Introduction to the Mathematics of Evolution


Chapter 15


The Probability of Evolution



"A statistician is a person who stands in a bucket of ice water, sticks their head in an over and says: 'on average, I feel fine!'"

K. Dunnigan



Gene Complexes


In prior chapters we talked about genes and DNA, among other things. While a "gene" is a template to make a protein, a "gene complex" is a gene plus all of the other sections of DNA which are needed in order for this gene to be converted into a protein and for the protein to be placed into the proper position inside the cell, etc.


A gene would be useless without the rest of the gene complex.


No one really knows what the average number of nucleotide pairs (generally just referred to as "nucleotides") are in the average "gene complex." In the book: Genetic Entropy & The Mystery of the Genome, by Dr. Sanford, there is a clue (what he calls a "whole gene" is called a "gene complex" in this book):


"While only a small fraction of the [DNA] directly encodes for proteins, every protein-encoding sequence is embedded within other functional sequences that regulate the expression of such proteins. This includes promoters, enhancers, introns, leader sequences, training sequences, and sequences affecting regional folding and DNA architecture ... While a typical protein-coding sequence may only be 3,000 nucleotides long or less, the typical 'whole gene'[i.e. gene complex] that controls the expression of that protein can be in the range of 50,000 nucleotides long."

Genetic Entropy & The Mystery of the Genome, page 38


The numbers he quotes are for humans. In this chapter it will be assumed that the average "gene complex" for human beings, and for other very advanced animals, is 15,000 nucleotides. This number is just a guess since no one really has a clue what the exact number is.


Before getting into human evolution, let us apply the concept of "gene complex" to the "first living cell."



The Probability of the "First Living Cell"


Every gene of the "first living cell" had to form totally by random mutations of amino acids or nucleotides. There were no prior living cells (by definition) from which to serve as a pattern for the ordering of its amino acids or nucleotides.


To understand what the totally random formation of nucleotides is like, let us talk about Shakespeare. Suppose we put Shakespeare's King Henry VIII play into a computer and then scrambled the letters up randomly (we will also scramble up the spaces between words). Then, suppose we isolated 900 of these randomly generated letters and spaces. This is what the scrambled King Henry VIII might look like (note: a period ('.') is really a space in this list):












The gene complexes of the "first living cell" did not have viable patterns of nucleotides to serve as a pattern, thus the above attempt to replicate Shakespeare, from scratch, is a visual example of what the DNA of the "first living cell" would have looked like if we could "read" DNA as easily as we could read Shakespeare.


In other words, the first attempt to create a DNA strand for the "first living cell" would have been total gibberish because there was no prior pattern or ordering from which to pull nucleotides.


What if we randomly modified pure gibberish? I hope you understand that if you take gibberish, and randomly mutate it with more gibberish, you will still have gibberish.


So what mechanism converted pure gibberish into a viable DNA strand for the "first living cell?" There was no such mechanism because there was no life on this earth prior to the "first living cell."


The important thing to note is that there is no intelligence in the above Shakespeare rearrangement of its letters.


Actually, the above chart was generated by random numbers, but the random numbers were "weighted" by the exact proportion of letters in Shakespeare's play. For example, a letter of the alphabet that appeared very rarely in the play would appear very rarely in a "weighted" or "biased" randomly generated listing.


You won't get a better grade in literature class by reading thousands of pages of randomly generated letters of the alphabet, even when they are "weighted" by the actual proportion of each letter in the actual play.


Likewise, when we randomly scramble nucleotides, we would not expect to have a sequence of nucleotides which would provide any "information" or "intelligence" which would be useful to the "first living cell."


A scrambled; or randomly put together sequence of nucleotides; would not be expected to make a viable gene complex any more than a scrambled King Henry VIII play would tell us much about who King Henry VIII was and what his part was in the play. The play was named after him so you can assume he was one of the main characters (I suppose most people would consider him a villain, but others might consider him to be a role model).


