A Black Life in Physics [1]

by George Campbell Jr., President Emeritus, The Cooper Union for the Advancement of Science and Art


In 1876, Edward Bouchet received a Ph.D. in physics from Yale University. Just two years earlier, he had graduated Summa Cum Laude and Phi Beta Kappa, also from Yale, with a bachelor’s degree in physics. His remarkable academic success and substantial early contributions to research as a graduate student suggested a promising future in physics. Except for one thing. Edward Bouchet was Black. Bouchet’s doctorate was, in fact, the first-ever Ph.D. awarded to an African American by an American university in any field. Initially intent on a research career after graduation, Bouchet could find a job only at the Institute for Colored Youth in Philadelphia. At the pinnacle of his career, his last job, he served as principal of a high school in Ohio. [2]

The tragic story of Edward Bouchet’s life is not a surprise to anyone familiar with American history. It is, nevertheless, noteworthy that physics was the first profession to allow penetration of the previously impervious barrier to education for Black people. This was just before the dawn of the twentieth century when the development of relativity and quantum mechanics, fundamental breakthroughs in physics, created an authentic Kuhnian paradigm shift. Physicists in this emerging era of enlightenment were steeped in the pursuit of objective truth. It might, therefore, have been natural at that time to anticipate a leadership role for physics in breaking down the irrational, obsessive American practice of racial exclusion.

It was not to be. In fact, a half century later, the decidedly unscientific voice of William Shockley, a Bell Labs physicist who had shared the Nobel Prize for the invention of the transistor, used his prestigious, highly visible platform to promote a thinly veiled hypothesis of white supremacy. From the day that Bouchet received his Ph.D. almost a full century would go by—coincidentally, until the time I was in graduate school—before the doors to an advanced physics degree and to a career in physics would slowly begin to creak open. While I was a graduate student, the average annual number of physics doctorates received by African Americans in the United States was seven out of a total of about 1,000 awarded. During the more than 40 years since, considerable resources spent by private philanthropy, the National Science Foundation, the National Academies, Congress and others have been devoted to improving access to education and careers in science for minorities. Most of the resources were distributed to a multitude of colleges, universities, and a cottage industry of minority programs. The undertakings have been piecemeal, uncoordinated, incoherent; and no one entity has ever had enough resources to move the needle alone.

A substantial fraction of the finances was dedicated to conducting studies aimed at determining the best strategies and corrective measures, deciphering what the data tells us, uncovering what works and what doesn’t. There now have been enough studies to populate a moderately sized library. I have frequently suggested to funding sources that current resources would better serve the goal of equity if they were devoted to taking action based on knowledge we have already accumulated. In the annals of education research we have copious examples of successful practices and strategies to overcome the gaps in educational opportunities and professional development of minorities. NACME, Inc., the National Action Council for Minorities in Engineering, which I had the honor of leading during the 1990s, is a non-profit organization that began at the National Academy of Engineering in 1971 to address the underrepresentation of minorities in engineering. It was funded by a coalition of private philanthropy, led by the Sloan Foundation and the nation’s largest technology-intensive corporations. Its board was comprised of Chief Executive Officers of those corporations, several university presidents and president of the National Academy of Engineering. Over the years, NACME conducted several financial studies, yielding compelling recommendations and outlining the amount of financial programmatic resources required to achieve equity. Collective funding from all sources to all relevant programs has never reached more than 20 percent of what was recommended. Of course, with a serious commitment to the mission, the founding organizations could easily have fully supported the effort.

George Campbell Jr.
George Campbell Jr.

While in some disciplines, there has been measurable, though marginal progress, the bottom line in physics is that in 2017, the number of Ph.D.s awarded to African Americans in the U.S. was 14 out of 2,000, the identical proportion as in the 1970s. We have made virtually no progress toward racial inclusiveness over the last half century. We have not embraced the considerable talents, creative energy and abilities underrepresented and underdeveloped in the field. Rectifying this historical pattern would substantially enhance and enrich scientific advancement in this country. Resounding studies have shown that diverse groups of professionals devoid of racial hang-ups working in collaboration have considerably higher performance potential than heterogeneous groups. [3]

Over the course of my career at one time or another, I have been intensely engaged with the entire educational pipeline. I have worked both in academia and industry, and in what follows, I will share some of the insights I have gained into what strategies are effective in eliminating impediments to education and career advancement in the sciences for African Americans.

The Corporate Sector

During my early physics career at Bell Laboratories, I suggested to a colleague, another distinguished Nobel Laureate—not of the Shockley disposition, but a very thoughtful physicist who cared about issues of equity—that the company should be putting a greater effort into identifying, recruiting and hiring Black physicists. His very sincere response was, “Anybody in the country who is capable of doing what we do here at Bell Labs is bound to eventually come to our attention, so we don’t have to go out beating the bushes.” What he was missing was that the opportunities for young Black scientists to demonstrate their capabilities both as students and as professionals were extremely limited as a consequence of the still prevalent social structures encumbered by racial bias. To be fair, Bell Laboratories did have among the nation’s most successful scholarship and fellowship programs in the sciences—essentially growing our own—and at one time employed almost one half of all Black Ph.D. physicists in the United States. Equally important, Bell Labs was a pioneer in developing and delivering innovative, hard-hitting programs to educate managers about cultural and structural biases inherited from centuries of ill treatment of Black people. 

One such program that began in the 1970s was called the Urban Minorities Workshop. After going through a developmental phase, the top executives at Bell Labs went through the Workshop and decided to make it a requirement for all new managers. The one-week Workshop thoroughly immersed participants in the Black experience. There were tours of depressed Black neighborhoods in Newark, NJ and visits with civil rights and other community organizations. More importantly, the Workshop confronted participants with their conscious and unconscious biases, latent and overt racial attitudes and learned instinctive assumptions and behaviors toward Black people. 

Most white managers came into the program with little or no experience interacting with African Americans either socially or professionally, without having ever given much thought to racial issues and largely ignorant of America’s history of oppressive treatment of African Americans. This was not surprising. Very few Americans then and now were well educated with respect to the history of the African American experience in the United States. It remains virtually impossible to this day to find a public or private school K-12 curriculum that includes more than a perfunctory mention of slavery or any mention whatsoever of its successor policies and outcomes—Jim Crow laws legalizing segregation, de facto legalized lynching, voter suppression, mass incarceration, economic inequities, wealth disparities and daily mistreatment, racial discrimination and systemic police brutality against African Americans. Few, if any, had any inkling of how different the Black experience is from other ethnic groups in the United States. 

I’m reminded of a conversation I had with a senior executive of AT&T in the 1970s, during my time at Bell Laboratories. I recounted a then-recent experience with the police, when two officers accosted me on my front lawn, with guns in my face. I was apparently “suspicious” to them while immersed in and tending to my shrubs. The executive’s honest and understandably incredulous reply was, “Surely you weren’t concerned for your safety in the moment. After all, they were police officers holding the guns!” For him, it was unfathomable that a police officer might have posed a danger to an innocent person. This had to be an example of a simple mistake that had nothing to do with race, a “single isolated incidence.”

Beyond the anecdotal, it would have been rare for any of the Bell Labs managers to encounter any rigorous historical academic treatment of these matters. In any case, the managers universally rejected responsibility for America’s history of oppressive policies. After all, they had taken no part in slavery, in lynching or other such practices. Up to that point, they had undergone no conscious intellectual engagement with the benefits of what we now call white privilege, which the Urban Minorities Workshop brought to the fore. Led by three young Black urban professionals, the program was raw, hard-hitting, contentious, dissonant. Black managers, too, were not spared confrontation in the Workshop. They, too, were prodded over lifestyles that afforded them, at least in part, those privileges conferred by economic class not available to the majority of African Americans. 

