Genetic algorithms and the changing face of scientific theories

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

Philosophy of GNSFinis

References

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

Ioan Muntean

Department of Philosophyand

History and Philosophy of ScienceUniversity of Leeds

March 9, 2010

1

ioan

Sticky Note

Comments are enabled in Acrobat Reader



References

What are Numerical Simulations (NS)?Philosophical questionsThree stancesThe “glorified slide rule argument”My position

Outline1 Philosophy of Numerical Simulations?


2 Genetic Algorithms in Numerical Simulations (GNS)Beyond TuringSurvival and chance in computer scienceInductive programming (skip)Genetic numerical algorithms (GNS)

3 Philosophy of GNSWhat philosophy for GNS?Arguments for GNSMetaphysics of GNSGNS and mathematicsGNS and invarianceGNS and laws of natureObjections

4 FinisRisky conclusionsWeaker conclusions

5 References

2



References


Definitions

Standard: “the use of a computer to build a model involvingequations that we cannot solve analytically”. (P. Humphreys,E. Winsberg)Non-Standard: NS track the dynamical evolution of realsystems (St. Hartmann).Broad: NS is a computational model that includes theequations of a model, assumptions, corrections,interpretations, justifications, and representations (Humphreys2004, 110).History prone NS: more fine-grained, historical distinctionsare needed (E. F. Keller).

I take them as “working definitions”

I agree that we need to be more philosophically nuanced

3



References


Definitions

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

Non-Standard: NS track the dynamical evolution of realsystems (St. Hartmann).Broad: NS is a computational model that includes theequations of a model, assumptions, corrections,interpretations, justifications, and representations (Humphreys2004, 110).History prone NS: more fine-grained, historical distinctionsare needed (E. F. Keller).



3



References


Definitions

Standard: “the use of a computer to build a model involvingequations that we cannot solve analytically”. (P. Humphreys,E. Winsberg)Non-Standard: NS track the dynamical evolution of realsystems (St. Hartmann).

Broad: NS is a computational model that includes theequations of a model, assumptions, corrections,interpretations, justifications, and representations (Humphreys2004, 110).History prone NS: more fine-grained, historical distinctionsare needed (E. F. Keller).



3



References


Definitions

Standard: “the use of a computer to build a model involvingequations that we cannot solve analytically”. (P. Humphreys,E. Winsberg)Non-Standard: NS track the dynamical evolution of realsystems (St. Hartmann).Broad: NS is a computational model that includes theequations of a model, assumptions, corrections,interpretations, justifications, and representations (Humphreys2004, 110).

History prone NS: more fine-grained, historical distinctionsare needed (E. F. Keller).



3



References


Definitions




3



References


Definitions




3



References


Definitions




3



References


What are they? What is their status?

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

Are NS mere experiments? E. Winsberg, W. Parker: they arenot

Are numerical experiments mere applications or spinoffs ofscientific theories? We’ll discuss this.

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

Witness the philosophical importance of some scientific tools:

the microscope (I. Hacking),the thermometer (H. Chang).

Why not a philosophy of NS?

4



References










4



References










4



References










4



References










4



References










4



References







Witness the philosophical importance of some scientific tools:the microscope (I. Hacking),

the thermometer (H. Chang).


4



References







Witness the philosophical importance of some scientific tools:the microscope (I. Hacking),the thermometer (H. Chang).


4



References







Witness the philosophical importance of some scientific tools:the microscope (I. Hacking),the thermometer (H. Chang).


4



References


Mongrels and halfway houses

E. Winsberg: NS are “mongrels”between experiments and theories andhave features of both theories and ofexperiments, without being theories orexperiments.

S. Ulam (the father of the MonteCarlo method, late 1940s): NS are a“halfway house” between eleganttheory and experimental hardware(quoted in Keller 2003, 205)

5



References



E. Winsberg: NS are “mongrels”between experiments and theories andhave features of both theories and ofexperiments, without being theories orexperiments.S. Ulam (the father of the MonteCarlo method, late 1940s): NS are a“halfway house” between eleganttheory and experimental hardware(quoted in Keller 2003, 205)

5



References




5



References




5



References


The enthusiasts

It is thus reasonable to conclude that we are at thethreshold of an era of new scientific methodology. Inview of further technical developments in the near future,computer experts suggest that we are at present only atthe very beginning of this new era. [...] computersimulation offers a new tool for science: theoreticalmodel experiments of a scope and richness far exceedinganything available before. (Rohrlich 1990, 512,516)

Galison: NS constitute a new epistemology, as a new methodof extracting information from physical measurements, as wellas a new metaphysics that presupposed discrete entitiesinteracting through stochastic processes (Galison 1996, 120).

6



References


The enthusiasts

It is thus reasonable to conclude that we are at thethreshold of an era of new scientific methodology. Inview of further technical developments in the near future,computer experts suggest that we are at present only atthe very beginning of this new era. [...] computersimulation offers a new tool for science: theoreticalmodel experiments of a scope and richness far exceedinganything available before. (Rohrlich 1990, 512,516)

Galison: NS constitute a new epistemology, as a new methodof extracting information from physical measurements, as wellas a new metaphysics that presupposed discrete entitiesinteracting through stochastic processes (Galison 1996, 120).