In addition to randomness, there was no "survival of the fittest" in creating the "first living cell," meaning there were no intermediate semi-live cells which would provide a clue as to what the nucleotide sequences should look like.



Chemical Issues - Binding Sites


Proteins are nothing but a long string of amino acids. However, the amino acids need to be chemically bound together and then "folded" so that they form a shape so that they can be functional to the cell, even in the "first living cell."


Let us assume there was a "protein structure" in the "first living cell" which needed 50 different proteins (i.e. 50 different genes would be used to make 50 different proteins, and then the 50 different proteins were folded together make one very large protein structure).


Physically, the 50 different proteins must "fit together" much like you would build a toy robot using several different kinds of Lego building blocks and fit the pieces together. For example, the toy robot may have 15 "subsystems," where each of the "subsystems" are made of several or many different blocks, and where the sum total of the 15 "subsystems" or "structures" makes the complete toy robot.


With this analogy, the "subsystems" are the protein structures and the individual building blocks are individual proteins.


But such a concept is only half the problem for the "first living cell."


Unlike building a toy robot, individual amino acids, from different proteins in the protein structure, must "stick" or "bind" to each other at certain locations so that the entire protein structure is strong. This would be like gluing the Lego building blocks together at certain points so it could be carried to another room.


But with living structures, some sections of the proteins in a protein structure in a cell must repel each other. There are no building blocks that do that.


What this means is that not only must the 50 different proteins (that form one protein structure) have shapes that fit together "like a complex glove," certain amino acids (in different proteins in the protein structure) must have very specific amino acids, in exactly the right place, so that some of the 50 protein parts "stick" to each other or repel each other, etc.


Thus, proteins not only must have the right amino acids in the right places in order for the proteins to fold in the right places, there must also be just the right amino acids in just the right places so the proteins with bind together, will repel each other, will repel water, will attract water, and so on. Designing complex protein structures is an insanely complex process.


The focus of the book: The Edge of Evolution, by Dr. Michael J. Behe, totally disproves the theory of evolution by talking about "binding sites." His claim is that it is impossible that random mutations of nucleotides could produce enough binding sites to create a single complex protein structure. He is right, it is a superb book. However, like his other book, his "Edge" book is not very popular among the evolutionists.



Probability and the First Living Cell


Let us assume the "first living cell" had 300 gene complexes, with an average length of 3,000 nucleotides (or nucleotide pairs). Human gene complexes are far more complicated, and longer, than the gene complexes of the "first living cell" (if such a cell ever existed).


Now let us assume the probability of a random permutation of 3,000 nucleotides, being able to create a gene complex for the "first living cell," was 10‑5. This number is ridiculously generous to the theory of evolution (i.e. the real probability is much, much less than that).


Thus, we have a probability that an RNA or DNA strand for the "first living cell" would have a viable permutation of nucleotides is: 10(‑5x300) which is equal to 10‑1,500. The "‑5" is the probability of a single new gene complex forming from a randomly generated permutation of 3,000 nucleotides; and the 300 is the number of gene complexes which must be made.


Using the above example, 50 of the 300 gene complexes would be used to create one protein structure.


But even the above probability of 10‑1,500 ignores a lot of things, such as the viability of different combinations of proteins (remember, proteins must fit together, thus just having a bunch of proteins doesn't help at all, they must be a "set" of proteins which have very specific shapes and have specific amino acids in just the right places), but we will use the above numbers.


Remember, 10‑100 is an impossible probability. A probability of 10‑500 is an insane probability because it is 10400 times smaller than an impossible probability.


Now we are talking about a number which is 101,000 times smaller than an insane probability (i.e. 10(1,500‑500) equals 101,000).



Randomly Creating a "First Living Cell" in a Lab


Now let us assume a group of scientists claimed that they used a randomly generated DNA or RNA strand of 900,000 nucleotides, and ended up creating life from non-life. The "life" would include at least 300 very complex gene complexes (i.e. the proteins made from the gene complexes are mainly used to create protein structures). 50 of them are assumed to create one of the key protein structures inside the "first living cell."


