"Stuff Piles Up" Fails to Explain Stupendous Biology Systems

Mark Rober's Crunchlabs is a TV show available on Netflix. It is a reality TV show that I would guess was inspired by the long-running TV show MythBusters. The MythBusters show would involve various informal experiments performed by two experimenters interested in doing weird experiments that would make good television footage. Mark Rober's Crunchlabs takes a similar approach. One of the Season 1 episodes is entitled "World's Largest Jello Pool."

We see a swimming pool filled with red jello, the gelatin product that forms a semi-solid substance. We are told that this is 30,000 pounds of jello. We see (at the 4:55 mark) an experiment in which small children without any attached rope are jumping onto the swimming pool of jello. It seems like a reckless stunt that might have caused one of the children to be injured, or possibly even drown. The pool of jello is a dark fluid, making it hard to see where a child is in the pool if the child is submerged in the jello. We seem to not see or hear about any precautions taken to prevent injury or death to the children involved in this experiment. We are told the swimming pool of jello is the first ever constructed, so how could the people doing this TV show have had any confidence that their experiment would not cause death or injury to a small child? At one point (the 7:14) the host says that when he dived into the swimming pool of jello, the jello filled up his ears; and who knows what risk would be involved in filling up an ear (filled with delicate components) with semi-solid gelatin material. 

Similarly, in a Season 1 episode entitled "Unbeatable Rock Paper Scissors Robot" we see a 10-year-old child skateboarding on some super-slippery surface of 3.5 million BB pellets, which the host describes (at the 2:13 mark) as "the most slippery surface I've ever stood on." At the 3:16 mark the child makes a high-speed skateboard fall and says, "I think I broke all my bones." Why endanger a child for such a stunt?

For much of the time in the show, host Mark Rober talks way too fast, so fast that many viewers will not be able to understand what he is saying. 

Another episode in Season 1 of the show is entitled "Octopus vs. Underwater Maze." At the 10:16 mark in the show we get what we call "a very simplified version of a tree of life." Rober tells us, "These kind of diagrams show you how all life is related and what evolved from what." No, they sure do not. "Tree of life" diagrams are visual depictions of scientist speculations about an ancestry of one type of living creature and another. 

Such "tree of life" diagrams are called cladograms. A scientific paper says this:

"Since the early 1990s, cladograms have found their way into high school biology textbooks, yet we know little about their effectiveness as interpretive and instructional tools in biology education. In this article we document the frequency and types of cladograms found in 31 textbooks, and classify and survey the other types of evolutionary diagrams used in the texts. Although cladograms comprised approximately 72 percent of the diagrams overall, we found virtually no attempt to explain their structure and theoretical underpinnings."

Speaking of such cladogram "trees of life," another scientific paper says, " There is much evidence that even professional biologists lack a true understanding of phylogenetic trees (Morrison 2013). "

If you do a Google image search for "tree of life," you will find dozens of different diagrams which do not agree with each other.  A common characteristic of such diagrams is the existence of many unlabeled nodes. Below is a modified version of what I get when I ask the Google Gemini AI to produce a "tree of life" diagram. I'll omit the left part, so that it is easier to read. The diagram is pretty worthless in terms of explaining any evolutionary relationships, because of all the unlabeled nodes. I have placed yellow X marks to point out places where we have an unlabeled node, typically one that corresponds to no species ever discovered. 

Such unlabeled nodes can be called "missing links."  When a "tree of life" has as many missing links as we see in the one above, the diagram fails to convincingly substantiate claims of common descent. The "tree of life" shown in the TV show  entitled "Octopus vs. Underwater Maze" (at the 10:16 mark) also has very many unlabeled nodes that  correspond to missing links. 

The show then gives us some reasoning trying to support ideas of common descent. We are told that there are 7 vertebrae in the necks of humans, giraffe, elephants, whales mice, lions, horses and bats. We are told "that's a clue they all share a common ancestor." No, it's merely a structural similarity in some mammals; and some other mammals such as sloths and manatees have a different number of neck vertebrae.  All automobiles have four wheels, but all automobiles do not have a common ancestor. 

The chart below shows how many vertebrae exist in the types of organisms mentioned. The numbers in each colored bar show how many vertebrae of a particular type exist for an organism of a particular type. The number 7 is found in all the red bars. But the numbers found in the yellow bars differ (ranging from 3 to 15);  the numbers found in the orange bars differ (ranging from 1 to 20);  the numbers found in the green bars differ (ranging from 1 to 7); the numbers found in the blue bars differ (ranging from 4 or less to 28). 

