CUMULATIVE SELECTION AS A MULTI-DISCIPLINE META-THEORY:
AN ANALYSIS AND COMPUTER SIMULATION
Michael E. Mills, Ph.D.
Loyola Marymount University
Los Angeles, CA 90045
Copyright (c) 1989 Michael E. Mills, Ph.D.
You are about to witness a computer simulation of a very powerful and
extremely important process: cumulative selection. Other than creation by
an intelligent being, it is the only known natural process that can
produce highly organized complexity from an initial state of disorder and
randomness. Amazingly, this complex organization is built up gradually
and blindly. It is the moving force that shapes and increases the
evolution of complexity of biological, behavioral and cultural phenomena.
In this tutorial and computer demonstration the process of
cumulative selection will be defined and described. It will then be
compared with a process with which it has been often confused: single
The differences between single step and cumulative selection are
unclear to many people. However, the differences are truly profound.
Single step selection does not have the capacity to produce organized
complexity; only cumulative selection does.
Finally, we will discuss how cumulative selection represents a
fundamental "meta-theory" that transcends traditional academic discipline
boundaries. Via analogies, we'll see cumulative selection operating in
biological evolution, behavioral learning, the formulation of cultural
practices, scientific research, and even in the development of your own
THE GENESIS OF COMPLEXITY IN AN ENTROPYING UNIVERSE
Physicists tell us that, taken as a whole, the universe is
continuously and inexorably losing information and complexity. This is
the second law of thermodynamics--a process called 'entropy.' This
continually increasing disorder started moments after 'big bang,' it
continues to this day, and it will continue into the future. The end
result will be a universe that is almost completely void of order and
organization. Molecules will no longer exist and even atoms will have
broken down into elementary particles and radiation--all complexity will
have been dissolved.
Fortunately for us, there is a counter-force to entropy also at work
in the universe. Against this general backdrop of increasing disorder,
in perhaps a few extremely isolated corners in the universe (such as the
Earth), exist biological and cultural systems that are gradually
increasing in complexity and organization.
This would appear to violate the second law of thermodynamics. In
fact it does not. By "extracting" order from the universe, cumulative
selection actually increases the overall amount of entropy in the
universe as a whole. This is because cumulative selection is a process
that requires either an internal (biological) or external (environmental)
energy source for it to operate.
For example, let's say that you will expend 200 calories to analyze
and store information the information presented in this tutorial in your
brain. After this tutorial, presumably your brain will have become an
even more highly ordered system--a reverse entropy process. To accomplish
this, you will have had to convert a form of highly ordered energy (food)
into very disordered energy (heat). The resulting increased order of
your brain will have decreased the order in the food by a factor of 10
million million million times the amount of the increase of the order of
your brain. By thinking about and memorizing the information in this
tutorial, you are actually accelerating entropy!
But don't worry--there is a great deal of ordered energy left in the
universe! We won't run out for many billions of years (Hawking, 1988).
A DEMONSTRATION OF SINGLE-STEP SELECTION
For this exercise, please close both of your hands into a fist, with
the exception of your two index fingers, which are to be fully extended.
Now, position your two hands over the keyboard before you. In a moment,
I would like you to close your eyes and randomly type out 28 letters on
the keyboard. You will alternate tapping with each finger, and
reposition each finger "randomly" each time. The computer will
acknowledge each letter you type in with a short "beep." After you have
typed in 28 letters, I'll notify you with 3 rapid beeps on the computer's
speaker, at which time you can open your eyes again! Ready? As soon as
you press return, start tapping out 28 letters, one letter at a time.
@ THE TYPING 28 LETTERS RANDOMLY DEMO IS HERE.
Answer: The number of attempts, or "generations," required to randomly
type the sentence 'methinks it is like a weasel' is very large. In fact,
it is unthinkably large. You could spend the rest of your life
repeatedly typing random series of 28 letters and never produce the
sentence 'methinks it is like a weasel.'
Exactly what are the odds? Let's calculate them. The chance of
getting the first letter, 'm', correct is 1 in 27 (the 26 letters of the
alphabet plus the 'space' character). We have the same 1 in 27 chance
of getting any of the other letters in the correct position. But the
chance of getting all the letters in the correct position, at the same
time, in one try, is the probability of getting any one character (1 in
27) multiplied by the total number of letters in the sentence (28,
including the spaces). Twenty seven to the 28th power is a very large
number. You have about 1 chance in 10,000 million million million
million million million of getting the entire phrase correct in one try.
How long do you think it would it take a monkey randomly pecking at a
typewriter to produce the entire works of Shakespeare?
First we need to know how many letters there are in the complete
works of Shakespeare. Well, on second thought, perhaps we'll save that
exercise for another day.
