Σ.4. Library of Links

The mathematical literature and webpages we've consulted and recommend for further reading. To show more library items, select the page extension option -- or ++ in the control form on the top left.
The items are marked as:

σ.4.1. Big number news, art & fun

• Yee & Kondo's improved New World Record - 10 Trillion Digits of Pi 17-10-2011
• Ai Weiwei's 100 million Sunflower seeds at Tate Modern Guardian 11-10-2010
• Carl Bialik The Numbers Guy The World's Best Agers 23-7-2010
• "The 2,000,000,000,000,000th digit is 0" Pi record smashed... BBC News 16-9-2010
• Austin Sendak's Make Hella Official links to CNN, New York Times, etc. 14-3-2010
• "$1,784 billion trillion" Bank claim that is out of this world BBC News 23-10-2009
• Tallest structure on Earth is the Dubai 828 meter Khalifa Tower on 1-10-2009
• Steve's The Googillion Journal Google vs. Googillion 1-12-2007
• Mary & John Gribbin "Big Numbers" 2003
• Kokogiak media – The MegaPenny Project
• Math cats – Can you say really big numbers?
• Eames Office film for IBM – APOD YouTube – Powers of Ten 1968
  after the book: Cosmic View by educator Kees Boeke 1957

σ.4.2. Home grown Big numbers

• Giga Gerard "Beatrix matrix system sets number record!" 30-4-2013
• Novaloka "A binary variation with brackets" in functions and matrix 27-1-2011
• Novaloka "Construction of Big and Infinite Numbers" 9-4-2009
• Novaloka "Constructie van Grote getallen" [Dutch] 29-1-2009
• Novaloka Binary Big Number Systems the signs and the story 18-10-2008
• Novaloka blog "Spreading fingers across the universe" [Dutch] 2008-9-22
• Novaloka blog "Operator generation as a motor for an operator function" 25-8-2008
• Novaloka & Mathmuis "Plaatsen een Record Getal" [Dutch] 2008-8-8
• Novaloka blog "Number distances" Difficult numbers + BigOpera 10000 Jul.2008
• Novaloka blog "Neuropol 0" goes far beyond counting in dimensions 2-5-2008
• Novaloka blog "Numbers from 0 to many more..." milk & jazz numbers 23-1-2008
• Novaloka blog series "On the number horizon" Big information theory Oct.2007
• Novaloka essay "One Last Thing" Buddha in recursive progression 22-9-2007
• Novaloka blog "I love big numbers" tetration up to 7^^3 in Java 24-6-2006

σ.4.3. Big numbers on the web

• Christopher M. Bird "Super Huge Numbers" – Bird's array notations, 4-4-2006
• Jonathan Bowers – Big Number Central – Exploding Array Function
  Richard Morris tidied up all Bowers' names for large numbers from BEAF.
• G.A. Edgar "Transseries: Composition, Recursion, and Convergence" arXiv 7-9-2009
• Ioannis Galidakis – Mathematics Lambert's W Function, Infinite Exponents, etc.
• Ioannis N. Galidakis "On Extending hyper4 and Knuth's Up-arrow..." 2005
• Peter Hurford – Large numbers part 1, 2, 3, 4, essays on Moser & Conway
• Susan Stepney Factoids ..Steinhaus polygons, Moser polygons.. 2008
• Heiner Marxen Busy Beaver 2009
• Alistair Cockburn's CCWiki with Stephan Houben Really Big Numbers 2007
• Robert Munafo – Large Numbers with references 2009
• Andrew Robbins "Solving the Analytic Extension of Tetration..." 2005
  Henryk Trappman, Andrew Robbins "Tetration Forum FAQ" [drafts] 2008
• Rubtsov, Romerio "Ackermann's function and new arithmetical operations" 2004
• Sam Hughes on Bowers' linear, planar and multidimensional array notation, 2007
• Sbiis Saibian's blog "1977 IS LONG OVER, AND SO IS G" 2008, and new website
• The Grzegorczyk hierarchy, extended to the fast-growing Löb-Wainer hierarchy,
  the Bachmann-Howard ordinal from Ordinal collapsing function in Wikipedia.
• Wolfram MathWorld – Large Numbers index in online maths encyclopedia