After several years, there had developed a critical mass of white managers who had been outraged by the Urban Minorities Workshop experience, and who petitioned the company to eliminate it. They felt ambushed, coerced, abused and belittled in the program. To some extent that was part of the design—to expose them briefly to the ignominies that are all too common for Black people. Admittedly, a less caustic, more amiable approach may have found greater acceptance. However, the managers’ rebellion was also consistent with a long standing American pattern of resistance to the nation’s history with respect to race, a resistance to change. Ultimately, under threat of legal action, the company capitulated and abandoned the Workshop. Nevertheless, throughout the corporate sector, the need remained for a rigorous program to educate the workforce about the history of racism and their own, perhaps passive, role in its perpetuation.

In a broader context, for scientists—or indeed any professional—to flourish, whether in corporate America or in academia, it’s important to know the unwritten, often socially constructed, rules and processes that underpin success. And for Black scientists, it’s important to understand that the rules are different for them relative to their white peers, in much the same way that the criminal justice system works differently for Blacks relative to white citizens. The presumption of innocence does not work the same way. Mistakes are weighed more heavily. Forgiveness is nonexistent. Just as decisiveness among women can be regarded as vitriolic, brilliance among Black scientists can be interpreted as arrogance. Isabel Wilkerson describes these rules as “a subconscious code of instructions for maintaining a 400 year old social order.”[4]

Over the years, I’ve often been called upon to investigate specific issues of diversity at a variety of technology based or research-intensive corporations and institutions: hiring practices, performance evaluation fairness, promotion outcomes, incidences of overt discrimination, cultural biases etc. One detailed longitudinal study of an annual review process uncovered particularly interesting insights. It’s worth noting that the specific company’s process was, on the surface, exceptionally rigorous, objective and fair. The contributions of each member of the scientific staff was discussed in detail with input from a range of managers beyond the direct supervision. An immediate observation was that there was a marked difference in the first projects approved or assigned to the new Black scientist relative to peers with virtually identical academic backgrounds, reflecting a clear difference in expectations or level of confidence. 

The conduct of science is inherently collaborative, but ignoring the possibility of overt racism, there is an enduring discomfort interacting across ethnic boundaries. Consequently, white managers, perhaps unconsciously, were often not forthcoming in communicating crucial information to Black scientists. Beyond inhibiting the work, this substantially impacted the extent to which those scientists acquired knowledge of the company’s unwritten rules, strategic objectives, policies and practices. Supervisors, too, were less candid in communicating performance rankings, whether positive or negative. Informal mentoring was less available to the Black scientist. While risk-taking and creativity are nurtured in a healthy scientific culture, risk aversion is almost necessary for Black scientists to survive. The evidence demonstrates that, for them, deviation from the norm is less acceptable by their managers, and a failed project is virtually impossible to overcome. 

Later in the Black scientists’ career, whatever exceptional performance and expertise they have achieved, when entering a new environment, a new organization, they must over and over again re-earn the reputation, the respect and acknowledgement even of competency that routinely accrues to high achieving scientists of other ethnicities. As a manager or leader, climbing the career ladder, Black scientists encounter the, often unconscious, psychological resistance to his or her leadership. This leads to behaviors that undermine or outright sabotage their decisions and their success. The Black scientist is subjected to the invisibility and ever present microaggressions that are well-documented throughout the literature on race relations. A quote from Toni Morrison captures one consequence of racism on the professional:

…the very serious function of racism is distraction.
It keeps you from doing your work. It keeps you explaining,
over and over again, your reason for being. [5] 

The ultimate outcome I found in studying the annual review process was, for white scientists, the usual normal distribution. Black scientists, on the other hand, exhibited a distinctively bifurcated distribution, with one mean at the low end of the overall distribution and the other mean at the very high end. After much sifting of the data, enhanced by personal interviews with managers, it became clear that the Black scientist who did not quickly get anointed as a superstar entered a rapidly spiraling decline. The non-superstar Black scientist did not get well supported financially and otherwise, did not get opportunities to work on high profile, high visibility projects, did not get access to leadership in the company. Settling in the middle of the rankings was not a possibility.


Access to a physics career begins well before college with considerably greater preparation and prerequisite courses than for most other disciplines. For the typical Black precollege student in this country, this presents a considerable access barrier. It is well known that public schools in Black communities typically are woefully deficient in science and mathematics. In the small proportion of high schools in those communities that offer college preparatory mathematics and science courses, those who teach them frequently do not have even the minimum qualifications to carry out their assignments. 

Looking at the pipeline from a broad perspective, we can incontrovertibly assume that among the approximately two million African Americans in underperforming high schools there are thousands of students who would have exceptional potential, if only given the necessary educational opportunity. NACME programs during the 1990s developed highly successful methods for identifying those high potential students, ignoring traditional measures. We know, for example, that measures, such as standardized tests, are artificial, largely reflective of family income and educational experience. The programs also demonstrated that intervention, exposing these students to exciting ideas in physics, providing intense accelerated college preparation in the mathematics and science “gatekeeper courses” can overcome the gaps in their earlier educational experience. Adequate financial support for college is also essential. The NACME program that took on students with triple digit combined SAT scores and marginal GPAs produced graduates from top ranked engineering colleges with 3.5 to 4.0 GPAs.

Throughout the academic pipeline, from precollege student through professional academic careers, Blacks have experiences similar to those discussed above in corporations. Assumptions about academic potential are made about students based on the color of their skin. At a prestigious private school, in eighth grade, my oldest son was placed in the lowest level mathematics course offered, despite having been selected through national competition for the prestigious Johns Hopkins Gifted Mathematics Program. Reviewing his homework assignments, I recognized immediately the misalignment and intervened to get him properly placed at his school. He wound up getting a degree in mathematics at Swarthmore College when he was 19 years old, solved a famous unsolved problem in number theory while a graduate student, and is now a professor of mathematics and Provost at a major university. This experience begs the question, how many exceptionally capable young Black boys who don’t have a parent proficient in mathematics get inappropriately channeled out of the possibility of a scientific career very early because of race-based decisions. 

As aspiring Black physicists progress through college and graduate school and into an academic career, they are typically immersed in a community that has no other Blacks. Their career paths are wholly reliant on those from other ethnic groups to judge their work equitably without prejudice. But faculty members, peers, university leaders are subject to the same conscious and unconscious biases found among corporate managers. They too are bereft of understanding of the history of the Black experience in America and of white privilege. They too could benefit from the kinds of educational experiences and training necessary to become “antiracist.” Being an antiracist demands more than intellectual acceptance of abstract principles of social justice, equity and equal opportunity. It demands proactive behaviors that expunge deeply ingrained racist behaviors and proactive refutation of white privilege.


On a personal level, as a Black physicist who has had what might retrospectively look like an enviable career, I have been asked what I could possibly have to complain about. Life is difficult. Everyone has problems of one sort or another. The truth is that the opportunities that I’ve had—getting a great education in physics; then in the 1970s and 1980s, working at what was then one of the world’s premiere research and development enterprises; in the 1990s, closely collaborating with the CEO’s and other senior executives of the nation’s most prominent technology-based corporations and research entities to formulate policies to advance the equity agenda; then ascending to the highest level in academia, as president for eleven years of The Cooper Union, then one of the nation’s top three specialized colleges—have been all I could have dreamed of growing up as a Black male under segregated conditions in the 1950s and early 1960s. My career as a physicist and subsequently as a manager and leader in the scientific field has been enormously satisfying. I have personally been fortunate enough to have had a great many physicist friends and colleagues of all ethnic backgrounds—Black, white, Latinx, Asian and others—faculty members, peers, leaders in the scientific community, university administrators and board members to thank for their unbridled support and confidence as I traversed my career. But my personal history notwithstanding, systemic barriers remain, and those barriers intercept success from K-12 through college, graduate school and the workplace. Those barriers have prevented the physics community from making any meaningful progress in the fifty years since the end of legal segregation. 