So what went on in the TV show was data cherry-picking. Overall the data on vertebrae numbers in these animals fails to strongly suggest any idea of common descent. But if you cherry-pick data by only telling people about the number of neck vertebrae,  it may sound like "a clue they all share a common ancestor."

We then have in the TV show a visual showing the arm bones of humans, bats, chickens, turtles and dolphins. They look very different, as you can see in the diagram below. 

But with some arbitrary color-coding not corresponding to colors in nature, the TV show (around the 10:49 mark) suggests some similarity, giving us a diagram looking like the one below:

"Similarity of anatomy" cases like this never provide good evidence for unguided Darwinian evolution as an explanation for biological innovations, as opposed to purposeful design. A designer might tend to use similar designs, rather than using a completely different design each time. 

At the 10:54 mark the host tells us, "It's wild what tiny beneficial mutations and millions of generations can produce." That's the standard Darwinist story, a "stuff piles up" explanation appealing to accumulation. But it makes no sense, because those tiny mutations would almost always not have been beneficial when they occurred; so they would not have been preserved and proliferated by any "natural selection" effect. To credibly explain dazzling biology wonders resembling products of purposeful engineering, you need a theory of organization, not a mere theory of accumulation. 

At the core of Darwinism is a fallacy we may call property misattribution.  The fallacy consists of attributing to "tiny mutations" a property of advantageousness that such mutations would almost never have by themselves. I can explain the fallacy with a little story involving alphabet cards, cards that each have only one letter of the alphabet printed on them. 

On his birthday a cruel person gave blind Will a deck of cards, each of which had a letter of the alphabet printed on it. "I will now spell out a message that is very helpful," said Will. "How will you do that?" asked his puzzled mother, knowing that blind Will could not see. "It's so easy," said Will. "I will just divide the cards into two piles, putting the helpful cards in one pile, and the cards that are not helpful in another pile. Then it will be easy to spell out a helpful message, by using only the cards from the pile of helpful cards." 

Will has made an error in logic, committing a fallacy of property misattribution. Individual letters do not have any property of being helpful or beneficial or advantageous. You can use the letters to spell out a message that is helpful or beneficial or advantageous, a message such as "Remember to look both ways when crossing the street." But that useful result does not arise until there is a special arrangement of letters.  The helpfulness or advantageousness only arises "late in the game," once such a special arrangement has occurred. 

Darwinist theorists make a similar error. They assume that great wonders of biological innovation are accumulations of random mutations, with each tiny mutation being preserved by a blind, mindless process of so-called "natural selection" because the mutation was beneficial. But if there are 100 or 1000 tiny mutations needed for some very complex biological innovation requiring a special arrangement of many parts, it would not be that each mutation (or that most of the mutations) would be beneficial when they occurred. So no "survival of the fittest" or "natural selection" effect could explain the preservation and proliferation of such tiny mutations if they occurred in some individuals, before a requirements threshold was met. The requirements threshold would only be reached "very late in the game," when there had occurred a sufficient arrangement of parts to produce the useful function (an arrangement enormously unlikely to ever occur by chance).

What good is half an eye? No good at all -- you can't see with half an eye. What good is 100% of an eye? No good at all, unless that eye is part of a vision system requiring much more than just an eye, including different types of protein molecules (each requiring a special arrangement of hundreds of amino acids), an optic nerve, and a specialized region of the brain allowing vision. 

The system that allows humans to hear is one of the many stupendous biology systems in the body, marvels of purposeful engineering which are often systems of systems of systems. In my post "Human Anatomy Structures and the Cell Types Each Requires" I detailed the cell types different body parts require. While writing that post, I was struck by how many different cell types are required for hearing. I listed all of these cell types as being involved in hearing:

Ceruminous gland cell, Planum semilunar epithelial cell, Organ of Corti interdental epithelial cell, Elastic cartilage chondrocyte, Inner pillar cells of organ of Corti, Outer pillar cells of the organ of Corti, Inner phalangeal cells of organ of Corti, Outer hair cells of vestibular system of ear, Inner hair cells of vestibular system of ear, Outer phalangeal cells of organ of Corti, Border cells of organ of Corti, Hensen's cells of organ of Corti

When you consider how every one of these cell types is itself an incredibly organized component consisting of many types of organelles that are themselves extremely organized components, you may realize the sky-high levels of organization required for hearing. 

Mark Rober should study at length the extremely high organization of many parts or extremely complex components needed to achieve stupendous biology systems such as the hearing system, the vision system, the reproductive system and the blood circulation system; and he should also study how such systems require very many interdependent components, with components only becoming useful when most of the system exists.  If he studies how a capability such as hearing requires the most fine-tuned arrangement of very many delicate and interdependent parts, he may be less likely to give fallacious biology explanations, and be less likely to be involved in some risky stunt such as one in which children dive into a swimming pool of jello gelatin, with the possibility of their ears getting filled with gelatin that may damage the intricate delicate fine-tuned mechanism required for good hearing. 