The exercise you just performed is an example of what is called
"single step selection"--the probability of getting a series of letters
(or genes, or behaviors, or scientific ideas, or lottery numbers, etc.)
correct in one random try. As you can see, the probably of single step
selection producing anything interesting, such as a meaningful sentence,
is pretty close to nil. The probability of it producing anything truly
complex, such as a living organism, is, to a mere mortal, as close to nil
as you can get.
The reason that single step selection performs so poorly in
producing complex things is that no information is passed between
generations. Without surviving information, each generational "attempt"
must start again entirely from scratch, without any "assistance" provided
In contrast, cumulative selection "breeds" the next generation--
information developed so far about the "solution" to the problem is
passed on to the next generation. The "problem" may be how to guess a
sentence that I am thinking, or it may be how a biological organism can
adapt to an environment. The problem may also be to learn how to behave
in a way that will help you obtain what you find rewarding and avoid
stimuli that are punishing.
The next computer simulation is truly dramatic--because you will see
actual cumulative selection in the process of producing complexity (in
this case, cumulative selection will, by itself, produce the sentence:
'methinks it is like a weasel'). The computer will repeatedly generate a
random series of 27 letters. When a randomly generated letter happens to
be the correct letter in the correct position (given our target sentence)
it then is "selected" and passed on to the next generation. This
successive inheritance of "correct" letters will eventually produce the
While cumulative selection is progressively "finding the solution"
to this problem by repeated breeding, you will see that single step
selection is performing very poorly in comparison.
Keep in mind that the computer is not preprogrammed to produce the
target sentence after a certain number of generations. Rather, with each
new generation, cumulative selection must work with the "raw material" of
each random series of 27 letters that are fed to it. It may take 20
generations or 220 generations before it the sentence 'methinks it is
like a weasel' is produced--there is simply no way to predict. So what
you are about to see is actual cumulative selection in progress. This is
not just a simulation of cumulative selection, it is a real demonstration
of cumulative selection in action.
@ THE WEASEL2 (RAPID GENERATIONS) IS HERE
Wow! Pretty fast!
How did cumulative selection do it?
There are two essential processes that we need understand to
comprehend how cumulative selection operates: "replicators" (or
"repeators") and "sieving" (or "selection").
"REPEATORS" AND "REPLICATORS"
In the last demonstration, you noted that a number of successive
attempts, or "generations," were required to produce the target sentence.
Repeating a "sieving" process over and over many times is a prerequisite
for the occurrence of cumulative selection. Each successive generation
"breeds" the next generation, and that subsequent generation "inherits"
the results of the previous breeding.
The repetitions that are required for cumulative selection to occur
in the biological world are performed by "replicators." These are
molecules that have the ability to replicate themselves, such as DNA.
Cumulative selection can also operate in the nonbiological world,
via a what might be termed a "repeator" process. For example, as noted
by Dawkins (1986), if you walk along a pebbly beach, you may notice that
the pebbles and rocks are not randomly distributed. Rather, the rocks
are often clearly sorted into various lanes or rows. As you walk from
the berm to the water, you often walk over several zones of rocks. Each
zone is characterized by rocks of a particular size. The "repeator"
process in this case has been the repeated action of the waves and tides.
The "sieving" or "selection" process has been the amount of force that
the waves apply to each rock. Pebbles and rocks have been selected into
zones according to their size and weight.
@ Show the illustration of the rock sieves
SIEVING AND SELECTION
We can of think another situation wherein rocks can be sorted by
size via a cumulative selection process. Imagine that we have a series
of 10 sieves, stacked one on top of the other. They are stacked
according to how fine each sieve is. Let's say that the sieve at the top
will catch rocks a foot across or wider; anything smaller will pass
through it to the sieve below. The second sieve, a foot below the first,
is a slightly finer sieve, and so on. The middle sieve might be a chain
link fence; at the bottom the final sieve is a window screen.
We now put several shovel fulls of sand, gravel and rocks into a
wheel barrel, and mix it up thoroughly. Imagine that we then dump the
contents of the wheel barrel on the top sieve. What will happen? We will
see order quickly emerge from disorder as the rocks, gravel and sand drop
down through the series of sieves.
When the dust settles, the rocks and gravel will be neatly sorted by
size. The top sieve will have caught the largest rocks, the second sieve
the next largest rocks, and so on. Each level will have a particular
size of rock or gravel. Order is derived from disorder.
Observing cumulative selection produce a target sentence by feeding
in random letters generated by a computer is interesting. But how can
cumulative selection produce such immensely complex phenomena as
organisms, behavior, and culture while operating without a goal, and
@ Show gene sieves in the bottom window.
Read the screen in the bottom window, then continue reading here.
In biological evolution, each generation represents a sieve. What is
being sieved are not rocks, but genes. The siever is not a chain link
fence, but "fitness" (reproductive success). Genes that promote the
fitness of an individual make it through the generational sieve of
biological evolution to the next generation. Genes that do not promote
reproductive success of an organism are left behind. In the gene pool,
genes that do a better job of increasing the reproductive success of
their particular organism will come to dominate, while the less effective
genes are left behind in the "genetic dump heap."