To be clear, the goal is equitable—not preferential—treatment. I’ve often heard the argument from white colleagues: “Why should my neighbor’s family get any special acknowledgement for being Black. They live in a nice house, their earnings are equivalent to mine, they have all the same privileges that my family has.” What this argument misses is that, in this country, skin color trumps socio-economic status. Even as a college president, I was never immune to the external racist forces that are deeply ingrained in our society. When driving with my three sons, we became four Black men in a car, automatically seen by police and, in certain neighborhoods, by residents, as suspicious, there for nefarious purposes. I will invariably be pulled over, and usually not politely. We are ordered to get out of the car and put our hands on the roof while they approach with weapons drawn. I venture a guess that not many of my fellow college presidents who are white have suffered such indignities or, indeed, as we all have come to realize now, serious risks of bodily harm, including death.

 In the wake of the George Floyd murder, it has often been suggested that the mushrooming examples of police brutality and aggression are recent phenomena due to the increased militarization of urban police forces or the presence of a few “bad apples.” The truth is that the only thing that is recent is the undeniable evidence resulting from the presence of cell phone cameras, CCTV and other video sources. The inequities are deeply rooted in our culture; the violence against Blacks is systemic in police culture and always has been. Even Black police officers are indoctrinated into that culture.

However, as the unequivocal evidence of white privilege and systemic mistreatment of Black people have recently emerged, there appears to be a renewed vigor to right the wrongs in this country with respect to race. Many young whites are accepting the evidence and acknowledging the reality of white privilege.  While some efforts that appear responsive to a moral imperative are merely commercial ventures to advance a profit agenda, there has been an unprecedented commitment of philanthropy and other capital investments to reduce the economic inequities in our systems. Various government entities, corporations and other pillars of our society are contemplating, if not enacting, sweeping policies to modify policing practices and to embrace diversity in all its dimensions.

I’m, of course, mindful of the exhilarating hopefulness we experienced in 1964 and 1965 following the passage of the Civil Rights Act and the Voting Rights Act, a hopefulness seen also following the Emancipation Proclamation (and, in Texas, Juneteenth), during Reconstruction, following the 13th, 14th, 15th, 19th, 24th and 26th Amendments to the U.S. Constitution, following Great Migration, following the Brown v. Board of Education Supreme Court decision, following the election of Barack Obama. I’m mindful that each the joyful moments was followed by a feverish backlash by “conservatives” to reclaim the prior conditions, severely moderating the anticipated progress. The relentless, persistent, cyclical history notwithstanding, I am going to allow myself to believe that the current generation is more enlightened and, through modern technology, more informed, than those of the past. I’m going to allow myself at this moment in the great American experiment, to exult in a hopeful optimism for the future of our nation. I’m going to allow myself to believe that we in the physics community will seize this moment of heightened consciousness to lower the barriers to access and reduce the impediments to career advancement for African Americans. With an honest commitment to change, I know that we can finally begin to make progress towards genuine equity in physics. We can recapture the 19th century promise we saw in Edward Bouchet’s achievements.

Notes and References

[1] The Introduction is adapted and updated from G. Campbell Jr., “United States Demographics” and “Critical Issues,” essays in Access Denied: Race, Ethnicity and the Scientific Enterprise,  eds. G. Campbell Jr., R. Denes and C. Morrison, Oxford University Press, 2000.

[2] Ronald E. Mickens. “Bouchet and Imes: First Black Physicists,” in A. M. Johnson, ed., Proceedings of the 12th Annual Meeting and 16th Day of Scientific Lectures of the National Society of Black Physicists, pp. 1-14, National Scoiety of Black Physicists, 1989.

[3] See, for example, Vivian Hunt, Dennis Layton, and Sara Prince. “Why diversity matters,” McKinsey & Co., January, 2015; or J.J. DiStefano and M.L. Maznevski, Effective management of diversity: A theoretical model with empirical evidence. Presented at the American Association for the Advancement of Science Annual Meeting, 1994.

[4] Isabel Wilkerson. “America’s Enduring Racial Caste System,” The New York Times Magazine, July 5, 2020

[5] Toni Morrison, “A Humanistic View.” Speech delivered at Portland State University, May 30, 1975

The Roles of SIR Mathematical Models in Epidemiology [1]

by Ronald E. Mickens, Department of Physics, and Talitha M. Washington, Department of Mathematics, Clark Atlanta University

Abstract: Many human-based diseases are analyzed using so-called SIR mathematical models. Our major goals are to examine the structure of these models, discuss what useful information can be derived from them, and indicate how they may be used to make general predictions on the possible courses of the associated diseases when particular types of actions are taken. We conclude that the simplest SIR models are valuable as tools for deriving critical qualitative features of the spread of disease. Various issues are also considered relative to the successes and failings of these models.


Currently, October 2020, the world is engaged in a pandemic caused by “severe acute respiratory syndrome coronavirus-2”, better known as ARS-CoV-2 [2]. This not previously seen disease in humans can spread easily from person to person. It is estimated that the median time from onset to clinical recovery for mild cases is approximately two weeks and is on the range of 3 to 6 weeks for patients with severe or critical disease [3]. A major non-laboratory tool used to analyze, understand, and predict the course of this disease in humans is mathematical modeling [4]. The most basic of such models is the SIR model where the total population is assumed to be constant is divided into three sub-populations:


susceptible and individuals who are uninfected;


infected individuals who upon contact with susceptible individuals can infect the susceptible;


recovered and/or removed individuals who have either recovered from their infection or have removed themselves by dying, etc.

The task of such models is to predict the trajectory of the epidemic as transitions are made from one population class to another, i.e.,

S(t) → I(t) → R(t).                                              (1)

SIR models are explicitly constructed to provide this information or estimates of it. These results are important since “there is a critical need to understand both the likely number of infections and their time course to inform both public health and health care system responses” [5].

Mathematical modeling is important because we wish to both understand and manipulate the universe, so that predictions can be made of its future states or conditions. Mathematical modeling allows for a partial resolution of this goal. However, different models may, in general,

Talitha Washington and Ronald Mickens

Talitha Washington and Ronald Mickens
(Photo by Talitha Washington)

only allow the probing of different aspects of our original system. Thus, it should be kept in mind that the models are not the actual system. They are abstract mathematical representations of some of its features, the ones (hopefully) of relevance for our needs.

The purposes of this paper are several:

  1. Show the construction of a SIR model where the total population is assumed to be constant. This model consists of three coupled ordinary differential equations and is perhaps the simplest of possible SIR models.
  2. Provide appropriate interpretations of the parameters appearing in the equations and their connection to epidemiology data.
  3. Derive, using elementary mathematics, a number of the significant aspects or features of the solutions.
  4. Give a direct geometrical explanation of the effects of “stay-at-home-orders” and their relaxation.
  5. Provide “an abundance of evidence,” as a consequence of the above results, that a simple SIR differential equation mathematical model allows detailed predictions to be made for all the major qualitative feature for the spread of a disease such as COVID-19.

This paper is organized as follows: In the next section, we present the general methodology for the construction of a SIR mathematical model with the total population constant. Section 3 presents on explicit SIR model and shows how it may be used to calculate quantities such as the conditions necessary for an epidemic to occur, the general time dependent behaviors expected for S(t), I(t), and R(t), and the number of total persons infected. Section 4 gives a geometrical argument to show the consequences of stay-at-home orders. In Section 5, a SIR model, satisfying all the conditions given in Section 2 is presented and discussed briefly. An important aspect of this model is that an exact, explicit solution to it can be calculated. Finally, we summarize our general results in Section 6 and briefly indicate how the simple SIR model can be generalized to include an exposed, but not infectious population class, how to include vaccination, and how to model vaccination with limited immunity.

Methodology of SIR Models

The most elementary SIR models are based on certain (simplistic) assumptions [6, 7]:

  1. The total population is composed of only three sub-populations, i.e., susceptibles, S(t); infected, I(t); and recovered, R(t). Susceptibles are uninfected and susceptible to the disease; the infected population is, by definition, infected and they can in turn infect susceptibles; and recovered individuals have recovered from the disease and are now immune to re-infection.
  2. The total population is taken to be constant, i.e.,

    (t) + I(t) + R(t) = N = constant.                                 (2)

    This constraint means that over the time interval for which the model is relevant, the birth and death rates are equal.