How to Answer the Question "Do You Trust Science?"

Nowadays a person may try to get someone to "fall into the line" or conform by asking him, "Do you trust science?" A conversation may go like this:

John: Blah blah blah blah blah you're just some molecules bouncing around in a body blah blah blah blah blah blah you're just electricity firing around in a brain blah blah blah blah blah blah blah our species arose merely because of lucky random mutations blah blah blah blah blah blah blah.

Jane: I don't think so. 

John: But you trust science, don't you?

Jane: Uh, well...I guess so. 

John: Then you should agree with what I said!

Jane's answer to the "do you trust science" question was not a good answer. That question should be answered with an answer longer than a simple "yes" or "no."

What is meant by the word "science"? You get very different definitions when you look for the definition of that word in major dictionaries or other leading sources:

• The Merriam Webster dictionary defines science primarily as "knowledge or a system of knowledge covering general truths or the operation of general laws especially as obtained and tested through scientific method."  It also offers a definition of "a particular area of scientific study." 
• The Cambridge Dictionary defines science primarily as "(knowledge from) the careful study of the structure and behavior of the physical world, especially by watching, measuring, and doing experiments, and the development of theories to describe the results of these activities." Note that there is a very big difference between this definition and the Merriam Webster definition. The Merriam Webster definition spoke as if science meant only "knowledge" (making it sound like science is beyond question), but the Cambridge Dictionary definition says that science is also "theories" (things that may reasonably be questioned). Also the Cambridge Dictionary gives this secondary definition of "science": "the facts and opinions that are provided by scientists who have studied a particular subject or situation." Now we have a definition of something much different from pure knowledge. We may very reasonably be entitled to distrust opinions of scientists that are not facts or knowledge. 
• Dictionary.com defines science primarily as "the systematic study of the nature and behaviour of the material and physical universe, based on observation, experiment, and measurement, and the formulation of laws to describe these facts in general terms." This is an "activity" definition of science very different from the "knowledge" definition of science given by the Merriam Webster dictionary.  This "activity" definition of science is no fluke. Other major sources have defined "science" in such a way, describing it not as knowledge but as the process of attempting to gather knowledge by systematic efforts based on observations and experiments. Clearly we may be entitled to doubt "science" if it is defined in such a way.  Human beings are prone to error, particularly when they become members of belief communities where belief traditions arise; and scientists are members of such belief communities. As a wise old saying stated, "Error circles the globe while truth is still putting on its boots." Or as Murphy put, "If anything can go wrong, it will go wrong."
• Like dictionary.com, the American Heritage Dictionary (a leading American dictionary) gives as its primary definition of science an "activity" definition rather than a "body of knowledge" definition. It gives as its primary definition of science this definition: "the observation, identification, description, experimental investigation, and theoretical explanation of phenomena." It is notable that under this definition doing things such as ESP tests and doing tests with psychic mediums are just as much "science" as digging up fossils or observing with a telescope. It is also notable that by using the term "theoretical explanation" this definition reminds us of how scientist explanations are largely speculative or debatable. 

What is a good description of "science" as it now exists? A good literature-centered description might be this: science is a mixture of very important truths and also dubious claims and bad errors, being advanced by economically and ideologically motivated individuals who tend to be members of conformist belief communities that keep repeating a mixture of facts, speculation, triumphal legends and belief traditions. A good activity-centered description of science might be this: the process of attempting to establish truth or understand reality by a systematic use of experiments, observations or theorizing, a process that is very difficult to do right, and very easy to do wrong. 

Do you think I am exaggerating how ideological today's scientists tend to be? I recently got out from my local library seven books by mainstream scientists and doctors, which I read. (Over the past 13 years I have spent gigantic amounts of time reading, quoting and analyzing the writings of those who largely teach the exact opposite of what I believe, and this is proven by my extremely abundant links to their papers, articles and books, on this blog and another blog of mine.  Conversely, most mainstream scientists seem to spend no time studying works of those who criticize their dogmas and no time studying the works of those who report spooky things inconsistent with such dogmas.)  One of those books I got out from the library was by an evolutionary biologist who on his very first page told us that he would be teaching "the foundation of a worldview"; and we later learn in the book how this worldview has all kinds of metaphysical presumptions and atheist dogmas. Such "worldview warrior" scientists often are candid about how shaping and controlling your worldview is a key item of their agenda. 

