This document summarizes a lecture on complexity and computation in nature given by Hector Zenil. It discusses how natural systems like slime molds and cellular automata can be viewed as computing substrates. It also examines definitions of life and computation, exploring whether living systems and phenomena in nature can be said to compute. The document proposes using algorithmic information theory and analyzing dynamical properties and programmability to assess computational abilities in natural systems.

1. How can we test for artificial life?
Complexity and Computation in Nature
Hector Zenil
hector.zenil@ki.se
November 7, 2013
ShangAI Lectures on Natural and Artificial Intelligence
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2. Complexity and Computation in Nature
Natural computing
We all believe we know how computers look like
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3. Complexity and Computation in Nature
Natural computing
And how they definitely don’t look like. Right?
(Yellow slime mold: a single cell! with thousands of nuclei. They are formed
when individual flagellated cells swarm together and fuse.)
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4. Complexity and Computation in Nature
Natural computing
Human computers
But they did use to look like this!
A computer at work, c. 1940.
Oxford English Dictionary: “A person employed to make calculations in an
observatory, in surveying, etc.”
When Computers Were Human by Grier, David Alan (Nov 1, 2013)
http://www.computerhistory.org/revolution/calculators/1/65/2209
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5. Complexity and Computation in Nature
Natural computing
Turing’s computing model
Other computationally equivalent models: Post Tag systems, Church lambda
calculus, Kleene recursive functions.
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6. Complexity and Computation in Nature
Natural computing
Richard Feynman
I don’t believe in computer science.... To me science is the study of the
behaviour of nature...
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7. Complexity and Computation in Nature
Natural computing
Natural computing
Some computer scientists are trying to compute with completely different
substrates.
Physarum (slime mold) (left) and Electrified liquid crystals (right) Slime moulds are
especially adept at finding optimal solutions to transportation network problems, such
as paths and even inspiring a solution to the (NP complete) travel salesman person
problem and Voronoi partitions.
Computers Made Out of DNA, Slime and Other Strange Stuff (04.02.13)
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8. Complexity and Computation in Nature
Natural computing
What is a computer? A Digital? Electronic?
Quantum device?
(e.g. circadian clock in plants and animals: computing time in a 24hr period)
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9. Complexity and Computation in Nature
Natural computing
Can a computer simulate the universe?
In fact, Feynman asked what kind of computer could simulate the universe...
Classical computers cannot simulate the universe because the full description
of quantum physics requires too many variables. If one particle is described
by 2 variables, for example, then to simulate 100 particles need 2100 (a 1
followed by 30 zeroes).
Quantum computers: qubits. They keep up with the world capacity. (and can
solve faster some classical computations)
Whether quantum computers are actually possible and scalable is yet
unknown. Nor it is known whether a more fundamental classical substratum
gives rise to quantum phenomena. But we can ask about natural
computation, even if not quantum mechanical.
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10. Complexity and Computation in Nature
Natural computing
Natural computation and computation in nature
Fungi “fairy” circles and lava stone hexagons.
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11. Complexity and Computation in Nature
Artificial life and synthetic biology
Reengineering vs creating life
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12. Complexity and Computation in Nature
Artificial life and synthetic biology
John von Neumann
J. von Neuman’s self-replication interest (1950s).
von Neumann (with S. Ulam) started the field of Cellular Automata
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13. Complexity and Computation in Nature
Artificial life and synthetic biology
Cellular Automata
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14. Complexity and Computation in Nature
Artificial life and synthetic biology
Rule 30 long run
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15. Complexity and Computation in Nature
Artificial life and synthetic biology
Rule 30 operating in nature?
Image: Zenil, 2012.
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16. Complexity and Computation in Nature
Artificial life and synthetic biology
von Neumann’s universal constructor (cont.)
J. von Neumann’s universal constructor (claimed to have 28 states).
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17. Complexity and Computation in Nature
Artificial life and synthetic biology
RepRap
The RepRap machine (University of Bath , UK) prints all its components, it
(almost) self-replicates (it does not assemble the pieces).
In computer science a self-reproducing computer program is a computer
program that, when executed, outputs its own code. This is also called a quine.
Here is an example program in the Python programming language:
a=’a=%r;print a%%a’;print a%a
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18. Complexity and Computation in Nature
Artificial life and synthetic biology
Conway’s Game of Life
Mimics many properties of life (movement, persistence, interaction,
evolution).
