One of life’s most fundamental revelations is change. Presenting the fascinating view that pattern is the manifestation of change, this unique book explores the science, mathematics, and philosophy of change and the ways in which they have come to inform our understanding of the world. Through discussions on chance and determinism, symmetry and invariance, information and entropy, quantum theory and paradox, the authors trace the history of science and bridge the gaps between mathematical, physical, and philosophical perspectives. Change as a foundational concept is deeply rooted in ancient Chinese thought, and this perspective is integrated into the narrative throughout, providing philosophical counterpoints to customary Western thought. Ultimately, this is a book about ideas. Intended for a wide audience, not so much as a book of answers, but rather an introduction to new ways of viewing the world.

One of life’s most fundamental revelations is change. Presenting the fascinating view that pattern is the manifestation of change, this unique book explores the science, mathematics, and philosophy of change and the ways in which they have come to inform our understanding of the world. Through discussions on chance and determinism, symmetry and invariance, information and entropy, quantum theory and paradox, the authors trace the history of science and bridge the gaps between mathematical, physical, and philosophical perspectives. Change as a foundational concept is deeply rooted in ancient Chinese thought, and this perspective is integrated into the narrative throughout, providing philosophical counterpoints to customary Western thought. Ultimately, this is a book about ideas. Intended for a wide audience, not so much as a book of answers, but rather an introduction to new ways of viewing the world.

One of life’s most fundamental revelations is change. Presenting the fascinating view that pattern is the manifestation of change, this unique book explores the science, mathematics, and philosophy of change and the ways in which they have come to inform our understanding of the world. Through discussions on chance and determinism, symmetry and invariance, information and entropy, quantum theory and paradox, the authors trace the history of science and bridge the gaps between mathematical, physical, and philosophical perspectives. Change as a foundational concept is deeply rooted in ancient Chinese thought, and this perspective is integrated into the narrative throughout, providing philosophical counterpoints to customary Western thought. Ultimately, this is a book about ideas. Intended for a wide audience, not so much as a book of answers, but rather an introduction to new ways of viewing the world.

One of life’s most fundamental revelations is change. Presenting the fascinating view that pattern is the manifestation of change, this unique book explores the science, mathematics, and philosophy of change and the ways in which they have come to inform our understanding of the world. Through discussions on chance and determinism, symmetry and invariance, information and entropy, quantum theory and paradox, the authors trace the history of science and bridge the gaps between mathematical, physical, and philosophical perspectives. Change as a foundational concept is deeply rooted in ancient Chinese thought, and this perspective is integrated into the narrative throughout, providing philosophical counterpoints to customary Western thought. Ultimately, this is a book about ideas. Intended for a wide audience, not so much as a book of answers, but rather an introduction to new ways of viewing the world.

One of life’s most fundamental revelations is change. Presenting the fascinating view that pattern is the manifestation of change, this unique book explores the science, mathematics, and philosophy of change and the ways in which they have come to inform our understanding of the world. Through discussions on chance and determinism, symmetry and invariance, information and entropy, quantum theory and paradox, the authors trace the history of science and bridge the gaps between mathematical, physical, and philosophical perspectives. Change as a foundational concept is deeply rooted in ancient Chinese thought, and this perspective is integrated into the narrative throughout, providing philosophical counterpoints to customary Western thought. Ultimately, this is a book about ideas. Intended for a wide audience, not so much as a book of answers, but rather an introduction to new ways of viewing the world.

Elizabeth Monroe, married Boggs (1913−1996), trained as a mathematician at Bryn Mawr, as a mathematical chemist at Cambridge, and as a theoretical chemist at Cornell, before joining the Manhattan Project at the Explosives Research Laboratory. Although her contributions to the fields of computational quantum chemistry, statistical mechanics, and explosives had lasting legacies, her scientific career nevertheless ended with World War II. The birth of her son, who suffered from severe developmental disabilities, prevented her from ever rejoining the research workforce. She pivoted instead to a remarkable life of public advocacy for people with disability, building on her scientific training to move research and policy forward. This chapters retraces how Monroe Boggs went from an early quantum chemistry enthusiast to a key figure of the disability rights movement.