Would you believe the scientists? Note that in the above paragraph is the phrase: "randomly generated DNA or RNA."


If they carefully designed the order of the nucleotides for the DNA of a "first living cell;" good for them, they should win the Nobel Prize (and no doubt they would).


But in this case the scientists are claiming that they used a totally random sequence of nucleotides to simulate true evolution to order the amino acids and proteins necessary to create life from non-life. They claimed they were simulating the pre-biotic world.


Should you believe these scientists? No, you should not believe them. They are trying to deceive you. It is not the accumulation of 900,000 amino acids which is the problem (though this is actually a very severe problem because amino acids do not chemically bind to each other); rather it is the permutation of nucleotides which is the problem.


Even though there would be many successful permutations of nucleotides which would create a living cell; even taking this into account, if these scientists had had a thousand failures, the chances of a success would still be 10‑1,497. Simply put, such a claim would be a clear case of fraud and deceit.


The point is that in nature, the same statistics apply. Not only would you not believe the scientists if they said they randomly created a "first living cell," you would also not believe them if they said nature randomly created a "first living cell" by using random mutations.



Building a New Species Randomly


Let us, for the sake of argument, assume that the average gene complex, for very advanced animals and plants, including humans, consists of 15,000 nucleotides (i.e. "nucleotide pairs"). Dr. Sanford says they can be as large as 50,000 nucleotides (i.e. "nucleotide pairs").


By the way, Dr. Sanford's book is one of the best sources for understanding genetic entropy. Genetic entropy is, by itself, an absolutely superb evidence that the theory of evolution cannot be true as will be seen later.


But let us assume that in the "evolution" from the first complex animal (an "animal" which had circulating blood or some other circulating fluid) to human DNA, that the average size of a gene complex was only 5,000 genes. This is an average for a lot of different species, some of which were much simpler than human DNA.


There are exactly 45,000 different ways that a sequence of 5,000 nucleotides can be ordered (remember, each way they can be uniquely ordered is called a "permutation"). Converting from base 4 to base 10, this number is approximately 103,000. This number is about 102,920 times larger than the number of atoms in our Universe and it represents the number of permutations in just one gene complex.


Once the "first living cell" was alive; its DNA needed to be mutated to make new species of single-celled animals.


Eventually, simple complex animals needed to be formed. Considering the "evolution" from the first complex animal to human DNA, do you think the probability of "evolution" got easier or harder as time passed, speaking from a probability standpoint?


Well, it got harder, much harder. From the first complex animal (which was an ancestor of humans according to the theory of evolution), many, many species were needed before humans could "evolve" into existence.


In this book it will be assumed there were 3,000 different species, meaning "ancestor species" of humans, meaning different species of animals which were ancestors of humans and were complex species (i.e. some fluid circulated).


First, we need to analyze how a single new species could "evolve" from an existing species.


Random mutations (in this context where viable DNA already existed) are events that occur to an existing species (starting with the "first living cell," but actually we will start with the first complex animal which is an ancestor of humans - meaning one of our "ancestor species").


Remember, an "ancestor species" is a species from which we are descended on our phylogenetic tree or evolutionary tree (assuming the theory of evolution is true for a moment).


To create a single new species, from an existing species, we will take the DNA of an existing species, and

1) Randomly copy one or more DNA strands from an existing species and place this copy somewhere else on the DNA (other options will be discussed in later chapters);

2) Randomly mutate some of the nucleotides (i.e. randomly change one nucleotide into another nucleotide, randomly add nucleotides or randomly delete nucleotides) which were copied from the DNA of the existing species; and

3) Randomly mutate (add, change or delete) some of the nucleotides of the DNA of the existing species which were not part of the copied DNA segments (e.g. for the nucleotides involved in the morphing of the embryo algorithms); and


A single gene complex of a new species would likely consist of about 5,000 randomly chosen nucleotides, as mentioned above. A "gene complex" is very specialized for a specific type of animal or plant. All mutations must be effective for the specific type of animal or plant they occur inside of.