σ.4.4. Big numbers on paper

• Wilhelm Ackermann "On Hilbert's construction of the real numbers" 1928
  in Jean van Heijenoort's source book "From Frege to Gödel" 1967
• Archimedes "The Sand Reckoner" annotated by James R. Newman, 1956
  from: "The works of Archimedes" 3d century BC, by Th. Heath 1897
  also in: Hutchins "Great Books of the Western World, vol.11" 1952
• Brian Clegg "A brief history of Infinity" 2003
• John H. Conway, Richard K. Guy "The Book of Numbers" 1996, pp.59-62
• R. Crandell, C. Pomerance "Prime Numbers, a computational perspective" 2005
• Philip J. Davis "The lore of large numbers" 1961
• Martin Gardner "Mathematical Games" 1977, on Graham's number
• R.L. Graham, B.L. Rothschild "Ramsey's Theorem for n-Parameter Sets" 1971
• Bhikshu Jin Yong "How Large is One Asamkhyeya?" Nov. 2008
• Edward Kasner, James R. Newman "New Names for Old" 1940
  in James R. Newman "The world of mathematics, vol.3" 1956, p.2009
• Donald Knuth "Mathematics and Computer Science: Coping with Finiteness" 1976
  in Campbell, Higgins "Mathematics people problems results, vol.2" 1984, pp.210-211
• David Wells "The Penguin Dictionary of Curious and Interesting Numbers" 1997

σ.4.5. Recursion theory

• C.J. Ash, J.F. Knight "Computable Structures and the Hyperarithmetical Hierarchy" 2000
• Gregory Chaitin "Meta Maths, the quest for omega" 2005
• P. Clote, J.B. Remmel, ed. "Feasible Mathematics II" 1995
• Ershov, Goncharov, Nerode, Remmel "Handbook of Recursive Mathematics"
  vol.1 "Recursive model theory" 1998
  vol.2 "Recursive algebra, analysis and combinatorics" 1998
• M.C. Fitting "Fundamentals of Generalized Recursion Theory" 1981
• R.L. Goodstein "Recursive Number Theory" 1957
• Edward R. Griffor, ed. "Handbook of Computability Theory" 1999
• Andrzej Grzegorczyk "Some classes of recursive functions" 1953
• Peter G. Hinman "Recursion-Theoretic Hierarchies" 1978
• A.I. Mal'cev "Algorithms and recursive functions" 1970
• Dag Normann "Recursion on the countable functionals" 1980
• Piergiorgio Odifreddi "Classical Recursion Theory" 1989
  and his "Classical Recursion Theory Volume II" 1999
• Rózsa Péter "Recursive Functions" 1967, 3d ed. (1st ed. German 1951)
• H. Rogers "Theory of recursive functions and effective computability" 1967
• H.E. Rose "Subrecursion, Functions and hierarchies" 1984
• Luis E. Sanchis "Recursive Functionals" 1992
• Andrea Sorbi, ed. "Complexity, logic and recursion theory" 1997
• R.M. Smullyan "Recursion Theory for Metamathematics" 1993

σ.4.6. Foundations

• J.L. Bell, M. Machover "A Course in Mathematical Logic" 1993
• R.D. Carmichael "Groups of Finite Order" 1937
• C.C. Chang, H. Jerome Keisler "Model Theory" 1977
• Dirk van Dalen "Logic and Structure" 4th ed. 2004
• Paul R. Halmos "Naive Set Theory" 1960
• David Hilbert "On the infinite" 1925
  in: Heijenoort "From Frege to Gödel" 1967
• Wilfred Hodges "Building Models by Games" 1985
• Thomas Jech "Set theory" 2002
• Akihiro Kanamori "The Higher Infinite" 1997
• Stephen C. Kleene "Introduction to Meta-mathematics" 1952
• Ulrich Kohlenbach "Applied Proof Theory: proof interpretations..." 2008
• S. Mac Lane "Categories for the working mathematician" 1997
• S. Mac Lane, I. Moerdijk "Sheaves in Geometry and Logic" 1992
• Jerome Malitz "Introduction to Mathematical Logic" 1979
• Yu. I. Manin "A Course in Mathematical Logic (for Mathematicians)" 2010
• Elliott Mendelson "Introduction to Mathematical Logic" 1964
• J. Donald Monk "Mathematical Logic" 1976
• Wolfram Pohlers "Proof Theory, the first step into impredicativity" 2009
• S. Shelah "Classification Theory" 1990
• Edwin H. Spanier "Algebraic Topology" 1966
• Paul-Hermann Zieschang "Theory of Association Schemes" 2005

