Scientists From Massachusetts

"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."

"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."

"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."

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

"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."

"To the Editor of the Bulletin: In Professor Hart's most interesting and illuminating article printed in the Alumni Bulletin he remarks that barring certain exceptions "petticoats are considered to have no place in Harvard or a Harvard Catalogue." Unfortunately this statement is only too true, and I believe the time is ripe to take serious account of the important and indispensable services that women are rendering to the University in technical and administrative positions in her offices and her institutions. We have recently read in the papers of the death of Miss Henrietta S. Leavitt of the Astronomical Observatory, whose work in photographic photometry gave her an international reputation... in fact, the services that the women have rendered at the Observatory are too well known in the scientific world to need further comment. ...Harvard should follow the lead already taken by the other large universities of the country, including California, Chicago, Columbia, Princeton, and Yale, in recognizing high grade service afforded by women on its staff, and this recognition should be not merely the inclusion of their names in the Catalogue... but should carry with it privileges of retirement and pension funds and of leave of absence at stated periods in order to afford opportunity for study and research. Several of the universities named are already ahead of Harvard in this respect, and in some of them women occupying high grade technical positions take rank with instructors and assistant professors when their acquirements and the nature of their work make them worthy of it. ...my heading "Petticoats in Harvard" is not an attempt to bring up the question is... only a plea for fitting recognition of scholarly work efficiently and faithfully performed in our midst by an unrecognized body of experts."

"Miss Henrietta Swan Leavitt, for more than twenty years a member of the staff of the Harvard Astronomical Observatory, died at her home in Cambridge on Dec. 12. She was a graduate of Radcliffe College, and had studied astronomy as a graduate student. She joined the staff of the Harvard Observatory in 1895, and finally was in charge of the department of photographic stellar photometry. She determined the brightness of a series of stars near the north pole ranging from the fourth to the twentieth magnitude; discovered four new stars and 2,400 variables of about half of all the known variable stars; formulated a law establishing a definite relation between the brightness and the length of period of such variables; and made other noteworthy achievements in astronomy. The scientific results of her work form parts of volumes 60, 71, 84, and 85 in the "Annals of the Harvard Observatory.""

"How far are the spiral nebulae? How large is the universe? We cannot begin to answer these questions unless we measure the distance of heavenly objects. The breakthrough was made by Henrietta Leavitt, who was interested in a rather special class of stars, the Cepheids. The intensity of light coming from Cepheids rises and falls regularly with time... Concentrating on one of the Magellanic Clouds, she found that there was a very close relationship... The brighter the Cepheid was, the longer its period. The distance of the Magellanic Cloud is so great that the stars there can be regarded as all being effectively the same distance from the Earth. If you are in Los Angeles, everybody in Carnegie Hall is about the same distance from you. ...Suppose that a Cepheid in the cloud has a certain brightness and a period of one week. Now look at another Cepheid in some more distant galaxy. If it has the same period, we can assume it has the same intrinsic brightness, and yet it is dimmer than it should be. ...we can work out the relative distance from Earth. A star of the same intrinsic brightness that is twice as far away will be four times dimmer. ...It is slightly complicated by the effects on brightness of interstellar dust clouds, but it was a huge step forward."

"By the death of Miss Leavitt on December 12, 1921, the Observatory lost an investigator of the highest value. She had obtained a comprehensive experience in photographic photometry, and had developed a clear appreciation of the difficulties involved in the theory and practice of this important research. Her work on standard magnitude sequences was nearly concluded at the time of her death, but she had hardly begun work on her extensive program of photographic measures of variable stars. In the foregoing summary no mention has been made of Miss Leavitt's work on standard photometry..."

"The following statement regarding the periods of 25 variable stars in the Small Magellanic Cloud has been prepared by Miss Leavitt."

"I should be willing to pay thirty cents an hour in view of the quality of your work, although our usual price, in such cases, is twenty five cents an hour."

