Although gravity is by far the weakest force of nature, its insidious and cumulative action serves to determine the ultimate fate not only of individual astronomical objects but of the entire cosmos. The same remorseless attraction that crushes a star operates on a much grander scale on the universe as a whole.

Any chemist reading this book can see, in some detail, how I have spent most of my mature life. They can become familiar with the quality of my mind and imagination. They can make judgements about my research abilities. They can tell how well I have documented my claims of experimental results. Any scientist can redo my experiments to see if they still work—and this has happened! I know of no other field in which contributions to world culture are so clearly on exhibit, so cumulative, and so subject to verification.

Cells are required to stick precisely to the point. Any ambiguity, any tendency to wander from the matter at hand, will introduce grave hazards for the cells, and even more for the host in which they live. … There is a theory that the process of aging may be due to the cumulative effect of imprecision, a gradual degrading of information. It is not a system that allows for deviating.

Human evolution is nothing else but the natural continuation, at a collective level, of the perennial and cumulative process of “psychogenetic” arrangement of matter which we call life. … The whole history of mankind has been nothing else (and henceforth it will never be anything else) but an explosive outburst of ever-growing cerebration. … Life, if fully understood, is not a freak in the universe—nor man a freak in life. On the contrary, life physically culminates in man, just as energy physically culminates in life.

I have never had reason, up to now, to give up the concept which I have always stressed, that nerve cells, instead of working individually, act together, so that we must think that several groups of elements exercise a cumulative effect on the peripheral organs through whole bundles of fibres. It is understood that this concept implies another regarding the opposite action of sensory functions. However opposed it may seem to the popular tendency to individualize the elements, I cannot abandon the idea of a unitary action of the nervous system, without bothering if, by that, I approach old conceptions.

If the Weismann idea triumphs, it will be in a sense a triumph of fatalism; for, according to it, while we may indefinitely improve the forces of our education and surroundings, and this civilizing nurture will improve the individuals of each generation, its actual effects will not be cumulative as regards the race itself, but only as regards the environment of the race; each new generation must start de novo, receiving no increment of the moral and intellectual advance made during the lifetime of its predecessors. It would follow that one deep, almost instinctive motive for a higher life would be removed if the race were only superficially benefited by its nurture, and the only possible channel of actual improvement were in the selection of the fittest chains of race plasma.

It is easy without any very profound logical analysis to perceive the difference between a succession of favorable deviations from the laws of chance, and on the other hand, the continuous and cumulative action of these laws. It is on the latter that the principle of Natural Selection relies.

It is this ideal of progress through cumulative effort rather than through genius—progress by organised effort, progress which does not wait for some brilliant stroke, some lucky discovery, or the advent of some superman, has been the chief gift of science to social philosophy.

No history of civilization can be tolerably complete which does not give considerable space to the explanation of scientific progress. If we had any doubts about this, it would suffice to ask ourselves what constitutes the essential difference between our and earlier civilizations. Throughout the course of history, in every period, and in almost every country, we find a small number of saints, of great artists, of men of science. The saints of to-day are not necessarily more saintly than those of a thousand years ago; our artists are not necessarily greater than those of early Greece; they are more likely to be inferior; and of course, our men of science are not necessarily more intelligent than those of old; yet one thing is certain, their knowledge is at once more extensive and more accurate. The acquisition and systematization of positive knowledge is the only human activity which is truly cumulative and progressive. Our civilization is essentially different from earlier ones, because our knowledge of the world and of ourselves is deeper, more precise, and more certain, because we have gradually learned to disentangle the forces of nature, and because we have contrived, by strict obedience to their laws, to capture them and to divert them to the gratification of our own needs.

Organization is simply the means by which the acts of ordinary men can be made to add up to extraordinary results. To this idea of progress that does not wait on some lucky break, some chance discovery, or some rare stroke of genius, but instead is achieved through systematic, cumulative effort, the engineer has contributed brilliantly.

Science began to be powerful when it began to be cumulative, when observers began to preserve detailed records, to organize cooperating groups in order to pool and criticize their experiences.

The transition from a paradigm in crisis to a new one from which a new tradition of normal science can emerge is far from a cumulative process, one achieved by an articulation or extension of the old paradigm. Rather it is a reconstruction of the field from new fundamentals, a reconstruction that changes some of the field's most elementary theoretical generalizations as well as many of its paradigm methods and applications. During the transition period there will be a large but never complete overlap between the problems that can be solved by the old and by the new paradigm. But there will also be a decisive difference in the modes of solution. When the transition is complete, the profession will have changed its view of the field, its methods, and its goals.

Theory provides the maps that turn an uncoordinated set of experiments or computer simulations into a cumulative exploration.

This ability to incorporate the past gives the sharpest diagnostic tool, if one asks whether a body of knowledge is a science or not. Do present practitioners have to go back to an original work of the past? Or has it been incorporated? … Science is cumulative, and embodies its past.