6



References


Some skeptical stances

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

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

3 “Rage against the machine”: philosophical argumentspertaining to show that: “computers are dummy” “computerscannot create” etc.

7



References






7



References






7



References






7



References


Short answers to skeptics

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

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

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)

8



References





I focus on 3

It’s more subtle!



8



References





I focus on 3

It’s more subtle!



8



References





I focus on 3

It’s more subtle!



8



References





I focus on 3

It’s more subtle!



8



References





I focus on 3

It’s more subtle!



8



References


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

For instance, if, rather than spilling much ink onconvincing ourselves that simulations are unlikeeverything else, we recognize that the epistemologicalproblems presented to us by simulations have much incommon with the ones that arise in connection withmodels, we can take the insights we gain in both fieldstogether and try to make progress in constructing thesought-after new epistemology. (Frigg and Reiss 2009,611).

With this, I agree

I will try to do something similar in last section

9



References




With this, I agree


9



References




With this, I agree


9



References


Stance 2: The Greek Chorus attitude

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

10



References


Stance 2: The Greek Chorus attitude

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

10



References


Stance 3: NS as “glorified slide rules”

claim C-1

A computer algorithm is no better than the assumptions which itwas built on

The Analytical Engine has no pretensions to originateanything. It can do whatever we know how to order it toperform. A letter of A. Lovelace quoted in (Hatree, 1949)

An argument

Computers do not thinkScience is a creative process that involves reason and skillsComputers do not contribute to progress (or discovery) in science

Computers are erring in anything, like slide rules do.

I call this argument and those of its ilk: the “glorified sliderules” argument

11



References


Stance 3: NS as “glorified slide rules”

claim C-1

A computer algorithm is no better than the assumptions which itwas built on

The Analytical Engine has no pretensions to originateanything. It can do whatever we know how to order it toperform. A letter of A. Lovelace quoted in (Hatree, 1949)

An argument

Computers do not thinkScience is a creative process that involves reason and skillsComputers do not contribute to progress (or discovery) in science

Computers are erring in anything, like slide rules do.I call this argument and those of its ilk: the “glorified sliderules” argument

11



References


Consequences of the glorified slide rules argument

Demoting NS again

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

Nothing that NS have achieved could not have been done byan “army of well-trained scientists working with slide rules”.

12



References


Consequences of the glorified slide rules argument

Demoting NS again

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

Nothing that NS have achieved could not have been done byan “army of well-trained scientists working with slide rules”.

12



References


The inherently limited nature of NS

NS are subordinate in their nature because they do providenovel scientificknowledge only when other, more rigorous ways ofrepresenting the real world fail:

NS are unreal because unlike experiments and models, theydo not latch directly onto reality

NS lack materiality; Materiality, maybe the most relevant, isdiscussed in (Parker 2009).NS bear no causal connection to the world;NS are very brute idealizations (Parker, M. Morgan2005-2009) etc. argue for or against some of these.

NS are fundamentally flawed.

computers cannot simulate the continuum quantities ofphysics,there are inherent errors of digitization and,computer arithmetic is fundamentally limited by Godel’sincompleteness theorem.Hence: mathematics can show us what “machines cannot inprinciple do”.

13



References



NS are subordinate in their nature because they do providenovel scientificknowledge only when other, more rigorous ways ofrepresenting the real world fail:NS are unreal because unlike experiments and models, theydo not latch directly onto reality




13



References




NS lack materiality; Materiality, maybe the most relevant, isdiscussed in (Parker 2009).

NS bear no causal connection to the world;NS are very brute idealizations (Parker, M. Morgan2005-2009) etc. argue for or against some of these.



13



References




NS lack materiality; Materiality, maybe the most relevant, isdiscussed in (Parker 2009).NS bear no causal connection to the world;

NS are very brute idealizations (Parker, M. Morgan2005-2009) etc. argue for or against some of these.



13



References







13



References







13



References






computers cannot simulate the continuum quantities ofphysics,

there are inherent errors of digitization and,computer arithmetic is fundamentally limited by Godel’sincompleteness theorem.Hence: mathematics can show us what “machines cannot inprinciple do”.

13



References






computers cannot simulate the continuum quantities ofphysics,there are inherent errors of digitization and,

computer arithmetic is fundamentally limited by Godel’sincompleteness theorem.Hence: mathematics can show us what “machines cannot inprinciple do”.

13



References






computers cannot simulate the continuum quantities ofphysics,there are inherent errors of digitization and,computer arithmetic is fundamentally limited by Godel’sincompleteness theorem.

Hence: mathematics can show us what “machines cannot inprinciple do”.

13



References







13



References


science and NS

NS are not able to falsify or confirm scientific theories;

NS do not explain

NS do not augment scientific knowledge.

NS are limited predicting tools, at best, and only when apre-existing theoretical model permits it.

Science is about explanation/understanding/unification etc.

No philosophy of slide rules

In philosophy of science, no country for old slide rules

14



References


science and NS


NS do not explain






14



References


science and NS


NS do not explain






14



References


science and NS


NS do not explain






14



References


science and NS


NS do not explain






14



References


science and NS


NS do not explain






14



References


science and NS


NS do not explain






14



References


A rejoinder to the “glorified slide rules” arguments

How do we argue against the “glorified slide rules” arguments?

