Acts of creation are ordinarily reserved for gods and poets, but humbler folk may circumvent this restriction if they know how. To plant a pine, for example, one need be neither god nor poet; one need only own a shovel. By virtue of this curious loophole in the rules, any clodhopper may say: Let there be a tree—and there will be one.

Animals, even plants, lie to each other all the time, and we could restrict the research to them, putting off the real truth about ourselves for the several centuries we need to catch our breath. What is it that enables certain flowers to resemble nubile insects, or opossums to play dead, or female fireflies to change the code of their flashes in order to attract, and then eat, males of a different species?

Former arbiters of taste must have felt (as so many apostles of ‘traditional values’ and other highminded tags for restriction and conformity do today) that maintaining the social order required a concept of unalloyed heroism. Human beings so designated as role models had to embody all virtues of the paragon–which meant, of course, that they could not be described in their truly human and ineluctably faulted form.

It is the constant attempt in this country [Canada] to make fundamental science responsive to the marketplace. Because technology needs science, it is tempting to require that scientific projects be justified in terms of the worth of the technology they can be expected to generate. The effect of applying this criterion is, however, to restrict science to developed fields where the links to technology are most evident. By continually looking for a short-term payoff we disqualify the sort of science that … attempts to answer fundamental questions, and, having answered them, suggests fundamentally new approaches in the realm of applications.

Lakatos realized and admitted that the existing standards of rationality, standards of logic included, were too restrictive and would have hindered science had they been applied with determination. He therefore permitted the scientist to violate them (he admits that science is not “rational” in the sense of these standards). However, he demanded that research programmes show certain features in the long run—they must be progressive. … I have argued that this demand no longer restricts scientific practice. Any development agrees with it.

Pauling was shocked by the freedom with which the X-ray crystallographers of the time, including particularly Astbury, played with the intimate chemical structure of their models. They seemed to think that if the atoms were arranged in the right order and about the right distance apart, that was all that mattered, that no further restrictions need to be put on them.

Physics does not endeavour to explain nature. In fact, the great success of physics is due to a restriction of its objectives: it only endeavours to explain the regularities in the behavior of objects.

Progress imposes not only new possibilities for the future but new restrictions.

Science must be free. We can permit no restrictions to be placed upon the scientists’ right to question, to experiment, and to think. Because America has held liberty above all else, distinguished men of science have come here to live, to work, and to seek new knowledge. The world has been the benefactor and science has moved forward.

Scientists and particularly the professional students of evolution are often accused of a bias toward mechanism or materialism, even though believers in vitalism and in finalism are not lacking among them. Such bias as may exist is inherent in the method of science. The most successful scientific investigation has generally involved treating phenomena as if they were purely materialistic, rejecting any metaphysical hypothesis as long as a physical hypothesis seems possible. The method works. The restriction is necessary because science is confined to physical means of investigation and so it would stultify its own efforts to postulate that its subject is not physical and so not susceptible to its methods.

Suppose we divide the space into little volume elements. If we have black and white molecules, how many ways could we distribute them among the volume elements so that white is on one side and black is on the other? On the other hand, how many ways could we distribute them with no restriction on which goes where? Clearly, there are many more ways to arrange them in the latter case. We measure “disorder” by the number of ways that the insides can be arranged, so that from the outside it looks the same. The logarithm of that number of ways is the entropy. The number of ways in the separated case is less, so the entropy is less, or the “disorder” is less.

The belief that mathematics, because it is abstract, because it is static and cold and gray, is detached from life, is a mistaken belief. Mathematics, even in its purest and most abstract estate, is not detached from life. It is just the ideal handling of the problems of life, as sculpture may idealize a human figure or as poetry or painting may idealize a figure or a scene. Mathematics is precisely the ideal handling of the problems of life, and the central ideas of the science, the great concepts about which its stately doctrines have been built up, are precisely the chief ideas with which life must always deal and which, as it tumbles and rolls about them through time and space, give it its interests and problems, and its order and rationality. That such is the case a few indications will suffice to show. The mathematical concepts of constant and variable are represented familiarly in life by the notions of fixedness and change. The concept of equation or that of an equational system, imposing restriction upon variability, is matched in life by the concept of natural and spiritual law, giving order to what were else chaotic change and providing partial freedom in lieu of none at all. What is known in mathematics under the name of limit is everywhere present in life in the guise of some ideal, some excellence high-dwelling among the rocks, an “ever flying perfect” as Emerson calls it, unto which we may approximate nearer and nearer, but which we can never quite attain, save in aspiration. The supreme concept of functionality finds its correlate in life in the all-pervasive sense of interdependence and mutual determination among the elements of the world. What is known in mathematics as transformation—that is, lawful transfer of attention, serving to match in orderly fashion the things of one system with those of another—is conceived in life as a process of transmutation by which, in the flux of the world, the content of the present has come out of the past and in its turn, in ceasing to be, gives birth to its successor, as the boy is father to the man and as things, in general, become what they are not. The mathematical concept of invariance and that of infinitude, especially the imposing doctrines that explain their meanings and bear their names—What are they but mathematicizations of that which has ever been the chief of life’s hopes and dreams, of that which has ever been the object of its deepest passion and of its dominant enterprise, I mean the finding of the worth that abides, the finding of permanence in the midst of change, and the discovery of a presence, in what has seemed to be a finite world, of being that is infinite? It is needless further to multiply examples of a correlation that is so abounding and complete as indeed to suggest a doubt whether it be juster to view mathematics as the abstract idealization of life than to regard life as the concrete realization of mathematics.

There are about 3,000,000 people seriously ill in the United States…. More than half of this illness is preventable. If we count the value of each life lost at only $1700 and reckon the average earning lost by illness at $700 a year for grown men, we find that the economic gain from mitigation of preventable disease in the United States would exceed $1,500,000,000 a year. … This gain … can be secured through medical investigation and practice, school and factory hygiene, restriction of labor by women and children, the education of the people in both public and private hygiene, and through improving the efficiency of our health service, municipal, state, and national.

When a conjecture inspires new hopes or creates new fears, action is indicated. There is an important asymmetry between hope, which leads to actions that will test its basis, and fear, which leads to restriction of options frequently restricting testing of the basis for the fear. As we know only too well, many of our hopes do not survive their tests. However, fears accumulate untested. Our inventory of untested fears has always made humanity disastrously vulnerable to thought control. While science was independent of politics, its greatest triumph was the reduction of that vulnerability.