  3. It is assumed that there is homogeneous mixing of the three populations. This means that all individuals in the total population have exactly the same probability of coming into contact with each other and interacting [5]. Further, it is assumed that the disease can be transmitted between any two individuals regardless of their location and age.

The explicit construction of a SIR model begins when a framework is formulated for determining how the three populations transfer from one population to another; see Eq. 1. For our purposes, we use the scheme where


T1(S I) = transition rate from the S population to the I population,

T2(I R) = transition rate from the I population to the R population.

Note that adding Eqs. 3 through 5 gives 

which is equivalent to the result expressed in Eq. 2. Also, observe the placement of the negative signs in Eqs. 4 and 5. This convention allows us to define the transition functions to be non-negative, i.e.,

T1(S I) > 0, T2(I R) > 0, S > 0, I > 0.                              (8)

So what about the mathematical structure of T1(S I) and T2(I R)? To be definitive in what follows, we will only examine deterministic, ordinary differential equation models and doing this gives for Eqs. 3 to 5 the three coupled equations

This particular structure is easy to understand. First, take the transition rate functions, T1 and T2, to be non-negative. It follows that there must be a negative sign on the right-side of Eq. 9 since each S that gets infected gets transferred into the I-population. Thus, the S-population decreases and the I-population increases. Similarly, the first term on the right-side of Eq. 10 corresponds to additions to the I-population coming from newly infected members of the S-population. The second term on the right-side of Eq. 10 represents those members of the I-population that have recovered from the disease and now get transferred to the R-population.

A deep, careful consideration of the general dynamics of the systems to be modeled by an SIR representation allows us to conclude that the simplest transition functions must have the following mathematical properties:

T1(S → I) ≡ T1(S,I)

  1. T1(S,I) > 0, for S > 0, I > 0;
  2. T1(0,I) = T1(S,0) = 0;
  3. T1(S,I) is a monotonic increasing function of S and I.

T2(I R) ≡ T2(I)

  1. T2(I) > 0, for I > 0;
  2. T2(0) = 0;
  3. T2(I) is a monotonic increasing function of I.

T1(S1,I) and T2(I) indicate that the respective transition amplitudes are functions of S and I, and I. There are many possible selections of functions T1(S,I) and T2(I) which satisfy these restrictions. The papers of Korobeinikov and Maini [9], and Hethcote and Driessche [8] provide some choices.

Standard SIR Model

The standard, most used, SIR model is constructed using the following choices for the transition functions [6, 7]


The β and γ are constant parameters and are usually interpreted as being related to important aspects of the progression of the disease as seen in the following argument.

The left-hand sides of Eqs. 13 to 15 have the physical units of populations number over unit time. Therefore, all the right-hand side terms must also have these physical units. Examination of T1(S,I) and T2(I) allows the conclusion that the two parameters, β and γ, have the physical unit of inverse time. From this result, they are then given the interpretations

tc = 1/β = average time between contacts of the S and I populations,

tr = 1/ γ = average time a member of the infected population stays infected, and then gets transferred to the removed population.

It is important to observe that Eqs. 13 and 14 do not involve R. A major consequence of this fact is that in the analysis of this SIR system of equations only Eqs. 13 and 14 need to be considered since R can be determined from Eq. 2, i.e., R = N S I.

Note that the equation for dI/dt can be algebraically manipulated into the following expression where

Keep in mind the fact that dI/dt > 0 implies that I(t) is increasing, while dI/dt < 0 means that I(t) is decreasing. Also, both S(t) and I(t) are always non-negative. With this information, the following conclusions can be immediately drawn from an examination of Eq. 16:

  1. Let at time t = 0, S(0) = S0 > 0 and I(0) = I0 > 0, with I0 << S0. If S0 > S*, then I(t), for t > 0, initially will increase. But from Eq. 13, S(t) will decrease. At some future time, S(t) will fall below S and I(t) will begin to fall. This situation is depicted in Figure 1(a). For this case, we have a classical epidemic.
  2. For the same initial conditions as in (i), but with S(0) < S, I(t) decreases to zero; see Figure 1(b). No epidemic takes place.

Thus, we are led to the famous threshold theorem of epidemiology [4, 6, 7]. The placement of a single infective in a susceptible population will only initiate an epidemic if the number of susceptibles in larger than a certain threshold value, in our case it is S. Another way of stating this result is to note that this is equivalent to the condition


that the rate at which susceptibles become infectives must be larger than the rate at which infectives are eliminated from the population; see Eq. 16.

An alternative way to proceed is to introduce r0, the so-called “basic reproduction number” [6, 7]. We define r0 as

The parameter r0 plays a fundamental role in SIR based epidemiology and is generally interpreted as the average number of secondary infections caused by the introduction of a single infective individual into a susceptible population. It is easily seen that if r0 > 1, then an epidemic will occur, while for 0 < r0 < 1, the infective population decreases from the start and no epidemic takes place.

The curve of I versus S provides further insights into the dynamics of the SIR model. It can be shown (with just a knowledge of first-year calculus) that the slope of the I(s) versus S curve is given by the expression [6, 7]

and this equation can be integrated to give the result

where S = S(t), I = I(t) and S0 = S(0), I0 = I(0), and R(0) = R0 = 0.

Figure 2 gives a plot of the I versus S curve for two situations: (i) S0 > S, leading to an epidemic; and (ii) S0 < S, for which no epidemic occurs. These two cases correspond, respectively, to whether r0 > 1 or r0 < 1. Note that in terms of time behaviour, the motion along these curves goes from the right to the left sides of the graph and exactly correspond to the plots presented in Figure 1.

For the remainder of this section, only the case of an epidemic will be considered.

Of interest is a determination of Imax, S, and Itotal where



the maximum value of the number of infectives during the course of the epidemic;



the number of susceptibles who do not succumb to the epidemic;



the total number of susceptibles who become infected.

Using Eq. 20, it follows that these quantities are given by the expressions

Note that we are “given” the parameters β and γ, and the total population N, and this allows S to be calculated, see Eq. 17. In addition, the initial numbers of the infectives and susceptibles, i.e., I0 and S0, are also specified. Thus, Imax, S, and Itotal may be determined, respectively, from Eqs. 21, 22, and 23.

Comment: The equation to be solved for S, given in Eq. 22, allows for it to be expressed in terms of a “new elementary function.” the so-called Lambert-W function [10].

In summary, given the elementary SIR model where the parameters β and γ are known, given the size of the total population, N = S0 + I0, it follows that all of the general qualitative features can be determined, and values for Imax, S, and Itotal can be calculated. This realization is important since for this model explicit, exact, close-form solutions do not exist for S(t) and I(t), expressible in terms of a finite combination of the elementary functions.

Flattening the Curve

The curve that is being talked about is the plot of I(t) versus t, i.e., the number of infectives as a function of time, t.

Hospitals generally have a maximum capacity for treating acute illnesses in terms of the number of beds and available care teams. Further, some hospitals and emergency facilities may already be operating close to their maximum capacity under normal circumstances.

If the sharply peaked curve (see Figure 3) could be changed into a broader, flatter, lower curve, lying below the capacity curve of the hospital, then this would help hospitals provide better care for their patients and allow some relief to their emergency care staff. Figure 3 illustrates this situation [11].

Note that what we wish to achieve is a lowering of the total number of cases who are in the hospital at any given time to a number smaller than the maximum capacity and spread them out over a longer period of time [10]. This lowering and spreading can be achieved, in the absence of an actual effective vaccine through the use of physical distancing, stay-at-home orders, the appropriate wearing of face masks and a number of other measures. All of these actions may be characterized as non-pharmaceutical interventions [12].

We now study the consequences of a non-pharmaceutical intervention on the out-

comes of the simple SIR model. This can be done without any new mathematical effort. The purpose of the intervention is to “flatten the curve” and for ease of interpretation and explanation, we consider a stay-at-home order. In the immediate discussion, all of our comments and observations will refer to the curves in Fig. 4.