It is capable of Turing universality!
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19. Complexity and Computation in Nature
Artificial life and synthetic biology
Cellular automata as models of nature
“Fairy” circles explained with cellular automata.
Image: Norbert Juergens and Science (2013).
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20. Complexity and Computation in Nature
Artificial life and synthetic biology
Life as self-replication?
Langton’s loop shows that self-replication does not require Turing
universality.
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21. Complexity and Computation in Nature
Artificial life and synthetic biology
Crystals...
However, self-replication is not enough by itself to characterise life:
Crystals self-replicate too!
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22. Complexity and Computation in Nature
Artificial life and synthetic biology
Essential requirements for life?
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23. Complexity and Computation in Nature
Artificial life and synthetic biology
Information, computation and life
An informational definition (G.F. Joyce, Bit by Bit: The Darwinian Basis of Life,
2012) of life:
A (genetic) system that contains more bits than the number that were
required to initiate its operation. (added parenthesis)
A computational view (John Hopfield, J. Theor. Biol. 171, 53-60, 1994):
All biological systems perform some kind of computation. Computation
is inherent to adaptive systems and makes biology different from physics.
Leroy Cronin (TEDx conference, 2011) proposes that:
Life is anything that can undergo evolution (survival of the fittest).
Matter that can evolve is alive.
Borderline case: Virus evolve (not exactly by their own though) yet they are
only matter (encapsulated genetic material).
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24. Complexity and Computation in Nature
A behavioural approach to computation
Do things really compute?
There is a current debate around the concept of natural computationalism.
Do things and living systems compute?
Stephen Wolfram (A New Kind of Science, (2002)):
There is a simple rule for our universe.
“Rule” here means a Turing computable rule.
Seth Lloyd (Programming the Universe, (2007)):
The universe computes itself.
“Computes” here means quantum computes.
Hillary Putnam’s “Multiple realizability” criticism to computationalism
(functionalism).
Chalmer’s “Does a Rock Implement Every Finite-State Automaton?”
I want a measure to associate it to (and try answer) these claims/questions.
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25. Complexity and Computation in Nature
A behavioural approach to computation
Algorithmic information theory to the rescue?
Which string looks more random?
(a) 1111111111111111111111111111111111111111
(b) 0011010011010010110111010010100010111010
(c) 0101010101010101010101010101010101010101
Definition
KU (s) = min{|p|, U(p) = s}
(1)
Compressibility and algorithmic randomness
A string with low Kolmogorov complexity is c-compressible if |p| + c = |s|. A
string is random if K(s) ≈ |s|.
[Kolmogorov (1965); Chaitin (1966)]
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26. Complexity and Computation in Nature
A behavioural approach to computation
Example of an evaluation of K
The string (b) 01010101...01 is not algorithmic random (or has low K
complexity) because it can be produced by the following program:
Program A(i):
1: n:= 0
2: Print n mod 2
3: n:= n+1
4: If n=i Goto 6
5: Goto 2
6: End
The length of A (in bits) is an upper bound of K(010101...01).
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27. Complexity and Computation in Nature
A behavioural approach to computation
Behavioural classes of abstract computing
machines
Wolfram’s computational classes of behaviour:
Class I: system evolves into a homogeneous state.
Class II: system evolves in a periodic state.
Class III: system evolves into random-looking states.
Class IV: system evolves into localised complex structures.
Living systems clearly fall in class IV systems.
[Wolfram, (1994)]
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28. Complexity and Computation in Nature
A behavioural approach to computation
Asymptotic behaviour of compressed evolutions
[Zenil, Complex Systems (2010)]
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29. Complexity and Computation in Nature
A behavioural approach to computation
A behavioural approach to computation (and life
recognition)
A Turing-test like test strategy to the question of life (instead of Turing’s
original question of artificial intelligence):
[Zenil, Philosophy & Technology and SAPERE, (2013)]
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30. Complexity and Computation in Nature
A behavioural approach to computation
Answering Chalmer’s rock question
Figure : ECA R4 has a low Ct value for any n and t (it doesn’t react much to external
n
stimuli).
[Zenil, Philosophy & Technology, (2013)]
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31. Complexity and Computation in Nature
A behavioural approach to computation
Turing universality
Figure : ECA R110 has large asymptotic coefficient Ct value for large enough choices
n
of t and n, which is compatible with the fact that it is Turing universal (for particular
semi-periodic initial configurations).
