The diverse animal kingdom exemplifies nature's complexity.
These animals, unique is many ways, incredible in their
creative abilities, skills, physical and mental attributes
to compete and survive to pass on their genes, astound
and at the same time enlighten us to reach new heights
in our own evolutionary struggle. DNA and embryonic
similarity suggest that all these animals are all common
is some way. That we evolved from one source. Nature
also displays amazing interactions: predator and prey,
different species working together to benefit one another,
patterns of evolution and changes in population due
to sudden changes in external forces.
Darwin explains this complexity in nature in the concept
of natural selection in his book, The Origin of Species.
Its basic premise is that all living organisms are continually
improving and optimizing: the strongest survive to pass
on their genes while the weaker, less competitive die
off. Stephen Wolfram, the inventor of Mathematica, holds
a different viewpoint of natural selection in his book
A New Kind of Science. He believes that natural selection
is too simple and cannot fully explain nature's complexity.
Classes of Natural Selection
In this section, I'd like to introduce my classification
for natural selection. This classification is derived
from Wolfram's classification for CAs.
Like CAs, natural selection patterns can also mimic
each category. Class 1 is an example of when a species
becomes extinct. Class 2 describes a simple repetitive
pattern. The pattern of population growth is an example.
A study was conducted by Italian mathematician Vito
Volterra in the1920s on the population of sharks and
the population of food-fish. The results show a cyclic
pattern of ups and downs. As the food-fish population
grows, the sharks will breed more readily. At a certain
point the shark population will "overflow"
and eat up all the food. With little food supply, many
sharks will die of starvation. This contradicts the
rule of natural selection and optimization. Intuitively,
one would suspect that optimization would lead to a
balanced and stabled relationship.
Another example of Class 2 behavior is found in a species
of salamander and snake. This prey-predator situation
is one of competition and evolution. The salamander
produces a toxin that defends it against its predators.
However, this snake has evolved a tolerance of the poison.
The poison doesn't kill the snake, but leaves it paralyzed
and vulnerable for a few hours. At the same time, the
production of toxin is very energy consuming for the
salamander. Through this interaction of species, future
generations of salamanders produce more and more of
the toxin. And likewise, the species of snake also gradually
evolves to become more and more tolerant of the poison.
As a result of such competition, today, the situation
is such that the salamander's toxin is ridiculously
high and is extremely poisonous. This predictable pattern
is a clear example of Class 2 behavior.
The inclusion of external forces gives rise to Class
4 behavior. According to the Darwin's theory, the evolution
of species progresses towards an optimal peak. If coupled
with the ever-changing faces of nature, these animals
are forced to adapt to their environment. Thus, the
evolution process is predictable but yet can dramatically
and instantly change towards a different pattern: the
definition of Class 4.
Class 3 behavior in natural selection is very rare.
Periods in history where there is wide spread changes
lasting for a very long time are examples of Class 3
behavior. For example, the theory of evolution states
that the dinosaurs became extinct because a large meteorite
hit the earth. This meteorite created an environment
that affected the whole earth, and this condition did
not revert back to its original state. The population
sizes and evolution of all animals during this time
was extremely random and chaotic. Population sizes of
large animals virtually disappeared. Changes in the
environment were dramatic. Many elements were changing
concurrently and the rippling effects of each were felt.
This situation is different than that described in
Class 4 because it affected all areas of life and prevailed
throughout a long period. Class 4 has chaotic patterns
but also displays symmetric patterns as well. The external
forces in Class 4 are things like hurricanes or earthquakes,
which only affects a limited population and does not
last very long. And because of this, patterns of animal
populations recuperate and return to evolve in a predictable
Wolfram vs. Darwin
In this section, we will look at Wolfram's viewpoint
of CAs and it's correlation with natural selection.
Wolfram will dispute the evidences of natural selection
and give his reasoning for the complexity that we see
in nature. An example will then be given for further
Too Many Parts
Wolfram argues the significance of natural selection
by saying that an organism is too complex. Natural selection
cannot determine which characteristic is the better
one. That is, organisms are made up of many parts. All
these parts are changing at once. There are simply too
many of these changes taking place that natural selection
cannot pin point one individual part to improve.
Another important point is that animals interbreed.
If a mutation occurred and it gives an animal an advantage,
it will counterbalance when the advantage character
is mixed with a non-advantage character. Let's say,
10 percent of an animal changes for the better, but
another 10 percent or even less changes for the worse.
This animal will breed with a normal animal that doesn't
have this mutation. Or the second animal could have
a disadvantage in the parts that the first animal has
an advantage over. Thus interbreeding and the fact that
there are too many parts to be accounted for causes
a balancing effect such that one trait cannot be optimized.
