealing with the complexity of the universe, whether mathematically or logically, we cannot grasp all factors at once, and so are obliged to regard some sides to the exclusion of others, to disregard the variable and dependent nature of some factors in the consideration of that of others. ”

“ We must therefore, and this seems to me the practical conclusion of the whole matter, proceed to form means of intellectual apprehension of a greater and greater degree of complexity, both dimensionally and in extent in any dimension. Such means of representation must always be artificial, but in the multiplicity of the elements with which we deal, however incipiently arbitrary, lies our chance of apprehending nature. ”

“ This latter alternative will be considered in another relation by-and-by, so I will not dwell upon it now. But with reference to all these possible contingencies, I may observe that we are not without clear indications of the great fact that the high order of complexity which has been reached by the social organism is accompanied by evidence of something which we may least dimly define as resembling subjectivity. In numberless ways, which I need not wait to enumerate, we perceive that society exhibits the phenomena both of thought and conduct. ”

“ A thousand men in a crowd are not distinguishable from nine hundred and ninety-nine. But in all cases, in which the complexity of the idea arises from the repetition of the same idea, names can be invented upon a plan, which shall render them distinct, up to the very highest degree of complication. ”

“ It seems to us, then, that the complexity of the material elements and the mathematical order that binds them together must arise automatically when within the whole a partial interruption or inversion is produced. Moreover, as the intellect itself is cut out of mind by a process of the same kind, it is attuned to this order and complexity, and admires them because it recognizes itself in them. But what is admirable in itself, what really deserves to provoke wonder, is the ever-renewed creation which reality, whole and undivided, accomplishes in advancing ”

“ In their territory not only the factors of the particular occurrence mix in almost inextricable complexity, but even the fate of a given element, that may be analyzed out of the confusion, is beyond determination by mathematics and experiment. ”

“ And if there is any force in the claim that diversity and complexity in an object, with the relatively greater subjective activity which they imply, tend to hold the attention to the ideated object about which this activity is employed, the result could hardly be other than it is. ”

“ 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. ”

“ This is a problem for someone who wants to embrace position in a strict hierarchy as a measure of complexity: there may be no strict hierarchy to which we can appeal. Dynamical complexity cheerfully acknowledges this fact, and judges complexity on a case-by-case basis, rather than trying to pronounce on the relative complexity of all biological systems, or all psychological systems. ”

“ 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. ”

“ Pass now to a conception of still greater complexity—say that the ratio of A to B varies as the ratio of C to D. Far more numerous things have now to be represented in consciousness with approximate simultaneity. ”

“ 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. ”

“ We would like to have a more enduring result than awareness of complexity, and therefor we adopt the Definition & Reality methodology. As said, a proposition - as a statement on reality - can be regarded as a mathematical theorem about/within a model of stylized facts. When there is a tautology, we attain truth by definition. ”

“ 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. ”

“ Because we can often arrange the series of structures in a line extending from the very simple to the more complex, we are apt to become unduly impressed by this fact and conclude that if we found the complete series we should find all the intermediate steps and that they have arisen in the order of their complexity. ”

“ Nor does it admit of doubt, that similar adaptations and precautions are indispensable in sociology. In applying to that most complex of all studies what is demonstrably the sole method capable of throwing the light of science even upon phenomena of a far inferior degree of complication, we ought to be aware that the same superior complexity which renders the instrument of Deduction more necessary, renders it also more precarious ”

“ In this section, I will argue that dynamical complexity succeeds in cherry-picking the best features of the mereological size measure, the hierarchical position measure, the information-theoretic measure, and the fractal dimension measure, while avoiding the worst difficulties of each of them. ”

“ The complexity of the individual organism, which corresponds strictly to the political, economic and scientific complexity of societies, adds neither to the possibilities of life, nor to its scope of activity, nor to its hopes. ”

“ The complexity of some parts of the present work is due to the inevitable dovetailing of problems which results from approaching philosophy in such a way. But through this complexity, which is due to the complexity of reality itself, we believe that the reader will find his way if he keeps a fast hold on the two principles which we have used as a clue throughout our own researches. ”

“ 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. ”