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Self-reference and Evolution of Evolvability Collaborators: Michael
of “blueprints” needed to construct other components of cells and copy itself. M. C. Escher
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Jul 17 2019 You can then use these primitives to draw more realistic plants or more artistic tessellations (see Escher's work for inspiration [Wikipedia
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Why is Escher a famous mathematician?
Escher's art became well known among scientists and mathematicians, and in popular culture, especially after it was featured by Martin Gardner in his April 1966 Mathematical Games column in Scientific American. Apart from being used in a variety of technical papers, his work has appeared on the covers of many books and albums.
Who was Maurits C Escher?
The Dutch artist Maurits C. Escher (1898-1972) was a draftsman, book illustrator, tapestry designer, and muralist, but his primary work was as a printmaker. Born in Leeuwarden, Holland, the son of a civil engineer, Escher spent most of his childhood in Arnhem.
How many Escher works are there?
The Gallery's collection includes more than 400 works by Escher: drawings, illustrated books, technical materials, and impressions of 330 of the artist's 450 prints. Hand with Reflecting Sphere, 1935, lithograph, Rosenwald Collection All M.C. Escher works © Cordon Art-Baarn-the Netherlands.
How did Escher influence popular culture?
Escher's special way of thinking and rich graphics have had a continuous influence in mathematics and art, as well as in popular culture . The Escher intellectual property is controlled by the M.C. Escher Company, while exhibitions of his artworks are managed separately by the M.C. Escher Foundation. [j]
Self-reference and
Evolution of
Evolvability
C ollaborators: Michael Harré, Joseph T. Lizier, Fabio Boschetti, Pavlos Peppas, Stuart Kauffman,Adam Svahn, Emanuele Crosato, RamilNigmatullin,
Richard E. Spinney,Matthew Chadwick, Daniel PolaniCentre for Complex Systems
Faculty of Engineering Prof. Mikhail Prokopenko
Workshop "Evolution of Social Complexity"
Sydney, 13 February 2020
Outline
Self-reference and "tangled hierarchies"
The halting problem and The Liar paradox
Edge of chaos, criticality and phase transitions
Meta-simulation and novelty generation
Emergence of functional self-descriptions
Self and a functional description of "self"
Drawing Hands:
the product, the hands, are undertaking the operation - the drawing of the handsDNA: genetic instructions (sequence) used in
development and functioning of a living organism (function and structure) -a set of "blueprints" needed to construct other components of cells, and copy itselfM. C. Escher, Drawing Hands, Wikipedia Wikipedia
Self-reference
Drawing Hands:
the product, the hands, are undertaking the operation - the drawing of the handsEl FarolBar Problem:
if less than 60% of the population go to the bar, then if more than 60% of the population go to the bar, then KaterynaDirenko: stylized human silhouettes M. C. Escher, Drawing Hands, WikipediaThe Liar paradox
The Liar paradox
Outline
Self-reference and "tangled hierarchies"
The halting problem and The Liar paradox
Edge of chaos, criticality and phase transitions
Meta-simulation and novelty generation
Emergence of functional self-descriptions
Turing Machine (...not that one)
The Imitation Game, 2014
Turing Machine
LudgerHumbert / TEXample/ CC BY 2.5
Turing Machine
Wikipedia
Universal Turing Machine:
can simulate any other machineGlenn D. Blank et al., 2003 http://www.cse.lehigh.edu/~glennb/um/1intro.pdf
M M'sUniversal Decider Turing Machine:
does it exist?M. Prokopenko, M. Harré, J. Lizier, F. Boschetti, P. Peppas, S. Kauffman, Self-referential basis of undecidable
dynamics: from The Liar Paradox and the halting Problem to the edge of chaos, Physics of Life Reviews,
31: 134-156, 2019.
Universal Decider Turing Machine:
does it exist?Universal Decider Turing Machine:
does not exist!Outline
Self-reference and "tangled hierarchies"
The halting problem and The Liar paradox
Edge of chaos, criticality and phase transitions
Meta-simulation and novelty generation
Emergence of functional self-descriptions
Motivation: dynamics of computation
Chris Langton, "Computation at the edge of chaos: Phase transitions and emergent computation" (1991): -how can emergence of computation be explained in a dynamic setting? -how is it related to complexityof the system in point? complex high level structuresGame of Life
self-organisingstructuresGame of Life: convergence?
fixed point or limit cycle ?Conway's game of life:
Game of Life: convergence?
