Harvard University Alumni

"In addition to these larger labors, Miss Leavitt took part in various minor investigations. She gave considerable time to the discovery of new celestial objects. Altogether, she found 4 new stars, 2400 variable stars, or about one half of the known variables, and various asteroids and other objects."

"About 1906 a Durchmustering of variable stars was proposed at the Harvard Observatory. Somewhat later this was undertaken on plates included in the Map of the Sky... A comparison of the photographs of a number of these regions by Miss Leavitt led to the discovery of several hundred variables and other special objects. Among them were a number of stars of the Algol type."

"One of the most striking accomplishments of Miss Leavitt was the discovery of 1,777 variable stars in the Magellanic Clouds. These results were [made] possible by photographs of long exposure made at Arequipa with the 24-inch Bruce refractor and forwarded to Cambridge. Some of these plates had exposures of from two to four hours and showed very faint stars, among which nearly all the variables are found. ...from a study of 25 of them, the important law was derived, that the length of period bears a definite relation to the absolute magnitude."

"Hubble tackled two of the most fundamental questions of the universe: how old is it, and how big? To answer both it is necessary to know two things—how far away certain galaxies are and how fast they are flying away from us. The red shift gives the speed at which galaxies are retiring, but doesn't tell us how far away they are to begin with. For that you need what are known as "standard candles"—stars whose brightness can be reliably calculated and used as benchmarks... Hubble's luck was to come along soon after an ingenious woman named Henrietta Swan Leavitt had figured out a way to do so."

"It is to be hoped, also, that the parallaxes of some variables of this type may be measured."

"It is hoped that systematic study of the light changes of all the variables, nearly two thousand in number, in the two Magellanic Clouds may soon be undertaken at this Observatory."

"Since the Cepheid] variables are probably at nearly the same distance from the Earth, their periods are apparently associated with their actual emission of light, as determined by their mass, density, and surface brightness."

"As a senior in 1892 Leavitt was introduced to astronomy. She was fascinated by it, and after graduation she enrolled in a course to study the subject full time. Tragically Henrietta Leavitt was suddenly struck down by a serous illness, and she was forced to spend over two years at home recovering. Her illness left her profoundly deaf. ...when she felt fit enough she put forward her name in 1895 as a volunteer worker at Harvard College Observatory."

"A determination of the visual magnitudes of the stars had a very large place in the work of the Observatory during the first half of Professor Pickering's directorate. As soon as the need of photographic magnitudes became urgent, the importance of a standard sequence, from which the photographic magnitudes could be derived for stars anywhere in the sky, became evident. A sequence of stars of varying magnitudes had been early selected near the North Pole, and the determination of the magnitudes of the stars involved was assigned to Miss Leavitt. This work was carried out with unusual originality, skill, and patience."

"It is worthy of notice that in Table VI the brighter variables have the longer periods. It is also noticeable that those having the longest periods appear to be as regular in their variations as those which pass through their changes in a day or two."

"The discovery of variable stars, at this Observatory and elsewhere, has progressed so rapidly during the last five years, that the difficulty of keeping pace in observing and discussing them has become very great. In the study of distribution now in progress here, the actual time devoted to the search for new variables is small, but thorough observation requires much time, while the discussion of results may be prolonged almost indefinitely. When new lists of variables are published, therefore, it should be remembered that their discovery does not interfere materially with the study of individual objects. The number of these is so large that the publication of full results for all must be greatly delayed."

"Apparently no sharp dividing line can be drawn between true Algol stars and those whose variations are continuous. Periods of nine variables in this region, which are of the Algol type or closely resemble it, have been determined and are here discussed."

"The range of H 1255 is only four tenths of a magnitude, and on account of its brightness it is difficult to observe on all plates except those taken with the 1-inch Cooke lens. It seemed necessary, therefore, to take unusual precautions in order to secure accurate observations, and to give each one its full weight. Accordingly, one hundred and thirty six photographs were selected, including nearly all of those taken with the Cooke lens, and also those taken with the 8 inch Bache Telescope on which the variable was certainly faint. Four independent estimates of brightness were made on each plate, and means were taken, thus reducing the probable error one half. The phase was computed for each observation, thus covering all parts of the light curve. ...H 1255 and H 1303 differ from the other variables in a marked degree as in each case the duration of the phase of minimum is very long in proportion to the length of the period. This fact led to considerable difficulty in determining their periods as they were apparently at their minimum brightness for some time before and after the actual minima occurred. In H 1255, the change in brightness is obviously continuous throughout the period, although it is much more rapid near minimum than near maximum. This is clearly seen in Plate IV, Figs. 5 and 6."