We must remember that each animal or plant has a very sophisticated set of highly coordinated functions. In other words, you cannot take a rat liver and put it in a horse. The horse liver must be compatible with the other organs in a horse.


All the computers in the world, in a trillion years, could not calculate the probability of accidentally creating a single viable gene complex for a specific type of animal.


So we have to use some common sense (or use sampling). It will be assumed the probability of randomly mutating (i.e. copying, changing, deleting and adding nucleotides), which will result in the formation of a new gene complex for a new species, is 10‑10 (1 in 10 billion), though in reality it is probably worse than 10‑40 (which is why it is impossible to calculate without taking samples or using common sense).


This probability is lower than for the "first living cell" because the gene complexes for advanced animals are longer and more complicated.


The number 10‑10 is very, very generous to the theory of evolution.



How Many Unique Gene Complexes Per Unique Species?


The next assumption we must make is to calculate how many unique gene complexes are in a typical unique species.


Human DNA has 30,000 gene complexes. The "first living cell" would have had about 300 gene complexes. Thus, we have an increase of 29,700 gene complexes going from the DNA of the "first living cell" to human DNA (obviously assuming evolution, which is what we are trying to calculate the probability of).


However, the gene complexes of human DNA are huge compared to the gene complexes of the "first living cell" or even the first complex animal which was an ancestor species of humans (assuming evolution), plus human DNA would have to be far, far more complex. So we can ignore the "first living cell" DNA or the DNA of the first complex ancestor of humans. Thus, for all practical purposes, we need to build 30,000 gene complexes from scratch, even if we start with the first complex animal.


Assuming there are 3,000 unique species between the DNA of the first complex animal (which is an ancestor of humans), and human DNA, the average "ancestor species" (i.e. a species which is on our evolutionary tree) would have 10 unique gene complexes (30,000 divided by 3,000).


In summary, we will make these assumptions in our next calculation:


1) The average "gene complex" of a complex species is 5,000 nucleotides.

2) The probability of a randomly generated sequence of 5,000 nucleotides being able to form a single, viable gene complex for a specific species: 10‑10

3) Each unique species, of our ancestor species, has an average of 10 unique gene complexes.


With these generous assumptions, the probability of a new species "evolving" by random mutations of nucleotides (which is the only way that the theory of evolution can work) is:

10(‑10x10) = 10‑100


This probability is for one new species using randomly generated and modified nucleotides from an existing species.


This probability applies to every one of the unique species which have lived, and do live, on this earth. In other words, for every complex species which has ever lived on this earth (including extinct species), there is a probability of 10‑100 that this species was derived by random mutations of nucleotides (actually this is an average).


And even this probability is very, very generous to the theory of evolution.


There are actually other factors which have been ignored which would be very damaging to the theory of evolution if they had been included.


For example, consider the male and female issue. When there is a new species, which has a male and female, the DNA (after the random mutations in each of their germ cells) must be identical; meaning their DNA must "align," meaning all the functional sections of the DNA must be in the same order, in the germ cells of both the male and female, in every generation, in order for them to have viable offspring.


What this means is that the probability that a male and female will have the same random mutations in the same generation in the same location of earth is impossible. The 10‑100 probability does not even begin to take this absurdity into account.


Another example is the morphing of the embryo algorithm (i.e. computer program) in the DNA of each and every complex species which converts a single egg into a living animal. Every time there is a physical structural change in the species, the highly complex morphing of the embryo algorithm must change in a very precise way in the male and female. This, by itself, is an insane probability.


Multi-generational issues are also ignored. Multi-species issues are also ignored.


In any case, the 10‑100 applies to 3,000 ancestor species of humans. This means that the probability of human evolution is about: 10(‑100x 3000) or 10‑300,000.



A Consecutive Lottery


It is critical that the reader does not think of evolution as a single event with a probability of 10‑300,000.