σ.4.7. Mathematics

• Stephen Abbott "Understanding Analysis" 2001
• P. Abramenko, K.S. Brown "Buildings: theory and applications" 2008
• Martin Aigner "A Course in Enumeration" 2007
• Jörg Arndt, Christoph Haenel "Pi-unleashed" 2001
• Avner Ash, Robert Gross "Fearless Symmetry" 2006
• Jerome Barkley Improved lower bound on a Euclidean Ramsey problem
  Graham's hypergraph has minimal dimension 13, arXiv 2008
• John L. Casti "Five Golden Rules" 1996
• P.M. Cohn "Further Algebra and Applications" 2002
• Mariana Cook "Mathematicians, an outer view..." 2009
• Dedekind "Essays on the Theory of Numbers" 2nd ed. 1893
  in Stephen Hawking "God created the Integers" 2007
  online: Project Gutenberg ebook, Internet Archive 1901 ed.
• Ebbinghaus, Hermes, et al. "Numbers" 1991
• George Gheverghese Joseph "The Crest of the Peacock" 1991
• Gowers, ed. "The Princeton Companion to Mathematics" 2008
• Graham, Rothschild, Spencer "Ramsey Theory" 1990
• Peter D. Grünwald "The Minimum Description Length Principle" 2008
• Julian Havil "Gamma" 2003
• Heikkilä, Lakshmikantham "Monotone iterative techniques..." 1994
• Georges Ifrah "... A universal history of numbers" 1985
• Nathan Jacobson "Basic Algebra I" 1974
• Khalil Jaouiche India's contribution to Arab mathematics 1997
• Eli Maor "e: the Story of a Number" 1998
• Jun-Iti Nagata "Modern Dimension Theory" 1965
• Marcus du Sautoy "Finding Moonshine" / "Symmetry" 2008
• H.A. Thurston "The Number System" 1956
• Eric W. Weinstein "CRC Concise Encyclopedia of Mathematics" 1999

σ.4.8. Science and programming

• Abiteboul, Hull, Vianu "Foundations of Databases" 1995
• Darren Aronofsky "Π faith in chaos" 1999, film (+book fiction)
• Roel Bloo "Preservation of Termination for Explicit Substitution" 1997
• Peter J. de Bruin "Inductive Types in Constructive Languages" 1995
• Doets, van Eijck "The Haskell road to logic, maths and programming" 2004
• David Flanagan "JavaScript, the definitive guide" O'Reilly 2006
• Franklin, Powell, Emami-Naeini "Feedback Control of Dynamical Systems" 2002
• Jeffrey Friedl "Mastering Regular Expressions" O'Reilly 2006
• Douglas R. Hofstadter "Gödel, Escher, Bach" 1979
• Jan van Leeuwen "Rule-labeled programs" 1972
• Seth Lloyd "Computational capacity of the universe" arXiv 24-10-2001
• Nielsen, Chuang "Quantum Computation and Quantum Information" 2000
• Jennifer Niederst Robbins "Web Design in a Nutshell" O'Reilly 2006
• Sullivan, Goerzen, Stewart "Real World Haskell" O'Reilly 2008
• Hermann Weyl "The Theory of Groups and Quantum Mechanics" 1931
• Ludwig Wittgenstein "Tractatus logico-philosophicus" 6.4, 1918