In another of the seven books I got out from the library a biologist mentioned one little thing and then said "And that's basically all there is to biochemistry."  Eager to make biological life look very simple for the sake of selling an ideology, the biologist made the most absurd misstatement, rather like someone mentioning one type of thing and then saying, "And that's all there is to history."  Biochemistry actually has oceans and oceans of the deepest complexities beyond the one thing that the biologist had mentioned.  On another page, the same biologist tried to pretend as if anatomy does not even exist, by making this blundering statement: "My body is some 10 trillion cells. Period." No, actually, bodies have things larger than cells, such as tissues, organs, organ systems and useful appendages such as the hands I am using to write this post.  

In a previous trip to the same library, I took out a very bad book ("Until the End of Time") by physicist Brian Greene in which he stated on page 125 the enormous falsehood that "you are a swarm of interacting particles." Human bodies actually have many levels of enormous organization that make them the exact opposite of "a swarm of interacting particles," a phrase suitable for describing a tornado or a Martian dust storm. Greene makes an equally false statement on page 237. Such "speak the exact opposite of the truth" falsehoods by Greene are ideologically motivated.  Guys like Greene don't want you to understand the sky-high levels of organization in your body, because the better you understand that, the less likely you will be to believe in the dogma of unguided human origins. For decades Greene has peddled the groundless scientist fantasy that is string theory. 

The visual below illustrates what a "hit and miss" affair science is:

So what is a good answer to give when asked, "Do you trust science?" It is not a one-word answer of "yes" or "no."  A good answer might be something like this: 

I trust that large portion of science which consists of well-observed things, and facts established by well-replicated "best practices" experiments using large study groups. I largely distrust the large portion of science which consists of shaky dogmas, belief traditions of scientist communities, and experimental work involving poor methods and badly designed experiments guilty of procedural sins such as the use of way-too-small study groups. I am also very concerned about the very high level of clickbait, hype and exaggeration in today's online science literature, where we very often read groundless boasts and the repetition of socially constructed triumphal legends. 

Another good answer might be something like this:

I trust Science with a capital "S," defined as facts established by observations, well-designed experiments and systematic inquiry. I largely distrust much of science with a small "s," defined as the attempt to establish knowledge by observations, experiments and theorizing.  The reason I largely distrust much of that is because humans are very erring creatures who seem to do things wrong as commonly as they do things right, particularly when they try to do grand things that are very hard to do.  There are a vast number of ways to do things wrong when you try to do science, and a far fewer number of ways to do things right. 

ESP Marvels Documented by Rhine

In his book New Frontiers of the Mind: The Story of the Duke Experiments, Duke University professor Joseph Rhine discussed his search for people who would perform highly on tests of ESP. Rhine discusses tests that are mainly tests of clairvoyance, not telepathy. (The term ESP refers to both telepathy and clairvoyance.)  In a laboratory test of telepathy, one person will typically attempt to transmit a thought (or will look at some image), and another person will attempt to receive that thought or guess what image the other person saw. In a laboratory test of clairvoyance, one person will attempt to perceive something that cannot be seen with his senses at that time. 

Rhine and Hubert Pearce

The tests Rhine describes were done with Zener cards depicted below. Each card in the deck would have five possible symbols, the symbols depicted below. Each symbol would appear in the deck of cards the same number of times. 

 

In a test such as the one shown above, a subject would attempt to guess what was the symbol of a card at the top of the deck. The pack of cards would be like a deck of playing cards, in that all of the cards have an identical appearance on one side, but different symbols on the other side. By looking at the top of the deck, you could not see what was the symbol you would see when the card was turned the other way. 

On page 74 Rhine discusses tests he did with A. J. Linzmayer. We read that in card-guessing tests using Zener cards in which the chance of guessing the card symbol correctly is 1 in 5, Linzmayer guessed nine consecutive cards correctly. We read that he did the same feat the next day. The chance of getting such a result with nine consecutive guesses of these cards is 1 in 5 to the ninth power, or 1 in 1,953,125. 

On page 76 we read that instead of guessing about 60 cards correctly in a series of 300 card guesses (about the result expected by chance), Linzmayer guessed 119 cards correctly. The probability of a result that good can be calculated using a binomial probability calculator such as the Wolfram Alpha binomial probability calculator. Below are the inputs you can use. That calculator uses the confusing term "endpoint." It would be better if it used the clearer term "number of successes."

As the screen above indicates, the probability of getting a result as good as the result reported for Linzmayer is less than 1 in 10 to the 14th power, less than 1 in 100 trillion. 

