“And then came the grandest idea of all! We actually made a map of the country, on the scale of a mile to the mile!"

"Have you used it much?" I enquired.

"It has never been spread out, yet," said Mein Herr: "the farmers objected: they said it would cover the whole country, and shut out the sunlight! So we now use the country itself, as its own map, and I assure you it does nearly as well.”

-- Lewis Carol

Schematic Models are more useful than Realistic Models...

Mathematical Models of Evolution

Artificial LifeSelf-replicating computer code•A-life systems (Tierra, Avida...)• Computer viruses

Genetic Algorithms•population of structureswith heritable features•replicate with mutations• test for “fitness”•select

“Nature, red in tooth and claw” --Tennyson

Darwinian Evolution -- The Paradox of Delicacy

“Survival of the Fittest” -- Darwin

•In Biological Evolution:Expect: Muscle, armor, aggression, robustness

Find: Flower petals, butterfly wings, naked ape with delicate brain

•In Cultural Evolution:Expect: Warriors, Loan-sharks, Lawyers

Find: Teddy bears, florists, poets, Mother Theresa

Could be “survival value of altruism,” or...

Our intuition about evolution is wrong...

•Selection leads naturally to evolution of delicate structures,together with the machinery to protect them from a harsh world.

Why?

•Because complexity is needed in order to occupy new niches,and complexity implies vulnerability.

warriors

poetspoets

Homeostasis• Self-regulation: Organisms maintain stabilized internal milieu in the face of external fluctuations.• Information theory point of view: Organisms exclude “noise” information. This has an entropic cost.• Why? “Obviously,” stability is conducive to carrying out complex adaptive tasks.• Says Who???

If the exclusion of environmental noise from a delicate sub-system is a universal evolutionary

imperative, would it evolve in an abstract mathematical model of natural selection?

12xy

z

A K=2 Boolean Element Truth Table of Element 12

xy

T F

FTTF FT

N

11

71

1248

11

Fragment of Boolean Network, Showing Propagation of Noise

Boolean Networks

At each time-step, the output of an element is thespecified boolean function of its inputs on theprevious time-step.

The Model• A population of M (~100) organisms, each of which is a boolean network consisting of N (~100) discrete-time synchronous boolean elements, each with K (usually 2) inputs and one output.• A subset of nout (~25) arbitrarily chosen elements are considered “output elements” of the network.• A subset of nin (~5-20) elements have their first terminal connected to boolean “noise.”• Each organism is “developed” through T (~100) steps and an output function n(t) is determined by counting the number of output elements in the TRUE state at each step.• “Fitness” of an organism is defined as F = -t[n(t)-f(t)]2/T where f is a user-specified target function.• Initial organism is randomly constructed.• One generation of evolution: Replicate organisms by factor R, allowing rare, random mutations. From new population of RM organisms, select the best M in order of fitness.

Will evolution recognize and exclude noise?

Variable

LockedFrozen Phase: Isolated Oscillators

Variable

LockedChaotic Phase: Entire Network Coupled

Variable

LockedCritical Boundary: Coupled Regions on All Scales

Generations10 100 1000

-Fitn

ess

0

30

60

Time (steps)

0 100T

rue

elem

ents

0

5

10

15

20

25

Output function

Target function

Evolution in the Absence of NoisePart I: Adaptation of Function

Concept of “Fitness Landscape”

A boolean network with 100 2-input elements has 2.58x10520 possible genotypes!

q0.0 0.5 1.0

K

1

2

3N=1000, gens=1000, Thresh=15

Chaotic

Frozen

K = inputs/elementq = prob. output TRUE

Evolution in the Absence of NoisePart II: Evolvability

•Boolean networks of different statistical structures differ in their ability to adapt by natural selection.•Evolvability is greatest near the critical boundary, where the network consists of separated subsystems.•The principle of “component parts” is a natural “engineering method” of evolution.

Hypothesis: Noise will be excluded because of:• Irrelevance: noise carries no information about the task• Complexity: noise chosen randomly from 2T > 1030 sequences

Stereotyped Noise:

Single realization for all organisms in all generation

Time, steps

0 50 100

No.

of T

RU

E o

utpu

ts

0

22

Generations

0 2500-F

itnes

s1

10

100

A B

D E

Generations

0 2500

Noi

se D

isse

min

atio

n

0.0

0.5

1.0

C

c

d,e

Output elementsAll elements

Time, steps

0 50 100Num

ber

of T

RU

E o

utpu

ts

0

10

20

Time, steps

0 50 100Num

ber

of T

RU

E o

utpu

ts

0

10

20

Output

Template

Noise

Generations

0 2500

-Fitn

ess

1

10

100

Population AverageNoise Average

•Networks that evolved in the presence of a given (but arbitrary) noise representation require that particular noise in order to function.•Even though the fitness evolves just as rapidly in the presence of stereotyped noise as in the absence of noise, there is no improvement in the average fitness in other, randomly chosen, noise environments.