1 Deny C-1: computers do help us understanding and explainbecause they show us how to decompose systems, separatelevels and see the organization of mechanisms. (Simon 1969)

2 Show that historically it is inaccurate (Keller, 2003): CellularAutomata (CA), Neural Networks (NN) and GeneticAlgorithms (GA) are counterexamples to C2. (CA illustratethe third stage in Keller).

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

Here I combine 1 and 2, but insist on the paradigm shift a laKeller.

15



References








15



References








15



References








15



References








15



References


What do i argue for?

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

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

More attention to the historical developments of NS (a laKeller and Galison)

Some NS are able to:

build models,find invariants,discover non-trivial conserved quantities etc.

The NS under scrutiny here are: Genetic Algorithms

16



References









16



References









16



References









16



References









16



References







build models,

find invariants,discover non-trivial conserved quantities etc.


16



References







build models,find invariants,

discover non-trivial conserved quantities etc.


16



References









16



References









16



References

Beyond TuringSurvival and chance in computer scienceInductive programming (skip)Genetic numerical algorithms (GNS)






5 References

17



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 machineparadigm.

Are all machine Turing machines?

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

Hence adopt biomimetics

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

18



References



Biomimetics







18



References



Biomimetics







18



References



Biomimetics







18



References



Biomimetics






1 Go stochastic in building algorithms!

2 Go Darwinian in programming computers

18



References



Biomimetics







18



References


Do philosophers talk about non-Turing machines?

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

Are these solutions philosophically attractive?

The literature on NS ignores GA

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

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

I focus here on GA and GP

19



References









19



References









19



References









19



References









19



References









19



References


Evolution of algorithms

Speculated by Turing in 1948.

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

Turing in Mind (1950): “the child-machine needs to be taughtand surveyed. Then another child-machine tried andcompared to the first etc.”

the child machine = hereditary material,the changes within it = genetic mutation andnatural selection = “judgment of the experimenter”

In a unpublished paper, Turing realized that such a geneticsearch implied randomness (Turing 1996).

20



References








20



References








20



References








20



References






the child machine = hereditary material,

the changes within it = genetic mutation andnatural selection = “judgment of the experimenter”


20



References






the child machine = hereditary material,the changes within it = genetic mutation and

natural selection = “judgment of the experimenter”


20



References








20



References








20



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 andGenetic Algorithms: 1986 to 1995

21



References


J. Holland’s genetic programming

Starts from a given number of initial programs randomlydistributed in a given space of solutions.Based on relative results, the best competitors are chosen andreproducedOffspring have some (randomly chosen) features of thepredecessors.The best competitor wins and constitutes the solutions of theproblem.GA are implementations of the biological evolutionOptimization: searching for the best solution is based on somepre-established criteriaUnlike in Turing, selection occurs at the level of population,not at the level of individual algorithms.

Adaptation in Natural and Artificial Systems (1975)

22



References



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

Based on relative results, the best competitors are chosen andreproducedOffspring have some (randomly chosen) features of thepredecessors.The best competitor wins and constitutes the solutions of theproblem.GA are implementations of the biological evolutionOptimization: searching for the best solution is based on somepre-established criteriaUnlike in Turing, selection occurs at the level of population,not at the level of individual algorithms.


22



References



Starts from a given number of initial programs randomlydistributed in a given space of solutions.Based on relative results, the best competitors are chosen andreproduced

Offspring have some (randomly chosen) features of thepredecessors.The best competitor wins and constitutes the solutions of theproblem.GA are implementations of the biological evolutionOptimization: searching for the best solution is based on somepre-established criteriaUnlike in Turing, selection occurs at the level of population,not at the level of individual algorithms.


22



References



Starts from a given number of initial programs randomlydistributed in a given space of solutions.Based on relative results, the best competitors are chosen andreproducedOffspring have some (randomly chosen) features of thepredecessors.

The best competitor wins and constitutes the solutions of theproblem.GA are implementations of the biological evolutionOptimization: searching for the best solution is based on somepre-established criteriaUnlike in Turing, selection occurs at the level of population,not at the level of individual algorithms.


22



References



Starts from a given number of initial programs randomlydistributed in a given space of solutions.Based on relative results, the best competitors are chosen andreproducedOffspring have some (randomly chosen) features of thepredecessors.The best competitor wins and constitutes the solutions of theproblem.

GA are implementations of the biological evolutionOptimization: searching for the best solution is based on somepre-established criteriaUnlike in Turing, selection occurs at the level of population,not at the level of individual algorithms.


22



References



Starts from a given number of initial programs randomlydistributed in a given space of solutions.Based on relative results, the best competitors are chosen andreproducedOffspring have some (randomly chosen) features of thepredecessors.The best competitor wins and constitutes the solutions of theproblem.GA are implementations of the biological evolution

Optimization: searching for the best solution is based on somepre-established criteriaUnlike in Turing, selection occurs at the level of population,not at the level of individual algorithms.


