Genetic algorithms and the changing face of scientific theories

Philosophy of Numerical Simulations?
Genetic Algorithms in Numerical Simulations (GNS)
Philosophy of GNS
Finis
References

Numerical Simulations and Scientiﬁc Discovery
paper available at: http://papers.imuntean.net

Ioan Muntean

Department of Philosophy
and
History and Philosophy of Science
University of Leeds

March 9, 2010

1

Philosophy of Numerical Simulations? What are Numerical Simulations (NS)?
Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions
Philosophy of GNS Three stances
Finis The “gloriﬁed slide rule argument”
References My position

Outline
1 Philosophy of Numerical Simulations?
What are Numerical Simulations (NS)?
Philosophical questions
Three stances
The “gloriﬁed slide rule argument”
My position
2 Genetic Algorithms in Numerical Simulations (GNS)
Beyond Turing
Survival and chance in computer science
Inductive programming (skip)
Genetic numerical algorithms (GNS)
3 Philosophy of GNS
What philosophy for GNS?
Arguments for GNS
Metaphysics of GNS
GNS and mathematics
GNS and invariance
GNS and laws of nature
Objections
4 Finis
Risky conclusions
Weaker conclusions
5 References
2


Deﬁnitions

3


Deﬁnitions
Standard: “the use of a computer to build a model involving
equations that we cannot solve analytically”. (P. Humphreys,
E. Winsberg)

3


Deﬁnitions
E. Winsberg)
Non-Standard: NS track the dynamical evolution of real
systems (St. Hartmann).

3


Deﬁnitions
E. Winsberg)
Broad: NS is a computational model that includes the
equations of a model, assumptions, corrections,
interpretations, justiﬁcations, and representations (Humphreys
2004, 110).

3


Deﬁnitions
E. Winsberg)
2004, 110).
History prone NS: more ﬁne-grained, historical distinctions
are needed (E. F. Keller).

3


Definitions
E. Winsberg)
2004, 110).
History prone NS: more fine-grained, historical distinctions
are needed (E. F. Keller).

I take them as “working definitions”
I agree that we need to be more philosophically nuanced
3


4


What are they? What is their status?
Are numerical simulations similar to models? M. Morrison
(2009): they have the same epistemic status)

4


Are NS mere experiments? E. Winsberg, W. Parker: they are
not

4


not
Are numerical experiments mere applications or spinoﬀs of
scientiﬁc theories? We’ll discuss this.

4


not
How do NS contribute to the progress of science? Not yet,
not signiﬁcantly.

4


not
not signiﬁcantly.

Witness the philosophical importance of some scientiﬁc tools:

4


not
not signiﬁcantly.

the microscope (I. Hacking),

4


not
not signiﬁcantly.

the thermometer (H. Chang).

4


not
not signiﬁcantly.

the thermometer (H. Chang).
Why not a philosophy of NS?
4


Mongrels and halfway houses

E. Winsberg: NS are “mongrels”
between experiments and theories and
have features of both theories and of
experiments, without being theories or
experiments.

5


Mongrels and halfway houses

E. Winsberg: NS are “mongrels”
between experiments and theories and
have features of both theories and of
experiments, without being theories or
experiments.
S. Ulam (the father of the Monte
Carlo method, late 1940s): NS are a
“halfway house” between elegant
theory and experimental hardware
(quoted in Keller 2003, 205)

5


The enthusiasts

6


The enthusiasts
It is thus reasonable to conclude that we are at the
threshold of an era of new scientiﬁc methodology. In
view of further technical developments in the near future,
computer experts suggest that we are at present only at
the very beginning of this new era. [...] computer
simulation oﬀers a new tool for science: theoretical
model experiments of a scope and richness far exceeding
anything available before. (Rohrlich 1990, 512,516)

Galison: NS constitute a new epistemology, as a new method
of extracting information from physical measurements, as well
as a new metaphysics that presupposed discrete entities
interacting through stochastic processes (Galison 1996, 120).
6


Some skeptical stances



1 “Old stew in a new pot”: NS are not special for philosophy of
science (Frigg and Reiss 2009; Stockler 2000).