By analogy with our rock and gravel siever, imagine that over time
unfit genes swell up and get larger. Of course, this really does not
happen, but this visual analogy will help illustrate the process of gene
selection. These "large," unfit genes won't make it down very many
A little earlier, we saw that cumulative selection could relatively
quickly produce order out of randomness. Let's look at this again, but
this time we will slow things down a bit, so that we can see more clearly
what is happening.
@ CUMULATIVE SELECTION SLOW DEMO (@ must follow each screen)
In the window below, we will compare cumulative and single step selection
generation by generation. Here is what each of the headings mean:
Random Mutation--> this is a computer generated series of
random letters "fed" to this generation.
Current (Bred) Generation--> the current, "descendant" generation
produced so far by the process of cumulative selection.
Current (Random) Mutation--> this is a computer generated series
of letters "fed" to this generation of single step selection.
Remember, single step selection does not "inherit" any of the
correct letters from previous generations.
Best approximation so far--> although single step selection
does not retain its closest approximation to the target, we'll
save the best approximation here just for comparison.
CUMULATIVE SELECTION IN BIOLOGICAL EVOLUTION
To understand how cumulative selection operates in biological evolution,
imagine that a series of randomly generated letters represent a genetic
code. For our demonstration, let's say that most any randomly produced
series of 28 letters actually do produce a viable organism of some type.
However, although viable, such organisms are far from well adapted to
In fact, they may die out relatively soon if the environment changes or
they meet some hardship. In order to be "best" adapted to this
hypothetical environment, an organism must have a genetic code that (just
happens!) to spell out the sentence:
"methinks it is like a weasel"
By imagining that the randomly generated letters below represent a
genetic code, we can see how, every so often, that genetic code is slowly
improving to produce an organism progressively better adapted to its
The random fluctuations in the letters each generation represent genetic
mutations. As you can see, the vast majority of these mutations do not
improve the fitness (reproductive success) of the organism. These non-
adaptive genetic mutations do not make it to the next generation. They
are discarded. They may have helped some other organism in a different
environment, but not this one.
The "sieve" in this process of biological evolution is natural selection.
Genes that make it through the generational sieve of natural selection
are genes that improve the reproductive success of its host "vehicle."
Organisms are vehicles for genes in the sense that they are temporary
"throw away" shells for them. Organisms protect genes from a hostile
environment, and from other organismic vehicles created by competing
genes. (By the way, these competing organisms can indeed compete very
nastily--some have evolved elaborate fighting weapons, such as incisor
teeth and claws.)
The primary "task" of organisms, and the biological reason for their
existence, is to copy genes. Of course, genes don't "want" to
reproduce--the process of natural selection simply makes it appear that
way since only those genes that promote reproductive success in fact
survive. And, as they say, nothing succeeds like success!
What is cumulative selection accumulating? Information! DNA is simply a
repository of information, developed over an unthinkingably long period
of time (about 3 to 4 billion years), about how to produce an organism
that can facilitate survival and reproduction in a sometimes changing and
progressively more competitive environment.
CUMULATIVE SELECTION IN BEHAVIORAL LEARNING.
We can also see cumulative selection operating in the ontological
(individual) behavioral development of an organism. To understand how
cumulative selection operates in behavioral evolution, imagine that each
of the randomly generated letters represents a behavior. Suppose you
worked as a dolphin trainer at Sea World. A new, untrained dolphin might
display a variety of "random" behaviors. Your task, as the trainer, is to
wait for the behavior you want repeated to appear. When it does, you
reward the dolphin with a fish.
Rewarded behavior is more likely to appear again. You are "selecting"
the behavior of the dolphin through contingent positive reinforcement. A
behavioral trainer in this sense might be called a "Behavioral Selector"
or "Behavioral Siever." Suppose you wanted the dolphin to swim around
the tank, jump through a hoop, and fetch a life ring. Let's say that the
letter 'm' represents the behavior of swimming around the tank in a
You guessed, it: the letter 'e' represents jumping through a hoop, and so
on. We can imagine that the sentence 'methinks it is like a weasel'
represents a chained series of discrete behaviors. The "repeator" process
in this case are the number of learning trials (analogous to generations
in biological evolution). Analogous to reproductive success is
behavioral success (getting the fish for a correct, or 'adaptive,'
behavior). As the trainer, you are like Mother Nature! You are doing the
In this process of cumulative behavioral evolution, what is being
accumulated? Again, it is information. The information this time is not
about how to produce a biological vehicle well adapted to a particular
environment; rather it is how to behaviorally adapt to an environment to
obtain positive reinforcement. The repository of information is not
DNA--it is in the neurons of the dolphin's brain. The cumulative memory
of positive reinforcement (and punishment) is basically what we call
There is an interesting parallel between biological evolution and
behavioral evolution. Life (reproductive success) and death are to
biological evolution what positive reinforcement (pleasure) and
punishment (pain) are to behavioral evolution. Both are part of a
"sieving" process. Life and death sieve genes; pleasure and pain sieve
behaviors. Both add to a store of information about how to adapt to a
particular environment, either biologically in phylogenetic (species)
time, or behaviorally in ontological (an individual's lifetime) time.
