207 captures

23 Aug 2000 - 07 Oct 2025

Nov	FEB	Mar
	15
2013	2015	2016

success

fail

About this capture

COLLECTED BY

Organization: Internet Archive

The Internet Archive discovers and captures web pages through many different web crawls. At any given time several distinct crawls are running, some for months, and some every day or longer. View the web archive through the Wayback Machine.

Collection: Survey Crawl Number 2 - Started Dec 17th, 2014 - Ended Jul 31st, 2015

The seed for this crawl was a list of every host in the Wayback Machine

This crawl was run at a level 1 (URLs including their embeds, plus the URLs of all outbound links including their embeds)

The WARC files associated with this crawl are not currently available to the general public.

TIMESTAMPS

Sans les mathématiques on ne pénètre point au fond de la philosophie. Sans la philosophie on ne pénètre point au fond des mathématiques. Sans les deux on ne pénètre au fond de rien. — Leibniz [Without mathematics we cannot penetrate deeply into philosophy. Without philosophy we cannot penetrate deeply into mathematics. Without both we cannot penetrate deeply into anything.] Tribute to Leibniz: Essay on Leibniz, Complexity and Incompleteness

[Note on George Bernard Shaw (1856-1950): The first use of the term metabiology of which I am aware is in Shaw's 1921 play Back to Methuselah: A Metabiological Pentateuch. A better play of Shaw's that is also on evolution is his 1903 Man and Superman. Shaw's idea-filled plays, which feature lengthy prefaces, were originally meant to be read rather than performed.]

Ursula Molter, Gregory Chaitin and Hernán Lombardi opening the Buenos Aires Mathematics Festival (Argentina, May 2009)

G J Chaitin Home Page

Chaitin is a professor at the Federal University of Rio de Janeiro and an honorary professor at the University of Buenos Aires, and has honorary doctorates from the National University of Córdoba in Argentina and the University of Maine in the United States. He is also a member of the Académie Internationale de Philosophie des Sciences (Brussels) and the Leibniz-Sozietät der Wissenschaften (Berlin).

Carnival in Rio de Janeiro, 1970. Photo by Peter Albrecht

     

     

• Foreword for the Chinese edition of Proving Darwin

• IACAP 14 Invited Talk (Foils)

• Conceptual Complexity and Algorithmic Information (Preprint)

  "In this essay we propose that the fundamental philosophical concept of conceptual complexity
  is captured mathematically by the notion of algorithmic information content, and we discuss
  the complexity of physical and mathematical theories, the complexity of biological mutations,
  and the most complex system in biology, the human brain."

• Metabiología: los orígenes de la creatividad biológica (Investigación y Ciencia)

• Los límites de la razón (Investigación y Ciencia)

• The Limits of Reason (Scientific American)

• Randomness in Arithmetic (Russian Scientific American)

• L'Univers est-il intelligible? (La Recherche)

• Computers, Paradoxes and the Foundations of Mathematics (American Scientist)

• Ordenadores, paradojas y fundamentos de las matemáticas (Investigación y Ciencia)

• Grenzen der Berechenbarkeit (Spektrum der Wissenschaft)

• Life as Evolving Software
  Universidade Federal do Rio Grande do Sul, 2 May 2011

• Hacia una teoría matemática de la evolución y de la creatividad biológica
  Instituto de Sistemas Complejos de Valparaíso, 30 de noviembre 2010

• Leibniz, Complexity and Incompleteness
  Hebrew University, Jerusalem, 13 September 2008

• LISP interpreter as Java applet
• LISP interpreter in C
• LISP interpreter in Mathematica (Original Mma v2 version)
• LISP interpreter in Mathematica (Mma v4.1 version contributed by Joe Yoon)
• LISP Tutorial (from The Unknowable)
• LISP Manual (from Exploring Randomness)
• LISP Manual—Advanced Features (from Exploring Randomness)

The Limits of Mathematics (1998)

LISP Code

• "Manual" for our LISP (alternate version)
• You can't prove that an S-expression is elegant! (commented version)
• The universal Turing machine used to define our complexity measure H (alternate version)
• You can't prove lower bounds on the complexity H! (commented version)
• Ω in the limit from below—stupid version (with additional output)
• Ω in the limit from below—elegant version (with additional output)
• Ω in the limit from below—fast version
• Ω is algorithmically incompressible/random (commented version)
• You can't prove what Ω's bits are! (commented version)

LISP Runs

• "Manual" for our LISP (alternate version)
• You can't prove that an S-expression is elegant! (commented version)
• The universal Turing machine used to define our complexity measure H (alternate version)
• You can't prove lower bounds on the complexity H! (commented version)
• Ω in the limit from below—stupid version (with additional output)
• Ω in the limit from below—elegant version (with additional output)
• Ω in the limit from below—fast version
• Ω is algorithmically incompressible/random (commented version)
• You can't prove what Ω's bits are! (commented version)

The Unknowable (1999)

LISP Code

• Elementary set theory in LISP
• A self-reproducing LISP expression
• Gödel's proof of his incompleteness theorem
• Turing's proof of the unsolvability of the halting problem
• My proof that you can't show that a LISP expression is elegant

LISP Runs

• Elementary set theory in LISP
• A self-reproducing LISP expression
• Gödel's proof of his incompleteness theorem
• Turing's proof of the unsolvability of the halting problem
• My proof that you can't show that a LISP expression is elegant

Exploring Randomness (2001)

• Preface

Part I—Introduction

• Historical introduction—A century of controversy over the foundations of mathematics

• What is LISP? Why do I like it?

• How to program my universal Turing machine in LISP
  utm2 code, utm2 run

Part II—Program-Size

• A self-delimiting Turing machine considered as a set of (program, output) pairs
  exec code, exec run

• How to construct self-delimiting Turing machines: the Kraft inequality
  kraft code, kraft run

• The connection between program-size complexity and algorithmic probability: $H(x) = -\log_2 P(x) + O(1)$.
  Occam's razor: there are few minimum-size programs
  occam code, occam run

• The basic result on relative complexity: $H(y|x) = H(x, y) - H(x) + O(1)$
  decomp code, decomp run, lemma code, lemma run

Part III—Randomness

• Theoretical interlude—What is randomness? My definitions

• Proof that Martin-Löf randomness is equivalent to Chaitin randomness
  martin-lof code, martin-lof run, martin-lof2 code, martin-lof2 run

• Proof that Solovay randomness is equivalent to Martin-Löf randomness
  solovay code, solovay run

• Proof that Solovay randomness is equivalent to strong Chaitin randomness
  chaitin code, chaitin run, chaitin2 code, chaitin2 run

Part IV—Future Work

• Extending AIT to the size of programs for computing infinite sets and to computations with oracles

• Postscript—Letter to a daring young reader

\[ \Omega = \sum_{\text{program $p$ halts}} 2^{-(\text{size in bits of $p$})} \] \[ \Omega_U = \sum_{\text{$U(p)$ halts}} 2^{-|p|} \] \[ \Omega' = \sum_{n \,=\, 1,\, 2,\, 3,\, ...} 2^{-H(n)} \]