The Giant Number That Is Only a Bound
In short: A short history of naming enormous numbers, from Archimedes' sand grains to Graham's number, a famous upper bound on a problem whose true answer lies somewhere between 13 and a much smaller, later bound.
A 1:23 short film in the series “From Fingers to Qubits”, narrated by intellect_voice_01.
Sources used in this film: Scott Aaronson, essay 'Who Can Name the Bigger Number?' (1999, revised by Florian Mayer), hosted on a University of Illinois Chicago mathematics course page, “Aaronson99.pdf”; Elsevier (European Journal of Combinatorics, via ScienceDirect), “Improved upper and lower bounds on a geometric Ramsey problem”; California State University, Los Angeles (Vignettes of Ancient Mathematics, translation by Henry Mendell), “Archimedes, Sand-Reckoner, Intro.”; Joseph Muscat, University of Malta (staff page; notes last revised 15 Sep 2019), “Archimedes.pdf”; SciHi Blog (PDF hosted by the MacTutor History of Mathematics archive, University of St Andrews), “sci_hi”; TIME (TIME USA, LLC), archive article 'Science: Googol', dated Feb 28, 1938, “Science: Googol”; Science (American Association for the Advancement of Science); article by Donald E. Knuth, 17 December 1976, hosted on a Texas A&M University course page, “finiteness.pdf”; Science (American Association for the Advancement of Science, AAAS), “Mathematics and Computer Science: Coping with Finiteness”; Carnegie Mellon University, Algorithms, Combinatorics and Optimization (ACO) Seminar, “ACO Seminar, 2012-2013”; arXiv (preprint by Mikhail Lavrov and John Mackey of Carnegie Mellon University and Mitchell Lee of MIT), “1304.6910v2.pdf”.
Sources used in this film
- Scott Aaronson, essay 'Who Can Name the Bigger Number?' (1999, revised by Florian Mayer), hosted on a University of Illinois Chicago mathematics course page — Aaronson99.pdf · View →
- Elsevier (European Journal of Combinatorics, via ScienceDirect) — Improved upper and lower bounds on a geometric Ramsey problem · View →
- California State University, Los Angeles (Vignettes of Ancient Mathematics, translation by Henry Mendell) — Archimedes, Sand-Reckoner, Intro. · View →
- Joseph Muscat, University of Malta (staff page; notes last revised 15 Sep 2019) — Archimedes.pdf · View →
- SciHi Blog (PDF hosted by the MacTutor History of Mathematics archive, University of St Andrews) — sci_hi · View →
- TIME (TIME USA, LLC), archive article 'Science: Googol', dated Feb 28, 1938 — Science: Googol · View →
- Science (American Association for the Advancement of Science); article by Donald E. Knuth, 17 December 1976, hosted on a Texas A&M University course page — finiteness.pdf · View →
- Science (American Association for the Advancement of Science, AAAS) — Mathematics and Computer Science: Coping with Finiteness · View →
- Carnegie Mellon University, Algorithms, Combinatorics and Optimization (ACO) Seminar — ACO Seminar, 2012-2013 · View →
- arXiv (preprint by Mikhail Lavrov and John Mackey of Carnegie Mellon University and Mitchell Lee of MIT) — 1304.6910v2.pdf · View →
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Sources
- Summary by Intellect · source: Scott Aaronson, essay 'Who Can Name the Bigger Number?' (1999, revised by Florian Mayer), hosted on a University of Illi: Aaronson99.pdf
- Also: Elsevier (European Journal of Combinatorics, via ScienceDirect): Improved upper and lower bounds on a geometric Ramsey problem
- Also: California State University, Los Angeles (Vignettes of Ancient Mathematics, translation by Henry Mendell): Archimedes, Sand-Reckoner, Intro.
- Also: Joseph Muscat, University of Malta (staff page; notes last revised 15 Sep 2019): Archimedes.pdf
- Also: SciHi Blog (PDF hosted by the MacTutor History of Mathematics archive, University of St Andrews): sci_hi
- Also: TIME (TIME USA, LLC), archive article 'Science: Googol', dated Feb 28, 1938: Science: Googol
- Also: Science (American Association for the Advancement of Science); article by Donald E. Knuth, 17 December 1976, hosted on a: finiteness.pdf
- Also: Science (American Association for the Advancement of Science, AAAS): Mathematics and Computer Science: Coping with Finiteness
- Also: Carnegie Mellon University, Algorithms, Combinatorics and Optimization (ACO) Seminar: ACO Seminar, 2012-2013
- Also: arXiv (preprint by Mikhail Lavrov and John Mackey of Carnegie Mellon University and Mitchell Lee of MIT): 1304.6910v2.pdf
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