"He acknowledges the use and calibration of her period-luminosity relation first by Hertzsprung and later by Shapley and ends the “Period- Luminosity Relations to Cepheids” section in his book without ever mentioning that he, Hubble, had used Shapley’s technique. ...Hubble’s underwhelming acknowledgment of Henrietta Leavitt is an example of the ongoing denial and lack of the professional and public recognition that Henrietta Leavitt suffers from, despite her landmark discovery. With the exception of naming a moon crater after her, the profession of astronomy has not done much to celebrate her work. No astronomy prize is named after her and the period-luminosity relation has not been renamed as the H. Leavitt law."

"She deserved the Nobel Prize for her work."

"She and others realized that one needed only to calculate the distance to these [Magellanic] Cepheids, which almost certainly were roughly the same distance to the earth, to have a useful yardstick for measuring other distances."

"The photographic plates from Peru that Leavitt was studying in Harvard covered two clouds of stars, known as the Large and Small Magellanic Clouds... During the course of her painstaking work, Leavitt noticed that the Cepheids in the Small Magellanic Cloud (SMC) showed an overall pattern of behaviour in which the brighter Cepheids... went through their cycle more slowly. The initial discovery was reported in 1908, and by 1912 Leavitt had enough data to pin down this period-luminosity relationship in a mathematical formula, established from her study of twenty-five Cepheids in the SMC. ...Leavitt found a clear mathematical relationship between the apparent brightness of a Cepheid in the SMC and its period... This could only mean that the absolute magnitudes of Cepheids are related to one another in the same way, since the distance effect is essentially the same for all of the Cepheids in the SMC. All that was needed now was to find the distance to just one or two Cepheids in our neighborhood... so that distances... could be worked out from the period-luminosity law that Leavitt had discovered."

"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."

"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."

"Apart from her few and very important scientific papers, Leavitt left behind almost no traces of her life. She was born on the Fourth of July 1868 in Lancaster, Mass., and died of cancer on Dec. 12, 1921. Her will tells nearly all. She left an estate worth $314.91, mostly in Liberty Bonds, with a few items such as a desk valued at $5. She never married and had few living relatives. She also left behind a legacy of a great astronomical discovery."

"Miss Leavitt was of an especially quiet and retiring nature, and absorbed in her work to an unusual degree. She had the highest esteem of all her associates at the Harvard Observatory, where her loss is keenly felt."

"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."

"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."

"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."

"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."

"You Become what You Disrupt"

"For every dollar spent in failure, learn a dollar’s worth of lesson."

"The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data."

"Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise."

"The tool that is so dull that you cannot cut yourself on it is not likely to be sharp enough to be either useful or helpful."

"There is no concept in the whole field of physics which is more difficult to understand than is the concept of entropy, nor is there one which is more fundamental."

"...the more accurate the calculations became, the more the concepts tended to vanish into thin air."

"Whatever work you undertake to do in your lifetime, it is very important that first you have a passion for it — you know, get excited about it — and second, that you have fun with it. That's important. Otherwise, you see, your work becomes nothing but an idle chore. Then, you hate the life you live."

"My first TV series on demonstrations in physics — titled Why Is It So? were now seen and heard over the land. The mail was massive. The academics were a special triumph for me. They charged me with being superficial and trivial. If I had done what they wanted my programs would be as dull as their classes! I knew my purpose well and clear: to show how Nature behaves without cluttering its beauty with abtruse mathematics. Why cloud the charm of a Chladni plate with a Bessel function?"

"We are approaching a darkness in the land. Boys and girls are emerging from every level of school with certificates and degrees, but they can't read, write or calculate. We don't have academic honesty or intellectual rigor. Schools have abandoned integrity and rigor."

"Kids are my favorites … their spirit and curiosity has not yet been dulled by schools."

"If I want a word, I make it. I don't like combustion. It's too quiet. I have some stuff in a state of combustication."

"My view is this: We teach nothing. We do not teach physics nor do we teach students. (I take physics merely as an example.) What is the same thing: No one is taught anything! Here lies the folly of this business. We try to teach somebody nothing. This is a sorry endeavour for no one can be taught a thing. What we do, if we are successful, is to stir interest in the matter at hand, awaken enthusiasm for it, arouse a curiosity, kindle a feeling, fire up the imagination. To my own teachers who handled me in this way, I owe a great and lasting debt."