7



2 “Wait-and-see”: We do not know what are the long-term
consequences of the NS

7



2 “Wait-and-see”: We do not know what are the long-term
consequences of the NS
3 “Rage against the machine”: philosophical arguments
pertaining to show that: “computers are dummy” “computers
cannot create” etc.

7


Short answers to skeptics

My answer to 1: what is a novel philosophical problem? We
risk to get to “nothing new under the sun”



My answer to 2: philosophy of science is the history of future
science (so to speak). Wait what? The next Ice Age? NS are
here, alive and kicking.




I focus on 3
It’s more subtle!




I focus on 3
It’s more subtle!
It has a respectable philosophical pedigree (Descartes, Leibniz,
Kant)




I focus on 3
It’s more subtle!
It has a respectable philosophical pedigree (Descartes, Leibniz,
Kant)
It is mathematically and scientiﬁcally challenging (see Godel,
Turing, J.R. Lucas)


Stance 1: “Look! This is something new”?



For instance, if, rather than spilling much ink on
convincing ourselves that simulations are unlike
everything else, we recognize that the epistemological
problems presented to us by simulations have much in
common with the ones that arise in connection with
models, we can take the insights we gain in both ﬁelds
together and try to make progress in constructing the
sought-after new epistemology. (Frigg and Reiss 2009,
611).

With this, I agree



For instance, if, rather than spilling much ink on
convincing ourselves that simulations are unlike
everything else, we recognize that the epistemological
problems presented to us by simulations have much in
common with the ones that arise in connection with
models, we can take the insights we gain in both ﬁelds
together and try to make progress in constructing the
sought-after new epistemology. (Frigg and Reiss 2009,
611).

With this, I agree
I will try to do something similar in last section


Stance 2: The Greek Chorus attitude

10


Stance 2: The Greek Chorus attitude

Wait and see who’s winning the battle. Do not hedge your bets
too early in the game. Philosophers are like Greek chorus, they
come at the end to explain the victory.

10


Stance 3: NS as “gloriﬁed slide rules”
claim C-1
A computer algorithm is no better than the assumptions which it
was built on
The Analytical Engine has no pretensions to originate
anything. It can do whatever we know how to order it to
perform. A letter of A. Lovelace quoted in (Hatree, 1949)

An argument
Computers do not think
Science is a creative process that involves reason and skills
Computers do not contribute to progress (or discovery) in science

Computers are erring in anything, like slide rules do.


Consequences of the gloriﬁed slide rules argument

Demoting NS again
Whenever the analytic solution is discovered, a real experiment
is possible or new data is available, NS can be tossed away.


Consequences of the gloriﬁed slide rules argument

Demoting NS again
Whenever the analytic solution is discovered, a real experiment
is possible or new data is available, NS can be tossed away.
Nothing that NS have achieved could not have been done by
an “army of well-trained scientists working with slide rules”.


The inherently limited nature of NS
NS are subordinate in their nature because they do provide
novel scientiﬁc
knowledge only when other, more rigorous ways of
representing the real world fail:

13


novel scientiﬁc
NS are unreal because unlike experiments and models, they
do not latch directly onto reality

13


novel scientiﬁc
NS lack materiality; Materiality, maybe the most relevant, is
discussed in (Parker 2009).

13


novel scientiﬁc
NS bear no causal connection to the world;

13


novel scientiﬁc
NS are very brute idealizations (Parker, M. Morgan
2005-2009) etc. argue for or against some of these.

13


novel scientiﬁc
NS are fundamentally ﬂawed.

13


novel scientiﬁc
computers cannot simulate the continuum quantities of
physics,

13


novel scientiﬁc
physics,
there are inherent errors of digitization and,

13


novel scientiﬁc
physics,
computer arithmetic is fundamentally limited by G¨del’s
o
incompleteness theorem.