On page 78 Rhine says that he tested Linzmayer and saw him guess correctly 15 consecutive times, using the Zener ESP test cards. The probability of getting this result by chance is 1 in 5 to the 15th power, or 1 in 30,517,578,125, about 1 in 30 billion. When continued for a total of 25 guesses, the result was 21 correct out of 25. The probability of getting a result that good by chance is about 1 in 100 billion.

On pages 94 to 95 of his book, Rhine discusses an experiment with Zener cards done with Hubert Pearce. Pearce correctly guessed 25 consecutive times the symbol of the top card of a deck of Zener cards that was cut each time. The probability of getting this result by chance is 1 in 5 to the 25th power, or 1 in 298,023,223,876,953,125. Rhine says it was the most phenomenal thing he ever witnessed. On page 104 Rhine says that George Zirkle duplicated Pearce's feat of making 25 consecutive correct guesses when being tested with Zener cards. 

On page 100 Rhine says that June Bailey averaged between 8 and 10 correct guesses on "thousands of trials" in which the expected chance result is only 5 correct guesses. On the same page we read that T. Coleman Cooper "was able to score reliably about 8 hits per 25 over thousands of trials."

In a set of 2000 guesses with Zener cards, the expected chance result is about 400 correct guesses. Getting 8 hits per 25 in a set of 2000 guesses would mean a number of successes of about 640. (8 out of 25 is .32, and 2000 multiplied by .32 is 640.)  To calculate the probability of getting the results discussed above for Bailey and Cooper, you can use the inputs below in the Wolfram Alpha binomial probability calculator:

The calculator tells us that the likelihood of getting the results reported for Bailey and Cooper is less than 1 in 1,000,000,000,000,000,000,000,000,000.

On the next page we read this about May Frances Turner: "Her averages through many thousands of trials were in the neighborhood of 9." The probability of getting such a result by chance would be much smaller than the tiny probability just mentioned. 

The account below appeared on page 90 of  the April 15, 1940 edition of Life magazine, which during its heyday was one of the three or four leading weekly magazines in the United States. We read of tests with Zener cards that have five possible symbols, on one side of the card. The chance probability of guessing one of the cards correctly is 1 in 5. 

On page 92 the same Life magazine article tells us of the remarkable success in a long-distance test carried out over a span of 250 miles. It is a test that can be considered either a test of clairvoyance or a test of telepathy:

The wording is ambiguous, leaving us in doubt whether the 16 out of 25 result was obtained on two consecutive days, or whether it was one result of 16 out of 25 spanning two days. I cleared up the ambiguity by searching in the writings of Joseph Rhine, to find his account. It occurs on page 60 of his book Extra-sensory Perception. We read this:

So the results on the first three tests were:

Test 1: 19 out of 25 correct

Test 2: 16 out of 25 correct

Test 3: 16 out of 25 correct

Rhine does not do a good job of explaining how unlikely this result is. But by using what is called a binomial probability calculator, we can estimate that. The first three tests add up to being 51 successes out of 75, in a test in which the expected chance result is about 15 (which is one fifth of 75). Using the Wolfram Alpha binomial probability calculator, we can calculate the chance of that level of success, by using the inputs below:

The probability of getting a result as good as this by chance is calculated above. It is roughly 1 in 10 to the 19th power or 1 in 10,000,000,000,000,000,000.

The Life magazine article also discusses on page 95 tests of clairvoyance and ESP that Joseph Rhine did with the medium Eileen Garrett.  These were very unusual, in that the medium would go into a trance, and then start speaking as if she were another personality called Uvani. Often when this occurs with mediums, there is an impression of communication with some unearthly realm, such as an afterlife realm.  The original report of these tests appear at the beginning of this edition of the scientific journal Character and Personality, the December 1934 edition (Volume 3, Issue 2). On page 100 we read this report by Rhine:

"The experimentation with the Mrs. Garrett personality began on April 10 and lasted until April 28, approximately three weeks. During this period 14,425 tests or trials were given her in the normal state in clairvoyance and telepathy combined.

The work with the Uvani personality in clairvoyant and telepathic perception began on the 17th of April and lasted until the 25th. The amount of work per day, as well as the number of days, was limited by Uvani’s disinclination toward the experiments, which was in contrast to Mrs. Garrett’s willingness and patience. Only 1,575 trials were obtained with Uvani.

In all there were performed 16,000 trials at clairvoyant and telepathic perception. This number includes all the results, high scores and low. The most probable number of hits expected by chance for this number of trials would be 3,200 but the actual results were 4,018, or 818 hits above the chance mean. This gives an average per 25 of 6.3, and when evaluated for anti-chance significance, a value of X (i.e., deviation divided by probable error) equal to 24.0. This gives odds against the chance hypothesis of such a huge number—one with well over 50 digits—that it is beyond a moment’s question that chance is not the explanation."

