Why We Do Not Understand the Origin of Complex Biological Innovations

Darwinism is the “this explains it all” dogma that enjoys a smug reign in modern biology. A Darwinist will try to explain every organism's capabilities as being due to random mutations and natural selection, just like a dogmatic Marxist will try to explain every major historical event as being an example of class struggle. Without offering any firm answer as to what causes biological innovations, in this post I will take a candid look at why Darwinism fails as an explanation for the origin of species and the origin of biological complexity.  I may note that the points below are not by any means crucial to the issue of whether minds are produced by brains.  The idea that minds do not come from brains can be held without contradiction by both those who follow Darwinism and those who are skeptical about it.  

There are three aspects of Darwinism: (1) common descent, the idea that all life is descended from a common ancestor ; (2) gradualism, the idea that species gradually change over eons into very different species; (3) the idea that biological innovations occur because of a combination of natural selection and random mutations. None of these claims has been proven.

We have no proof of the doctrine of common descent. The fact that all life uses the same genetic code is not at all proof that all life descended from the same ancestor. If some divine creator or series of extraterrestrial expeditions to Earth had decided to populate our planets with organisms, such a force might well have chosen to introduce organisms with a common genetic code, so that a harmonious ecosystem could develop, without organisms getting poisoned because they fed on some other organism with a different genetic code.

To try to support the doctrine of common descent, scientists use what is called phylogenetics, which attempts to create “trees of life” showing how species evolved from a common ancestor. But phylogenetics is very much guesswork. We have almost no DNA from species that lived very long ago, because DNA decays fairly quickly. The half-life of DNA is 521 years, meaning every 521 years half of the DNA in a dead organism will decay.

What happens is that speculative “trees of life” are generated using computer programs run by phylogenetics experts. Such computer programs use massive amounts of guesswork all over the place. They do not arrive at likely solutions, but merely at estimates that are “most likely” given the inputs and given a starting assumption of common descent. Here “most likely” does not mean probable, but simply “more likely than any other guess.” You can make a “most likely” estimate that is very probably wrong. If I ask you to pick a word at random from a book, then the word “the” is the “most likely” answer, but it is not a likely answer (the word you picked will probably be some other word).

The doctrine of common descent (that all organisms descend from a common ancestor) is also not proven by the fossil record. Because of events such as the Cambrian Explosion, the fossil record is actually very much at odds with the predictions of Darwinism. The largest classification of species (below a kingdom) is called a phylum. According to Darwinism, we should have seen animal phyla appear very gradually. But instead the fossil record shows almost all animal phyla appearing in a relatively short period of time, about 530 million years ago, in the event called the Cambrian Explosion. Such a dramatic appearance of almost all the animal phyla is incompatible with Darwinism. Darwinists have done nothing to plausibly explain how the Cambrian Explosion could have occurred under their assumptions. 

Darwinists will often use the rhetorical trick of saying "evolution is fact." But it is only microevolution that is fact. Microevolution is  relatively minor changes in a species caused by some trait already existing in a population become more common in a gene pool or less common in a gene pool. We have no proof of macroevolution, that complex biological innovations appear in a species through a gradual process.  Referring to speciation (the origin of new species) in an interview, the distinguished biologist Denis Noble states, "So I go along with the view that there has been no really clear proof that speciation occurred via gradual mutation followed by selection."  

Shockingly, the fossil record supplies relatively little support for the idea that species gradually evolve into different species. By far the most common pattern in the fossil record looks like this:

1. A species will suddenly appear in the fossil record, with no obvious ancestor.
2. The species persists in the fossil record for a certain length, perhaps many millions of years.
3. The species then disappears from the fossil record, for no obvious reason.

Now it is true that Darwinists have been able to come up with a few cases of what are called fossil series, in which you can line up a series of fossils, order them by age, and have something that may suggest an evolutionary progression between forms. But the number of such series is actually much less than we would expect if Darwinian evolution had been occurring constantly during the past billion years. If Darwinian evolution had been occurring constantly during the past billion years, we should see such fossil series all over the fossil record. Instead they seem to occur only here and there, in relatively small numbers.

What we also must remember is that in a random fossil record in which no Darwinian evolution occurred, we should actually expect to see (purely by chance) some cases in which fossils coincidentally can be arranged in a “fossil series” suggesting evolution. We must remember that for decades our paleontologists have been diligently combing through the fossil record, looking for series of fossils that can be grouped together in a line suggesting a Darwinian progression. We would expect that purely by chance quite a few such series could be found, even if Darwinian evolution had not occurred.

