Algorithmic Complexity
Appendix to
The Prophets of
the Thinking Machines:
Artificial General Intelligene and Transhumanism
History, Theory and Pioneers
Past, Present and Future
by Todor Arnaudov
Edition: 20.7.2025 (32 pages)
Edition: 19.7.2025 (30 pages)
Edition: 18.7.2025 (27 pages)
http://twenkid.com/agi
https://github.com/twenkid/sigi-2025
#complexity #сложност
©Authors: The authors
of all cited and reviewed works, such as:
Hector Zenil, Felipe Abrahao, Andrey Kolmogorov, Gregory Chaitin, Ray Solomonoff, Leonid Levin;
Charles Benett, David Deutsch, Nicolas Gauvrit, Jesper Tegnér, Leong Ting Lui, Santiago
Hernández-Orozco, Jean-Paul Delahaye, Cristian S. Calude, Gordana
Dodig-Crnkovic, Oliver Korten Noam Nisan, Avi Wigderson, Martin Davis, Alexander
Shen, Marvin Minsky et al., ; various encyclopaedic sources such as Wikipedia
etc.
… & Todor Arnaudov – author of The Prophets of the Thinking Machines and
editor, summarizer, introductory texts, notes and author of the contextual reviews
and mini-sub-articles.
Read the paper at:
https://twenkid.com/agi/Algorithmic-Complexity_Prophets-of-the-Thinking-Machines-18-7-2025.pdf (32 pages)
Or from the SIGI-2025 github's page.
(...)
One
specific reason for compiling this work now was that I recently discovered
a paper from the circle of Hector Zenil about the SuperARC[1]
test, and then a recent strategic program paper about the Simulation
Intelligence[2]. I
decided to refresh and deepen my knowledge by doing a literature review, using Hector’s
works as a starting point[3].
This
work intends to be food for thought for readers who also want to improve and
widen their knowledge. Other goals are to share my comments and additions to
some of the reviewed ideas from the papers and in the context of The Prophets…
– to shed light on ...
[1] See below. This paper has technical and extensive
continuations of generalizations done also in TUM in the early 2000s
[2] Simulation
Intelligence: Towards a New Generation of Scientific Methods Alexander Lavin,
David Krakauer, Hector Zenil et al., 2021/2022,
https://arxiv.org/abs/2112.03235
[3] Part of the reviews here are included also in the bigger
appendix #Listove which has broader and interdisciplinary scope and currently
is bilingual - Bulgarian and English.
(...)
[This work is a continuation of the Lecture #4 from the AGI course]
Complexity and The Universe Computer from the “Sacred
Computer”
* World’s first university course in Artificial General Intelligence,
Plovdiv 2010, 2011,
https://artificial-mind.blogspot.com/2010/04/universal-artificial-intelligence.html
https://research.twenkid.com/agi/2010/ https://research.twenkid.com/agi/2010/Complexity_Probability_Chaos_10-2010_MTR.pdf
* Lecture slides (Bulgarian):
Complexity and Theory of Information. Probability Theory – statistical
(empirical) probability. Chaos Theory. Systems Theory. Emergent functions and
behavior. Universe as a computer – digital physics. Algorithmic Probability.
Kolmogorov's Complexity and Minimum Message Length. Occam's Razor. (slides originally in Bulgarian)
* Definition
of Machine Intelligence, Legg and Hutter, 2007 – Slides for the
course:
Bulgarian: “Универсална интелигентност: Дефиниция на агента на Маркус Хутер” по работата: …
Universal
Intelligence:”
https://research.twenkid.com/agi/2010/Intelligence_by_Marcus_Hutter_Agent_14_5_2010.pdf
* Slides in English “Universal Intelligence According to Marcus
Hutter's Definition”
https://research.twenkid.com/agi/2010/en/Machine_Intelligence_Hutter_Legg_Eng_MTR_Twenkid_Research.pdf
(...)
Overview of Basic Concepts about Turing Machines and Computation
A tape, divided
into cells; a head; state register, a finite table
of instructions: given the state and the symbol that is read from the tape (...)
Selected papers, summaries and notes in Algorithmic
Complexity, Randomness etc.
(...)