In 1896, Edward Charles Pickering, Director of the Harvard College Observatory (HCO), reported in a trio of publications on the observation of “peculiar spectra” of the southern star ζ Puppis, which he attributed to an “element not yet found in other stars or on earth.” Supported by laboratory spectra obtained by Alfred Fowler, Niels Bohr showed in 1913 that this “element” was ionized helium. Its spectrum has become known as the Pickering series, even though Pickering credited Williamina Fleming (1857−1911), one of HCO’s “computers” and the future curator of the Astronomical Photographic Glass Plate Collection, for the discovery. The series of spectral lines associated with Pickering’s name played a unique role on the path to quantum mechanics,serving as a proving ground for Bohr’s model of the atom. Our examination of the discovery of the Pickering series relied on the records held at the Center for Astrophysics | Harvard & Smithsonian, especially the notebooks and diaries of Fleming, and on the center’s glass plate collection. Glimpses of the “peculiar sociology” of a research institution, half of whose staff were women employed on grossly unequal terms with men, are also given.

This chapter examines the contributions to quantum physics made by Lídia Salgueiro (1917–2009) and a team of women researchers at the Laboratory of Physics of the University of Lisbon. Between 1929 and 1947, the Lisbon laboratory rose to prominence as a successful research school in atomic and nuclear physics. The 1947 political purge by the dictatorial regime of the Estado Novo, however, led to a drastic reorganization, including the ousting of one of its leaders, Manuel Valadares. The right-wing physicist Julio Palacios was then appointed director. We here analyze how these institutional changes impacted Salgueiro’s agency. While Palacios opted for a new research agenda on electrochemistry, Salgueiro and women researchers gathered around her took responsibility for continuing research along the lines previously set up by Valadares. This group of women successfully extended their research into quantum physics to the study of radiation emitted at the atomic and nuclear levels, with a particular emphasis on X-ray spectroscopy. They asserted themselves as a relevant group within the Portuguese emerging research community in the field, participating in the many avenues asserting experimental atomic and nuclear physics on a global scale.

Spanish physicist Maria Lluïsa Canut (1924–2005) specialized in the application of X-ray diffraction to the determination of molecular crystal structures, a field at the intersection of crystallography and quantum mechanics. She completed her PhD at the University of Barcelona under the supervision of José Luís Amorós (1920–2001). After becoming a couple, the two developed joint research projects. In the 1960s, they moved to Southern Illinois University, where she notably built computing programs to analyze molecular structures from X-ray diffraction patterns. In parallel, Canut became involved in the struggle for pay parity at the university. This participation in the US second feminist wave sparked her interest in science policy. After the couple moved back to Madrid in the 1970s, Amorós continued with crystallographic research, whereas Canut became involved in American–Spanish scientific cooperation and computing systems applied to university libraries. This chapter analyzes Canut’s scientific contributions against the backdrop of her gender and across the changing contexts of her career, including the role played by scientific couples in the research enterprise.

In 1925, as matrix mechanics was taking shape, Lucy Mensing (1901−1995), who earned her PhD with Lenz and Pauli in Hamburg, came to Göttingen as a postdoc. She was the first to apply matrix mechanics to diatomic molecules, using the new rules for the quantization of angular momentum. As a byproduct, she showed that orbital angular momentum can only take integer values. Impressed by this contribution, Pauli invited her to collaborate on the susceptibility of gases. She then went to Tübingen, where many of the spectroscopic data were obtained that drove the transition from the old to the new quantum theory. It is hard to imagine better places to be in those years for young quantum physicists trying to make a name for themselves. This chapter describes these promising early stages of Mensing’s career and asks why she gave it up three years in. We argue that it was not getting married and having children that forced Lucy Mensing, now Lucy Schütz, out of physics, but the other way around. Frustration about her own research in Tübingen and about the prevailing male-dominated climate in physics led her to choose family over career.

The first four women to obtain a PhD in physics at Leiden University all graduated with Nobel laureate Hendrik Lorentz, among them Hendrika Johanna (Jo) van Leeuwen (1887−1974). She and her younger sister Cornelia (Nel) van Leeuwen finished their undergraduate studies in physics in Leiden in the early twentieth century. Whereas the younger sister left physics in 1917 after a relatively short period as a graduate student, Jo van Leeuwen went on to earn a PhD in 1919. Her thesis elucidates that magnetism is exclusively a quantum phenomenon – a result that was independently also obtained by Niels Bohr and that is now commonly known as the Bohr–van Leeuwen theorem. From 1920 onwards Van Leeuwen worked at the Technische Hoogeschool in Delft (now Delft University of Technology). Initially serving as an assistant, she was appointed as a reader in theoretical and applied physics in 1947, becoming the first female reader in Delft. This chapter outlines the foray into physics by the two sisters, focusing specifically on Jo van Leeuwen, detailing her work and early contributions to the quantum theory of magnetism.