chaotic or strange attractor?Conway's game of life:
a kinetic phase transition driven by •nearest neighbours N c •alignment strength J = v 0 a E. Crosato, R. Spinney, R. Nigmatullin, J. T. Lizier, M. Prokopenko, Thermodynamics of collective motion near criticality, Physical Review E, 97, 012120, 2018.Swarming (collective) motion
The two kinetic phases
disordered motion phasecoherent motion phaseEdge of chaos in collective motion
Outline
Self-reference and "tangled hierarchies"
The halting problem and The Liar paradox
Edge of chaos, criticality and phase transitions
Meta-simulation and novelty generation
Emergence of functional self-descriptions
Universal Cellular Automata: a Metapixel
"Life in Life" by Phillip Bradbury: https://www.youtube .com /watch ?time _continue =4 &v =xP5 -iIeKXE8
CC BY license
Three-way equivalence
M's MSelf and a functional description of "self"
Drawing Hands:
the product, the hands, are undertaking the operation - the drawing of the handsDNA: genetic instructions (sequence) used in
development and functioning of a living organism (function and structure) -a set of "blueprints" needed to construct other components of cells, and copy itselfM. C. Escher, Drawing Hands, Wikipedia Wikipedia
Coding threshold
genotype-phenotype mapping: a self-referential relationship between an encoded description of a living organism (data) and the organism itself (program) "how the genotype-phenotype relationship had come to be?" how a functional self-description ("encoding") could evolve? "Coding threshold" separates an earlier evolutionary stage and the RNA world with the capacity to represent nucleic acid life symbolically, in terms of amino acid sequencesWoese, C.R., A new biology for a new century, Microbiology and Molecular Biology Reviews, 68(2):173-186, 2004
h 3 h 2 h 1Entrapment and Horizontal Gene Transfer
X 1 X 2 X 3 g 1 g 2 g 3Entrapment
Transfer
M. Prokopenko, D. Polani, M. Chadwick. Stigmergicgene transfer and emergence of universal coding,HFSP Journal, 3(5): 317-327, 2009.
Selection pressure: information preservation
how a functional self-description ("encoding") could evolve? hypothesis: maximisation of information preservation through selected channels is one of the main evolutionary pressures information preservation is a consistent motif in biology: evolution extracts valuable information and stores it in the genes this process is relatively slow and noisy ĺa selective advantage: to preserve this information, once capturedModelling evolutionary dynamics
cell (source) replicated cell (receiver) cell in noisy environment (source + noise) self-description (an encoding sequence) encoding translationObjective (fitness) function
max subject to minRecovery of structure
encodingtranslation h "Error interval"Fitness
d over external noiseOutline
Self-reference and "tangled hierarchies"
The halting problem and The Liar paradox
Edge of chaos, criticality and phase transitions
Meta-simulation and novelty generation
Emergence of functional self-descriptions
Genetic code: a functional self-description
DNA: genetic instructions (sequence) used in development and functioning of a living organism (function and structure) -a set of "blueprints" needed to construct other components of cells, and copy itselfWikipedia
Language: a functional self-description
Speech, language, grammar: A ௗ
depicting a person emitting a speech scroll from his mouth, symbolizing speechWikipedia
Culture: a functional self-description
Culture
: Petroglyphs in modern-dayGobustan, Azerbaijan, dating back
to 10,000 BCEWikipedia
The Tower of Babel
by Pieter Bruegel the Elder,1563.Conclusions
universal computation and undecidable dynamics undecidabilityis generated by self-reference, infinite computation and negation computational novelty can be created by agents with universal computation and functional self-description information preservation via functional self-description drives novelty generation across major transitions (genetic, linguistic, cultural) complex systems aredynamical systems with undecidable dynamicsAcknowledgements
Acknowledgements
Acknowledgements
References
Bennett C. H. Undecidable dynamics. Nature, 346: 606-607, 1990.BuldtB. On fixed points, diagonalization, and self-reference. In: FreitagW, RottH, Sturm H, ZinkeA, eds. Von Rang und Namen: essays
in honour of Wolfgang Spohn . Münster: Mentis, 47-63, 2016.CRC Press, 1991.
Cook M. Universality in elementary Cellular Automata. Complex Systems, 15(1): 1-40, 2004.CrosatoE., Spinney R., NigmatullinR., LizierJ., ProkopenkoM. Thermodynamics of collective motion near criticality, Physical Review E,
97: 012120, 2018.
IlachinskiA. Cellular Automata: a discrete universe. Singapore: World Scientific, 2001. Kauffman S. Humanity in a creative universe. New York, NY, USA: Oxford University Press, 2016.Langton C. G. Computation at the edge of chaos: phase transitions and emergent computation. PhysicaD, 42(1-3): 12-37, 1990.
MarkoseS. M. Novelty in complex adaptive systems (CAS) dynamics: a computational theory of actor innovation. PhysicaA: Statistical
Mechanics and its Applications, 344(1): 41-49, 2004.Moore C. Unpredictability and undecidabilityin dynamical systems. Physical Review Letters, 64(20): 2354-2357, 1990.
ProkopenkoM., HarréM., LizierJ., BoschettiF., PeppasP., Kauffman S., Self-referential basis of undecidable dynamics: from The Liar
Paradox and the halting Problem to the edge of chaos. Physics of Life Reviews, 31: 134-156, 2019.Prokopenko, M., Polani, D., Chadwick, M., Stigmergicgene transfer and emergence of universal coding, HFSP, 3(5): 317-327, 2009.
SipserM. Introduction to the theory of computation, 1st edition. Thomson Publishing: International, 1996.
SutnerK. Computational classification of Cellular Automata. International Journal of General Systems, 41(6): 595-607, 2012.
Woese, C.R., A new biology for a new century, Microbiology and Molecular Biology Reviews, 68(2):173-186, 2004.
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