22



References



Starts from a given number of initial programs randomlydistributed in a given space of solutions.Based on relative results, the best competitors are chosen andreproducedOffspring have some (randomly chosen) features of thepredecessors.The best competitor wins and constitutes the solutions of theproblem.GA are implementations of the biological evolutionOptimization: searching for the best solution is based on somepre-established criteria

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


22



References





22



References





22



References


Stochastic algorithms

Output is manifestly stochastic.

23



References


Developments in GA

Crossover takes two individuals (parents) and produces twonew individuals, the offspring,

by swapping parts of the parents (the simplest crossoveroperator exchanges substrings of the parents)

Crossover moves the search towards those regions of thesearch space in which results are most likely to befound.(Tomassini 1995)

Mutation is a background redistribution of strings to preventpremature convergence to local optima.

Termination condition: when the sought-for level of optimalityis reached or when all the solutions converge to one candidate

24



References


Developments in GA






24



References


Developments in GA






24



References


Developments in GA






24



References


Developments in GA






24



References


Results of GA/GP

GA

are able to reinvent patented inventions: the negativefeedback (Black 1927)

are able to find algorithms in quantum computing–toocomplicated to be discovered by humans.

find patterns in the EEG before the epileptic seizure (butcan’t predict it!)

find more interesting patterns before earthquakes (but too lateand in general without impact)

25



References


Results of GA/GP

GA





25



References


Results of GA/GP

GA





25



References


Results of GA/GP

GA





25



References


A simple result

The algorithm takes pairs of numbers between −1 and +1that fit perfectly the quadratic polynomial x2 + x + 1 and aset of elementary or “desired” operators F = {+;−;×; / }used as primitive of the symbolic regression.

The initial population randomly constructed had theindividuals: x + 1; x2 + 1; 2; x and were fitted with the databased on a classical metric: the area covered by the curverepresented by the competitor and the given set of data.

After the second generation and after applying the crossoveroperator, the result was as expected x2 + x + 1.

26



References


A simple result




26



References


A simple result




26



References


A simple result




26



References


GA in a snapshot

produce an initial population of individuals

while termination condition not met do

evaluate the fitness of all individuals

select fitter individuals for reproduction

produce new individuals

generate a new population by inserting some new good

individuals and by discarding some old/bad

individuals

mutate some individuals

endwhile

27



References


GA in a snapshot

produce an initial population of individuals

while termination condition not met do

evaluate the fitness of all individuals

select fitter individuals for reproduction

produce new individuals

generate a new population by inserting some new good

individuals and by discarding some old/bad

individuals

mutate some individuals

endwhile

27



References


Problems of GA

GA are sensitive to the initial population. For a different set ofinitial population, the generation can take several iterations, butfor simple enough expressions, the GA converge

28



References


BACON, the software

BACON is a software best on induction (1980s by H. Simon,P. Langley, J. Shrager, etc)

Other software: OCCAM, GALILEO, HUYGENS.

BACON rediscovered Kepler’s laws, Prout’s hypothesis aboutatomic structure, etc.

Bacon had a bad reception among philosophers, despiteSimon’s arguments (Simon, 1992).

BACON is marred with the problem of induction, does notexplain, does not help us with understanding.

It’s based on a totally weak analogy.

It threatens rationality of science

Does not explain and help us with understanding science.

29



References


BACON, the software









29



References


BACON, the software









29



References


BACON, the software









29



References


BACON, the software









29



References


BACON, the software









29



References


BACON, the software









29



References


BACON, the software









29



References


BACON, the software









29



References


Planck’s discoveryFrom:

To:U(ν) = U(ω)dωdν = 8π

c3hν3

e~ω/kT−1

30



References


BACON against the roulette (skip)

GA score better than BACON because they avoid localoptima.

Too complicated to discuss here.

31



References


BACON against the roulette (skip)

GA score better than BACON because they avoid localoptima.


31



References


ADAM, the robot scientist (skip)

R.D. King coined this term in 2004.

ADAM is a new software based on inductive reasoning. Itidentifies genes encoding orphan enzymes in Saccharomycescerevisiae for which the encoding gene(s) are not known

A robot scientist automatically originates hypothesesto explain observations, devises experiments to testthese hypotheses, physically runs the experiments byusing laboratory robotics, interprets the results, andthen repeats the cycle.

Limitations of Adam: the scientific knowledge “discovered” byAdam is implicit in the formulation of the problem and istherefore not novel.

We accept that the knowledge automatically generatedby Adam is of a modest kind. However, this knowledge isnot trivial, and in the case of the genes encoding 2A2OA,it sheds light on, and perhaps solves, a 50-year-oldpuzzle. (King et al. 2009, 88)

32



References



R.D. King coined this term in 2004.ADAM is a new software based on inductive reasoning. Itidentifies genes encoding orphan enzymes in Saccharomycescerevisiae for which the encoding gene(s) are not known




32



References







32



References







32



References







32



References


What’s GA Got To Do With NS?

There are genetic numerical algorithms ( GNS)

Best example I know of is (Schmidt&Lipson 2009)

GNS do not output data, but symbolic representations, i.e.laws and mathematical expressions from data based on GA.