The alleged transitional series found in the fossil record could be the result of a kind of “paleontology pareidolia,” in which people find a few patterns they are hoping to find after spending great lengths of time scanning a large data collection, rather like people who spend countless hours scanning Mars photos and who occasionally find things on the surface they claim are evidence of ancient Mars civilizations. Dictionary.com defines pareidolia as “the imagined perception of a pattern or meaning where it does not actually exist.” The scientist who spends decades searching for transitional series of fossils (and who eventually finds one or two series that seem to please him) may be like some person who for 40 years carefully checks his toast for dark spots that look like the face of Jesus, and who eventually finds something that pleases him.

Imagine I go into the Yankee Stadium parking lot during many different baseball games. If I am determined to find evidence that one car has evolved into another car, I will probably be able to take car photos that I can arrange in a line, and offer as evidence of “car evolution.” I might for example have a series that first shows a dark blue convertible, then a dark blue car with a roof, and then a dark blue van. I might cite these as proof that one type of vehicle is evolving into another, but it's merely me finding a pattern I was hoping to find, in a way that is not surprising given a large data set to comb through. The few “transitional fossil series” presented by paleontologists may be the same type of thing – examples of pareidolia.

In the case of the human species, paleontologists produce “transitional fossil series” supposedly showing a transition leading ape-like ancestors to humans. But such series involve guesswork. We do not have the DNA needed to put such guesses on a firm basis. The half-life of DNA is 521 years, meaning there is very little DNA for any organisms older than 100,000 years. Attempts to use mitochondrial DNA derived from fossils are very dubious indeed, since less than one percent of an organism's DNA is mitochondrial DNA.

It is dogmatically claimed that humans and chimpanzees had a common ancestor. But no such common ancestor has been found in the fossil record. In 2017 BBC.com had a long article entitled, “We have still not found the missing link between us and apes.” The article notes a disagreement over whether chimpanzees or orangutans are the “sister species” of humans. A scientific article tells us, “Few fields of research are subject to so many competing hypotheses, as illustrated by the variable number of ancestral species assigned to the human lineage by different authors, ranging from four to a maximum of 25.” In recent decades a bewildering variety of hominid fossils have been found, making it harder and harder to extract any clear tale of human ancestry.

A study based on fossil teeth is described in the science story here, which is entitled, “No known hominin is common ancestor of Neanderthals and modern humans, study suggests.” Although it is often claimed that humans and chimpanzees have a common ancestor, the wikipedia.org article on "Chimpanzee-human last common ancestor" (CHLCA) confesses, "no fossil has yet been identified as a probable candidate for the CHLCA." 

To back up their claim that humans and chimpanzees share a common ancestor, Darwinists are very fond of citing the similarity of human DNA and chimpanzee DNA. But we are not built from the linear chains of amino acids found in DNA – we are built from the three-dimensional proteins that mysteriously arise from such linear chains. When we compare chimpanzees and humans on a protein basis, taking into account the shapes of the proteins, it is found that 80 percent of the proteins in humans differ from those of chimpanzees. See the scientific paper entitled “Eighty percent of proteins are different between humans and chimpanzees” at this URL.

The most plausible fossil candidate for a human ancestor is not the Neanderthals (who lived at the same time as early humans) but a species referred to as Homo heidelbergensis.  But the wikipedia.org article on Homo heidelbergensis tells us that the case for such an ancestry is far from clear. It states that "there is no direct evidence that suggest the Homo heidelbergensis is related to modern-day humans."

Such a statement should shock every person who believes that humans are descended from more ape-like ancestors.  The statement tells us that there is "no direct evidence" that this best candidate for a human ancestor is related to modern-day humans. 

We are told that men and chimpanzees have a common ancestor. But chimpanzees use knuckle-walking, which involves four limbs. In order to believe that humans and chimpanzees arose from a common ancestor, we have to believe in a progression like this occurring over many thousands or millions of years:

4-limb walking (works well) → Intermediate stage (works poorly) → Bipedal walking (works well)

The problem is that this progression is unbelievable under a theory of natural selection, which should stop any progression that works against survival value. 

 
Anthropology professor Henry M. McHenry stated this on page 270 of the book Evolution: The First Four Billion Years: "The published hominin fossil record does not yet have a true intermediate stage between an apelike and a humanlike body."

Biological organisms show almost unfathomable complexity and coordination. The innovations we see in biological organisms are more impressive from an engineering standpoint than all of the works of man. How do Darwinists attempt to explain such marvels? They offer an explanation that is not at all a deep explanation, but merely a tissue-thin explanation. The explanation they offer is that all of the wonders of biology appeared because of random mutations and natural selection. The idea is that random mutations cause great innovations to appear once or twice in a population, and that natural selection then caused these innovations to spread through a gene pool, because the innovations increased the survival likelihood or reproduction likelihood of an organism.