An example will clarify the above statements. Let's
look at the varying species of finches on the Galapagos
Island. How did they evolve? According to Darwin, the
birds were probably blown in by some storm. There they
were isolated from the rest of the world. The finches
evolved into many different species of finches: each
one with varying beak size and shape. The different
shapes and sizes give each finch species an advantage,
specializing it to accommodate certain food categories
and also reducing competition amongst each other.
Wolfram says this diversity cannot be explained by
natural selection. If the bird's beak gradually gets
smaller, then this change should be transparent with
all the birds. Why did some birds stay the same and
some get bigger. If something was an advantage, why
do some not change or diverge. Darwin's explanation
is that the small beaks gave some birds an advantage
while big beaks gave those a different advantage as
well. The problem with this explanation is that the
species interbreed. Because of this interbreeding, the
varying beak sizes should balance each other out. That
is, the only way that this divergence can occur is that
species were selective in whom their mates were or that
somehow the interbreeding stopped. Darwin's explanation
is that somehow, these birds were isolated from each
other and developed their speciation apart from one
another, and thus evolved into different species. And
after some time has past, these differences were so
great that when the two came together, breeding between
them cease to exist. However, for this example, it is
hard to imagine that so many of these isolations can
take place on an island. These are birds. They fly around
and can cover large distances. It's hard to imagine
how they can be isolated from themselves on an island.
Too Many Parts
Wolfram also says that even if interbreeding does not
take place (assuming the isolation theory is correct),
natural selection still cannot explain the varying beak
size. The reason, as mentioned earlier, is that there
are too many parts that make up the animal. The large
number of parts makes it hard for natural selection
to distinguish the good part from the bad part. For
instance, say one bird had a large beak. Another bird
will be lucky and have great speed but a very small
beak. However, the second bird survives to pass on its
genes because of its great speed. Thus the variations
will even out. Natural selection would not work simply
because it cannot distinguish or separate the good traits
from the bad traits when there are so many traits to
This section will look at natural selection's theory
of progressive optimality. First, we will discuss how
optimal characteristics are ambiguous. Then we will
look at what Wolfram has to say about optimality and
What does Optimal Mean?
Natural selection says that organisms move towards
an optimal state. But what does optimal mean? Does it
mean survival and having many offspring? If this is
the case as, then viruses and other bacteria are the
optimal organisms. That is, we should evolve into them
in the future according to the laws of natural selection.
But that won't happen. Another important point is that
these viruses have existed since the beginning of time.
The whole backbone of evolution says that in the beginning
of life, there existed simple one-cell organisms and
then they evolved into more complex organisms. But why
evolve, when you are already "optimal". Why
did the virus or bacteria change into something more
complicated when they were already "optimal"?
The funny thing is, many didn't change and stayed the
It is a little tricky to define what is optimal. After
all, optimal, in a sense, is perfection, and perfection
can never be achieved. The truth is, we don't know what's
optimal. But we do know when certain animals have advantages
over others. Is that animal moving towards optimality?
I would say yes, but Wolfram says no. One thing is for
sure, some species clearly have an advantage over other
However, there is the opposite case. There are lots
of systems that migrate in the opposite direction into
simpler organisms. Wolfram gives the analogy of a new
technology introduced into the market. At first, this
technology is used in many different ways. But eventually,
this technology settles down and is used in a conventional
way that is much simpler that the ones that were tried.
The fact that it's hard to distinguish what characteristic
is optimal and that some viruses evolve to something
more complex while the some of the same type of viruses
does not, tells us that nature is moving back and forth
(simple to complex, complex to simple). Nature might
not be moving towards optimality but instead just moving
But Many Animals have Advantages
Although Wolfram claims that natural selection doesn't
advance towards an optimal state, it is evident that
many of species are well adapted to complete in their
environment. Humans are simply amazed as to the complexity,
but more important is the "optimality" that
is endowed in each and every species. A couple of examples
to clarify are the cheetah with its great speed and
the kangaroo with its ability to carry its young in
its pouch. They are designed for peak performance in
their own special niche. And within all these specialization,
we see incredible diversity as each animal compete for
Wolfram's Explanation of Optimality
Wolfram does not deny the existence of optimality.
It's more accurate to say that Wolfram acknowledges
the fact that some animals have an advantage over other
animals. However, he doesn't give the credit to natural
selection. The reason that we see animals with advantages
over others is because of chance. It is just diversity.
And out of this diversity, there will be organism that
happens to have an advantage over the next. The key
thing here is that Wolfram never agrees to the fact
that organisms move towards an optimal state. That is,
the organism doesn't "evolve".