It may have a direct impact on science in the future.(remember I started by rejecting the the wait-and-see attitude)

I also want to defuse blind optimism

33



References








33



References








33



References








33



References








33



References








33



References


GNS and meaningfulness

Here things are getting really exciting:

These GNS can discover : Hamiltonians, Lagrangians, laws ofconservation, symmetries, and other invariants.

Based on meaningfulness and interestingness.

34



References






34



References






34



References






34



References


A simple illustration of a “best expression”

35



References


Schmidt and Lipson about their result

We have demonstrated the discovery of physical laws,from scratch, directly from experimentally captured datawith the use of a computational search [...] detectnonlinear energy conservation laws, Newtonian forcelaws, geometric invariants, and system manifolds invarious synthetic and physically implemented systemswithout prior knowledge about physics, kinematics, orgeometry. The concise analytical expressions that wefound are amenable to human interpretation and help toreveal the physics underlying the observed phenomenon.[...] Might this process diminish the role of futurescientists? Quite the contrary: Scientists may useprocesses such as this to help focus on interestingphenomena more rapidly and to interpret their meaning.

(Schmidt and Lipson 2009, 85)

36



References


Can BACON and ADAM compete with the roulette? (skip)

difficult to compare directly.

But GNS score better than BACON because they avoid localoptima.


37



References






37



References






37



References

What philosophy for GNS?Arguments for GNSMetaphysics of GNSGNS and mathematicsGNS and invarianceGNS and laws of natureObjections






5 References

38



References


Are GNS philosophically attractive?

In the framework of the debate about the “philosophy of NS”they are!In GNS we simulate:

the process of scientific discovery.the relation between experiments, theories and models.

With GNS, we do not rely on theories, we discover them!

It is prima facie a bottom-up view!There is literally a guesswork in GNS, but:

It optimizes the result based on meaning and “interestingness”If in science we transform data into phenomena (Woodwardand Bogen), then GNS qualifies as a possible candidatetogether with experimentsIn the context of discovery, science is, for better or worse,guesswork

39



References



In the framework of the debate about the “philosophy of NS”they are!

In GNS we simulate:





39



References








39



References




the process of scientific discovery.

the relation between experiments, theories and models.




39



References








39



References








39



References






It is prima facie a bottom-up view!

There is literally a guesswork in GNS, but:


39



References








39



References







It optimizes the result based on meaning and “interestingness”

If in science we transform data into phenomena (Woodwardand Bogen), then GNS qualifies as a possible candidatetogether with experimentsIn the context of discovery, science is, for better or worse,guesswork

39



References







It optimizes the result based on meaning and “interestingness”If in science we transform data into phenomena (Woodwardand Bogen), then GNS qualifies as a possible candidatetogether with experiments

In the context of discovery, science is, for better or worse,guesswork

39



References








39



References


Creativity, Luck and Chance in GNS

In the context of scientific discovery, yes GNS arephilosophically interesting

GNS make room to chance in scientific discovery.

Novelty and chance may be stronger related.

As a biological metaphor, GNS are up to their neck instochasticity.

How is chance (as part of a search procedure) related tocreativity?

F. Crick “chance is the only source of true novelty” (Crick1981, 58).

Maybe scientific discovery is in fact closer to playing a gameand hedging one’s bets.

40



References










40



References










40



References










40



References










40



References










40



References










40



References










40



References


How inventive are we?

We are extremely inventive beings! Can you read this?

To xllxstxatx, I cxn rxplxce xvexy txirx lextex of x sextexce xitx anx, anx yox stxll xan xanxge xo rxad xt wixh sxme xifxicxltx.

Then be happy, because no Turing machine can!

Searching patterns and comparing them is a difficult business.

41



References







41



References







41



References


Stochasticism (a philosophical view)

Maybe the nature is stochastic/chancy (we don’t know, butwe have reasons to think so)

Our representation of the world should mimic it

Then we’d better go stochastic in modeling the world

If the world is not stochastic, no big fuss: as humans we takechances: we are built to be stochastic (gamble, guess)

We can go intuitionistic in mathematics (as opposed toPlatonism, formalism,etc.)

42



References








42



References








42



References








42



References








42



References








42



References


Argument from stochasticity

world/science The world is:

deterministic non-deterministic

Non-stochastic Long Live Laplace! Ooops! We are off!!

Stochastic It is OK1 The best combination

1It’s ok, it’s just a representation. Some deterministic systems are betterrepresented by statistical models

43



References


GNS as better “epistemic enhancers” (Humphreys)

P. Humphreys thinks that NS in general are epistemicenhancers.

They extend ourselves

If so, GNS pushes the limits farther than ordinary NS.Pushes the limits of what is “scientifically discoverable”

44



References






44



References






44



References





If so, GNS pushes the limits farther than ordinary NS.

Pushes the limits of what is “scientifically discoverable”

44



References






44



References


Mathematics as a constraint?

Think of the “unreasonable effectiveness of mathematics”argument (Steiner, Colyvain, etc)

Parenthetically, I have doubts about this argument.

In some cases mathematics is not the driving force but theconstraint.