This explanation entirely fails to be a credible explanation for biological innovations, because of a very simple reason. Natural selection cannot do anything to explain the first appearance of a biological innovation, because natural selection only starts working in regard to a biological innovation after that innovation has appeared. For example, imagine a species does not have any vision system. Once a vision system appears in one organism of that species, natural selection can start blessing that organism with a higher chance of survival and a higher chance of reproduction. But until the innovation of a vision system appears, natural selection will do nothing to make it more likely that a vision system will appear. And so it is in general for every type of biological innovation. Natural selection does nothing to explain the first appearance of any type of biological innovation.  Natural selection involves the survival of the fittest, but does not explain the arrival of the fittest.  The point is illustrated in the diagram below. How did those "good designs" of the yellow circles appear? Natural selection doesn't explain that. 

We can compare natural selection to a sneeze. A sneeze is a proliferation agent that will help a virus spread once the virus already exists in a particular person. But a sneeze does absolutely nothing to explain how the virus appeared in the first person infected. And so it is with natural selection, which does nothing to explain the first appearance of any biological innovation.

Therefore the Darwinist's “explanation” of random mutations and natural selection ends up being an account that is really 99% an account of random mutations. And saying something was caused by random mutations is just a non-explanation, simply saying that it appeared by pure chance. 

 An MIT professor wrote a paper "Inadequacies of Neo-Darwinian Evolution as a Scientific Theory" in which he stated this:

The process of speciation by a process of random variation of properties in offspring is usually too imprecisely defined to be testable. When it is precisely defined it is highly implausible. 
 

We know that for every random mutation that is helpful, there are very many that are harmful. A random mutation is like a typo, a random letter typed on a keyboard. The chance that a set of random mutations will produce something useful is as small as the chance that a monkey typing at a keyboard will produce a useful computer program or a story or poem good enough to get published in The New Yorker.

In a New Scientist article recently published, a biologist made a candid confession: that while most random mutations are neutral (having no effect), the number of random mutations that are harmful vastly outnumbers the number of mutations that are helpful. I'll quote from the article (and note carefully the use of “extremely”):

“The vast majority of mutations don’t matter, says Leo Schalk at the University of Essex. “There might be the occasional mutation that is deleterious, or the extremely occasional mutation that is beneficial.” He compares the impact of mutations to swinging a hammer at a car engine. “There’s a chance that you will improve its function, but it’s much more likely that the hammer will either just bounce off or break something.”

A recent scientific paper cites multiple sources that assert harmful mutations are vastly more common than helpful ones:

The predominance of deleterious mutations over beneficial ones is well established. James Crow in (1997) stated, “Since most mutations, if they have any effect at all, are harmful, the overall impact of the mutation process must be deleterious”. Keightley and Lynch (2003) given an excellent overview of mutation accumulation experiments and conclude that “...the vast majority of mutations are deleterious. This is one of the most well-established principles of evolutionary genetics, supported by both molecular and quantitative-genetic data. This provides an explanation for many key genetic properties of natural and laboratory populations”. In (1995), Lande concluded that 90% of new mutations are deleterious and, the rest are “quasineutral” (Also see Franklin and Frankham (1998)). Gerrish and Lenski estimate the ratio of deleterious to beneficial mutations at a million to one (Gerrish and Lenski 1998b), while other estimates indicate that the number of beneficial mutations is too low to be measured statistically (Ohta 1977; Kimura 1979; Elena et al. 1998; Gerrish and Lenski 1998a).

The paper can found at the link here.

In one scientific paper, some scientists say, “We predict 27–29% of amino acid changing (nonsynonymous) mutations are neutral or nearly neutral (|s|<0.01%), 30–42% are moderately deleterious (0.01%<|s|<1%), and nearly all the remainder are highly deleterious or lethal (|s|>1%).” The authors give us no estimate for the number for beneficial mutations, as such things are apparently so improbable that they can be ignored.

Very clearly, beneficial mutations are so improbable that the dogma of biological innovations by random mutations is utterly implausible. When a Darwinist tells us that something like the vast complexity of a vision system appeared from random mutations, he is telling us a modern-day miracle story. 

In the book Evolution and Ecology: The Pace of Life by Cambridge University biology professor K. D. Bennett, this mainstream authority comments on speciation (the origin of species). He says on page 175, "Natural selection has been shown to have occurred (for example, among populations of Darwin's finches), but there is no evidence that it accumulates over longer periods of time to produce speciation in the Darwinian sense."

Let us imagine there is a parent who doesn't want to believe that his toddler son is smart. One day he comes into the nursery and finds a beautiful house of cards next to the child on the floor. If the parent tried to explain this by saying that the child merely threw a deck of cards into the air, and that the house of cards was created by “random spatial positioning and friction” this would be pure nonsense. Friction would not help cards form such an arrangement, but merely help to preserve such an arrangement if (by a 1 in 1,000,000,000,000,000,000,000,000 coincidence) such an arrangement happened to appear by chance.