As for the diversity that we witness, it is an occurrence
of probability and mutation. Wolfram uses CAs to explain
the "illusion of optimality" and diversity
of nature. Assumed that our DNA strands can be interpreted
into a long binary string of bits. Just flipping one
random bit will cause major changes in the final outcome.
For example, in a 1D CA, we see that completely different
patterns arise even from adjacent rules. That is, rule
110 is completely different that rule 111. From this
perspective, Wolfram says that a mutation in DNA causes
the same type of effect. So that the small bit of a
DNA change has the possibility of creating enormous
physical change. Thus, it is easy to cause changes and
since the change (mutation) does not cause death, it
is passed on and we see diversity.
Also, it is evidence against natural selection in that
the sudden and drastic changes in so many traits would
make it hard for the natural selection theory to work
properly. In other words, since there are drastic changes,
there are too many characteristics to identify as the
primary reason for the advantage. (This was mentioned
earlier in the section "To many parts".)
The properties in CAs can be applied to animals. The
variations that we see are just random. Somewhere along
the timeline, a mutation occurred that drastically changed
the animal. The random mutation does not prove fatal
to the animal (the animal lives on to reproduce). This
animal is not better or worst that before. It's just
different. The strongest of each species do survive,
but there isn't this progression towards some optimal
state. Thus, the high standards that are characteristic
of the animal are kept, but the animal does not get
faster and faster and faster (the animal does not evolve).
Wolfram goes on to say that higher organism (e.g.,
humans) has nothing to do with optimality. Again, it
is simply a consequence of random strings of mutations.
If natural selection causes one to move to more complicated
animals, why do there exist organisms that have been
subjected to natural selection for over billions of
years and have not changed at all. Examples already
mentioned are viruses and bacteria.
Only One Type of "Human": An argument
Natural selection says that we move towards some type
of optimality. Every species must progress. But this
is not true. When you look at intelligence, humans are
far superior to all animals. Why are there no such animals
with similar intelligence since greater intelligence
means greater ability to survive and dominate. For example,
say you have 4 species: A, B, C, and D. And all were
of equal intelligence. Why is it that species D mutated
(into humans) and achieved greater intelligence while
species A, B, and C did not. Species A, B, and C must
have observed that species D was getting smarter. They
therefore had to adapt and become smarter themselves.
One can argue that the mutations are random and that
only D was lucky enough to get it. But that's a weak
argument. I think the same mutations must also occur
in A, B, and C, and therefore, they too will benefit
from the greater intelligence, preserve that characteristic,
and be able to pass it on. Millions of years ago, of
all the animals/fish/insects/etc., there must have been
one other species that also mutated to achieve the same
level of intelligence as a human. If not the same level
at least something close. Why did this not happen? It
is obviously to their advantage. And if that mutation
occurs, the fundamental principle of natural selection
says that that animal will dominate and we would be
able to see it today.
This leads me to question the theory that Neanderthals
die off. They were much smarter than monkey and therefore
had an advantage over competition. They must have been
able to compete against monkeys and still live to present
day. That is, if there were no humans and only monkeys
and Neanderthals, then I would imagine that the Neanderthals
would be able to out compete monkeys and still be alive
today. The Neanderthals did not die off because of competition
from humans because there were plenty of land/territories
along time ago. And if they couldn't compete with humans,
why didn't they evolve towards a different direction
or back into monkeys?
The same arguments can be used for other attributes
such as flying. This is a definite advantage. There
should be many animals with this ability (just like
there should be many animals with human like intelligence).
Why is it not the case?
Even worse, some of these animals such as penguins
and ostriches lose their abilities to fly? That doesn't
make sense. The penguin or ostrich that is able to fly
will have a definite advantage over the others and that
advantage should carry over to the next generation.
Natural selection experts say that they didn't need
that characteristic anymore. What? That doesn't make
sense that they don't need to fly. The ability to fly
is so much greater than not being able to fly (e.g.,
penguins can easily escape from walruses).
Flying is more optimal that not flying yet instead
of evolving, these animals regressed. This point is
hard for us to imagine, but if we give an analogy to
humans, then it would be very obvious. Human intelligence
is a definite advantage, yet can you imagine humans
getting dumber? It doesn't make sense for humans to
lose their ability to think and regress back into a
monkey no matter what circumstances we find ourselves
What about the animals that have become extinct? Natural
selection says that these animals could not compete.
