David Sharp

A World Without War

[...] in an important sense, the sciences have solved the problem of communicating with one another more completely than has any human enterprise. To retell an old story, thirty-five years ago, Dirac and I were in Gottingen. He was developing the quantum theory of radiation, and I was a student. He learned that I sometimes wrote a poem, and he took me to task, saying, “In physics we try to say things that no one knew before in a way that everyone can understand, whereas in poetry... ”

Syntax, Semantics, and the Problem of the Identity of Mathematical Objects

The items of mathematics, such as the real line, the triangle, sets, and the natural numbers, share the property of retaining their identity while receiving axiomatic presentations which may vary radically. Mathematicians have axiomatized the real line as a one-dimensional continuum, as a complete Archimedean ordered field, as a real closed field, or as a system of binary decimals on which arithmetical operations are performed in a certain way. Each of these axiomatizations is tacitly understood by mathematicians as an axiomatization of the same real line. That is, the mathematical item thereby axiomatized is presumed to be the same in each case, and such an identity is not questioned. We wish to analyze the conditions that make it possible to refer to the same mathematical item through a variety of axiomatic presentations.

Tradition and Discovery

[...] when columbus sailed on his first voyage, his first voyage of discovery, it is told that the first evening with the ship standing out to sea he opened the pages of what would later be the log of this voyage, and on it he wrote Jesus cum Maria sit nobis in via.

The Einstein-Podolsky-Rosen Paradox Re-Examined

This paper discusses the Einstein-Podolsky-Rosen paradox from a new point of view. In section II, the arguments by which Einstein, Podolsky and Rosen reach their paradoxical conclusions are presented. They are found to rest on two critical assumptions: (a) that before a measurement is made on a system consisting of two non-interacting but correlated sub-systems, the state of the entire system is exactly represented by: ψ _a(r̄₁,r̄₂)=∑_ηa_ητ _η(r̄₁,r̄₂)=∑_i,kα _ikψ _i(r̄₁)σ _k(r̄₂) (b) that the exact measurement of an observable A in one of the sub-systems is possible. In section III it is shown that assumption (b) is incorrect. Thus we conclude, as did Bohr, that the results of Einstein, Podolsky and Rosen are not valid. The arguments of section III are quite distinct from Bohrs, and therefore in Section IV this work is related to that of Bohr.

On Science and Culture

we live in an unusual world, marked by very great and irreversible changes that occur within the span of a man’s life. We live in a time where our knowledge and understanding of the world of nature grows wider and deeper at an unparalleled rate; and where the problems of applying this knowledge to man’s needs and hopes are new, and only a little illuminated by our past history.

Can Science Education Cope with the Information Onslaught

Publisher Summary This chapter discusses whether students are getting adequate scientific education to enable them to deal with information onslaught. The situation with respect to science curricula and science teachers might be considerably worse today were it not for the development of national curricula and the support of in-service workshops funded by the National Science Foundation over the past 25 years. Besides the problems special to science education, there are well-known general problems of schools and society that interfere with effective education. Quality education, as understood by the present authors, has not always been a high priority in society, and educators outside of major universities are not generally accorded the esteem given to other professionals such as physicians, attorneys, or research scientists. It is clear that the numerous problems faced by science education require responses at local, state, and national levels. At the local level, an important priority should be to alter the way in which public school science teachers are regarded by the general public, and to increase the importance attached to public school science education. The problem of providing achievement incentives for school children is one of the most longstanding and difficult problems facing the educational community, and there are no easy solutions.

The Consequences of Action

[...] in the recent past much has changed. Our troops are at war in Korea. We are in a state of emergency, and are mobilizing. Many of the views of the American people have sharpened and altered. Errors that were prevalent six months ago are obvious as errors today. There is a deep anxiety about war, about the prevention and limitation of war, and about the defeat of our enemies should war break out. I thus thought it only right that I should address myself largely, though not exclusively, to the role of the atom in military matters, to the public aspects of this question, of which obviously not all aspects can be or are public. [...] This is a field in which there are many handouts and many classified lies, in which the wholesome give and take of question and answer are much needed. Where I can, I shall try to respond to these questions of concern and curiosity.

To Live with Ourselves

[...] i use the word “science” to mean really all those areas of human knowledge, still a small part of human life, all those areas of human knowledge where we can tell each other what we have done and what we have found. This knowledge is historical, sociological, economic, mathematical, anthropological, astronomical, among many other forms. It is in just such fields that you have been working. I know that the word “humanities” can be used to talk about the whole range of expression that men give to their experience. I think the analogies that bind archaeology to astronomy are not very much more remote than those that bind anthropology to astronomy; I speak to you in this sense as fellow scientists.

Physics and Man’s Understanding

we are celebrating a birthday, honoring the foresight of a man and the success of a great institution. This makes it fitting that we leave to one side the common plaints of our time: that physics is corrupted by money; microbiology and mathematics by pride, not unrelated to achievement; astrophysics and geophysics by access to novel and powerful instruments of exploration; the arts by alienation; and all by our lack of virtue. What truth there is, and there is some, to these anxieties is not for us today. We could begin with Joseph Henry, the first Secretary of this Institution, [... who said,] “Knowledge should not be viewed as existing in isolated parts but as a whole, each portion of which throws light on the other... the tendency of all is to improve the human mind... for they all contribute to sweeten, to adorn, and to embellish life.” When we think back on the prolonged and troubled debates with which the Congress moved toward accepting Smithson’s bequest, establishing this institution, we can only be moved to celebrate the extent to which it has managed to preserve and enlarge, not perhaps the unity, but the harmony between the sciences, between the arts and sciences, between nature and man, and between knowledge and practice, whose conflicts so troubled the Congress for almost two decades.

Travelling to a Land We Cannot See

this wry tale comes to mind often when one observes the efforts which the Government of the United States is making to turn the development of atomic energy to good ends, and the frustrations and sorrows of the negotiations within the United Nations Atomic Energy Commission to which these efforts toward international control have now been reduced.