The initiation of the epidemic is at point 0, where P0 = (S0,I0). The system then evolves to point P1 = (S1,I1) where

S1 < S0, I1 > I0.                                                      (24)

At P1, the stay-at-home order is made and we assume that some fraction of the susceptible population obeys this edict. (The exact value is not important; it just needs to remain constant for the arguments to be valid.) The system now goes from P1 to P2 = (S2,I1), i.e., S changes (decreases) from S1 to S2, with S2 < S1, but the number of infectives remains constant at the value I1.

At P2, the SIR system evolves in the usual manner, with S(t) steadily decreasing to the value S(1), and I(t), at first increasing to a peak and then decreasing to zero. A close inspection of Figure 4, allows the following conclusions to be made:

  1. The evolution of the system with the stay-at-home order gives a smaller value for the peak number of infectives as compared with having no such order.
  2. Because S(1) > S(0), the total number of infections during the epidemic is reduced with a stay-at-home order.
  3. Since the graphs in Figure 4 do not contain temporal information, we cannot directly show the peak in infectives occurs later for the situation where a stay-at-home order is in place. However, this does turn out to occur [13].

The graphs in Figure 5 illustrate what can happen when a stay-at-home order is released. Assume that the path connecting point 0 (P0) and point 1 (P1) corresponds to a stay-at-home situation. Let the order be released at P1 = (S1,I1). The system now goes to P2 = (S2,I1) and continues along the upper curve. Examining this graph gives the following results:

  1. The second peak in the infective curve is now larger after the stay-at-home order is dropped.
  2. After the epidemic has reached its course, the total infective population is also larger.
  3. In summary, a stay-at-home order, followed by letting the SIR system evolve and then releasing the order may lead to a situation where the second peak and spread of the disease increases. This is due mainly to the sudden infusion of new susceptibles into the population and they can now potentially be infected.

Model with Exact Analytical Solution

It turns out that an SIR model can be constructed satisfying all the requirements in Section 2, such that its explicit solutions may be calculated in terms of a finite combination of the elementary functions, namely, the trigonometric functions [14]. For our purposes, this model takes the form

Note that the total population is constant, i.e.,

and further, only the differential equation involving S(t) and I(t) need be investigated. The transformation gives

a pair of linear, coupled equations which may be easily solved [14]. This model does have the interesting feature that I(t) goes extinct in a finite time. See Mickens [14] for the full details.


An important feature of our investigation of the elementary SIR model is that no explicit knowledge of the solutions for S(t) and I(t) are needed to either analyze or understand the essential details of the evolution of these solutions. This means that all of the basic qualitative properties can be determined without the use of advanced mathematical techniques. Further, instances where exact solutions do exist, by means of a proper selection of T1(S,T) and T2(I), these solutions are in full agreement with the expectations obtained from the qualitative investigations. Consequently, we may expect that our modeling process can be applied to actual epidemics even if we only wish to know the various aspects of their major qualitative features as they evolve. Thus, in spite of the fact that we only have incomplete knowledge, there is enough value obtained from the use of these qualitative techniques to help policymakers make certain general but valid decisions to limit disease spread.

Also, it is critical to understand that simple SIR models can be readily generalized to include other components such as adding an exposed class (infected, but not infectious individuals)

the inclusion of vaccination

and putting in limited immunity

As a further complexity, these features can be combined in a mega-model, with time-dependent parameters [4, 6, 7, 12].

Finally, it should be observed that the modeling of the evolution of a disease is not dependent on a mathematical representation by a set of coupled, ordinary differential equations. There are many mathematical structures available for use: continuous versus discrete time, deterministic versus stochastic, qualitative versus quantitative methods, etc. Generally, the particular mathematical structure selected is the choice of the modeler(s). What this article indicates is that even elementary mathematical models can be used to provide important insights into how to limit the spread of disease.

Notes and References

  1. [Editor’s Note: This is an invited contribution, serving as an introduction to epidemic modeling, by two experts – APS Fellow Ronald Mickens and AMS Fellow Talitha Washington.]
  2. World Health Organization (WHO), Coronavirus disease (COVID-19) technical guidance. Accessed at: technical-guidance
  3. Centers for Disease Control and Prevention, Coronavirus disease 2019 (COVID-19), National Center for Immunization and Respiratory Diseases (NCIRD), Division of Viral Diseases. Accessed at:
  4. R.M. Anderson and R.M. May, Infectious Diseases of Humans, Oxford University Press, Oxford, 1991.
  5. J. Tolles and T-B. Luong, Modeling epidemics with compartmental models, Journal of the American Medical Association (JAMA). Vol. 323 (24), June 23/30, 2020, pp. 2515–2516.
  6. H.W. Hethcote, The mathematics of infectious diseases, Society for Industrial and Applied Mathematics Review, Vol. 42 (2000), pp. 599–653.
  7. F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Springer, New York, 2001.
  8. H. Hethcote and P. Driessche, Some epidemiological models with nonlinear incidence, Journal of Mathematical Biology, Vol. 29 (1991), pp. 271–287.
  9. A. Korobeinikov and P. K. Maini, Non-linear incidence and stability of infectious disease modes, Mathematical Medicine and Biology, Vol. 22 (2005), pp. 113–128.
  10. F.W.J. Olver, D.W. Lozier, R.F. Boisvert, and C.W. Clark, editors, NIST handbook of Mathematical Functions, Cambridge University Press, 2010.
  11. K. Gavin, Flattening the curve for COVID-19: What does it mean and how can you help?. Accessed at: flattening-curve-for-covid-19-what-does-it-mean-and-how-can-you-help
  12. C.N. Ngonghala, E. Iboi, S. Eikenberry, M. Scotch, C.R. MacIntyre, M.H. Bonds, and A.B. Gumel, Mathematical assessment of the impact of non-pharmaceutical interventions on curtailing the 2019 novel coronavirus, Mathematical Biosciences, Vol. 325 (July 2020), 108364.
  13. Z. Feng, J.W. Glasser, and A.N. Hill, On the benefits of flattening the curve: A perspective, Mathematical Biosciences, Vol. 326 (August 2020), 108389.
  14. R.E. Mickens, An exactly solvable model for the spread of disease, The College Mathematics Journal, Vol. 43 (2012), pp. 114–121.

      The Other-Worldly Career of Freeman Dyson

      by Phillip F. Schewe

      Freeman Dyson lived the life of ten men. By turns a mathematician, physicist, engineer, anti-nuke crusader, biologist, and writer, he considered himself a futurist. Dyson, who died 28 February 2020 at the age of 96, was especially drawn to the prospective human migration into space. His science background prepared him to weigh the aeronautics and biotech innovations needed; his intellectual curiosity led him to consider the likely ethical and economic implications. 

      Dyson’s ideas on humanity’s deep future made him a popular figure on college campuses and in magazines. What gave his vivid prognostications legitimacy was his proven scientific credibility. With the exception of the Nobel Prize, he won most of the great prizes for physics.  A longtime professor at the Institute for Advanced Study in Princeton, NJ, his most important physics work was in consolidating the theory of quantum electrodynamics.

      Among non-scientists, however, Dyson was better known for his opinions on climate change, rightly one of the most debated political and scientific issues of our time. Appearing on the cover the New York Times magazine in March 2009 in a picture that made him look like a war criminal, he was branded as a “global warming heretic.” Here was Dyson---Obama supporter, disarmament campaigner, nature-loving liberal---saying that leading climate scientists had gotten things wrong.

      Here is a compact summary of Dyson’s views on climate. He didn’t deny that the amount of carbon dioxide in the atmosphere was increasing or that human technology was largely responsible, or that some of the global changes would not be deleterious. He believed, however, that the good might outweigh the bad. Having performed some of the first climate computer modeling in the 1970s, he wasn’t confident enough in current projections to justify the large expense needed to dispense quickly with fossil fuels. He felt that it was better to spend scarce resources on other pressing needs, such as improving education, hygiene, diet, and reducing the threat of future wars.

      Dyson did not enjoy his participation in the climate debate. In the primary years of his research he had much preferred putting his mathematical abilities to practical use in a variety of other areas. For example, he designed the TRIGA nuclear reactor (used to this day) for training and for producing medical isotopes. Through his work with the Jason advisory group, he helped design a method for sharpening images of distant astronomical objects using a computer-controlled, frequently-adjusted set of mirror facets. This “adaptive optics” system is now employed by many of the largest optical telescopes in the world.

