On 29 October 1675, Gottfried Wilhelm Leibniz wrote a single elongated letter S in his notebook, creating the integral sign that would become the mathematical foundation of modern science. This episode explores how a simple symbol quietly rewired humanity’s understanding of the universe, then moves through three other significant moments from this date: John Glenn’s return to space at seventy-seven in 1998, the Lion Air Flight 610 tragedy in the Java Sea in 2018 that exposed fatal flaws in the Boeing 737 MAX, and China’s announcement ending its controversial one-child policy in 2015 after thirty-five years. From calculus notation that still powers every satellite launch to demographic experiments that reshaped a nation, these stories reveal how human ambition, tragedy, and policy decisions echo across centuries.

• Intro A German mathematician in Paris writes a single symbol that will quietly rewire human understanding of the universe.
• Leibniz and the Long S: The Symbol That Built the Modern World On 29 October 1675, Leibniz creates the integral sign, a stretched S for summa that becomes the visual grammar of calculus. His notation proves superior to Newton’s, spreading through European mathematics and becoming the foundation for classical mechanics, electromagnetism, quantum mechanics, and every engineering calculation since.
• John Glenn Goes Back to Space at Seventy-Seven In 1998, the first American to orbit Earth returns to space aboard Discovery at age seventy-seven. Glenn serves as a research subject studying how spaceflight affects older bodies, contributing to ageing science whilst proving extraordinary lives need not end at retirement.
• Lion Air Flight 610: The Java Sea Tragedy In 2018, Lion Air Flight 610 crashes into the Java Sea twelve minutes after takeoff, killing all 189 people aboard. A faulty automated system on the Boeing 737 MAX repeatedly pushes the nose down despite pilot efforts. A second MAX crash five months later leads to a worldwide grounding lasting nearly two years.
• China Ends the One-Child Policy In 2015, China announces the end of its thirty-five-year one-child policy, introduced in 1980 to address overpopulation. The policy slowed population growth but involved coercion, created gender imbalances, and reshaped family structures. Its end addresses an ageing population and shrinking workforce, though birth rates remain lower than officials anticipated.
• Outro Four moments from 29 October: a symbol, an astronaut, a tragedy, and a policy. History rarely arrives tidy.

• https://www.britannica.com/biography/Gottfried-Wilhelm-Leibniz
• https://mathshistory.st-andrews.ac.uk/Biographies/Leibniz/
• https://www.nasa.gov/mission_pages/shuttle/shuttlemissions/archives/sts-95.html
• https://www.nasa.gov/feature/john-glenn-s-return-to-space
• https://reports.aviation-safety.net/2018/20181029-0_B38M_PK-LQP.pdf
• https://www.bbc.co.uk/news/world-asia-46014463
• https://www.theguardian.com/world/2019/mar/10/ethiopia-airlines-crash-boeing-737-max-8-latest-news
• https://www.bbc.co.uk/news/world-asia-34665539
• https://www.theguardian.com/world/2015/oct/29/china-abandons-one-child-policy

On 28 October 1492, Christopher Columbus landed on Cuba and confidently declared he had found Japan. He had not. His catastrophic geographical error set in motion events that would reshape the world, devastating Caribbean populations and launching centuries of colonial expansion. Meanwhile, on the same date in 2008, Volkswagen briefly became the world’s most valuable company after a short squeeze sent its share price soaring, a financial mishap that cost hedge funds billions. In 1993, Japan’s football team lost World Cup qualification in the final 90 seconds of their match in Doha, a moment still remembered as national heartbreak. And in 1971, Britain successfully launched its first and only domestically built satellite, Prospero, using a rocket programme the government had already cancelled. From navigational disasters to financial chaos, sporting tragedy to inadvertent space success, the 28th of October offers a masterclass in human overconfidence and the unpredictable consequences of getting things spectacularly wrong.

• Introduction Clara introduces the theme of geographical overconfidence through Columbus’s catastrophic navigational error, setting up a 28 October journey through history’s most confident mistakes.
• Columbus Calls Cuba Japan On 28 October 1492, Columbus lands on Cuba believing it to be Japan. His underestimation of Earth’s circumference, reliance on Marco Polo’s descriptions, and refusal to accept contrary evidence led to the colonial devastation of Caribbean indigenous populations and reshaped world history.
• Volkswagen’s Two-Day Reign On 28 October 2008, Porsche’s surprise announcement of controlling 74% of Volkswagen shares triggers a massive short squeeze. Volkswagen briefly becomes the world’s most valuable company as desperate hedge funds scramble to cover positions, losing billions in the process.
• The Agony of Doha On 28 October 1993, Japan’s national football team loses World Cup qualification when Iraq equalises in the 92nd minute. The devastating two-all draw, remembered as the Tragedy of Doha, denied Japan its first World Cup appearance and remains a cultural touchstone for heartbreak.
• Britain’s Cancelled Satellite Success On 28 October 1971, Britain launches Prospero, its first and only domestically built satellite, using the Black Arrow rocket. The programme had already been cancelled due to cost, making Britain’s successful entry to the space club both triumph and footnote.
• Conclusion Clara reflects on the day’s stories of confident mistakes, from navigation to finance to sport, noting that history consistently makes a strong case against human overconfidence.

• https://www.britannica.com/biography/Christopher-Columbus
• https://www.history.com/topics/exploration/christopher-columbus
• https://www.reuters.com/article/idUSTRE49R3I920081028/
• https://www.ft.com/content/0a58b63a-4294-11dd-9661-0000779fd2ac
• https://www.bbc.com/sport/football/24354219
• https://www.theguardian.com/football/2013/oct/28/japan-iraq-doha-tragedy-world-cup
• https://www.esa.int/About_Us/ESOC/Prospero_Britain_s_first_and_only_satellite
• https://www.bbc.co.uk/news/science-environment-14877390