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32. Complexity and Computation in Nature
A behavioural approach to computation
A hierarchical view of computing systems (and life?)
The measure can be applied to other than computers.
Programmability of physical and biological entities sorted by variability
versus controllability:
The diagonal determines the degree of programmability.
[Zenil, Ball, Tegn´ r, ECAL MIT Press Proceedings, (2013)]
e
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33. Complexity and Computation in Nature
A behavioural approach to computation
Phorphyrins: mapping behaviour to stimuli
One can find the specific stimuli producing specific behaviours and go to the lab and
test it. Compound parameters that have highest or lowest behavioural impact can be
tested and programmed in silico.
(Hemes in hemoglobin. They give the red color to blood)
[Terrazas, Zenil and Krasnogor, Natural Computing (in press)]
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34. Complexity and Computation in Nature
A behavioural approach to computation
Programmable Medicine
Building on molecular (DNA and non-DNA, e.g. porphyrin computation)
imagine the introduction of an array of these molecules with a simple logic to
treatments releasing a payload if expressing cancer markers, etc.
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35. Complexity and Computation in Nature
A behavioural approach to computation
The EMBL-EBI BioModel’s Database
The EMBL-EBI BioModel DB is a curated database of mathematical published
(about 400) models related to living organisms.
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36. Complexity and Computation in Nature
A behavioural approach to computation
Cell cycle versus metabolic pathways
Variability analysis: Models cluster by their role in living processes.
[Zenil, Ball, Tegn´ r, ECAL MIT Press Proceedings, (2013)]
e
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37. Complexity and Computation in Nature
A behavioural approach to computation
Variability and controllability of biological
models
Information content trajectories
(from EMBL-EBI model simulations):
Programmability is a combination of variability and controllability
[Zenil, Ball, Tegn´ r, ECAL MIT Press Proceedings, (2013)]
e
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38. Complexity and Computation in Nature
A behavioural approach to computation
H. Zenil, Compression-based Investigation of the Dynamical Properties of
Cellular Automata and Other Systems, Complex Systems, Vol. 19, No. 1, pages
1-28, 2010.
H. Zenil, What is Nature-like Computation? A Behavioural Approach and a
Notion of Programmability, Philosophy & Technology (special issue on History
and Philosophy of Computing), 2013.
H. Zenil, On the Dynamic Qualitative Behavior of Universal Computation
Complex Systems, vol. 20, No. 3, pp. 265-278, 2012.
G. Terrazas, H. Zenil and N. Krasnogor, Exploring Programmable Self-Assembly
in Non DNA-based Computing, Natural Computing, DOI:
10.1007/s11047-013-9397-2.
H. Zenil and E. Villarreal-Zapata, Asymptotic Behaviour and Ratios of Complexity
in Cellular Automata Rule Spaces, Journal of Bifurcation and Chaos (in press).
H. Zenil, G. Ball and J. Tegn´ r, Testing Biological Models for Non-linear
e
Sensitivity with a Programmability Test. In P. Lio, O. Miglino, G. Nicosia, S. Nolfi
`
and M. Pavone (eds), Advances in Artificial Intelligence, ECAL 2013, pp.
1222-1223, MIT Press, 2013.
H. Zenil, A Turing Test-Inspired Approach to Natural Computation. In G.
Primiero and L. De Mol (eds.), Turing in Context II (Brussels, 10-12 October 2012),
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39. Complexity and Computation in Nature
A behavioural approach to computation
Historical and Contemporary Research in Logic, Computing Machinery and
Artificial Intelligence, Proceedings published by the Royal Flemish Academy of
Belgium for Science and Arts, 2013.
A Behavioural Foundation for Natural Computing and a Programmability Test. In
G. Dodig-Crnkovic and R. Giovagnoli (eds), Computing Nature: Turing Centenary
Perspective, SAPERE Series vol. 7, Springer, 2013.
H. Zenil, Turing Patterns with Turing Machines: Emergence and Low-level
Structure Formation, Natural Computing, 12(2): 291-303 (2013), 2013.
J.-P. Delahaye and H. Zenil, Numerical Evaluation of the Complexity of Short
Strings: A Glance Into the Innermost Structure of Algorithmic Randomness,
Applied Mathematics and Computation 219, pp. 63-77, 2012.
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