Although he states very exactly the experiment's results, Rhine is not expressing very clearly how above chance these results are. But with a binomial probability calculator, a more clear idea of the improbability can be revealed. Using the Wolfram Alpha binomial probability calculator, the improbability can be calculated using the inputs shown below:

The tests involving guessing the symbol shown on a Zener card with 5 possible symbols. The tests were done with a deck of cards with an equal number of each of the five symbols. The probability of guessing correctly 4018 or more out of 16,000 cards is 1 in 7.7  times 10 to the 56th power. This is a probability of less than 1 in 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. We would never expect chance to produce such a result, even if you spent half of every person's life doing telepathy tests on them. 

The reported test result is one of the best test results ever achieved in a test of telepathy. I can recall only one better result: the result of the Riess test, reported here. 

Rhine's results were very convincing evidence for ESP.  I think he may have got results far more convincing if he had varied his procedural methods more. In the book we read of years using the same type of Zener cards, containing only abstract symbols with no particular emotional associations. There are endless other ways in which ESP could be tested. A method involving a more emotional component might be much more successful. For example, tests could be done with cards having emotionally powerful photos. A test of telepathy with such cards might produce much higher scores than tests using cards with abstract symbols. 

The 1925 New York Times article below (which you can read here) has the large headline "Balfour Says Telepathy Is Proved Fact." The Balfour referred to (Earl Balfour) was once a Prime Minister. 

To Understand Why Chance Cannot Engineer Things, Understand Improbability Explosions

 Every computer programmer is aware or should be aware of the concept of a combinatorial explosion. The term refers to a situation where the number of possibilities rises exponentially, resulting in so many possibilities that it is impossible to test them all. For a computer programmer, the problem with a combinatorial explosion is that it results in so many possibilities that you cannot test them all before releasing your software.

For example, imagine a screen like the one below. There are two checkboxes, and a single radio button, which can have one of three possible values. The total number of possible states the form can be in before it is submitted is a mere 12 states. So it is easy to make a comprehensive test of whether the form works under all possible conditions. A programmer can simply test all 12 of the states. 

But consider the web page below. It has very many inputs, including lots of dropdown controls, each of which allow the selection of many possible options. There is now a combinatorial explosion. There are so many possible ways the form can be configured before pressing the Submit button that no software developer can test all of them. By merely multiplying by about ten the number of inputs on the form, the number of possible configurations has increased exponentially, rising to trillions or more. 

The same idea is relevant to a chemist. Let's imagine a chemist is trying to determine the safety of various combinations of chemicals. Imagine that the combinations consist of three different chemicals from a larger set of chemicals. If the set of chemicals consists of only 20 chemicals, the number of possible combinations isn't very large. It is 1140. We can calculate that using the web page below (you can do a Google search for "combinations calculator" to find similar sites).

But imagine the set of chemicals is much larger. Suppose that there can be any combination of three chemicals from a set of 1000 chemicals. This results in a number of combinations equal to 166,167,000, as shown on the screen below.

This is an example of a combinatorial explosion. By merely increasing the size of the available chemicals set from 20 to 1000, we made the number of possible combinations increase by more than 100,000,000. The result is a set of possibilities too large to be tested.

Below is a visual I got when I asked the Google Gemini AI to produce an infographic explaining the concept of a combinatorial explosion. The end of the visual lists some "real world consequences" such as the need to use long (e.g. 14-character) passwords, the difficulty of calculating the shortest route between more than a dozen locations, and the difficulty of testing software when there are many possible inputs. The most important real-world consequence of combinatorial explosions (not mentioned in the diagram) is that no theory of accidental origins of very organized fine-tuned systems is credible whenever such systems require a special arrangement of very many parts. 

Rather similar to the concept of a combinatorial explosion (but not too similar) is what we may call an improbability explosion. We can use the term “improbability explosion” to refer to cases in which the improbability of something skyrockets exponentially and geometrically, because of a simple linear increase in the number of things that must happen for the event to occur.

I can illustrate the concept by imagining that you and four friends buy five contiguous seats in the seats beyond the outfield of Yankee stadium. What is the chance that you will be able to catch a home run that falls and hits where you are seated? A reasonable rough estimate is about 1 in 4814. There are only 13,000 seats beyond the outfield in Yankee stadium, and there are  about 2.7 home runs hit per game. 13,000 divided by 2.7 is 4814. 

But what is the chance that you and the person to your right will both catch separate home runs in the same game? To roughly calculate this, we multiply this 1 in 4814 probability by itself. This results in a probability of about 1 in 23,174,596.