13


novel scientiﬁc
physics,
computer arithmetic is fundamentally limited by G¨del’s
o
incompleteness theorem.
Hence: mathematics can show us what “machines cannot in
principle do”.
13


science and NS

NS are not able to falsify or conﬁrm scientiﬁc theories;


science and NS

NS do not explain


science and NS

NS do not explain
NS do not augment scientiﬁc knowledge.


science and NS

NS do not explain
NS are limited predicting tools, at best, and only when a
pre-existing theoretical model permits it.


science and NS

NS do not explain
Science is about explanation/understanding/uniﬁcation etc.


science and NS

NS do not explain
Science is about explanation/understanding/uniﬁcation etc.

No philosophy of slide rules
In philosophy of science, no country for old slide rules

14


A rejoinder to the “gloriﬁed slide rules” arguments

15


How do we argue against the “gloriﬁed slide rules” arguments?
1 Deny C-1: computers do help us understanding and explain
because they show us how to decompose systems, separate
levels and see the organization of mechanisms. (Simon 1969)


2 Show that historically it is inaccurate (Keller, 2003): Cellular
Automata (CA), Neural Networks (NN) and Genetic
Algorithms (GA) are counterexamples to C2. (CA illustrate
the third stage in Keller).


3 Quantum computing may be the “best” candidate for
surpassing C-1.


3 Quantum computing may be the “best” candidate for
surpassing C-1.

Here I combine 1 and 2, but insist on the paradigm shift ` la
a
Keller.


What do i argue for?

16



Pace Frigg&Reiss, there is philosophical novelty in NS.

16



Not all NS are “dumb slide rules”; Some are more interesting
than others.

16



than others.
More attention to the historical developments of NS (` la
a
Keller and Galison)

16



than others.
a
Keller and Galison)
Some NS are able to:

16



than others.
a
Keller and Galison)
build models,

16



than others.
a
Keller and Galison)
build models,
ﬁnd invariants,

16



than others.
a
Keller and Galison)
build models,
ﬁnd invariants,
discover non-trivial conserved quantities etc.

16



than others.
a
Keller and Galison)
build models,
ﬁnd invariants,
discover non-trivial conserved quantities etc.
The NS under scrutiny here are: Genetic Algorithms

16

Beyond Turing
Philosophy of GNS
Finis
References

Outline
1 Philosophy of Numerical Simulations?
What are Numerical Simulations (NS)?
Philosophical questions
Three stances
The “gloriﬁed slide rule argument”
My position
2 Genetic Algorithms in Numerical Simulations (GNS)
Beyond Turing
3 Philosophy of GNS
What philosophy for GNS?
Arguments for GNS
Metaphysics of GNS
GNS and mathematics
GNS and invariance
GNS and laws of nature
Objections
4 Finis
Risky conclusions
Weaker conclusions
5 References
17

Beyond Turing
Philosophy of GNS
Finis
References

Stochasticity and NS
Biomimetics
Q-1: How can computers be made to do what needs to be done,
without being told exactly how to do it?

The “gloriﬁed slide rules” argument uses the Turing machine
paradigm.

18

Beyond Turing
Philosophy of GNS
Finis
References

Biomimetics

paradigm.
Are all machine Turing machines?

18

Beyond Turing
Philosophy of GNS
Finis
References

Biomimetics

paradigm.
Build machines inspired by learning, discovery, game playing,
solving real-life problems, etc.

Beyond Turing
Philosophy of GNS
Finis
References

Biomimetics

paradigm.
Hence adopt biomimetics

Beyond Turing
Philosophy of GNS
Finis
References

Biomimetics

paradigm.
1 Go stochastic in building algorithms!

Beyond Turing
Philosophy of GNS
Finis
References

Biomimetics

paradigm.
1 Go stochastic in building algorithms!
2 Go Darwinian in programming computers

Beyond Turing
Philosophy of GNS
Finis
References

Do philosophers talk about non-Turing machines?