The Darwinist who tries to explain fantastically coordinated arrangements of matter by saying they are caused by “random mutations and natural selection” is really offering an explanation as implausible as this parent's explanation. Just as friction does nothing to explain the original appearance of the fantastically unlikely arrangement of cards, natural selection does nothing to explain the first appearance of any biological innovation in a gene pool. In both of these cases, we have explanations that are 99% just appeals to blind chance. And whenever you have any very complex arrangement fantastically unlikely to appear by chance, you never have a decent explanation if you are mainly just appealing to blind chance.

When trying to show how natural selection and random mutations might create a biological innovation, an evolutionary biologist might reason light this:

Let's imagine some biological innovation requires 7 parts. The first part might appear because of a random mutation. That part might supply a survival benefit, and therefore spread though out the population of organisms. We call this a “classic sweep.” Then some other random mutation might produce the second part needed for the biological innovation. By then all of the organisms would have the first part, because of the previous “classic sweep.” This second mutation might also produce a benefit, producing another “classic sweep.” We need merely imagine this happening about five more times, and then the biological innovation would have been produced.

While this scenario may sound reasonable, it actually is not. For one thing, the scenario ignores the very careful placement and fitting together of parts that must occur for a biological innovation to occur. It seems that there is only a microscopic chance that random mutations would produce parts that fit together in just the right way to make a functional whole. But the main reason why the scenario is not reasonable is the fact that the first parts of an implementation (whether biological or non-biological) are almost never useful. So the “classic sweeps” imagined in this scenario would not be occurring until all of the parts needed for the biological innovation had occurred.

By considering a few cases outside of the world of biology, you can realize the general principle that the first stages of an implementation are not useful. No benefit arises from building one tenth of a suspension bridge, or one third of a television set, or one seventh of a rocket. Or consider the case of an ice cream shop, which requires all of these things for it to produce any benefit to its owner: (1) the physical shop; (2) either a delivery system for receiving ice cream deliveries or machines for making ice cream; (3) a refrigerator; (4) at least one employee; (5) cups or cones which ice cream can be put in. If any of these five things are missing, there is no way for the shop to make money.

The general principle that the first stages of an implementation are not beneficial can be stated as the principle of preliminary implementations. We can state this principle like this:

The principle of preliminary implementations: in almost all cases, with few exceptions, preliminary or fragmentary implementations by themselves yield no benefits or rewards.

This principle holds true in general life (as the examples above show), and also in regard to biological implementations. So if we are speaking of some biological implementation requiring a certain number of parts, we should not at all assume that the first stages of such an implementation will provide a benefit. A benefit will occur only when a certain degree of complexity and functional coherence has been achieved. In other words, no benefit will come unless some functional threshold has been reached. Such a functional threshold will typically require that several or many parts are arranged in the right way. The diagram below illustrates the point.

In general Darwinism fails to explain the first stages of useful structures. This was pointed out very clearly in Darwin's time by the biologist Mivart, who wrote the following at the beginning of Chapter II of his book On the Genesis of Species: "Natural Selection utterly fails to account for the conservation and development of the minute and rudimentary beginnings, the slight and infinitesimal commencements of structures, however useful those structures may later become."  Mivart devoted Chapter II of that book to many examples of "incipient stages" that Darwinism could not explain well, including the first small part of any limb such as an arm or leg or the first small part of a wing or the first small part of a mammary gland.

Darwinists have told many a tall tale to try to account for such things, such as suggesting that maybe wings grew out of wing stumps that were used to catch insects. Such tales are typically unbelievable.  Two of the attempts that Darwin made to suggest such stories are now believed to be erroneous (biologists now reject his "maybe mammals come from marsupials" explanation for the incipient stages of mammary glands, and also reject his "lungs come from swim bladders" explanation for the incipient stages of lungs). 

Consider the case of the biological implementation needed to produce vision. We can call this a vision system, and it requires much more than just an eye. Below are 4 requirements of a vision system.

1. Some type of eye.
2. An optic nerve leading from the eye to the brain.
3. Extremely complicated proteins used to capture light, such as rhodopsin.
4. Very complex brain changes need to interpret inputs from the eye.

Now if an organism had only or two of these things, it would receive no benefit. For example, merely having an eye and an optic nerve would not be useful unless the eye had the proteins needed to capture vision, and unless the eye also connected to changes in a brain needed to make use of visual inputs. And if there were only such proteins and such brain changes, and no eye and no optic nerve, that would not be beneficial.

Here is a very simplified “back of the envelope” calculation to calculate the probability of a minimally functional vision system arising by chance during a 100-million-year period in a population of a million organisms without any such system. Very greatly oversimplifying, we can imagine the visual system as requiring 8 separate mutations: two for the eye, one for the optic nerve, two to have a protein used by vision, and two for the brain changes needed to process vision. (In all probability, many more mutations than these would be required, and the required number of mutations might be in the hundreds or thousands.) Since some of these mutations would have to require things incredibly improbable to happen, particularly the incredibly improbable mutations needed for proteins necessary to capture light, the average chance of any one of these mutations occurring during the 100 million year period would be no more than 1 in 10.