We can use an analogy to help understand the relationship between
phylogenetic and ontological adaption. A sensitive radio, telescope or
microscope may have separate controls for 'gross' and 'fine' tuning. We
can think of the phylogenetic evolution of behavioral predispositions as
analogous to a "gross-tuning" device, and the learning of specific
behaviors by a particular individual during his or her lifetime as a
For example, the biological predisposition humans have to learn a
language was produced by successive sieving of genes in phylogenetic
time. However, the specific language(s) that an individual learns during
his or her lifetime is the result of the successive sieving of behaviors
in ontological time. Phylogenetic "gross tuning" of behavioral
predispositions and instincts help a specie to adapt to a particular
ecological niche. Ontological "fine tuning" of these behaviors via the
sieving process of learning further helps an individual to adapt to the
demands of his or her specific physical, interpersonal and cultural
environment. Additional ontological "fine tuning" of these behavioral
However, during the ontological development of an organism, this gross
behavioral predisposition may be "fine tuned" by a particular organism's
specific learning history. Life and death produce gross behavioral
(predisposition) tuning. Pleasure and pain are the ontological fine
tuning devices to help an organism further adapt to a specific
LANGUAGE: THE GENESIS OF CULTURE
Many researchers suggest that perhaps the only really important
distinction between humans and the higher primates is that humans have
the ability to communicate symbolically via a spoken (and written)
language. The evolution of language is an evolutionary quantum leap. The
reason that language, particularly written language, is so important is
that it allows for something entirely new to be sieved over generations:
ideas. The cumulative selection of ideas over generations produces
Humans without language or culture are indeed "barbaric savages"
and behave not too unlike other primates. Imagine a group of modern
humans that had somehow been stripped of their language and culture, and
were placed on a remote island, totally isolated from civilization. It
would take many generations for "higher" human characteristics to
reappear. These "higher" human characteristics of language and culture
would appear very gradually, via a long process of cultural cumulative
To bring home this point, look around you. The computer you are now
using, the car you drive, the stereo you listen to -- did you invent any
of these things? Of course not. The vast majority of what you know, and
the technology you use, you did not discover. Good ideas and inventions
were handed down to you by previous generations--a result of the
cumulative selection of ideas. You just happen to be one of the very
lucky few to have been born fairly recently to take advantage of the
cumulative selection of these ideas. We owe a heavy debt of gratitude to
the good ideas of many dead people that have been handed (or, "seived")
down to us.
CUMULATIVE SELECTION IN SCIENCE
Science, in particular, relies on cumulative selection. Without it,
scientific progress would come to a halt. Both science and evolution: a)
perform experiments, and b) pass the results of those experiments on to
succeeding generations in an ever accumulating fashion. For example,
scientists perform experiments and communicate their findings (via
journal articles and books) to the next generation of scientists to
inherit and build on.
In fact, the scientific method is simply a recipe for accelerating
the cumulative selection of ideas of a culture.
Ideas and theories that do not explain observed phenomena well are
discarded. "Mutant" theories are developed, a few of which will be
"adaptive" (explain the data more parsimoniously). Those ideas and
theories are retained. Both evolution and science are the ultimate
pragmatists: they only keep "what works" and pass that information on as
the starting point for the next generation.
IS A LOTTERY CUMULATIVE SELECTION OR SINGLE STEP SELECTION?
To play the California State Lottery "6-49" game you select six numbers
(each of which may range from 1 - 49). To win, the six numbers you
select must match the six numbers randomly generated by the lottery
machine. What is the probability that you would correctly guess all six
numbers? Unlike our 'methinks it is like a weasel" example, at least the
six numbers don't have to be in a particular order--they must only be the
correct six numbers.
Even so, the odds of winning are astronomical. But suppose that the same
set of winning numbers was retained from week to week. And suppose that
each week you were allowed to keep any "correct" number you had selected
that week for the next drawing. For example, if this week you got one
number correct, you could keep it for next week and select only 5 more
numbers (since you already have one correct).
How long would it take before you got all six numbers correct? Not long.
Now you know why a lottery is a always single step selection.
(But if you know of lottery that allows for the cumulative selection of
numbers, please let me know!)
Let's watch the process of cumulative selection occur below.
(Press Cntrl-C if you want to exit this part of the program.)