•Stereotyped noise was never excluded, but always resulted in noise-imprinting!•Does that mean that incorporating meaningless noise actually improves fitness?

Generations

0 5000 10000

-F

0

60

0 5000 10000

-F

0

60

0 5000 10000

-F

0

60

0 5000 10000

-F

0

60

Generations

0 5000 10000

0

60

0 5000 10000

0

60

0 5000 10000

0

60

0 5000 10000

0

60

No Noise Stereotyped Noise

“Annealing” Effect of Stereotyped Noise with “Difficult” Target Functions

Generations

0 14000 28000

-F

0

45

90

{

Maybe yes...

-F population average10 100 1000

-F n

oise

ave

rage

10

100

1000

10000

No noiseStereotyped noiseRandom noise (2000 generations)noise invariance line

Noise Imprinting is a Suboptimal Strategy for an Easy Target FunctionBut no!

-F1

10100

Genotypes

M0

9

Noi

se P

atte

rns

Vno

ise

0.0

0.5

1.0

Generations

101 102 103 104 105-F

itnes

s1

10

100

SeedMultiple Noise Imprinting is a Suboptimal Strategy

Generations

0 2500

-Fitn

ess

1

10

100

Population AverageNoise Average

•Symmetry Breaking:Once noise information has been accidentally incorporated into the computation, paths to noise exclusion lead through low-fitness valleys.

So why is evolution so stupid?

-Fitness

0 2000 4000 6000 8000 10000

Num

ber

of R

ealiz

atio

ns

0

10000

20000

30000

0 2000 4000 6000 8000 10000

0

2000

4000

6000

8000

0 2000 4000 6000 8000 10000

0

2000

4000

6000

8000

A

B

C

Fitness distribution ofa random startingnetwork over 106 noiseenvironments

After evolution in thepresence of a stereotypednoise input, the noise-imprintednetwork has a broad distributionof fitness, with some noise inputsgiving good fitness while others are“poison” producing worse outputsthan a random network.

Repeating the evolution gives acompletely different noise-imprintednetwork, showing that noise-imprinting results from randomcontingencies during evolution.

Time (steps)

0 100

TR

UE

Out

puts

0

25

Time (steps)

0 100

TR

UE

Out

puts

0

25

Time (steps)

0 100

TR

UE

Out

puts

0

25 -F=9289

-F=157

-F=62

-F

0 20 40 60 80 100

Pro

ba

bili

ty D

en

sity

0.000

0.025

No Noise

Time (steps)

0 100

Time (steps)

0 100

"Best" of 106 noise realizations

"Worst" of 106 noise realizations

-Fitness

0 2000 4000 6000 8000 10000

Num

ber

of R

ealiz

atio

ns

0

10000

20000

30000

A

“Quiet Imprinting”Random contingencies in evolution always impose semantic “meaning” on arbitrary features of the environment that have no intrinsic significance. Life imposes meaning on a random world.

Does Noise Imprinting Occur in Cultural Evolution?•Meaningless random information is entrained in the process of evolution•Though evolution, the random information acquires a “meaning” and so cannot be removed even though its presence is sub-optimal.

A visitor to a synagogue noticed that when the rabbi entered the room, the entire congregation stood up. No one could explain this unusual custom. It turned out that the previous rabbi had used a remote control to open the curtain exposing the Torahs when he entered, whereupon the congregation stood as required by Jewish law. The remote had broken and been discarded, as had the former rabbi, but the congregation continued to stand whenever a rabbi entered.

N

1

3

4

5

6

7

8

9

1 0

1 1

1 3

1 4

1 5

2

2

5

6

1 3

1 0

5

6

2

5

1 3

4

5

1

7

1 1

2

1 3

8

2

2

3

2

1 1

8

2

2

7

1 4

4

9

6

2

1 5

3

1

9

1 1

1 3

7

7

1

3

1 3

4

4

1 0

1

1 1

5

1 2

7

1 1

5

3

1 4

1 0

4

7

1 2

0

9

1 5

8

1 3

50

0

4

5

6

9

1 3

1 1

1 1

Generations

0 1750 3500

-Fitn

ess

1

10

100

Noi

se D

isse

min

atio

n

0.0

0.5

1.0

Ouput elementsAll elements

Truly Random Noise: a different noise realization for each organism in each generation

-F

0 30 60

No

. of g

en

oty

pe

s

0

35

70

-F

0

30

60

Generations

0 2000 4000No.

of

geno

type

s

0

35

70

Vno

ise

0.0

0.5

1.0Noise Exclusion

is followed by reduction in genetic diversity

Random noise is always excluded. Thenumber of generations required for noise-exclusion to evolve is lognormallydistributed and increases exponentially withthe length of the target computation.