But (and this is a crucial point) once a mutation occurred, it would not immediately tend to become more common in the population, because it would be merely a part of a complex system needed for vision, and the other parts would not yet exist. So, for example, a mutation merely causing an optic nerve (leading from the brain to the exterior of an organism) would not be rewarded and would not tend to spread in the population unless the other required parts were in place. And a mutation merely causing half of an eye would not be rewarded and would not tend to spread in the population unless the other required mutations had occurred.

So each mutation that was not the first of these mutation would have no more than 1 chance in 1 million of occurring in an organism in which the previous lucky mutation occurred (because the population consists of a million organisms). The odds would actually be worse than that, because a mutation that didn't prove useful would tend to die out entirely in the population. Based on the population size (1 million) and the average chance of getting the mutation during the period (less than 1 in 10), the odds of one of these mutations occurring (not the first) in an organism that already had one of the previous mutations can be roughly calculated as less than 1 in 10 million. So you would have math like this:

Chance of mutation 1: 1 in 10

Chance of mutation 2 in organism with mutation 1: < 1 in 10,000,000

Chance of mutation 3 in organism with mutations 1 and 2: < 1 in 10,000,000

Chance of mutation 4 in organism with mutations 1,2 and 3: < 1 in 10,000,000

Chance of mutation 5 in organism with mutations 1,2, 3, and 4: < 1 in 10,000,000

Chance of mutation 6 in organism with mutations 1,2, 3, 4, and 5: < 1 in 10,000,000

Chance of mutation 7 in organism with mutations 1,2, 3, 4, 5, and 6: < 1 in 10,000,000

Chance of mutation 8 in organism with mutations 1,2,3,4,5,6, and 7: < 1 in 10,000,000

The probability of all 8 of these mutations ending up in a single organism, and finally giving that organism vision, would be these probabilities multiplied together, which gives a number much less than 1 in 10 million to the seventh power, or 1 in 10⁴⁹. We would not expect such a thing to ever happen by chance in the history of the galaxy, even if life had arisen on a billion planets in our galaxy.

I call this type of difficulty “the scattering problem.” It is the problem that when we consider how the mutations needed for a complex innovation would be scattered across populations occurring over multiple generations, it is exceptionally unlikely that all of the required mutations would ever end up in a single individual. 

 

I can illustrate this scattering problem through an analogy. Let's imagine you're some genius who invented the first home computer in 1960. Suppose that this consisted of 7 key parts: a motherboard, a CPU, a memory unit, a keyboard, a monitor, a disk drive, and an operating system disk. If you were to mail one of these parts on 7 different days, sending a different part each day to the same person, there might be a reasonable chance that the person might put them all together to make a home computer. But imagine you did something very different. Imagine you mailed each part in a different year, sending out the parts gradually between 1960 and 1967. Imagine also that each part was mailed to a person you selected through some random process (such as picking a random street and a random time, and asking the name and address of the first person you saw walking down that street) – a process that might give you any of a million people in the city you lived. What would be the chance that the parts you had mailed through such a process would ever be assembled into a single computer? Basically no chance.

It is exactly such odds that a Darwinian process of random mutations and natural selection would constantly be facing in order to explain innovations consisting of multiple complex parts, none by itself causing a survival benefit. If it luckily happened that there somehow occurred all of the random mutations needed for such a biological innovation, such gifts would be scattered so randomly across the population and across some vast length of time that there would be less than 1 chance in 1,000,000,000,000,000,000 that they would ever come together in a single individual, allowing the biological innovation to occur for the first time. What good is “survival of the fittest,” when it is so hard by chance to get some new piece of fitness (a complex biological innovation) in the first place?

The previous analogy involving computer parts serves well as a rough analogy of the scattering problem. To make a more exact analogy, we would have to imagine some parts distribution organization that persisted for many generations. Such an organization might send out one part of a complex machine in one generation, to a randomly chosen person in a city, and then several generations later send out another part of the machine to some other randomly chosen person in the city (who would be very unlikely to be related to the previous person); and then several generations later send out another part of the machine to some other randomly chosen person in the city; and then several generations later send out another part of the machine to some other randomly chosen person in the city. The overall likelihood of the parts ever becoming assembled into a machine with all the required parts would be some incredibly tiny, microscopic probability. This more exact analogy better simulates the scenario in which favorable mutations supposedly accumulated over multiple generations.