"A remarkable relation between the brightness of these Cepheid] variables and the length of their periods will be noticed. In H.A. 60, No.4, attention was called to the fact that the brighter variables have the longer periods, but at that time it was felt that the number was too small the drawing of general conclusions. The periods of 8 additional variables which have been determined since that time, however, conform to the same law. The relation is shown graphically in Figure 1... The two resulting curves, one for the maxima and one for the minima, are surprisingly smooth, and of remarkable form. In Figure 2, the abscissas are equal to the logarithms of the periods, and the ordinates to the corresponding magnitudes, as in Figure 1. A straight line can readily be drawn among each of the two series of points corresponding to the maxima and minima, thus showing that there is a simple relation between the brightness of the variables and their periods. The logarithm of the period increases by about 0.48 for each increase of one magnitude in brightness."

"James R. Wible. "Economics, Christianity, and Creative Evolution: Peirce, Newcomb, and Ely and the Issues Surrounding the Creation of the American Economic Association in the 1880s," 2009."

"There is no difference between Time and any of the three dimensions of Space except that our consciousness moves along it. ...space, as our mathematicians have it, is spoken of as having three dimensions, which one may call Length, Breadth, and Thickness, and is always definable by reference to these planes, each at right angle to the others. But some philosophical people have been asking why three dimensions particularly—why not another direction at right angles to the other three?—and have even tried to construct a Four Dimensional geometry. Professor Simon Newcomb was expounding this to the New York Mathematical Society only a month or so ago. You know how on a flat surface, which has only two dimensions, we can represent a figure of a Three-Dimensional solid, and similarly they think that by models of three dimensions they could represent one of four—if they could master the perspective of the thing. See?"

"In the late 19th century, Newcomb was one of America’s best known and probably one of its most powerful scientists. He had spent most of his career as a professor at the naval observatory in Washington, D. C. He had served as President of the American Academy of Arts and Science and as President of the Political Economy Club in the 1880s. He eventually received numerous awards for his most important astronomical research more accurately measuring the movements of the moon and the planets in our solar system. In the 1880s, Newcomb joined the faculty of Johns Hopkins University and his views regarding the competence of junior faculty were often communicated to President Daniel Gilman. This was especially the case for Peirce and Ely. Newcomb also confronted America’s most prominent theologians on the relationship between theology and science and of course evolution and Christianity. For the nation’s centennial, Newcomb also had offered his harsh appraisals of American science and political economy maintaining that they were way behind European science and British political economy. Newcomb also thwarted Peirce’s career progress on numerous occasions playing a pivotal role in his exclusion from academia after 1885."

"I knew that flying machines were impossible; in engineering school I had studied Professor Simon Newcomb's well-known mathematical proof that the efforts of Professor Langley and others to build an aerodyne capable of carrying a man were doomed, useless, because scale theory proved that no such contraption large enough to carry a man could carry a heat-energy plant large enough to lift it off the ground — much less a passenger. That was science's final word on a folly and it put a stop to wasting public monies on a will-o'-the-wisp. Research and development money went into airships, where it belonged, with enormous success. However, in the past few days I had gained a new angle on the idea of "impossible". When a veritable flying machine showed up in our sky, I was not greatly surprised."

"Professor Fisher's The Purchasing Power of Money is dedicated to Simon Newcomb, from whom vid Professor Kemmerer the PT = MV formula ultimately derives. Newcomb was not a professional economist but a mathematician (Professor of Mathematics in the U.S. Navy and at Johns Hopkins). His Principles of Political Economy, published in 1886, is one of those original works which a fresh scientific mind, not perverted by having read too much of the orthodox stuff, is able to produce from time to time in a half -formed subject like economics."

"One of the most curious of these cases [geometrical paradoxers] was that of a student, I am not sure but a graduate, of the University of Virginia, who claimed that geometers were in error in assuming that a line had no thickness. He published a school geometry based on his views, which received the endorsement of a well-known New York school official and, on the basis of this, was actually endorsed, or came very near being endorsed, as a text-book hi the public schools of New York."

"Is the Airship Possible? That depends, first of all, on whether we are to make the requisite scientific discoveries... the construction of an aerial vehicle ... which could carry even a single man from place-to-place at pleasure requires the discovery of some new metal or some new force."

"It is a matter of historical record that Newcomb, one of the most eminent American mathematicians of his day, published on the topic of four-dimensional space from 1877, and he spoke about it to the New York Mathematical Society in 1893. Four dimensions (and more) were important research topics in mathematics and physics."