      Dyson often claimed to have a short attention span, which obliged him to change research topics frequently. Often he was able to devote a career’s worth of inquiry into just a few numbers of years or even months. For example he helped introduce field theory into condensed matter physics; pioneered the use of random matrices, used in nuclear and solid-state physics; demonstrated mathematically the stability of solid matter; was one the early writers about the possibility that fundamental physical constants might change over time; and wrote the first detailed mathematical study of the very late universe.

      He helped design a rocket ship, called Orion, whose propulsion would be supplied by exploding atom bombs and wrote a stirring manifesto about saving human society on earth by using atom bombs to hoist pioneers into space. Their motto was Saturn by 1970. Although Orion was never built, Stanley Kubrick borrowed some ideas (and filmed an interview with Dyson) as part of preparing for his movie 2001: A Space Odyssey. Dyson’s scientific and engineering knowhow allowed him to envision superior civilizations building immense solar-energy-collecting platforms for tapping stars’ energy. Around 1959 this “Dyson Sphere” idea helped launch the scientific search for extra-terrestrial intelligence and later figured in an episode of Star Trek.

      August 2013, physics meeting in Singapore in honor of Freeman Dyson’s 90th birthday.

      L to R: Lawrence Krauss, Freeman Dyson, Phillip Schewe

      Visionary, yes, but Freeman Dyson always had his feet planted firmly on Earth. Another of his Jason projects was to prepare a 1966 report (long kept classified) which argued against the use of tactical nuclear weapons in the Vietnam war. In 1963, while working at the Arms Control and Disarmament Agency, he participated in crafting the limited nuclear test ban treaty, still in effect to this day, greatly reducing the threat of nuclear war and the amount of radioactive debris in the air. For many years he sought to curb the use of nuclear weapons by persuading (unsuccessfully) the U.S. government to adopt a no-first-use policy.

       Notwithstanding this rich resume, Dyson’s legacy contribution to culture will, I believe, be his social writing in his later decades, conducted mostly in the New York Review of Books, where he confronted precisely those intractable issues---climate change, genetic engineering of humans, and planting colonies in space---that are so expensive to address and politically and technologically complicated to implement as to seem beyond the resources or consensus of any one generation. Dyson specialized in looking at topics about which even like-minded scientists could easily disagree. One prominent example was the subject of genetically modified food, where, he felt, the humanist view (feeding millions) could bump against the environmentalist view (insisting on “natural” ingredients).

      Are we running out of time? Will humans migrate to a place like Jupiter’s moon Europa, with its apparently large volume of sub-surface liquid water? Not any time soon. For right now, Dyson felt, space travel was a joke. It’s too expensive and too bound up with mechanical engineering. True habituation to space would require plants, and then later humans, to adapt to a low-temperature, low-gravity, low-pressure environment. Long before we send humans out into the universe, Dyson argued, we should send small “cosmic eggs,” containing seedlings designed to weather some of those expected hazardous conditions around the solar system.

      Dyson often compared the daunting prospective human migration across the cold emptiness of interplanetary space to the earlier Polynesian translocation into the vast Pacific Ocean. It was essential, he felt, for humans “to escape from their neighbors and from their governments, to go live as they pleased in the wilderness.” For this purpose, he figured, in the long run one world would not be enough.

      Probably even one species won’t be enough.  Like the finches on the Galapagos Islands, Homo sapiens will eventually come to occupy different niches, obliging its inhabitants to splinter into separate species. This, Dyson plainly admitted, was an exciting and scary prospect. The trouble with appraising this oversized vision of humans living on far moons or comets is that none of us now living will be around to see it happen.

      FHP Essay Contest Winners

      by Joseph D. Martin

      The Forum held its fourth annual history of physics essay contest in 2020, and is pleased to recognize a winner and two runners up.

      Garrett Williams, a second-year PhD student in Department of Physics and the Illinois Quantum Information Science and Technology (IQUIST) at the University of Illinois at Urbana-Champaign, won for his essay “Lewis Latimer: The Shadow Behind the Light Bulb.” Williams completed his B.S. dual-degree in Physics and Chemistry at Baylor University in Waco, Texas. His research is in ultracold atomic physics with the goal of investigating novel states of quantum matter for experimental approaches to quantum computing. He enjoys playing the piano and all kinds of formal writing from research-driven works to musical compositions.

      Garrett Williams, graduate student in physics

      at the University of Illinois-Urbana-Champaign

      Hannah Pell, co-runner up for her essay “The ‘Opinion Splitter’: How the Superconducting Super Collider Divided American Physicists,” currently works in science publishing and as a freelance science writer. She is a former Research Assistant for the Center for History of Physics at the American Institute of Physics and an alumna of the Fulbright Program. She earned her B.S. in Physics and B.A. in Music from Lebanon Valley College and her M.A. in Music Theory from the University of Oregon. Her current research interests include science policy and communication with regards to nuclear power, large-scale high energy physics collaborations, and intersections between science and labor history. She has also been appointed to the Citizens Advisory Panel for the Three Mile Island nuclear power plant decommissioning process.

      Hannah Pell, freelance science writer

      John Vastola, whose essay “Who’s Afraid of Max Delbrück?” also earned a co-runner-up award, is a Ph.D. candidate in the Department of Physics and Astronomy at Vanderbilt University. He currently uses theoretical tools from physics to better understand how individual cells regulate how many proteins and RNA of various kinds they have. More broadly, he is interested in asking and trying to answer questions about nature; for example, how do collections of apparently inanimate atoms conspire to form our friends and family?

      John Vastola,

      graduate student in physics at Vanderbilt University

      To see details of the award and to read the essays, visit:

      FHP News

      Coming in 2025:  The Quantum Century

      In 2018 members of FHP leadership met with APS staff and representatives of other APS units to discuss the development of a global celebration and public outreach event to mark 100 years of quantum mechanics in the year 2025 entitled “The Quantum Century.”  The title is meant to reflect not only the potential of this celebration to highlight the theoretical, experimental, technological, and cultural impact of quantum mechanics over the past 100 years, but also the potential for the next 100 years of science and technology to be dominated by quantum-themed developments.  Since the initial meeting, the FHP has gradually built up an international network of over 50 volunteers from over 20 countries with expertise in history of science, outreach, and international coordination to begin long-term planning of the Project.  After a presentation of an outline of the Project to the APS Council in November, more than ¾ of the Councilors polled rated the Project a “high” or “critically high” priority for their respective APS units.  One of the main tasks that the Quantum Century Working Group will pursuing in 2021 will be laying the groundwork for the United Nations to designate 2025 the “International Year of Quantum Mechanics” as has been done previously for other years such as the 2005 “International Year of Physics” and the 2015 “International Year of Light and Light-based Technologies.”  FHP members with diplomatic connections interested in volunteering to help with this aspect of the project can contact Quantum Century Working Group Chair, and FHP Past-Chair, Paul Cadden-Zimansky.

      FHP Executive Committee Election Results (for three-year terms beginning April, 2021)

      • Alberto Martinez, ViceChair
      • Jami Miller, Member-at-Large (senior)
      • Tiffany Nichols, Member-at-Large (early career)

      Report on the April 18 2020 FHP Executive Committee Meeting

      by Dwight E. Neuenschwander, FHP Secretary/Treasurer

      The Executive Committee (EC) meeting was to occur on this day at the APS April Meeting in Washington, DC, but the April Meeting was cancelled due to the Covid-19 pandemic.  Nevertheless, the EC meeting proceeded online at the scheduled time.