Suppose that we try to calculate the likelihood that a line consisting of you and two or more of your friends (seated in a line) will all each catch a separate home run that lands where you are seated? The math looks something like this:

Chance that you will catch a home run: 1 in 4814.

Chance that you will catch a home run, and that your friend to your right will also catch a separate home run: 1 in 23,174,596.

Chance that you will catch a home run, and that your two friends seated to your right will also each catch a separate home run: 1 in  111,562,505,144.

Chance that you will catch a home run, and that your three friends to your right will also each catch a separate home run: 1 in 5.37 X 10^14.

Chance that you will catch a home run, and that your four friends to your right will also each catch a separate home run: 1 in 2.58 X 10¹⁸

We see here a good example of an improbability explosion. Even though it is isn't terribly improbable that any one of you five catch a home run, when we have the requirement that all five of you have to each catch a separate home run, the improbability rises geometrically and exponentially, finally resulting in an improbability that is essentially zero. The final probability of about 1 in 2.58 in 10¹⁸ is a probability of only slightly more than 1 in 1,000,000,000,000,000,000. That is something so improbable that it would be unlikely to ever occur even if they keep playing baseball games for a billion years.

Here is another example of an improbability explosion. Imagine you go to a crowded party, and don't know anyone's name. You play a game in which you guess the name of each person before asking the name of the person. The probability of success on the first try is not terribly low – maybe about 1 in 200. But imagine you are trying to get an unbroken series of correct guesses. The probability of guessing the first two person's names correctly would be about 1 in 200 times 1 in 200, or 1 in 40,000. But the odds would increase geometrically and exponentially, like this:

Chance of guessing correctly first person's name: 1 in 200.

Chance of guessing correctly names of first two persons: 1 in 40,000.

Chance of guessing correctly names of first three persons: 1 in 8 million.

Chance of guessing correctly names of first four persons: 1 in 1,600,000,000.

Chance of guessing correctly names of first five persons: 1 in 320,000,000,000

Chance of guessing correctly names of first six persons: 1 in 6.4 x 10¹³.

Again, we have an improbability explosion. Very quickly, we get to a situation where there is no reasonable chance of success. This required only a simple linear increase in the number of unlikely successes required. 

Pretty much the biggest improbability explosion we can imagine would be the origin of life from nonliving chemicals. Such a possibility is called abiogenesis. Scientists frequently claim that abiogenesis occurred, even though they have zero scientific evidence for such a claim.  

Scientists have never been able to make a living thing under conditions simulating the early earth, and scientists have not been able to even make any of the building components of a living thing under experimental conditions realistically simulating the early earth.  The building components of visible organisms are cells, and the building components of a microorganism are proteins. Scientists have not been able to produce from scratch proteins or cells in experiments simulating the early earth. In fact, scientists haven't even been able to make appreciable amounts of any of the 20 building components (amino acids) of the building components of microorganisms under conditions realistically simulating the early earth.  

The famed Miller-Urey experiment that produced some amino acids used a mixture of gases (heavy in ammonia and methane) that is now widely regarded as not being the correct atmosphere of the early earth (as discussed here).  Such an experiment was never a realistic simulation of early Earth conditions, because it used a special glass apparatus unlike anything that would have existed billions of years ago, and because the experiment used continuous electrical bombardment for a week; and there is no reason to believe that any place on Earth ever received such a bombardment (lightning being something that only strikes any natural square meter no more than once or twice in a century).  Sequels to the Miller-Urey experiment using more realistic atmospheric mixtures (such as nitrogen and carbon dioxide) have never been realistic simulations of the early Earth, because they have depended on things such as 2-hour proton beam bombardments or strong electrical charges or artificial hydrochloric hydrolysis, things that do not correspond to what existed on the early Earth. 

To imagine the simplest living thing, we cannot imagine something like a virus. Viruses require living cells to reproduce, and biologists tell us that viruses did not exist until after living self-reproducing cells existed.  Nor can we imagine some mere self-reproducing molecule existing as a living thing before a cell exists. No such living self-reproducing molecule has ever been observed outside of the framework of cells, so the concept of such a thing is pure fantasy. Since it is a basic fact of biology that cells are the basis of all living things, we must imagine some kind of cell as the simplest living thing. 

A team of 9 scientists wrote a scientific paper entitled, “Essential genes of a minimal bacterium.” It analyzed a type of bacteria (Mycoplasma genitalium) that has “the smallest genome of any organism that can be grown in pure culture.” According to wikipedia's article, this bacteria has 525 genes consisting of 580,070 base pairs. The paper concluded that 382 of this bacteria's protein-coding genes (72 percent) are essential. So multiplying that 580,070 by 72 percent, we get a figure of about 418,000 base pairs in the genome that are essential functionality. This is all information that must be arranged in just the right way for the tiny microbe to be capable of self-reproduction. 

