Focusing on Menippus’ description of his celestial journey and the great cosmic distances he has travelled, I argue that Icaromenippus is a playful point of reception for mathematical astronomy. Through his acerbic satire, Lucian intervenes in the traditions of cosmology and astronomy to expose how the authority of the most technical of scientific hypotheses can be every bit as precarious as the assertions of philosophy, historiography, or even fiction itself. Provocatively, he draws mathematical astronomy – the work of practitioners such as Archimedes and Aristarchus – into the realm of discourse analysis and pits the authority of science against myth. Icaromenippus therefore warrants a place alongside Plutarch’s On the Face of the Moon and the Aetna poem, other works of the imperial era that explore scientific and mythical explanations in differing ways, and Apuleius’ Apology, which examines the relationship between science and magic. More particularly, Icaromenippus reveals how astronomy could ignite the literary imagination, and how literary works can, in turn, enrich our understanding of scientific thought, inviting us to think about scientific method and communication, the scientific viewpoint, and the role of the body in the domain of perhaps the most incorporeal of the natural sciences, astronomy itself.

This chapter presents new, annotated translations of the testimonia and fragments of Hipparchos of Nikaia (active 162–128 BC), arranged as 46 extracts. The chapter introduction reviews Hipparchos’ wide-ranging and original achievements in mathematics, astronomy, and climatology, his rigorous (but occasionally over-sceptical) criticisms of Eratosthenes’ geographical work, and his development of superior models of climatic zones and latitude. Though not a geographer as such, his advances in the mathematical underpinnings of geography were influential.

The Tokugawa period saw a transformation in the systematic inquiry into nature. In the seventeenth century scholars were engaging in discrete fields of study, such as astronomy or medicine. But over the course of the next two centuries the fields that initially seemed distant and unrelated gradually converged into one enterprise that we now call “science.” Although Japanese scholars were not isolated from European science, it was not the outside influence that caused this transformation. Rather, the new conceptualization of science came from within, as different scholars came to align themselves along different lines. What brought them together was no longer social status, practical goals, or even their respective disciplines, but the kind of questions they asked, the kind of evidence they considered acceptable, and the sources they deemed authoritative. Together, they now engaged in Science, with a capital S, that was greater than the sum of its parts.

The Mongols facilitated a great deal of Sino-Islamic scientific exchange. Though scholars patronized by the Mongols learned a great deal about developments on the other side of the Mongol realms, science from China did not affect the theoretical foundations of science in Iran, nor vice versa. Rather, materia medica and co-operation in observational astronomy endured. The western Mongol realms also greeted scholars from Europe and from the Islamic west. The Mongols were principally interested in specific benefits accruing to them from scientific exchanges. Thus they welcomed information about medicine, mapmaking, astronomy, and astrology, and supported exchanges in these fields.

Until recently, those wanting to escape the effects of terrestrial light pollution could leave cities and travel to the countryside to observe the night sky. But increasingly there is nowhere, and therefore no way, to escape the pollution from the thousands of satellites being launched each year. ‘Mega-constellations’ composed of thousands or even tens of thousands of satellites are designed to provide low-cost, low-latency, high-bandwidth Internet around the world. This chapter outlines how the application of the ‘consumer electronic product model’ to satellites could lead to multiple tragedies of the commons, from the loss of access to certain orbits because of space debris, to changes to the chemistry of Earth’s upper atmosphere, to increased dangers on Earth’s surface from re-entered satellite components. Mega-constellations require a shift in perspectives and policies. Instead of looking at single satellites, we need to evaluate systems of thousands of satellites, launched by multiple states and companies, all operating within a shared ecosystem.

The rapid development of mega-constellations raises difficult issues of international law, including liability for collisions involving satellites. Establishing ‘causation’ – that the actions of one satellite operator caused a specific collision with another space object and resulted in damage – could be a challenge, especially in the context of knock-on collisions where debris from an initial collision later collides with one or more spacecraft, including satellites. A further challenge is determining, in the absence of binding international rules on the design and operation of satellites, what is ‘reasonable’ behaviour and therefore what constitutes ‘negligence’. This chapter also addresses the interference to astronomy that is increasingly resulting from light and radio spectrum pollution from satellites. A full interpretation of the Outer Space Treaty leads to the conclusion that states are already required to take certain steps, including conducting an environmental impact assessment, before licensing mega-constellations, because of the obligation of ‘due regard to the corresponding interests of all other States Parties to the Treaty’.