σ.4.9. Religious literature

• John Daido Loori "The True Dharma Eye" 2005, case 300 (Linji d. 867)
  comments on: Zen master Dogen's 300 koans, collection 1227
• John Stevens "The Marathon Monks of Mount Hiei" 1988
  Cites on kaihôgyô (founder Sô-ô 859) "The Story of Wandering Saints" 1387
• Fred "Philémon – Simbabbad de Batbad" 1974 (Dutch)
• Yram "Practical Astral Projection" ch.8, translation of "Le Médicin de l'Ame" 1925
  Yram is the mystic Marcel Fourhan (1884-1927), electrical engineer in Shanghai
• B. Malinowski "Baloma; the Spirits of the Dead in the Trobriand Islands" 1916
  Journal of the Royal Anthropological Institute of Great Britain and Ireland, vol.46
  in his: "Magic, Science and Religion" 1954 (courtesy P.C. Willis), p.161
• Basho "Journal of a weathered skeleton" 1684, haiku 1,9,15
  see: Nobuyuki Yuasa "The Narrow Road to the Deep North"
• Sri Caitanya "Šrî Brahma-samhitâ" 16th century, vs.40
  from: Joan Wilder "The Hare Krishna Music Book" 1994, p.48
• Keizan "Denkoroku" 14th century, case 30 (Huike 6th century)
  translation: Thomas Cleary "Transmission of Light"
  in: Classics of Buddhism and Zen vol.4, Shambhala 2001
• Nichiren Shonin "Letter to Niike" 1280
  in: "The major writings of Nichiren Daishonin" vol.1 1991, p.260
  quotes: "Mahâparinirvâna sûtra" 2nd? century
• Wumen Huikai (Mumon Ekai) "Wumen-guan" (Mumonkan) 1228, case 3
  translation: Thomas Cleary "Unlocking the Zen Koan" 1993
• Snorri Sturluson "Gylfaginning" (in Prose Edda) 1220, p.XXXVIII
  Quoted poem: "Edda" Grímnismál 20 (Codex Regius 13th century)
• Wansong "Ts'ung jung lu" (Shoyo Roku) 12th century compilation, case 3
  in: Thomas Cleary "Book of Serenity" One hundred Zen dialogues 1988
• Xuedou Chongxiang (Setchô) "Pi-yen lu" (Hekigan Roku) 11th century, case 3
  after: R.D.M. Shaw "The Blue Cliff Records" 1961
  and: Katsuki Sekida "Two Zen Classics" 1977
• The "Great Vows" of the Bodhisattva, as chanted in Zen buddhism
  own rendering 2009, based on: D.T. Suzuki "Manual of Zen Buddhism" 1950 &
  Maha Karuna & Kanzeon Sangha "Shiguseigan" & San Francisco Conference 1997
• "The Sutra of Complete Enlightenment" 6th? century
  in: Lu K'uan Yü "Ch'an and Zen Teaching" vol.3, 1962
• "Prajñâpâramitâ Hrdaya sûtra" (Heart Sutra) 5th? century
  in: Thich Nhat Hanh "The Heart of Understanding" 1988
• "Vajrachchedika-prajñâpâramitâ sûtra" 4th? century
  compare: "The Diamond Sutra and the Sutra of Hui-neng" 1990, ch.11
• "Buddhâvatamsaka-mahâvaipulya sûtra" 3d? century
  translation: Thomas Cleary "The Flower Ornament Scripture" 1984-1993
  with: chapter 30 "The Incalculable" annotated by Novaloka 2010
• "Vimalakîrti-nirdeša sûtra" (Wei mo chieh so shuo ching) 2nd? century
  from: Charles Luk "The Vimalakirti Nirdesa Sutra" 1972, ch.4
• "Lalitavistara sûtra" 1st? century, as "The Voice of the Buddha" 1983, ch.12
  with: "The mathematical test" annotated by Asamkhyeya dasa 2011
• "Lañkâvatâra sûtra" 1st? century, translation: D.T. Suzuki 1932, ch.2:17
• "The Gospel of Mary" 2nd? century, in: Barnstone, Meyer "The Gnostic Bible" 2003
• King James version of the Holy Bible, St. Mark "The Gospel" 1st century, ch.8:1-9
  in Novak from: The Holy Bible NRSV-1989, "Gospel of Matthew" ch.19:23-26
  from Aramaic via Dutch back to English – Mark 15:34, Matthew 27:46
  St. John the Divine "Book of Revelation" 2nd? century, ch.13:18 (number 666)
• Apollodorus "The Library" 1st/2nd century,
  modelled on a lost 5th century BC mythography by Pherecydes of Leros?
  in: Atchity "The Classical Greek Reader" 1996, p.332
• "Anuyogadvâra sûtra" (Mûlagrantha 4, Švetâmbara canon) Jaina 1th? century
• "Bhagavad Gîtâ" 0th? century, ch.11.13
  A.C. Bhaktivedanta Swami Prabhupâda "Bhagavad Gita As It Is" 1968
• "Saddharma-pundarîka sûtra" (Lotus Sutra) 1st? century BC
  translation Bunno Kato, et al: "The Threefold Lotus Sutra" 1975, ch.25
  online: Digital Sanskrit Buddhist Canon, in article: "Drops of ink and dust..."
• Chuang Tsu "Nua-hua chen ching" 4th? century BC
  translation: Gia-Fu Feng "Chuang Tsu, inner chapters" 1974, ch.1
• Confucius "Li chi" 5th? century BC
  from: Philip Novak "The World's Wisdom" 1994, ch3.2b
  Li Ji - Li Yun (Book of Rites - Evolution of Rites)
• Lao Tsu "Tao te ching" 6th? century BC, ch.1
  free after Novak, Blok (NL) and a copy (DE) in: "I, WILL McBRIDE" 1997, p.196
• The Buddha "Udana" 8.3, 6th? century BC
  after: Philip Novak "The World's Wisdom" 1994, ch2.34e
• "Atharva Veda" 11th? century BC, hymn 8, vs.7-10
  online: Ralph T.H. Griffith – the Atharva Veda 1895
• "Rg Veda" 11th? century BC, book 10, hymn 90, vs.1-2
  in: Sacred Writings vol. 5 "The Rig Veda", translation: Ralph T.H. Griffith 1896?