Sufficiency Quotes (16 quotes)
A star is drawing on some vast reservoir of energy by means unknown to us. This reservoir can scarcely be other than the subatomic energy which, it is known exists abundantly in all matter; we sometimes dream that man will one day learn how to release it and use it for his service. The store is well nigh inexhaustible, if only it could be tapped. There is sufficient in the Sun to maintain its output of heat for 15 billion years.
And invention must still go on for it is necessary that we should completely control our circumstances. It is not sufficient that there should [only] be organization capable of providing food and shelter for all and organization to effect its proper distribution.
For many parts of Nature can neither be invented with sufficient subtlety, nor demonstrated with sufficient perspicuity, nor accommodated to use with sufficient dexterity, without the aid and intervention of Mathematic: of which sort are Perspective, Music, Astronomy, cosmography, Architecture, Machinery, and some others.
In many cases, mathematics is an escape from reality. The mathematician finds his own monastic niche and happiness in pursuits that are disconnected from external affairs. Some practice it as if using a drug. Chess sometimes plays a similar role. In their unhappiness over the events of this world, some immerse themselves in a kind of self-sufficiency in mathematics. (Some have engaged in it for this reason alone.)
Intellectual beauty is sufficient unto itself, and only for it rather than for the future good of humanity does the scholar condemn himself to arduous and painful labors.
It is imperative in the design process to have a full and complete understanding of how failure is being obviated in order to achieve success. Without fully appreciating how close to failing a new design is, its own designer may not fully understand how and why a design works. A new design may prove to be successful because it has a sufficiently large factor of safety (which, of course, has often rightly been called a “factor of ignorance”), but a design's true factor of safety can never be known if the ultimate failure mode is unknown. Thus the design that succeeds (ie, does not fail) can actually provide less reliable information about how or how not to extrapolate from that design than one that fails. It is this observation that has long motivated reflective designers to study failures even more assiduously than successes.
Logic does not pretend to teach the surgeon what are the symptoms which indicate a violent death. This he must learn from his own experience and observation, or from that of others, his predecessors in his peculiar science. But logic sits in judgment on the sufficiency of that observation and experience to justify his rules, and on the sufficiency of his rules to justify his conduct. It does not give him proofs, but teaches him what makes them proofs, and how he is to judge of them.
Parkinson's Law is a purely scientific discovery, inapplicable except in theory to the politics of the day. It is not the business of the botanist to eradicate the weeds. Enough for him if he can tell us just how fast they grow.
The combination of such characters, some, as the sacral ones, altogether peculiar among Reptiles, others borrowed, as it were, from groups now distinct from each other, and all manifested by creatures far surpassing in size the largest of existing reptiles, will, it is presumed, be deemed sufficient ground for establishing a distinct tribe or sub-order of Saurian Reptiles, for which I would propose the name of Dinosauria.
The intrinsic character of mathematical research and knowledge is based essentially on three properties: first, on its conservative attitude towards the old truths and discoveries of mathematics; secondly, on its progressive mode of development, due to the incessant acquisition of new knowledge on the basis of the old; and thirdly, on its self-sufficiency and its consequent absolute independence.
The logical feebleness of science is not sufficiently borne in mind. It keeps down the weed of superstition, not by logic but by slowly rendering the mental soil unfit for its cultivation.
The regularity with which we conclude that further advances in a particular field are impossible seems equaled only by the regularity with which events prove that we are of too limited vision. And it always seems to be those who have the fullest opportunity to know who are the most limited in view. What, then, is the trouble? I think that one answer should be: we do not realize sufficiently that the unknown is absolutely infinite, and that new knowledge is always being produced.
The rudest numerical scales, such as that by which the mineralogists distinguish different degrees of hardness, are found useful. The mere counting of pistils and stamens sufficed to bring botany out of total chaos into some kind of form. It is not, however, so much from counting as from measuring, not so much from the conception of number as from that of continuous quantity, that the advantage of mathematical treatment comes. Number, after all, only serves to pin us down to a precision in our thoughts which, however beneficial, can seldom lead to lofty conceptions, and frequently descend to pettiness.
The scientist, if he is to be more than a plodding gatherer of bits of information, needs to exercise an active imagination. The scientists of the past whom we now recognize as great are those who were gifted with transcendental imaginative powers, and the part played by the imaginative faculty of his daily life is as least as important for the scientist as it is for the worker in any other field—much more important than for most. A good scientist thinks logically and accurately when conditions call for logical and accurate thinking—but so does any other good worker when he has a sufficient number of well-founded facts to serve as the basis for the accurate, logical induction of generalizations and the subsequent deduction of consequences.
Upon the rivers which are tributary to the Mississippi and also upon those which empty themselves into Lake Michigan, there are interminable forests of pine, sufficient to supply all the wants of the citizens ... for all time to come.
We profess to teach the principles and practice of medicine, or, in other words, the science and art of medicine. Science is knowledge reduced to principles; art is knowledge reduced to practice. The knowing and doing, however, are distinct. ... Your knowledge, therefore, is useless unless you cultivate the art of healing. Unfortunately, the scientific man very often has the least amount of art, and he is totally unsuccessful in practice; and, on the other hand, there may be much art based on an infinitesimal amount of knowledge, and yet it is sufficient to make its cultivator eminent.