Some 66 billion years ago, a cataclysmic collision between the Earth and an asteroid ten to 15 kilometres in diameter caused the extinction of the non-avian dinosaurs. In 1908, an asteroid 50 to 70 metres in diameter levelled over 2,000 square kilometres of forest in Siberia, while in 2013 an asteroid 19 metres in diameter produced a shockwave over Chelyabinsk, Russia, sending over a thousand people to the hospital. The field of ‘planetary defence’ involves the detection, characterisation, risk assessment and, if necessary, deflection of asteroids and comets that have the potential to strike Earth. Yet there has been a lack of high-level diplomacy on this issue. In particular, the low probability of a major Earth impact happening in our lifetime makes planetary defence a low priority for political leaders, despite the existential consequences of impacts and their eventual certainty of occurring. There is also a shortage of widely agreed international law, including on the potential use of nuclear explosive devices for deflecting asteroids. Most importantly, there is a lack of agreement on who is responsible for vetting the science, assessing the risks and making decisions if Earth were faced with an actual impact threat. Is it the United Nations Security Council that decides? What if a Security Council decision is blocked by one of its veto-holding permanent members? Would a state that acted unilaterally be excused any illegality because of the necessity of its actions, according to the international law on ‘state responsibility’?

Elena Fratto examines Chekhov’s interests in the scientific advancements of his time, showing how his passion for horticulture, his knowledge of botany, and his interests in astronomy, optics, thermodynamics, and evolutionary and degenerative theory transferred directly to his fiction.

This paper offers a provocative re-reading of the passage about the sizes of the sun, moon, and stars late in Lucretius’ De Rerum Natura (5.564-613). Attention to not only details of argumentation but also shades of meaning and contorted syntax shows a more complex, ambiguous presentation than generally acknowledged. This paper suggests that Lucretius' narrator—rather than merely parroting wrong, ridiculed doctrines—pulls student-readers into the process of inquiry. It becomes the didactic audience’s task to receive data from sense-perception and use lessons learned earlier in the poem in making correct judgments based upon that data. In Epicurean and Lucretian accounts of reality, the senses themselves are infallible; so the Lucretius-ego’s assertion that the sun as big as perceived by our senses must also be infallible. But our interpretation of what that assertion entails about the sun’s actual size is a matter of judgment, and thus fallible and uncertain indeed.

In the seventeenth and eighteenth centuries, scientists, philosophers, writers, artists, and composers were interested in questions of order and structure – of the universe, human society, and the individual. So were the people who read, saw, heard, and discussed their works in clubs, coffeehouses, salons, newspapers, and journals. Many people developed new ways to contemplate the universe and the place of humans in it: physicians, chemists, and alchemists observed and experimented on the natural world; astronomers searched the skies with the newly invented telescope; mathematicians posited laws to explain how basic forces worked. Philosophers increasingly argued that reason was the best tool for understanding the world, though most thought that the capacity for rational thought varied widely between different types of people. Concern with order and the limits of human understanding emerged in literature as well, while art and music saw giant works on a huge scale but also smaller, more reflective pieces. The eighteenth century saw a broadening of culture and learning, but also a growing split between professional and amateur – both trends that created a larger market for many types of cultural products.

The efforts to decode the mystery of the Antikythera mechanism, a unique machine surviving from around 70–60 BC, extend more than a century since its discovery in an ancient shipwreck off the coast of a Greek island. Although the first experts who looked at the device were baffled by its gear mechanisms, dating, and purpose, this chapter explains how many of these inscrutable aspects slowly came to be clarified and deciphered. The author illustrates the immense efforts it can take to ‘solve’ an enigma: in this case, the combined work of historians, epigraphers, radiographers, X-ray machines, mechanics, filmmakers, and multinational technology companies. The chapter also displays the valuable insights which can come from such endeavours. Decoding the Antikythera mechanism challenged common assumptions about technological skill and astronomical knowledge in antiquity, but it also encouraged innovations in modern technology and revealed something of humanity’s search to understand the cosmos.

Plato’s dialoguesespecially the Republiclead us to wonder what the objects of mathematics are. For Plato, no perceptible three is unqualifiedly three, a necessary condition for being an object of knowledge. Aristotle controversially ascribes to Plato the view that mathematical objects are “intermediates,” between perceptibles and Forms: multiple but also eternal, lacking change, and separate from perceptibles. The hunt for or against intermediates in Plato’s dialogues has depended on two ways of understanding Plato on scientific claims, a Form-centric approach and a subject-centric (semantic) approach. Although Socrates does not present intermediates in the Republic, it is difficult to see how the units of the expert arithmetician or motions of the real astronomer could be simply Forms or perceptibles. The standard over-reading of the Divided Line, where the middle sections are equal, further obscures our understanding. The Phaedo and the Timaeus provide candidates for mathematical objects, although these have only some of the attributes ascribed to intermediates. We are left with no clear answer, but exploring options may be exactly what Plato wants.

Undergraduate research experiences have been identified as a high-impact practice in higher education.Within the physics community, research experiences were cited as a critical educational experience for undergraduate students by many thriving physics programs. Furthermore, the discipline has, for many years, supported undergraduate research experiences by advocating for and funding such programs as well as providing opportunities for undergraduate students to present their research at professional conferences and in peer-reviewed professional journals. In this chapter, the authors briefly highlight the benefits of research experiences to undergraduate physics students along with some of the known or community-accepted best practices for engaging undergraduate students in research. The authors also discuss the challenges faced by the community surrounding equity and our ability to engage all students in this meaningful professional and educational experience. While challenges exist, there are opportunities for the physics community to successfully address them through hard work, creativity, and innovation.