"It is important that we subscribe to the requirements of nature."

"Why is it so?"

"The very spirits of the winds, when they were sent to carry the grateful harvest to the thirsting fields of Calabria, did not forget the geometry which they had studied in the caverns of Æolus and of which the geologist is daily discovering the diagrams."

"There is proof enough furnished by every science, but by none more than geometry, that the world to which we have been allotted is peculiarly adapted to our minds, and admirably fitted to promote our intellectual progress. There can be no reasonable doubt that it was part of the Creator's plan. How easily might the whole order have been transposed! How readily might we have been assigned to some complicated system which our feeble and finite powers could not have unravelled!"

"Some definite interpretation of a linear algebra would, at first sight, appear indispensable to its successful application. But on the contrary, it is a singular fact, and one quite consonant with the principles of sound logic, that its first and general use is mostly to be expected from its want of significance. The interpretation is a trammel to the use. Symbols are essential to comprehensive argument."

"The familiar proposition that all A is B, and all B is C, and therefore all A is C, is contracted in its domain by the substitution of significant words for the symbolic letters. The A, B, and C, are subject to no limitation for the purposes and validity of the proposition; they may represent not merely the actual, but also the ideal, the impossible as well as the possible. In Algebra, likewise, the letters are symbols which, passed through a machinery of argument in accordance with given laws, are developed into symbolic results under the name of formulas. When the formulas admit of intelligible interpretation, they are accessions to knowledge; but independently of their interpretation they are invaluable as symbolical expressions of thought. But the most noted instance is the symbol called the impossible or imaginary, known also as the square root of minus one, and which, from a shadow of meaning attached to it, may be more definitely distinguished as the symbol of semi-inversion. This symbol is restricted to a precise signification as the representative of perpendicularity in quaternions, and this wonderful algebra of space is intimately dependent upon the special use of the symbol for its symmetry, elegance, and power."

"The strongest use of the symbol is to be found in its magical power of doubling the actual universe, and placing by its side an ideal universe, its exact counterpart, with which it can be compared and contrasted, and, by means of curiously connecting fibres, form with it an organic whole, from which modern analysis has developed her surpassing geometry."

"What is man? … What a strange union of matter and mind! A machine for converting material into spiritual force."

"I presume that to the uninitiated the formulae will appear cold and cheerless; but let it be remembered that, like other mathematical formulae, they find their origin in the divine source of all geometry. Whether I shall have the satisfaction of taking part in their exposition, or whether that will remain for some more profound expositor, will be seen in the future."

"Mathematics is the science which draws necessary conclusions."

"The sphere of mathematics is here extended, in accordance with the derivation of its name, to all demonstrative research, so as to include all knowledge strictly capable of dogmatic teaching. Mathematics is not the discoverer of laws, for it is not induction; neither is it the framer of theories, for it is not hypothesis; but it is the judge over both, and it is the arbiter to which each must refer its claims ; and neither law can rule nor theory explain without the sanction of mathematics. It deduces from a law all its consequences, and develops them into the suitable form for comparison with observation, and thereby measures the strength of the argument from observation in favor of a proposed law or of a proposed form of application of a law. Mathematics, under this definition, belongs to every enquiry, moral as well as physical. Even the rules of logic, by which it is rigidly bound, could not be deduced without its aid. The laws of argument admit of simple statement, but they must be curiously transposed before they can be applied to the living speech and verified by, observation."

"The branches of mathematics are as various as the sciences to which they belong, and each subject of physical enquiry has its appropriate mathematics. In every form of material manifestation, there is a corresponding form of human thought, so that the human mind is as wide in its range of thought as the physical universe in which it thinks."

"All relations are either qualitative or quantitative. Qualitative relations can be considered by themselves without regard to quantity. The algebra of such enquiries may be called logical algebra, of which a fine example is given by Boole. Quantitative relations may also be considered by themselves without regard to quality. They belong to arithmetic, and the corresponding algebra is the common or arithmetical algebra. In all other algebras both relations must be combined, and the algebra must conform to the character of the relations."

"There are many cases of these algebras which may obviously be combined into natural classes, but the consideration of this portion of the subject will be reserved to subsequent researches."