For example, if there are 3,000 species, between the first complex animal and human DNA, then each of these ancestor species had to be consecutive, meaning one after the other, because they are all our ancestor species.


Just like our grandfather (our father's father) and our father cannot both be born in the same year, our 3,000th ancestor species (starting with our oldest ancestor species with complex DNA) must have existed prior to our 2,999th ancestor species. Our 2,999th ancestor species had to exist prior to our 2,998th ancestor species. And so on.


Thus, human evolution, from the DNA of our oldest complex ancestor species to the DNA of human beings, would be like winning "3,000 consecutive or sequential (i.e. one after the other) lotteries," where the probability of each was 10‑100!!!


In other words, the probability of going from our 3,000th ancestor species to our 2,999th ancestor species was 10‑100. The probability of going from our 2,999th ancestor species to our 2,998th ancestor species was 10‑100. And note that our 2,999th ancestor had to completely exist before the process of creating our 2,998th ancestor could even begin, as one example!!


In other words, we could not start to create our 2,998th ancestor species until after our 2,999th ancestor species already existed, so essentially we have to start the lottery over again to create our 2,998th ancestor species. Thus, after our 2,999th ancestor species existed we could start a new lottery, with a probability of 10‑100, of creating our 2,998th ancestor species.


And so on.


Thus, the theory of evolution consists of 3,000 true "consecutive or sequential lotteries," each with a probability of 10‑100.


There is no word in the English language to describe just how ludicrous the theory of evolution is!!


The 10300,000 number is the number of atoms in 10299,980 Universes. Thus, the probability of the theory of evolution, even when making very generous assumptions, is the same probability as picking the single, correct atom from among 10299,980 Universes!!


But even the 10‑300,000 probability for the theory of evolution is ludicrously generous because evolution must have "won" about 3,000 consecutive or sequential "lotteries," each with a probability of 10‑100!!


The problem of consecutive lotteries for the theory of evolution is "time." Not only is the probability of evolution ludicrous for a Universe which is a trillion trillion years old, on the planet Earth evolution had to occur (from the first complex animal) in about 600,000,000 to 660,000,000 years.


Would you bet your life on winning a lottery which requires winning 3,000 consecutive lotteries, each with a probability of 10‑100, in a period of 660,000,000 years? Do the math.


Remember, never has new genetic information or new genetic intelligence ever been observed being created from random mutations of nucleotides. Now you know why.



How Many Species?


Let us define a "species" as having a unique DNA structure, meaning a species has a unique set of gene complexes, in the same order on their DNA, the same morphing of the embryo algorithms, etc.


How many unique species have existed on this earth? Scientists know of many millions of species which have lived on this earth (counting plants and animals). However, in these counts there are many examples of "microevolution," meaning variation in a single "species," as defined above.


The key question is how many unique species have lived, and do live, on this earth?


The answer will be assumed to be about 10 million unique species. This includes living plants and animals (including fish and other species in the deep ocean) and extinct plants and animals (including extinct fish and other species in the deep ocean).


This means that in the 5 billion years evolutionists claim this earth has existed (most of this time there was no life on earth, except single-celled organisms, according to science); an insane probability of 10‑100 had to have happened 10 million times!!!


Actually, all of this had to happen in less than a billion years because we are starting with animals with complex DNA (i.e. a "complex species" means there are multiple types of cells which perform some coordinated function necessary for life, specifically a circulating fluid).


But it gets worse.


Each species, whether living or extinct, would have needed unique ancestor species back to the point they have a mutual ancestor species with humans or other animals. We see in this case the need for literally hundreds of thousands of situations where 5 or 10 or 50 consecutive lotteries must be won, which have nothing to do with human DNA. And this is being very careful to avoid any duplication of ancestor species (i.e. no species is counted more than once).


Are you beginning to see the inane absurdity of the theory of evolution?



A Murder Mystery #1


To comprehend why the theory of evolution is scientific nonsense, let us consider a murder mystery.