      Paul Cadden-Zimansky (Chair)

      Daniel Kennefick (Past Chair)

      Michel H. P. Janssen (Vice Chair)

      Joseph D. Martin (Chair-Elect)

      Paul H. Halpern (Vice Chair-Elect)

      Virginia Trimble (Councilor)

      Melinda Baldwin (Member-At-Large)

      Liu Jinyan (incoming Member-At-Large)

      Katemari D. Rosa (Member-At-Large)

      Douglas Stone (Member-At-Large)

      Chanda Prescod-Weinstein (Member-At-Large)

      Rebecca Ulrich (Member-At-Large)

      Audra J. Wolfe (Member-At-Large)

      Ed Neuenschwander (Secretary/Treasurer)

      Greg Good (AIP Center for History of Physics)

      Robert Crease (outgoing FHP Newsletter editor)

      Don Salisbury (incoming FHP Newsletter editor)

      Brian Schwartz and Smitha Vishveshwara (guests invited to discuss the FHP-sponsored plays)

      The meeting was called to order by the Chair at 2:00 PM EST. Liu Jinyan asked if the Covid-19 upheaval would disrupt the annual $20K that the Forum receives from APS.  At the APS Leadership Convocation of Jan. 29-Feb. 1, everyone was informed that APS has a comfortable surplus, but an official answer to Jinyan’s important question was not known by April 18, 2020.


      For the upcoming election, the FHP needs Vice-Chair and two At-Large candidates, Daniel Kennefick described three sources of nominations: Persons asked to run, self-nominations, and persons nominated by a third party.  Although established physics history scholars have tended to dominate candidate slates, the EC welcomes more diversity.  With the desire to include early career EC members, graduate student who are FHP members are welcome on the slate of candidates.  Virginia Trimble reminded us that, as voted by APS Council, all Units are required to have at least one Early Career or Student member on their executive committee.  Paul Cadden-Zimansky and Audra Wolfe suggested the EC membership strive for half early career and half senior members.  Chandra Prescod-Weinstein commented that deep interest in physics history “coming from the physics side” may be a more important qualification than formal training in the history of physics.  Finalists in the FHP Essay Contest would be a good source of approachable early career candidates.

      Program Committee Report

      The Program Committee Report was presented by Joseph Martin.  The pandemic created the overriding issue: no meetings will go ahead for the duration.  Some sessions have fallen by the wayside for now, but other sessions must be held because of the Pais Prize. Until recently APS allocated to Forums three sessions per meeting, but now a Forum’s number of invited sessions is tied to its number of contributed papers.  APS now uses the session numbers in year N to determine the number of invited sessions for year N+1.  More contributed papers should therefore be encouraged.  Under this new policy FHP lost one session for the March meeting, although the original schedule for April “held steady.” Don Salisbury asked whether the Pais Prize presentation will be delayed. Martin replied “No, but we owe Dieter Hoffman [the 2020 winner] a trip to an APS meeting.” Whether there will be in 2021 two joint Pais Prize presentations, or one at the March meeting and the other at the April meeting, remains to be determined. Trimble asked if FHP had co-sponsors for the Cosmology session. The reply was the Division of Gravitational Physics was “involved,” and the Division of Applied Physics was consulted but “not officially co-sponsors.”

      Councilor’s Report

      As FHP’s representative on the APS Council, Trimble reported that APS is solvent but faces major uncertainties. The Bridge Program is at risk; REU’s are facing increased demand but diminished supply; some graduate students are not able to get international visas before the fall semester (APS has asked Congress to arrange extensions); undergraduates applying to grad schools are uncertain about TA funding. Some grad students face serious struggles even without a pandemic; e.g., in some locations over half of one’s TA salary goes towards rent; in shared apartments both students can be forced out if one loses their job; many dormitories have been closed and some students are reduced to living in their cars. TAs are not always paid through the summer, producing effects that vary from annoying to disastrous. Trimble suggested that returned conference registration fees be moved from the “travel” line in one’s grant budget to the “student support” line. Wolfe commented that students’ economic difficulties do not correlate with resource allocation—"does APS understand what’s  going on?”  Prescod-Weinstein asked if APS advocates for Federal financial bailouts on behalf of higher education. The reply came that APS has had good luck negotiating with Congress, but less so with states.

      Pandemic Challenges

      These woes let to a continuation of pandemic discussion. Salisbury asked how the pandemic has affected FHP’s mission. Wolfe asked about plans for next year’s meetings should the pandemic continue. Salisbury suggested virtual FHP meetings. Trimble remarked how, ironically, the cancelled 2020 April Meeting had more registrants than any other April meeting. Cadden-Zimansky turned the discussion of the pandemic to FHP’s response.  The Forum has about $10K in funding for a project to record the history of the pandemic. Trimble suggested a way be found to let people tell their stories—perhaps a repository for thousand-word essays, analogous to the Oral History interviews archived by the AIP Center for the History of Physics.

      Other Officer Reports

      Cadden-Zimansky reported briefly on the 2020 APS Leadership Convocation, held in Washington D.C. Jan. 29-Feb. 1.  The Convocation’s theme was “APS and the ethics of gender discrimination.”  Neuenschwander then reported on FHP finances.  FHP receives $20K from APS every January.  In 2020 approximately another $2K YTD was received, but as in years past the FHP found itself in December 2019 with a deficit (~$4K) which carries into to the following year as a debit.

      The FHP Newsletter

      Robert Crease has stepped down as editor of the FHP Newsletter, having recently become Chair of his department.  Donald Salisbury is the new editor. He said that upcoming articles will describe FHP events that would have occurred in the March meeting, notifications of what was cancelled or rescheduled, and the announcement of the next Pais Prize award. Cadden-Zimansky announced that the seldom-used newsletter editorial board has been disbanded. Salisbury added that the book review feature still exists and obituaries will be added.

      FHP-Sponsored Plays

      FHP-sponsored plays was the next topic on the agenda.  The plays began in 2013, and four plays have been produced so far. They cost about $5K/yr for actor payments, venue rental, travel for organizers, and publicity. Because the plays consume about a quarter of the FHP annual budget, continuing the program requires EC approval.  There was skepticism expressed about FHP sponsorship in the absence of a  mission statement for the program with clearly articulated objectives. It was suggested that if outreach is the motive for offering he plays, less expensive alternatives exist.  Kennefick spoke up for the plays, saying they make a case for the study of the history of science. Play organizers Brian Schwartz and Smitha Vishveshwara reported that typical attendance is 100-200, consisting mostly of younger people, noting the value of the Q&A sessions following performances. Kennefick remarked that an attendance of 80-100 persons in Unit invited sessions is considered a good turnout. Salisbury observed that by being held in the evenings the plays do not conflict with other APS meeting events. Neuenschwander asked if the plays have been given ample opportunity to show what they could do if they were emphatically supported, musing that one famous play at a physics conference has come down to us, the brilliant spoof “The Copenhagen Faust”, presented at the Bohr Institute in 1932 (Figure 1).

      Figure 1. Images from Thirty Years that Shook Physics by George Gamow. (In the Copenhagen version of Faust, the Task Force responsible turned Faust into Paul Ehrenfest, The Lord was Niels Bohr, Mephistopheles was Wolfgang Pauli, and Gretchen was the neutrino.)

      Schwarz is stepping down from managing the plays, and Vishveshwara will take his place if FHP continues sponsorship. The March 2020 meeting was to have seen a performance of David Cassidy’s “Einstein’s Wife,” but it may be rescheduled for the March 2021 meeting in Nashville and the April meeting in Sacramento. After being temporarily tabled, upon returning to the plays after dealing with other business a motion and vote produced the result that FHP will not discontinue sponsorship, at least not yet, but give the plays a fighting chance by (1) increasing promotional support for the plays, perhaps linking them to a session; (2) delegate to those responsible for the plays the task of drafting a statement of objectives articulating programmatic goals; and (3) collect more data about attendance, audience demographics, etc. Trimble suggested that if the plays are to be open to the general public, they need a presence on social media—APS marketing should be on board.  