GNS illustrates the mathematics as “constraint”: it generatessymbolic expression from data based on mathematicalconstraints

First you need to decide what limits to put to yourmathematics, and then GNS delivers an optimal result

45



References








45



References








45



References








45



References








45



References








45



References


Conceivability

Any experiment explores possible worlds

C’mon, that’s trite

Science is not only about the actual, but about the possible.

The typical way to explore possibility: change initialconditions of an experiment but keep the laws.

Is science indeed about the possible? Maybe more aboutcounterfactuals.

That’s a class of nomical worlds based on physical possibilities

Science teaches us that the world is richer that we canconceive with the “naked mind” (Van Fraassen)

My argument is that NS and GNS, enhance the mind bypushing the limits of conceivability.

46



References


Conceivability

Any experiment explores possible worlds

C’mon, that’s trite







46



References


Conceivability

Any experiment explores possible worldsC’mon, that’s trite







46



References


Conceivability








46



References


Conceivability








46



References


Conceivability








46



References


Conceivability








46



References


Conceivability








46



References


Conceivability








46



References


What is really new?

Strictly speaking, data are new.

The way we discover it.

47



References


What is really new?



47



References


What is really new?



47



References


GNS and possibilia

The “observable”

The “physical”

The “logical”

The “conceivable”

Other less discussed possibilia

The “computable” (a la Church-Turing). But is physicscomputable? (some systems in condensed matter physics arenot NP-computable)My proposal: the “evolvable” (a la GNS)

The only one that’s chancyIt’s natural (maybe too literally)It’s always open to re-runs (not replicable)You can always hope for a better solution

48



References


GNS and possibilia


The “physical”

The “logical”





48



References


GNS and possibilia


The “physical”

The “logical”





48



References


GNS and possibilia


The “physical”

The “logical”





48



References


GNS and possibilia


The “physical”

The “logical”





48



References


GNS and possibilia


The “physical”

The “logical”





48



References


GNS and possibilia


The “physical”

The “logical”



The “computable” (a la Church-Turing). But is physicscomputable? (some systems in condensed matter physics arenot NP-computable)

My proposal: the “evolvable” (a la GNS)


48



References


GNS and possibilia


The “physical”

The “logical”





48



References


GNS and possibilia


The “physical”

The “logical”




The only one that’s chancy

It’s natural (maybe too literally)It’s always open to re-runs (not replicable)You can always hope for a better solution

48



References


GNS and possibilia


The “physical”

The “logical”




The only one that’s chancyIt’s natural (maybe too literally)

It’s always open to re-runs (not replicable)You can always hope for a better solution

48



References


GNS and possibilia


The “physical”

The “logical”




The only one that’s chancyIt’s natural (maybe too literally)It’s always open to re-runs (not replicable)

You can always hope for a better solution

48



References


GNS and possibilia


The “physical”

The “logical”





48



References


The surplus mathematical structure

Physics is replete with surplus mathematical structure:

Newtonian spacetime has too many rest frames among theinertial frames;General Relativity has too many choices for the global inertialframe;Quantum Field Theory has unitarily non-equivalent butobservationally equivalent representations available;Gauge theories provide too many solutions to the fieldequations which are all acceptable from an empirical point ofview, etc.There are 10500 String Theories (models?) etc.

49



References





49



References




Newtonian spacetime has too many rest frames among theinertial frames;

General Relativity has too many choices for the global inertialframe;Quantum Field Theory has unitarily non-equivalent butobservationally equivalent representations available;Gauge theories provide too many solutions to the fieldequations which are all acceptable from an empirical point ofview, etc.There are 10500 String Theories (models?) etc.

49



References




Newtonian spacetime has too many rest frames among theinertial frames;General Relativity has too many choices for the global inertialframe;

Quantum Field Theory has unitarily non-equivalent butobservationally equivalent representations available;Gauge theories provide too many solutions to the fieldequations which are all acceptable from an empirical point ofview, etc.There are 10500 String Theories (models?) etc.

49



References




Newtonian spacetime has too many rest frames among theinertial frames;General Relativity has too many choices for the global inertialframe;Quantum Field Theory has unitarily non-equivalent butobservationally equivalent representations available;

Gauge theories provide too many solutions to the fieldequations which are all acceptable from an empirical point ofview, etc.There are 10500 String Theories (models?) etc.

49



References




Newtonian spacetime has too many rest frames among theinertial frames;General Relativity has too many choices for the global inertialframe;Quantum Field Theory has unitarily non-equivalent butobservationally equivalent representations available;Gauge theories provide too many solutions to the fieldequations which are all acceptable from an empirical point ofview, etc.

There are 10500 String Theories (models?) etc.

49



References





49



References


The GNS and symmetry, invariance and objectivity

Are invariance and symmetry related to objectivity? Redheadand Debs think they are not

Objectivity is conventional.

50



References





50



References





50



References


No more partial differential equations?

Laws of evolutions are based on partial differential equations:the most powerful tools in the history of science

51



References


No more partial differential equations?