Is there any way to reduce the scattering problem when considering the odds of complex biological innovations occurring by Darwinian evolution? You might try to do that by assuming a smaller population size. However, assuming a smaller population size is very much a case of “robbing Peter to pay Paul.” The reason is this: the smaller the population size, the smaller the the chance that some particular favorable random mutation will occur. So any reduction in the assumed population size should involve a corresponding reduction in the average chance of one of the favorable mutations occurring. The result will be that the incredibly low probability of the biological innovation will not be increased.

Here is a quick example to show the point. Let us imagine 100,000 generations of a population of 1,000,000 organisms, and calculate the chance of a particular biological innovation occurring in it. Let's suppose the biological innovation requires seven random mutations, and the average chance of one of these mutations occurring is 1 in 10 during this 100,000 year period. Since all of the mutations are needed for the biological innovation, the math looks like this:

Chance of mutation 1: 1 in 10

Chance of mutation 2 in organism with mutation 1: < 1 in 10,000,000

Chance of mutation 3 in organism with mutations 1 and 2: < 1 in 10,000,000

Chance of mutation 4 in organism with mutations 1,2 and 3: < 1 in 10,000,000

Chance of mutation 5 in organism with mutations 1,2, 3, and 4: < 1 in 10,000,000

Chance of mutation 6 in organism with mutations 1,2, 3, 4, and 5: < 1 in 10,000,000

Chance of mutation 7 in organism with mutations 1,2, 3, 4, 5 and 6: < 1 in 10,000,000

The overall probability is therefore less than 1 in 10 to the 42^th power, or less than 1 in 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000. But what if we assume the population is ten times smaller? Since the population is ten times smaller, the average chance of each mutation occurring should undergo a corresponding reduction, and become 1 in 100 rather than 1 in 10. Now the chance of mutation 2 occurring in an organism with mutation 1 is less than 1 in 100 multiplied by 1 in 100,000 (the population size). But that still gives you a probability of less than 1 in a 10 million. So now the math looks a tiny bit different, but the final probability of all seven mutations is no greater than it was before. Here is the new math.

Chance of mutation 1: 1 in 100

Chance of mutation 2 in organism with mutation 1: < 1 in 10,000,000

Chance of mutation 3 in organism with mutations 1 and 2: < 1 in 10,000,000

Chance of mutation 4 in organism with mutations 1,2 and 3: < 1 in 10,000,000

Chance of mutation 5 in organism with mutations 1,2, 3, and 4: < 1 in 10,000,000

Chance of mutation 6 in organism with mutations 1,2, 3, 4, and 5: < 1 in 10,000,000
Chance of mutation 7 in organism with mutations 1,2, 3, 4, 5, and 6: < 1 in 10,000,000

The overall probability is therefore less than 1 in 10 to the 42^th power, or less than 1 in 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000. This is no better than before.

The scattering problem is a show-stopper for evolution by random mutations and natural selection. The scattering problem shows that there is virtually no chance that any complex biological innovation would ever appear by such means, and that the odds against such a thing are utterly prohibitive.

We cannot say that such a calculation conflicts with calculations made by Darwin, because Darwin (who confessed that math was repugnant to him) never made any population-based calculations on the likelihood of any biological innovation occurring. He tried to get through by skipping the math.

The previous calculations involved the probability of only one organism in a population ending up with some biological innovation. The probability of such a biological innovation becoming common throughout the population (so that many organisms in the population have the innovation) is exponentially smaller. Evolution experts say that a particular mutation will need to occur an average of about 100 times before it becomes fixated in a population. I didn't even factor in such a consideration in making the calculations above. When such a consideration is added to the calculation, we would end up with some probability many, many times smaller than the microscopic probability already calculated. Instead of a probability such as 1 in 10⁴² we might have a probability such as 1 in 10⁷⁰ or 1 in 10¹⁰⁰.

Probability 1: Probability that the gene pool of some particular species will ever experience (possibly scattered in different generations and individuals) each of the random mutations needed for a complex biological innovation, in which there is no benefit until multiple required components exist arranged in a way providing functional coherence.	Some particular probability
Probability 2: Probability that all of these mutations will exist in the gene pool during one particular generation (possibly scattered among different individuals)	Some probability only a tiny fraction of Probability 1
Probability 3: Probability that all of these mutations will ever end up in one particular individual, arranged in the right way and with the right positions, allowing the biological innovation to occur	Some probability only a microscopic fraction of Probability 1-- perhaps a million trillion quadrillion times smaller.
Probability 4: Probability that all of these mutations will ever end up in most of the organisms in the population	Some probability many times smaller than Probability 3, and perhaps billions of times smaller.

These considerations help show that the odds against biological innovations appearing by chance are absolutely prohibitive. Darwinists have not at all identified a mechanism by which nature could produce impressive biological innovations by chance. Their claim to have identified such a mechanism is a bogus brag.  An article quotes the well-known philosopher and cognitive scientist Jerry Fodor as saying, "Natural selection can't be the mechanism of evolution." 