Suppose a person was murdered in a small town, a 4 hour drive from Paris, France, at exactly 1 A.M. Central Standard Time, U.S.A., on a Thursday morning.


Suppose for some reason the French government wanted to frame me (i.e. Webster Kehr) for the murder.


Thus, they gathered hundreds of pieces of evidence which implicated me in the murder.


Suppose that I did not know the person who was murdered, in fact I did not know a single person in the city where he lived. Nor do I speak French. Yet, supposedly, there was a ton of contrived "evidence" that I was guilty.


How could I prove my innocence?


Suppose on the week this person was killed, I was working 8 hours a day (from 7:30 AM to 4:30 PM, which includes a lunch break) in Ft. Leavenworth, Kansas. Suppose my activities at work were very, very well documented and there were lots of witnesses to my being at work on those days and during those hours.


To prove my innocence, I would prove that I was at work, as scheduled, every day in the week the person was murdered.


Let us assume the following facts:


1) It would take me 30 minutes to drive to the nearest large airport, the Kansas City International airport (KCI).

2) I would have to be at the airport at least 1 hour before the plane left, since it was an international flight.

3) I would have to change planes (there are no non-stop flights from Kansas City to Paris), which would take another 1 hour.

4) The total flying time to Paris would take 12 hours.

5) It would have taken me 4 hours to drive from the Paris airport to the city where the murdered man lived.


Thus, to get from Ft. Leavenworth to the city where the person was murdered, would have taken me at least 18 hours. It would have taken a similar amount of time to get back to work.


Thus, it would have taken me 37 hours to complete the trip to the city in France, murder the man, and come back home.


How much time did I have? The answer is 15 hours. From 4:30 P.M. to 7:30 A.M. is 15 hours.


I could not have killed the person. I was innocent.



A Murder Mystery #2


Now let us take all the above facts, but in this case the person was murdered on a distant planet, 5 light years away.


How long would it take for me to travel 5 light years, at 100,000 miles per hour?


It would take about 67,000 years to go to the star and back.


How could I travel for 67,000 years in 15 hours? Again, I was innocent.





The problem with the theory of evolution is time. The scientific establishment has tried to make it appear that the theory of evolution has had 600 million years to 1 billion years, since the first complex animal.


That is not enough time. Even 600 trillion trillion trillion trillion years is not enough time. The theory of evolution is more like Murder Mystery #2 than Murder Mystery #1. There simply hasn't been enough time on this earth for the theory of evolution to have occurred.


Could you win 3,000 "consecutive lotteries" in 660 million years, where the probability of each lottery was 10‑100? Such a belief would be mathematical and scientific nonsense. It is virtually impossible you could win 3 "consecutive lotteries" in 660 million years.


But even the problem of winning 3,000 "consecutive lotteries" is just a small tip of the iceberg for the theory of evolution.


Winning 3,000 "consecutive lotteries" is just for human DNA. How about the DNA of millions of other unique species and the "consecutive lotteries" each of them needed to have "won," which did not include any duplication of ancestor species.


You also have problems with the male and female issue. Both the male and female have to have DNA which aligns with each other in order to have offspring. Thus, each must have the same impossible mutations in their germ cells, and the male and female must live in the same geographical area and same time period. This alone generates insane probabilities.


Those who support the theory of evolution might say that the same "external" events caused the same mutations in the DNA of the male and female. This theory is totally absurd for many, many reasons, but this book will not take the time to discuss these issues.


The point is that six-hundred million years is not enough time for evolution to have worked.

Even 600 billion years would not be enough.

Even 10100,000 years would not be near enough time for evolution to have occurred by random mutations of DNA. Not even close.


Do the math. You will find out that adding a few numbers to an exponent do not help the overall problem the theory of evolution faces.


Evolution never happened, not on this earth or on any other earth, or on any other galaxy or on any other Universe.


This Universe, the planets, and life on this earth were created by intelligent beings, all under the watchful eye of God Himself or life was created by God Himself. There is no other explanation for the DNA of millions of different species of animals and plants.