"The opinion is widely prevalent that even if the subjects are totally forgotten, a valuable mental discipline is acquired by the efforts made to master them. While the Conference admits that, considered in itself this discipline has a certain value, it feels that such a discipline is greatly inferior to that which may be gained by a different class of exercises, and bears the same relation to a really improving discipline that lifting exercises in an ill-ventilated room bear to games in the open air. The movements of a race horse afford a better model of improving exercise than those of the ox in a tread-mill."

"Within contemporary philosophy, Spinoza’s position is very similar to Donald Davidson’s. Davidson also rejects at least certain kinds of explanatory connections between the mental and the physical and, like Spinoza, employs the lack of these connections as part of the basis for the identity between mental things and physical things. Nonetheless, there are significant differences between Spinoza and Davidson: Davidson rejects any strict science of the psychological. For Davidson, there are strict laws governing the physical, but no strict laws governing the psychological. Thus for Davidson, the psychological is special, not governed by the same kinds of principles at work throughout nature. This would be a violation of naturalism, according to Spinoza, and thus Spinoza would insist, contra Davidson, on a science of the mental that is every bit as strict and fundamental as the science of the physical, even though there are no explanatory connections between the mental and the physical."

"I cannot see that this view of radical interpretation possesses the relevance for historians that some of Davidson’s more enthusiastic followers, such as Macdonald and Pettit, have supposed. Davidson is merely proposing a general strategy for using assertions to get at underlying beliefs, the strategy of beginning by assuming general agreement. It may well be that we need to start with some such assumption if we are to find another culture intelligible. If I am to identify the nature of Bodin’s beliefs about witches, or even to establish that they are beliefs about that particular subject-matter, it certainly seems plausible to assume that Bodin and I must share a considerable number of ancillary beliefs. It is arguable, however, that Davidson has overemphasised the significance of this consideration and too comfortably ridiculed the notion of radically different conceptual schemes."

"There are three basic problems: how a mind can know the world of nature, how it is possible for one mind to know another, and how it is possible to know the contents of our own minds without resort to observation or evidence. It is a mistake, I shall urge, to suppose that these questions can be collapsed into two, or taken into isolation."

"I conclude that there is no such thing as a language, not if a language is anything like what many philosophers and linguists have supposed. There is therefore no such thing to be learned, mastered, or born with. We must give up the idea of a clearly defined shared structure which language-users acquire and then apply to cases. And we should try again to say how convention in any important sense is involved in language; or, as I think, we should give up the attempt to illuminate how we communicate by appeal to conventions."

"I thought... that the fact that in characterizing truth for a language it is necessary to put words into relations with objects was enough to give some grip for the idea of correspondence; but this now seems to me a mistake. The mistake is in a way only a misnomer, but terminological infelicities have a way of breeding conceptual confusion, and so it is here. Correspondence theories have always been conceived as providing an explanation or analysis of truth, and this, a Tarski-style theory of truth, certainly does not do."

"Donald Davidson has notoriously retorted that the resources of existing natural languages seem perfectly adequate for dealing with even the most dramatic cases of purported incommensurability reported by writers like Benjamin Whorf and Thomas Kuhn. But Davidson’s argument seems questionable in itself, relying as it does on such a strict application of the verification principle in order to rule out the idea of alternative conceptual schemes. Furthermore, Davidson’s scepticism is insufficient to undermine the sense in which I am defending anything resembling a thesis of incommensurability. I am merely contending that it will always be a mistake for an historian to assume that the task of explicating an alien concept can be reduced to that of finding a counterpart in his or her own language for the term that expresses it."

"The methodological advice to interpret in a way that optimizes agreement should not be conceived as resting on a charitable assumption about human intelligence that might turn out to be false. If we cannot find a way to interpret the utterances and other behaviour of a creature as revealing a set of beliefs largely consistent and true by our standards, we have no reason to count that creature as rational, as having beliefs, or as saying anything"

"In quotation not only does language turn on itself, but it does so word by word and expression by expression, and this reflexive twist is inseparable from the convenience and universal applicability of the device. Here we already have enough to draw the interest of the philosopher of language."

"The dominant metaphor of conceptual relativism, that of differing points of view, seems to betray an underlying paradox. Different points of view make sense, but only if there is a common co-ordinate system on which to plot them; yet the existence of a common system belies the claim of dramatic incomparability."

"Ecological rationality uses reason – rational reconstruction – to examine the behavior of individuals based on their experience and folk knowledge, who are ‘naïve’ in their ability to apply constructivist tools to the decisions they make; to understand the emergent order in human cultures; to discover the possible intelligence embodied in the rules, norms and institutions of our cultural and biological heritage that are created from human interactions but not by deliberate human design. People follow rules without being able to articulate them, but they can be discovered."