Vno

ise

0

1

Generations

0 2500 5000

-Fitn

ess

1

10

100

Noise averagePopulation average

Time

0 100

Vn

ois

e

0

1

All elementsOutput elements

a bc

de

f

g

a b c d e f g

Random Noise

Generations

0 600 1200

-Fitn

ess

1

10

100

Vno

ise

0.0

0.5

1.0

Generations

0 1750 3500

1

10

100

0.0

0.5

1.0

Generations

0 800016000

1

10

100

0.0

0.5

1.0

Vsi

gnal

0.0

0.5

1.0

Correlated Noise

Generations

0 750015000

1

10

100

0.0

0.5

1.0

Random NoiseIntercalated with Signal

Information Catastrophe

Generations

100 102 104 106

-Fitn

ess

0

35

70

Probability density

0.00 0.35

Generations

16400 16925 16950

-(Immediate fitness)

-(Long term fitness)

AB

C

• Noise, suitably defined, is excluded from environments within the organism, creating a protected subsystem which carries out “delicate” computations.

• Because organisms are dissipative thermodynamic systems, protected subsystems cannot be completely isolated from the outside world or parent system, which supplies the free energy to power their irreversible processes.

• Therefore, there is always a risk that a protected subsystem will be corrupted by inappropriate information, with consequences that can be catastrophic.

The Paradox of “Dynamic Irony”

“All Power Grows out of the Barrel of a Gun”

The paradox...

It’s anathema• Government of laws• Natural rights of man•Violence an aberration

It’s obviously true• Governments of laws created by violent revolutions• Still need police & military to protect gov’t of laws

We must deny its truth• Everyone would get gun to enforce his rights• This would destroy gov’t of laws

This paradox is a generic feature of cultural evolution...

Does Information Catastrophe Occur in Cultural Evolution?

-Fitness

0 30 60Num

ber

of R

ealiz

atio

ns

0

500

1000

-Fitness

0 30 60Num

ber

of R

ealiz

atio

ns

1

10

100

1000

Generations

0 4000 8000

-Fitn

ess

1

10

100

Ensemble average

Population average

amplitude

time

The Power of Forgetting: Exclusion of Initial-State Noise

Generations

0 1250 2500

-F

1

10

100

Population fitnessNoise averaged fitness

Vno

ise

0.0

0.5

1.0

All elementsOutput elements

Stereotyped noise

Random noise

Generations

0 900 1800

-F

1

10

100

Population fitnessNoise averaged fitness

Vn

oise

0.0

0.5

1.0

All elementsOutput elements

Father Mother Offspring

SEX: It won’t change anything between us

Generations10 100 1000 10000

-F

1

10

100

1000

Population MeanNoise Average

Generations10 100 1000 10000

-F

1

10

100

1000

Stereotyped noiseNout=45

Mask1 @ t=100Mask2 @ t=100

Stereotyped noiseNout=45

Mask1 @ t=99Mask2 @ t=100

Generations1 10 100 1000 10000

Nu

mb

er o

f Err

ors

0

30

60

Population MeanNoise Average

Stereotyped noiseNout=25

Masks @ t=25,50,75,100

A

BC

“Morphogenesis” by Boolean Networks.

Networks were selected for the accuracy with which they attained (randomly) specified ‘shapes” (i.e., patterns of states (T/F) of the output elements) at specified “stages” (i.e. values of development time. The fitness F was the negative of the sum of the squares of the number of errors at each specified stage. A. If two conflicting shapes were both specified at stage 100, the network evolved a poor compromise. B. If the two arbitrary shapes were specified at stages only a single step apart (99&100), the network evolved to pass through the required shapes with only a single error out of 90 values. C. A network evolved to pass perfectly through 25 arbitrary output values at each of 4 development stages 25 steps apart. Noise imprinting (dotted vs. solid curves) and rejection of unpredictable noise (not shown) were similar to the “curve fitting” problem.

STOP

Get A-Life

Generations

0 12000-F

itnes

s

0

80

Vno

ise

0

1

Generations

0 12000

-Fitn

ess

0

80

Vno

ise

0

1

Generations

0 12000

-Fitn

ess

0

80

Vno

ise

0

1

Generations

0 12000

-Fitn

ess

0

80

Vno

ise

0

1

No Annealing Effect of Random Noise!

• A more refined system (government by laws) evolves from a crude one (government by force). It is delicate and so must be isolated from the violence of it’s parent--an instance of homeostasis.• Because its protection and resources must come from the violent outside world, it remains vulnerable to flow of information from that world--an instance of dynamic irony.• Arbitrary or irrational beliefs become incorporated into cultural systems in ways so entwined with necessary functions that they resist elimination--an instance of noise imprinting.

Other Examples:Business AcademiaSexual Competition FamilyWar PeaceCarnivorous Primate Animal Rights

...a generic feature of cultural evolution:

Hypothesis: Value systems are the homeostatic environments created by cultural evolution.