Laws of evolutions are based on partial differential equations:the most powerful tools in the history of science

51



References


The Humeans and GNS

GNS mesh well with the Mill-Ramsey-Lewis view of laws ofnatureMRL=laws of nature supervene on the collection of intrinsicpropertiesLaws of nature are the best balance between strength,simplicity, expressiveness, etc.For GNS: new data, new laws. But some laws have a betterstability to new data. Those are “laws of nature”Statistical and stochastic MRL:If a large population of algorithms

for diverse datafor a large range of contraints,for a large number of runs of GNS

converge to the same expression, then dub it “a law of nature”Laws of nature as stable maximal sets (Lange, Woodward, S.Mitchell)

52



References


The Humeans and GNS

GNS mesh well with the Mill-Ramsey-Lewis view of laws ofnature

MRL=laws of nature supervene on the collection of intrinsicpropertiesLaws of nature are the best balance between strength,simplicity, expressiveness, etc.For GNS: new data, new laws. But some laws have a betterstability to new data. Those are “laws of nature”Statistical and stochastic MRL:If a large population of algorithms



52



References


The Humeans and GNS

GNS mesh well with the Mill-Ramsey-Lewis view of laws ofnatureMRL=laws of nature supervene on the collection of intrinsicproperties

Laws of nature are the best balance between strength,simplicity, expressiveness, etc.For GNS: new data, new laws. But some laws have a betterstability to new data. Those are “laws of nature”Statistical and stochastic MRL:If a large population of algorithms



52



References


The Humeans and GNS

GNS mesh well with the Mill-Ramsey-Lewis view of laws ofnatureMRL=laws of nature supervene on the collection of intrinsicpropertiesLaws of nature are the best balance between strength,simplicity, expressiveness, etc.

For GNS: new data, new laws. But some laws have a betterstability to new data. Those are “laws of nature”Statistical and stochastic MRL:If a large population of algorithms



52



References


The Humeans and GNS

GNS mesh well with the Mill-Ramsey-Lewis view of laws ofnatureMRL=laws of nature supervene on the collection of intrinsicpropertiesLaws of nature are the best balance between strength,simplicity, expressiveness, etc.For GNS: new data, new laws. But some laws have a betterstability to new data. Those are “laws of nature”

Statistical and stochastic MRL:If a large population of algorithms



52



References


The Humeans and GNS

GNS mesh well with the Mill-Ramsey-Lewis view of laws ofnatureMRL=laws of nature supervene on the collection of intrinsicpropertiesLaws of nature are the best balance between strength,simplicity, expressiveness, etc.For GNS: new data, new laws. But some laws have a betterstability to new data. Those are “laws of nature”Statistical and stochastic MRL:

If a large population of algorithms



52



References


The Humeans and GNS




52



References


The Humeans and GNS


for diverse data

for a large range of contraints,for a large number of runs of GNS


52



References


The Humeans and GNS


for diverse datafor a large range of contraints,

for a large number of runs of GNS


52



References


The Humeans and GNS




52



References


The Humeans and GNS



converge to the same expression, then dub it “a law of nature”

Laws of nature as stable maximal sets (Lange, Woodward, S.Mitchell)

52



References


The Humeans and GNS




52



References


Advice for NS coming from GNS

Take biomimetics seriously.

Take seriously the context of discovery.

Naturalize philosophy of science.

53



References






53



References






53



References






53



References


An argument for distributive discovery

P. Humphreys suggests that the future of science belongs tothe collaboration humans between computers (Humphreys2004, 2009)

We need a division of labor

This will be more evident in discovery than in justificationI do not think NS score better in justification

54



References






54



References






54



References





This will be more evident in discovery than in justification

I do not think NS score better in justification

54



References






54



References


Ways to retort: some objections

1 Wait-and-see (again!) GNS are not ripe to harvest.

2 GNS bring irrationality into science. Do we need it?

3 If the world is stochastic/chancy then we do not need torepresent it by stochastic tools.

4 You do not honor the discovery/justification distinction.

5 If nature is deterministic why should we go stochastic? (seebelow)

6 The “three armies” argument (see below)

7 This is anthropomorphism in sheep clothes!(see below)

55



References










55



References










55



References










55



References










55



References










55



References










55



References










55



References


Back to Objection 5: Maybe Nature abhors chance!

Maybe at the bottom She abhors chance.

If so, all our models are pseudo-stochastic

If so, we can represent parts the world with stochastic models

M. Strevens: “Not only is Nature red in tooth and claw; she isirrepresibly stochastic in her violence” (Strevens, 2009, 459)

models in biology have a probabilistic element.

56



References








56



References








56



References








56



References








56



References








56



References


O 6 The three armies argument against GNS

Whatever you told us, Nothing that NS have achieved couldnot have been done by:

an army of well-trained scientists working with slide rules

an army of well-trained evolutionary biologists

an army of well-trained poker dealers and gamblers

Computers, NS are still dumb tools

57



References








57



References








57



References








57



References








57



References








57



References


O 7: Wait: this is anthropomorhism!

is biomimetics nothing more than anthropomorphizing?

It seems the nature abhors many things

58



References





58



References





58



References

Risky conclusionsWeaker conclusions






5 References

59



References


What emerges from my analysis?