"One of the most intriguing discoveries of experimental economics is that (1) as we have seen, people invariably behave non-cooperatively in small and large group ‘impersonal’ market exchange institutions; (2) many (up to half in single play; over 90% in repeat play) cooperate in ‘personal’ exchange (two-person extensive form games); (3) yet in both economic environments all interactions are between anonymous players."

"Theory should be ever more demanding of our empirical resources. Simultaneously, data should be ever more demanding of the empirical relevance of theory and of the theorist's expertise in working imaginatively on problems of the world, rather than on stylized problems of the imagination."

"When the theory performs well you also think, “Are there parallel results in naturally occurring field data?” You look for coherence across different data sets because theories are not specific to particular data sources. Such extensions are important because theories often make specific assumptions about information and institutions which can be controlled in the laboratory, but which may not accurately represent field data generating situations. Testing theories on the domain of their assumptions is sterile unless it is part of a research program concerned with extending the domain of applications of theory to field environments"

"In economics the tendency of theory to lag behind observation seems to be endemic, and, as theorists, few of us consider this to be a "terrible state." But as noted by Lakatos (1978, p. 6), "where theory lags behind the facts, we are dealing with miserable degenerating research programmes.""

"Rules emerge as a spontaneous order–they are found–not deliberately designed by one calculating mind. Initially constructivist institutions undergo evolutionary change adapting beyond the circumstances that gave them birth. What emerges is a form of “social mind” that solves complex organization problems without conscious cognition."

"It is not possible to design a laboratory resource allocation experiment without designing an institution in all its detail."

"In defining a microeconomic system two distinct component elements will be identified: an environment and an institution. The environment consists of a list of N economic agents {l,...,N}, a list of K + 1 commodities (including resources) {O,l,...,K}, and certain characteristics of each agent … Hence, a microeconomic environment is defined by the collection of characteristics e = (e',...,e”)."

"Parallelism: Propositions about the behavior of individuals and the performance of institutions that have been tested in laboratory microeconomies apply also to nonlaboratory environments where similar ceteris paribus conditions prevail."

"The vast majority of individuals with Asperger Syndrome need help — without that help they won't be able to do very well. The individuals that I know have to overcome a great deal of difficulty to maximize their potential and get the things in life they deserve."

"Complexity. In general individual decision makers must be assumed to have multidimensional values which attach nonmonetary subjective cost or value to (1) the process of making and executing individual or group decisions, (2) the end result of such decisions, and (3) the rewards (and perhaps behavior) of other individuals involved in the decision process."

"Economics as currently learned and taught in graduate school and practiced afterward is more theory-intensive and less observation-intensive than perhaps any other science. I think the statement that "no mere fact ever was a match in economics for a consistent theory" accurately describes the prevailing attitude in the profession (Milgrom and Roberts, 1987, p. 185)."

"It is important to remove artificial barriers–stumbling stones, often local in origin and coming from incumbent opposition to entry–and to not burden businesses with taxes that reduce their internally generated funds for reinvestment, growth and striving to overcome market challenges."

"Microeconomics, including the study of individual choice and of group choice in market and nonmarket processes, has generally been considered a field science as distinct from an experimental science. Hence microeconomics has sometimes been classified as "non-experimental" and closer methodologically to meteorology and astronomy than to physics and experimental psychology (Marschak, 1950, p. 3; Samuelson, 1973, p. 7). But the question of using experimental or nonexperimental techniques is largely a matter of cost, and generally the cost of conducting the most ambitious and informative experiments in astronomy, meteorology, and economics varies from prohibitive down to considerable. The cost of experimenting with different solar system planetary arrangements, different atmospheric conditions, and different national unemployment rates, each under suitable controls, must be regarded as prohibitive."

"In the Autumn semester, 1955, I taught Principles of Economics, and found it a challenge to convey basic microeconomic theory to students. Why/how could any market approximate a competitive equilibrium? I resolved that on the first day of class the following semester, I would try running a market experiment that would give the students an opportunity to experience an actual market, and me the opportunity to observe one in which I knew, but they did not know what were the alleged driving conditions of supply and demand in that market"

"Even though Hayek, in my view, is the leading economic thinker of the 20th century who saw what must be the mainsprings of the extended order, Mises was the choice technician, and no one was better at articulating the primacy of the individual and the need to define and nurture individual rights."

"Three precepts are offered to constitute a foundation for the use of laboratory experimental methods in testing hypotheses about the behavior of allocation mechanisms."

"Nonsatiation (Smith, 1976a). Given a costless choice be ween two alternatives which differ only in that the first yields more of the reward medium (e.g., currency) than the second, the first will always be chosen (preferred) over the second by an autonomous individual, i.e., utility U(M) is a monotone increasing function of the reward medium."