      Essay Contest

      This 2019 essay contest saw 17 submissions, more than usual, and the quality of the finalist essays was very good.  The contest offers a venue for discovering graduate students with a passion for the history of physics.  The EC was unanimous in its consensus to continue the essay contest program. Discussion of the essay contest focused on logistical issues, such as: Should the 2500 word limit be reconsidered?  Should the September 1 submission deadline be changed, since that falls so near the beginning of the fall term?  Cadden-Zimansky opined that FHP should be receiving more submissions from grad students in the Science & Society or philosophy communities, in addition to those in physics.  He suggested aiming for a deadline around October 1.  No motion was forthcoming to move the due date or change other rules, but issues were usefully aired that need more data and more thought.

      The Quantum Century Celebration

      The Quantum Century celebration planned for 2025 was the next agenda topic. The APS working group charged with public information on this project is presently in limbo due to staff departures in the public outreach office. Trimble observed that representatives of small countries where developments in quantum mechanics originated (e.g., Denmark) would be the best messengers to take a Quantum Century proposal to UNESCO, adding that international APS Councilors should be involved. Halpern suggested that Quantum Century organizers reach out to the children, grandchildren, and great-grandchildren of the founders of quantum mechanics (someone wondered aloud if Olivia Newton-John, granddaughter of Max Born, would be a constructive celebrity face in the promotion of The Quantum Century). Martin suggested that the FHP approach APS to propose an ad hoc committee to be linked with groups in Copenhagen and other sites where important developments in quantum mechanics occurred, noting that the existence of a committee along such lines would be a prerequisite for moving the Quantum Century celebration forward. Greg Good added that a committee of people representing institutions where quantum mechanics began would “carry weight.” Halpern suggested reaching out to the Carlsburg Brewery[1] and the Solvay organization. It was decided that Cadden-Zimansky would chair FHP’s efforts on the Quantum Century, and that Salisbury and Janssen would also be members of the working group. Ideas are in the air; stay tuned.

      Bylaws Reformation

      The EC also heard from the Bylaws Working Group. Its mission, as discussed at the 2019 EC meeting, was to make suggestions for bringing the FHP Bylaws into coherence with actual practices which have evolved over time. An “operating manual” for procedures as they are actually done is needed. Martin recalled that the EC and FHP relied in the past on the institutional memory of former Secretary/Treasurer Cameron Reed.[2] One item missing in the Bylaws is an articulation of the linkage between the Forum’s Council representative and the Forum’s membership—a way for our Councilor to send questions and requests directly to all FHP members would increase efficiency and remove some burden of going always through the Chair for such communications. It was moved and passed that such a document be produced by the Working Group.

      FHP 🡪 FHPP

      The final agenda topic was addressing the proposed name change of the Forum, from “Forum on History of Physics” to “Forum on History and Philosophy of Physics.”  Motivations for the change include descriptions of how FHP sessions on the foundations of quantum mechanics have inevitably brought in philosophical issues. One member described how, when team-teaching a Philosophy of Science course with a philosophy professor, important topics in the philosophy of science were almost always illustrated with developments in the history of physics. It was moved and passed that the FHP EC approves the name change and that the procedure for carrying it out be taken to the next level of APS.

      Other Business

      Having completed the agenda items, the meeting turned to “other business.”  Martin commented that no one seems to be maintaining the FHP Twitter account anymore. Salisbury asked about the role of an FHP webmaster—“who does it?”  The reply came that APS maintains all APS websites, so the contents of the FHP website goes through them. Trimble reviewed topics arising in this meeting that she would take to Council: (1) inquire about APS support of universities during the pandemic; (2) recommendations that APS be aware of and respond to the effect of Covid-19 on physics grad students; and (3) ask if Forums will receive the usual $20K funding from APS next year. Trimble then moved that the meeting be adjourned, which was greeted with multiple “seconds.”  Meeting adjourned 5:00 PM EST. A splendid time was had by all.


      [1] The Carlsburg Foundation gave substantial help in founding the Bohr Institute in 1921.

      [2] The current  Secretary/Treasurer still keeps warm the lines of communication between he and Cameron. The latter’s mentoring has been oh so helpful.

      March 2021 FHP Sessions

      Monday 3/15 2:30 pm

      Farm Hall Revisited – Mark Walker (Chair), Union College

      • The Drama of Farm Hall, David Cassidy
      • New Light on Farm Hall, Ryan Dahn
      • Farm Hall and Carl Friedrich von Weizsäcker, Dieter Hoffmann
      • Farm Hall: Did Heisenberg Understand How Atomic Bombs Work?, Mark Walker

      Tuesday 3/16 11:15 am

      Materials Science Institutions (Co-sponsored by DMP)– Robert P. Crease (Chair), Stoney Brook University 

      • Overview of History of Materials Research, Arne Hessenbruch
      • TBA, Bernadette Bensaude-Vincent, 
      • From Hidden Utility to Heroic Machines, E. F. Spero
      • TBA, Lynn W. Hobbs
      • History of Materials Science Institutions, Robert P. Crease

      Tuesday 3/16 8:00 am

      The Author in Dialogue: Jeffrey Bub’s Banana World – Michel Janssen (Chair), University of Minnesota

      • The Roots of Information-theoretic interpretations of quantum, mechanics in pragmatism, Leah Henderson
      • Interpreting Quantum Mechanics, Michael E. Cuffaro
      • The Geometry of Correlations from Pearson to Quantum Information Theory, Michael Janas
      • Response to Readers, Jeffrey Bub

      Thursday 3/18 8:00 am

      Pais Prize Session

      April 2021 FHP Sessions

      Saturday 4/17 1:30 pm

      Connecting Science Policy with Science’s History – Melinda Baldwin (Chair), University of Maryland

      • How do Practitioners of Science Policy Integrate History into their Work?, Erin Heath
      • Uneasy Alliances: Consideration of Military Sites by the Laser Interferometer Gravitational-Wave Observatory (LIGO), Tiffany Nichols
      • Science Policy Past and Present: Perspective from AIP’s FYI Bulletin , William Thomas

      Sunday 4/18 8:30 am

      Physics in India – Somaditya Banerjee (Chair), Austin Peay State University

      • Bimla Buti, the First Female Fellow of the Indian National Science Academy, Indianara Silva
      • Disputes about Electric Meters in early-twentieth-century Calcutta, Animesh Chatterjee
      • Bhadralok Physics: Raman, Bose and Others, Somaditya Banerjee

      Monday 4/19 1:30 pm

      Physics and Computation – Samuel Fletcher (Chair), University of Minnestota

      • Computer Simulations and Large-scale Structure Formation, Melissa Jacquart
      • Computer Simulations and Models of Dark Matter and/or Modified Gravity , Eric Winsberg
      • Computer Simulations and Cosmology , Marie Gueguen
      • Computation and Landauer’s Principle, Katherine Robertson

      Monday 4/19 3:30 pm

      FHP Essay Contest Winners

      • Striving for Realism, not for Determinism: Historical Misconceptions on Einstein and Bohm, Flavio Del Santo
      • A Changing Dichotomy: The Conception of the `Macroscopic’ Worlds in the History of Physics, Zhixin Wang
      • Lewis Latimer: The Shadow Behind the Light Bulb, Garrett R. Williams

      Officers and Committees 2020 - 2021

      Forum Officers
      Chair: Paul Joseph D Martin
      Chair-Elect: Michel H P Janssen
      Past Chair: Paul Cadden-Zimansky
      Secretary-Treasurer: Dwight E Neuenschwander

      Forum Councilor
      Virginia Trimble

      Other Executive Board Members
      Melinda Baldwin
      Chanda Prescod-Weinstein
      Katemeri Rosa
      Audra Wolfe
      Gregory Good (AIP)
      Donald Salisbury (newsletter)

      Program Committee
      Michel H P Janssen (chair)
      Paul Cadden-Zimansky
      Joseph D Martin

      Nominating Committee
      Chair: Paul Cadden-Zimansky
      Michel H P Janssen
      Chanda Prescod-Weinstein
      Audra J Wolfe

      Fellowship Committee
      Chair: Paul Helpern
      Peggy Kidwell
      Katemari Rosa

      Pais Prize Committee
      Chair: Helge Kragh
      Melinda Baldwin
      Dieter Hoffmann
      Jinyan Liu
      Gregory Good (ex-officio)

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