I may note that there is no proof that a single complex biological innovation has ever appeared because of the so-called Darwinian “mechanism” of random mutations and natural selection. Our Darwinists want us to believe that all complex biological innovations have occurred through this process, but have yet to prove that even one complex biological innovation ever appeared for such a reason.  For an in-depth examination of the logical fallacies employed by one famous Darwinist arguing for Darwinian orthodoxy, see this lengthy post. 

When we dive down into the micro-world, we find that proteins are the basic building blocks of organisms. We are made of thousands of proteins, and each protein is like a fine-tuned machine.  An analysis of a functional protein will typically show that with a few changes here and there, its function will be broken.  Scientists have no plausible tale to tell explaining how all these fine-tuned proteins could have originated.  A scientific paper says, "A wide variety of proteins structures exist in nature, however the evolutionary origins of this panoply of proteins remain unknown." Protein expert Douglas Axe PhD has argued vigorously that we cannot explain proteins through Darwinian evolution. He has estimated in a scientific paper that the likelihood of getting a protein with the folds needed to perform a specific function may be as low 1 in 10 to the seventy-seventh power. There is no real origins answer offered by this long recent review of the topic of protein evolution, which states this near its end (referring to protein folds):

It is not clear how natural selection can operate in the origin of folds or active site architecture. It is equally unclear how either micromutations or macromutations could repeatedly and reliably lead to large evolutionary transitions. What remains is a deep, tantalizing, perhaps immovable mystery.

When it comes to explaining the origin of humanity, Darwinists have not overcome some gigantic difficulties. One difficulty is that it is believed that the human population was very small at a time such as 100,000 years ago or 200,000 years ago. It is believed that at such a time the human population was no more than about 10,000 or 20,000. The problem is that the smaller the population, the less likely that it will be blessed by some fantastically lucky series of random mutations needed for a biological innovation (just as the smaller the pool of lottery ticket buyers, the lower the chance that it will win the grand jackpot). When you have a very small population, it becomes fantastically unlikely that a series of mutations needed for a biological innovation will occur. So how could there have occurred all the helpful random mutations needed for Homo sapiens to appear about 100,000 years ago? The likelihood of such a development seems microscopic.

Two scientists (one from Cornell University) published a scientific paper entitled “The Waiting Time Problem in a Model Hominem Population,” which was published in the journal Theoretical Biology and Medical Modelling. Using a computer simulation, they “simulated a classic pre-human hominin population of at least 10,000 individuals, with a generation time of 20 years, and with very strong selection (50 % selective elimination).” They were basically trying to see how long it would take before you got a mutation consisting of two nucleotides (which is a fairly minor mutation, only some tiny fraction of the mutations needed for the evolution of human intelligence). This is called the “waiting time problem.” The authors summarize their results as follows:

Biologically realistic numerical simulations revealed that a population of this type required inordinately long waiting times to establish even the shortest nucleotide strings. To establish a string of two nucleotides required on average 84 million years. To establish a string of five nucleotides required on average 2 billion years. We found that waiting times were reduced by higher mutation rates, stronger fitness benefits, and larger population sizes. However, even using the most generous feasible parameters settings, the waiting time required to establish any specific nucleotide string within this type of population was consistently prohibitive.

Their paper show a "waiting time" of some 5 billion years to get a crummy little six-nucleotide mutation. But the mutations needed for man would have required many times more than six nucleotides – and our Darwinists ask us to believe that they occurred not in 5 billion years but in a span of time less than a thousandth of that. The chance of that seems less than the chance of you winning a hundred million dollars from the Powerball lottery on each of three consecutive drawings. 

According to Darwinist dogma, lucky random mutations occur and cause "classic sweeps" or "classic selective sweeps" in which some new trait becomes more and more common in the gene pool, eventually so common that most organisms in the population have that trait. This dogma has recently struck out at the plate, as more sensitive scans of the human genome have found little evidence of  such classic sweeps. A recent scientific paper was entitled "Classic Selective Sweeps Were Rare in Recent Human Evolution." By "recent human evolution" the paper meant the past 250,000 years.

A more recent scientific study in 2014 found there was virtually no sign of adaptive evolution in the human genome. The paper published in a mainstream science journal looked for traces of natural selection by looking for something called “fixed adaptive substitutions” in human DNA. The paper stated, “Our overall estimate of the fraction of fixed adaptive substitutions (α) in the human lineage is very low, approximately 0.2%, which is consistent with previous studies.”  It's hard to imagine a bigger fail or flop for Darwinian explanations. If such explanations were correct, we would have expected to find such signs of adaptive evolution in a large fraction of the human genome, not a fifth of one percent. 

