Larger Quotes (13 quotes)
A googleplex is precisely as far from infinity as is the number 1 ... No matter what number you have in mind, infinity is larger.
Because intelligence is our own most distinctive feature, we may incline to ascribe superior intelligence to the basic primate plan, or to the basic plan of the mammals in general, but this point requires some careful consideration. There is no question at all that most mammals of today are more intelligent than most reptiles of today. I am not going to try to define intelligence or to argue with those who deny thought or consciousness to any animal except man. It seems both common and scientific sense to admit that ability to learn, modification of action according to the situation, and other observable elements of behavior in animals reflect their degrees of intelligence and permit us, if only roughly, to compare these degrees. In spite of all difficulties and all the qualifications with which the expert (quite properly) hedges his conclusions, it also seems sensible to conclude that by and large an animal is likely to be more intelligent if it has a larger brain at a given body size and especially if its brain shows greater development of those areas and structures best developed in our own brains. After all, we know we are intelligent, even though we wish we were more so.
I am larger, better than I thought,
I did not know I held so much goodness.
I did not know I held so much goodness.
Our science is a drop, our ignorance a sea. Whatever else be certain, this at least is certainthat the world of our present natural knowledge is enveloped in a larger world of some sort of whose residual properties we at present can frame no positive idea.
Progress is achieved by exchanging our theories for new ones which go further than the old, until we find one based on a larger number of facts. Theories are only hypotheses, verified by more or less numerous facts. Those verified by the most facts are the best, but even then they are never final, never to be absolutely believed.
The advantage which science gained by Gauss long-lingering method of publication is this: What he put into print is as true and important today as when first published; his publications are statutes, superior to other human statutes in this, that nowhere and never has a single error been detected in them. This justifies and makes intelligible the pride with which Gauss said in the evening of his life of the first larger work of his youth: The Disquisitiones arithmeticae belong to history.
The larger our great cities grow, the more irresistible becomes the attraction which they exert on the children of the country, who are fascinated by them, as the birds are fascinated by the lighthouse or the moths by the candle.
The motive for the study of mathematics is insight into the nature of the universe. Stars and strata, heat and electricity, the laws and processes of becoming and being, incorporate mathematical truths. If language imitates the voice of the Creator, revealing His heart, mathematics discloses His intellect, repeating the story of how things came into being. And Value of Mathematics, appealing as it does to our energy and to our honor, to our desire to know the truth and thereby to live as of right in the household of God, is that it establishes us in larger and larger certainties. As literature develops emotion, understanding, and sympathy, so mathematics develops observation, imagination, and reason.
The so-called science of psychology is now in chaos, with no sign that order is soon to be restored. It is hard to find two of its professors who agree, and when the phenomenon is encountered it usually turns out that one of them is not a psychologist at all, but simply a teacher of psychology. Not even anthropology offers a larger assortment of conflicting theories, or a more gaudy band of steaming and blood-sweating professors.
The study of geometry is a petty and idle exercise of the mind, if it is applied to no larger system than the starry one. Mathematics should be mixed not only with physics but with ethics; that is mixed mathematics.
The world of organisms, of animals and plants, is built up of individuals. I like to think, then, of natural history as the study of life at the level of the individualof what plants and animals do, how they react to each other and their environment, how they are organized into larger groupings like populations and communities.
There might have been a hundred or a thousand life-bearing planets, had the course of evolution of the universe been a little different, or there might have been none at all. They would probably add, that, as life and man have been produced, that shows that their production was possible; and therefore, if not now then at some other time, if not here then in some other planet of some other sun, we should be sure to have come into existence; or if not precisely the same as we are, then something a little better or a little worse.
When I was 9, my parents gave me a Commodore 64, which was fun. At the time, the opportunity to program your own computer was easier than it is today. Today there are significantly larger barriers because of the complexity built into computing.