If sabbertooth tigers were still alive, would they not
be able to compete against today's tigers? Did the modern
tiger progress or regress? Which of the two is more
The Leopard has an Internal CA
As previously stated, Wolfram does not agrees with
the idea of optimality. Wolfram argues this idea by
saying that humans "invented" the optimal
characteristics and attributed them to animals. For
example, we see spots on an animal and we say it's there
for a purpose. Or that we see a leaf shaped a certain
way and we say it's optimal. The last part of this section
talks about the golden angle and shows us that these
coincidences are simply coincidences and has nothing
to do with being optimal.
All three sections lean on the idea of simplicity in
creating new patterns/shapes/etc. Just like the varying
beak size of the Galapagos finches, we see diversity
in plants and animals because of the ease in the rule
in which we can create new patterns.
Animal patterns are thought to be complex for most
people. Natural selection tries to explain this by claiming
that there is a purpose behind it. The spots provide
the leopard with camouflage so that it can hide in the
tree or grass from enemies or prey. A long time ago,
there were leopards that didn't have spots and one mutated.
The mutated leopard with spots gained an advantage over
the others and passed on his genes. The key thing that
distinguishes natural selection with Wolfram's explanation
with CAs is that the stronger leopard (the one with
spots) has a better chance of survival, and thus, leads
into the idea of progression towards an optimal state.
Pattern Created Because of CA
However, this is another one of man's attempt to give
reason as to the purpose of the different things that
he finds. Man tries to explain and clarify why things
are the way they are. The funny thing is, there does
not have to be a purpose, and the intricate patterns
do not have to be produced by some complicated rule.
The spots are there simply because of a rule that governs
it. The leopard has an "internal CA" if you
will that determine its skin pattern. These are the
same patterns that are generated by 2D CAs. The rules
used to produce the patterns are also very simple. An
interesting fact is that these same patterns are seen
in many different types of species and the patterns
are almost always stripes and/or spots.
Natural selection uses the same explanation for seashell
patterns and shapes. But wouldn't it be better if the
patterns were exactly like that of the environment?
Wouldn't that serve as better camouflage? The patterns
I see are not exactly like the environment. Some actually
make the animals stand out.
There is no reason for the patterns. It's not there
to attract mate or prey, either. The difference with
seashell and animal patterns is that the seashell patterns
are produced one line at a time. The pattern doesn't
change. Once it is produced then it is fixed. If the
pattern is produced one line at a time, then how are
complex patterns created. Either the animal remembers
what pattern it has created in the past so it can continue
where it left off or that it follows some type of rule
to determine the next line. Remembering everything is
too complicated. The rule theory is very probable. The
patterns seen on seashells are very similar to those
seen on 1D CAs. In fact, 1D CAs are created in a similar
space-time fashion (one line at a time). The similarity
seen on seashells and 1D CAs should not be taken lightly.
It is very probable that the patterns are created by
some type of 1D CA rule.
The biggest evidence against natural selection, however,
is that some mollusc have an extra layer that covers
the patterns that it creates. So why go through the
trouble of making a pattern (that is suppose to provide
it with some type of purpose, designed for its optimal
performance) and then making another layer to cover
it. The only answer for this is that there is no specific
reason for the patterns. They appear by chance mutations.
And the variety of patterns is just random changes to
the rules. Mollusc can't even see! How are they supposed
to recognize the patterns to find their mate? Mollusc
eat dead animals, plants, or things like that. How are
their patterns going to attract prey?
The shapes of seashells can also be produced by simple
three-dimensional geometric rules. And minor changes
to the rules also create all the patterns that we see
in nature. Natural selection explains the diverse forms
by saying that they allow specialization. That is, the
different shapes give the animals an advantage and thus
those animals prevail. That is why we see so many different
types. They are all in competition with one another.
But the fact that the variety of shapes are easily made
through minor adjustments in the rules that make them,
tells us that the diversity that we see is really coincidental
mutations in the rules. And the coincidences create
all sorts of different shapes. It's not hard to make
a wide range of different shapes. From one shape, one
can easily diverge to create many different shapes.
The rule that defines the shape just need minor adjustments.
Tree and Leaf Shape
The branching patterns of trees and their leaves are
also a result of rules. These patterns can be replicated
with simple substitution systems. And by varying the
angles of the substituted branches, we can make any
tree or leaf shape. It's that simple. The similarity
between the branches or leaves created via substitution
and the real shapes of trees and branches leads one
to have an open mind and the possibility that maybe
they are related. It is much easier for a tree to have
this rule encoded into its DNA. There is not much information
that needs to be store. Natural selection says that
we have different tree and leaf shapes because it gives
each one an advantage. And the shapes are optimal. At
the risk of sounding repetitive, the rules such as CAs
and substitutions are much more logical at explaining
the diversity and complexity of the leaves or pigmentation
(leopard spots). There are two reasons: one is that
the rules are simple yet they produce complex patterns,
two is that minor changes in the rules produce different
patterns, and the range of these rules cover the complete
shapes and patterns that are seen in nature. The clear
similarity between the patterns produced by these system
rules and the same patterns found in real life should
make one stop, ponder, and give it a second thought.
