How to Finish Infinitely Many Tasks in One Minute

Zeno proved that Achilles can never catch a tortoise. The proof is 2,500 years old, and it's surprisingly hard to find the mistake. We follow Zeno's stages until they spell out 111.111… metres, see why some never-ending sums are finite and others aren't, stack infinitely many tasks into a one-minute staircase, and zoom into the exact moment Achilles draws level. Then Zeno's arrow leads to calculus, a watched atom refuses to change, and Thomson's lamp asks a question that math can't answer. Chapters 0:00 Intro 1:19 Who was Zeno? 1:58 You can't cross a room 2:31 Where does Achilles catch up? 3:48 The tempting answers 5:02 Infinity in a square 6:04 The race as a picture 7:18 The arrow 8:50 Zeno in modern physics 9:31 Thomson's lamp 10:16 The takeaway Sources and further reading Huggett, N. Zeno's Paradoxes. Stanford Encyclopedia of Philosophy: https://plato.stanford.edu/entries/pa... Aristotle, Physics, Book VI, chapters 2 and 9 Plato, Parmenides, 127a-128e Salmon, W. C. (ed.). Zeno's Paradoxes (Bobbs-Merrill, 1970) Oresme, N. Quaestiones super geometriam Euclidis (c. 1350): the divergence of the harmonic series Cauchy, A.-L. Cours d'analyse de l'École royale polytechnique (1821) Thomson, J. F. (1954). Tasks and super-tasks. Analysis 15(1), 1-13 Misra, B. & Sudarshan, E. C. G. (1977). The Zeno's paradox in quantum theory. Journal of Mathematical Physics 18, 756-763 Itano, W. M., Heinzen, D. J., Bollinger, J. J. & Wineland, D. J. (1990). Quantum Zeno effect. Physical Review A 41, 2295-2300 Zeno's paradoxes, Wikipedia: https://en.wikipedia.org/wiki/Zeno%27... Harmonic series (mathematics), Wikipedia: https://en.wikipedia.org/wiki/Harmoni...) Planck units, Wikipedia: https://en.wikipedia.org/wiki/Planck_... Business inquiries: mathimationstv@gmail.com #math #paradox #MathImations