Surprisingly, a less central role for mathematics in scientificdiscovery

More or less a bottom up image of science

A new type of possibilia, the numerical possibility

60



References






60



References






60



References






60



References


Moving from Turing to stochastic algorithms makes NS moreattractive

Relevance and meaning can be generated by machines

For better, for worse, GNS are not mere glorified slide rules

61



References





61



References





61



References





61



References






5 References

62



References

References I

Affenzeller, M., 2009. Genetic Algorithms and GeneticProgramming: Modern Concepts and Practical Applications.No. v. 6 in Numerical insights. CRC Press, Boca Raton, Fla.

Barberousse, A., Franceschelli, S., Imbert, C., 2007. Cellularautomata, modeling, and computation.http://philsci-archive.pitt.edu/archive/00003579/.URLhttp://philsci-archive.pitt.edu/archive/00003579/

Callender, C., Cohen, J., 2010. Special sciences, conspiracyand the better best system account of lawhood.

63

http://philsci-archive.pitt.edu/archive/00003579/



References

References II

Chaitin, G., Feb. 1995. Randomness in arithmetic and thedecline and fall of reductionism in pure mathematics. Chaos,Solitons & Fractals 5 (2), 143–159.

Cohen, J., Callender, C., 2009. A better best system accountof lawhood. Philosophical Studies 145 (1), 1–34.

Crick, F., 1981. Life Itself: Its Origin and Nature, 1ST Edition.Simon and Schuster.

Davies, P. C. W., Brown, J. R., 1988. Superstrings: a theoryof everything? Cambridge University Press, Cambridge U.K.;New York, book, Edited.

64



References

References III

Debs, T., 2007. Objectivity, invariance, and convention :symmetry in physical science. Harvard University Press,Cambridge Mass.

Floridi, L., 2008. Philosophy of computing and information : 5questions. Automatic Press, [S.I.].

Frigg, R., Reiss, J., 2009. The philosophy of simulation: Hotnew issues or same old stew? Journal for Epistemology169 (3), 593–613.

65



References

References IV

Galison, P. L., 1996. Computer simulations and the tradingzone. In: Galison, P., Stump, D. J. (Eds.), The Disunity ofscience : boundaries, contexts, and power. Stanford UniversityPress, Stanford Calif.

Hacking, I., 1983. Representing and intervening: introductorytopics in the philosophy of natural science. CambridgeUniversity Press, Cambridge, Cambridgeshire ; New York,book, Whole.

Hartmann, S., 2008. Modeling in Philosophy of Science. OntosVerlag, Heusenstamm bei Frankfurt, book, Whole.

66



References

References V

Humphreys, P., 2004. Extending ourselves: Computationalscience, empiricism, and scientific method. 2004.

Humphreys, P., 2009. The philosophical novelty of computersimulation methods. Synthese 169 (3), 615–626.

Keller, E., 2003. Models, simulation, and ’Computerexperiments’. In: Radder, H. (Ed.), The Philosophy ofScientific Experimentation. University of Pittsburgh Press, pp.198–215.

67



References

References VI

Koza, J. R., Keane, M., Streeter, M., Mydlowec, W., Yu, J.,Lanza, G. (Eds.), 2003. Genetic Programming IV: RoutineHuman-Competitive Machine Intelligence. Kluwer AcademicPublishers, Norwell, Mass.

Maddy, P., 2007. Second philosophy : a naturalistic method.Oxford University Press, Oxford ;;New York.

Morrison, M., 2009. Models, measurement and computersimulation: the changing face of experimentation.Philosophical Studies 143 (1), 33–57, journal Article.

68



References

References VII

Parker, W., 2009. Does matter really matter? computersimulations, experiments, and materiality. Synthese 169 (3),483–496.

Simon, H., 1969. The sciences of the artificial,. M.I.T. Press,Cambridge Mass.

Simon, H. A., 1992. Scientific discovery as problem solving.International Studies in the Philosophy of Science 6 (1), 3.

Simon, H. A., Langley, P. W., Bradshaw, G. L., 1981.Scientific discovery as problem solving. Synthese 47 (1), 1–27.

Simonton, D. K., 2004. Creativity in Science: Chance, Logic,Genius, and Zeitgeist. Cambridge University Press, Cambridge.

69



References

References VIII

Steiner, M. A., 1998. The applicability of mathematics as aphilosophical problem. Harvard University Press, Cambridge,Mass., book, Whole.

Thagard, P., 1988. Computational philosophy of science. MITPress, Cambridge, Mass., book, Whole.

Tomassini, M., 1995. A survey of genetic algorithms. AnnualReviews of Computational Physics 3, 87–118.

Turing, A., 1950. Computing machine and intelligence. Mind:A Quarterly Review of Philosophy 59 (236), 433–460.

Turing, A., 1996. Intelligent machinery, a heretical theory.Philosophia Mathematica 4 (3), 256–260.

70



References

References IX

Winsberg, E., 1999. Sanctioning models: The epistemology ofsimulation. Science in context. 12 (2), 275.

Winsberg, E., 2001. Simulations, models, and theories:Complex physical systems and their representations.Philosophy of Science 68 (3), S442–S454.

Wolfram, S., 2002. A new kind of science. Wolfram Media,Champaign IL.

71

Education

Genetic algorithms and the changing face of scientific theories