It is very probable that this explanation is correct.
Another compelling reason that nature follows simple
rules is the frequent occurrences of Fibonacci numbers.
Here are the facts: lilies have 3 petals, buttercups
have 5, delphiniums have 8, corn have 13, asters have
21, and daisies and sunflowers have 34, 55, 89, or 144.
There are many more examples where Fibonacci numbers
come up. Its frequent occurrences suggest that there
are rules that are followed and the diversity that we
see is a minor alteration of the rule. One might be
incline to say that the numbers occur often because
they supply some sort of optimal condition for the plant.
But from what we've discussed, this doesn't have to
be the case. The golden angle is an example which looks
like its there for a purpose, but in fact is just coincidence.
The Golden angle (137.5) is another number that frequently
arises. This is the angle in which new branches grow
out of the tree if one were to take a birds-eye view
of the tree. This angle almost always comes out to be
137.5. When considering the growing tree, just focus
in on the tip. This is where the growing and branching
occurs. Since the stem is a cylinder, if one only considers
the top of the stem, then it is a circle. Now unwrap
that circle and you have a line.
This is how branching works: when chemical concentration
reach a level at a certain place in the line, branching
at that place in the line will occur, but it will also
soak up all the chemical around the surrounding area.
Therefore, the next branching point in the line will
occur somewhere farther away. When following this rule,
the distance at the beginning to not uniform, but after
a few steps, the distances are the same and produce
an angle of 137.5. That is incredible result. It just
happens to work out this way all the time. This angle
does not occur in order to achieve any optimality. It
Evidence Against Natural Selection
The Neck of the Giraffe
There is a lot of evidence against natural selection.
For one there are many gaps in the fossil records. The
fossil records fail to show gradual changes in a species.
There are always time jumps from one ancestor to the
next. For example, the neck of the giraffe is very long
and natural selection says that the animal's neck grew
longer and longer as it evolved because the longer necked
animal had an advantage of reaching the leaves that
others cannot. However, animals with in-between sized
necks were never found. Moreover, female giraffes are
a meter shorter than male giraffes and there were also
baby giraffes. Therefore, there must have been plenty
of food at different heights.
Natural selection says that we evolved from a single
cell. But where did that single cell come from. Natural
selection says that the single cell is a product of
chemical reactions. If this is true, then we should
be able to reproduce this chemical reaction and create
life (so far we haven't).
But the explanation that life came from inorganic chemicals
is very questionable to begin with. All living organism
comes from a parent. This is a fact that we see today.
Living organisms do not simply appear. Another point
is that although the single cell organism, thought of
as simple by you and me, has very complex DNA sequences.
The probability that these parts coming together to
make a living cell is astronomically low. To give an
analogy to the degree of low probability, it is like
saying that a hurricane passed through a junkyard and
the parts amazingly attached to create a Bowing 757.
In conclusion, the basic idea of natural selection is
questionable. If things were to continually evolve into
bigger and better things, then why haven't we seen dogs
the size of horses by now. Breeders know that there
are limitations. Try as they might, they can't get a
greyhound or horse to run as fast as a cheetah. Wolfram's
explanation as to the diversity of animals from the
idea of 1D CAs, 2D CAs, and substitution has some validity.
There is no push towards optimal performance. Instead
there is a haphazard approach given to chance and probability.
The higher complex organisms like humans are no more
"optimal" than the lower level viruses, we
just have more stuff.
 Hitching, Francis, The Neck of the Giraffe, Ticknor
& Fields, New haven and New York 1982.
 Johnson, E. Phillip, Darwin on Trial, Regnery Gateway,
Washington D.C., 1991.
 Leah, Edelstein-Keshet, Mathematical Models in
Biology, Random House, New York, 1988.
 Natural Selection and Evolution, Website found
 KurzweilAI, website found at: http://www.kurzweilai.net/index.html?flash=2
 Origin of Life, Website found at: http://christiananswers.net/q-eden/origin-of-life.html
 Stewart, Ian, What Shape is a Snowflake?, W.H.
Freeman and Company, New York, 2001.
 Wolfram, Stephen, A New Kind of Science, Wolfram
Media, Inc., 2002.