CA, GA and NN can go beyond what a Turing machine is
able to do. So did the Monte Carlo method (ﬁrst NS).

Beyond Turing
Philosophy of GNS
Finis
References


Are these solutions philosophically attractive?

Beyond Turing
Philosophy of GNS
Finis
References


The literature on NS ignores GA

Beyond Turing
Philosophy of GNS
Finis
References


There are interesting discussions on CA and NN. (Keller,
2003) (Barberousse, Franceschelli, and Imbert 2007) and,
more dogmatically, (Wolfram 2002).

Beyond Turing
Philosophy of GNS
Finis
References


The literature on NN is well-known to philosophers: (Paul
and Patricia Churchland)

Beyond Turing
Philosophy of GNS
Finis
References


The literature on NN is well-known to philosophers: (Paul
and Patricia Churchland)
I focus here on GA and GP

Beyond Turing
Philosophy of GNS
Finis
References

Evolution of algorithms

20

Beyond Turing
Philosophy of GNS
Finis
References


Speculated by Turing in 1948.

Beyond Turing
Philosophy of GNS
Finis
References


Based on genetic or evolutionary search by which a
“combination of genes is looked for, the criterion being the
survival value”.

Beyond Turing
Philosophy of GNS
Finis
References


survival value”.
Turing in Mind (1950): “the child-machine needs to be taught
and surveyed. Then another child-machine tried and
compared to the ﬁrst etc.”

Beyond Turing
Philosophy of GNS
Finis
References


survival value”.
the child machine = hereditary material,

Beyond Turing
Philosophy of GNS
Finis
References


survival value”.
the changes within it = genetic mutation and

Beyond Turing
Philosophy of GNS
Finis
References


survival value”.
natural selection = “judgment of the experimenter”

Beyond Turing
Philosophy of GNS
Finis
References


survival value”.
natural selection = “judgment of the experimenter”
In a unpublished paper, Turing realized that such a genetic
search implied randomness (Turing 1996).

Beyond Turing
Philosophy of GNS
Finis
References

The 1970s and 1980s

Alien (1979)
Aliens (1986)
Alien (1992)
Alien Resurrection (1997)
ABBA’s “Take a chance on me”
Koza, Holland et al.: Birth of the Genetic Programming and
Genetic Algorithms: 1986 to 1995

21

Beyond Turing
Philosophy of GNS
Finis
References

J. Holland’s genetic programming

22

Beyond Turing
Philosophy of GNS
Finis
References

Starts from a given number of initial programs randomly
distributed in a given space of solutions.

22

Beyond Turing
Philosophy of GNS
Finis
References

Based on relative results, the best competitors are chosen and
reproduced

22

Beyond Turing
Philosophy of GNS
Finis
References

reproduced
Oﬀspring have some (randomly chosen) features of the
predecessors.

22

Beyond Turing
Philosophy of GNS
Finis
References

reproduced
predecessors.
The best competitor wins and constitutes the solutions of the
problem.

22

Beyond Turing
Philosophy of GNS
Finis
References

reproduced
predecessors.
problem.
GA are implementations of the biological evolution

22

Beyond Turing
Philosophy of GNS
Finis
References

reproduced
predecessors.
problem.
Optimization: searching for the best solution is based on some
pre-established criteria

22

Beyond Turing
Philosophy of GNS
Finis
References

reproduced
predecessors.
problem.
Unlike in Turing, selection occurs at the level of population,
not at the level of individual algorithms.

22

Beyond Turing
Philosophy of GNS
Finis
References

reproduced
predecessors.
problem.
Unlike in Turing, selection occurs at the level of population,
not at the level of individual algorithms.
Adaptation in Natural and Artiﬁcial Systems (1975)
22

Beyond Turing
Philosophy of GNS
Finis
References

Stochastic algorithms

Output is manifestly stochastic.

23

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