In the 2018 book Who We Are and How We Got Here by David Reich, a professor of genetics at Harvard Medical School, the author makes this revealing confession on page 9: “The sad truth is that it is possible to count on the fingers of two hands the examples like FOXP2 of mutations that increased in frequency in human ancestors under the pressure of natural selection and whose functions we partly understand.” Judging from this statement, there are merely 10 or fewer cases where we know of some mutation that increased in the human population because of natural selection. The scientific paper “The Genomic Rate of Adaptive Evolution” tells us “there is little evidence of widespread adaptive evolution in our own species."

In the study here, an initial analysis found 154 positively selected genes in the human genome -- genes that seemed to show signs of being promoted by natural selection. But then the authors applied something they called "the Bonferroni correction" to get a more accurate number, and were left with only 2 genes in the human genome showing signs of positive selection (promotion by natural selection).  That's only 1 gene in 10,000. Call it the faintest whisper of a trace -- hardly something inspiring confidence in claims that we are mainly the product of natural selection. 

A 2018 paper published in the mainstream science journal Human Evolution found that "nine out of 10 species on Earth today, including humans, came into being 100,000 to 200,000 years ago," according to a press summary. The study is discussed in this post.  Besides suggesting a rapidity of biological innovation impossible to account for by the snails pace process of Darwinian evolution, the paper reminded us of Lewintin's paradox. This is the fact that genetic diversity does not vary with population size. This is not at all what we would expect given Darwinian assumptions.  

The number of humans that have lived has been estimated at 100 billion. But a web site discussing this issue tells us that 99% of these people have lived in the past 10,000 years. Since 8000 BC some 100 billion humans have lived, but in the period between about 400,000 BC and 8000 BC, the population of humans or pre-humans was no probably no greater than about a billion, and very probably less than 3 billion. But we know there has been very little evolution of humans since 8000 BC -- only a few minor things like better lactose digestion and better high-altitude breathing in some people.   So if you believe the conventional account, you must believe that a population of no more than 3 billion humans or pre-humans underwent enormous evolution (resulting in humans that had language and symbolic abilities), but that in 100 billion humans living since 8000 BC there has been almost no evolution.  Such an idea is not very credible.  Why would there be so much evolution during less than 3 billion lives, and so little during 100 billion lives? 

Then we have the fact that humanity has many intellectual characteristics that cannot be explained as being due to natural selection, simply because they do not provide any survival value.  See here for quite a few examples. 

What we see in biological organisms all over the place is mountainous amounts of organization.  Such gigantic levels of organization could only be explained by a real theory of organization. But Darwinism is not such a thing. It is merely something much less: a theory of accumulation.  Accumulation was the word Darwin used again and again, not organization.  Referring to the so-called "modern synthesis" or MS, a term meaning modern evolutionary theory, an evolutionary biologist recently confessed, "Indeed, the MS theory lacks a theory of organization that can account for the characteristic features of phenotypic evolution, such as novelty, modularity, homology, homoplasy or the origin of lineage-defining body plans."

To clarify the difference between the two (organization and accumulation), below we see a depiction of organization, the metabolic pathways in the human body:

    Credit: US Department of Energy

And here is an example of accumulation:

This post is not intended as a complete repudiation of Darwinian claims. Of the three claims of Darwinism, the first two (common descent and gradualism) cannot be ruled out as possibilities, despite the weakness of the evidence for them. It is only the third claim of Darwinism (that biological innovations are mainly caused by random mutations and natural selection) that can be ruled out as both unproven and unreasonable.  You might put it this way: if species have appeared through gradual evolution, we don't understand how that happens. 

See here for a list of hundreds of PhD's who have signed a statement saying the following:

We are skeptical of claims for the ability of random mutation and natural selection to account for the complexity of life. Careful examination of the evidence for Darwinian theory should be encouraged.

See here for a separate list of scientists who "have, in one way or another, expressed their concerns regarding natural selection’s scope and who believe that other mechanisms are essential for a comprehensive understanding of evolutionary processes."

What is the upshot of all the considerations in this post? The upshot is: the origin of species and the origin of mankind are profoundly mysterious. We do not yet have any convincing explanation for either of these things. So it is not at all true that we have to cling to some “minds come from brains” dogma out of a need to adhere to Darwinist orthodoxy. A kind of modern-day creation myth spread by a priesthood of academic apostles, the boastful claims of the Darwinist catechism are very shaky claims indeed that should not be some ball and chain attached to our feet, keeping us from adventurous thinking on the topic of what is the source of the human mind.

On this wikipedia page is a list of more than 100 of the most important scientific experiments ever done. None of the actual experiments listed are those that either prove Darwin's explanation for evolution, or the idea that minds come from brains. The page has a line saying, “Charles Darwin demonstrates evolution by natural selection using many examples (1859).” But there were no experiments showing any such thing, and the 1859 “demonstrations” referred to are merely Darwin's doubtful arguments in The Origin of the Species that natural selection had produced new species.