We can compare this complexity of the simplest self-reproducing organism to the complexity of a book.  A book of 250 pages has about 300 words per page, or about 1800 characters (or letters) per page. Such a book has about 450,000 characters. A single base pair in the genome can be compared to a letter or character in a book. So a rather good analogy for the simplest imaginable living thing is to compare it to a 250-page technical book, such as a 250-page book on how to build bridges or a 250-page book on how to construct computer programs using Java.  

What is the chance that such a thing could ever arise from a chance combination of chemicals? Such a probability is essentially zero. We have here an improbability explosion so big it can be called galaxy-sized. 

We do not get out of this jam by imagining that instead of having an inconceivably improbable arrangement of low-level chemicals, there might have been merely a combination of various functional proteins that happened to be floating about.  The functional proteins would not have existed prior to the origin of the first living thing. Before it folds into a three-dimensional shape, a protein typically consists of a sequence of hundreds of amino acids arranged in just the right way to achieve a functional end. If the existing genetic code is used, there are 20 possible amino acids that may be used in any position of this sequence. The average protein consists of about 375 amino acids arranged in just the right way to achieve a functional effect. Even assuming that merely half of such amino acids have to match the existing sequence of amino acids for the same protein functionality to be achieved, the probability of a protein appearing with similar functionality (based on chance combinations of amino acids) is therefore something like 1 in 20 to the 187th power, which is equal to about 1 in 10 to the 243rd power, or 1 in 10²⁴³.  That probability is essentially zero. 

You could summarize this situation by saying that the origin of each new protein molecule would require its own improbability explosion like the other improbability explosions I have discussed.  The origin of a self-reproducing cell from chemicals (requiring at least 300 different types of protein molecules) would require an improbability super-explosion consisting of at least 300 individual improbability explosions, each fantastically unlikely to occur. 

Calculations such as these actually vastly underestimate how big an improbability explosion would be required, because they assume an existing genetic code that limits the number of possible amino acids in a protein to only twenty.  But as a recent scientific article states,  "There are millions of possible types of amino acids that could be found on Earth or elsewhere in the universe, each with its own distinctive chemical properties....there are 10⁴⁸ ways of making sets of 20 amino acids." 

What this means is that we vastly overestimate the likelihood of the first living thing appearing by chance if we imagine an analogy such as a typing monkey producing the book of 450,000 characters by randomly striking keys on a keyboard. For a monkey at such a keyboard would always have his keystrokes restricted so that there would be something like a 1/30 chance of typing a valid character. Given all the possibilities for the genetic code (with 10⁴⁸ ways of making sets of 20 amino acids), a much better analogy is to imagine a monkey equipped with a pen and a 250-page book of blank empty pages. In this analogy, the monkey can make any type of mark, which may or may not be a valid character.  Similarly, chemicals randomly forming into amino acids (or base pairs representing amino acids) could make a vast number of combinations, with only the tiniest fraction corresponding to the twenty amino acids used in earthly proteins.  

The overall probability of a self-reproducing cell being accidentally produced would be incomparably smaller than the probability of a monkey at a keyboard producing a 250-page technical book all filled with relevant and coherent technical instructions. It would instead be more like the probability of a monkey equipped with a pen handwriting such a book, and producing the coherent 250-page technical book of useful instructions by making random scribbles on the blank pages. 

A scribble

How often would we expect such a result to be achieved by chance? Never in the history of the universe, even if there are 100 billion galaxies each containing billions of planets, and even if there were 13 billion years for such chance combinations. And similarly, if there were 100 billion galaxies each filled with 100 billion planets, and they were all populated with countless billions of monkeys scribbling on blank pages, we would not expect that any such monkey would ever produce even one full page with hundreds of words giving coherent technical instructions on how to do anything, even if there were 13 billion years for monkeys to engage in such scribbling. I haven't even discussed the issue of homochirality, an entirely separate requirement for abiogenesis, one that worsens the chance of it by very many additional orders of magnitude, probably making such a thing even trillions of quadrillions of quintillions of times less likely. 

And so abiogenesis (the imagined accidental origin of biological life from lifeless chemicals) must be described not merely as an improbability explosion, but the mother of all improbability explosions. 

Most people do not understand the simple mathematics involved in estimating the likelihood of accidents producing useful inventions. Part of the reason is that while students are tortured in high school with required mathematics courses such as algebra and trigonometry (involving calculations that almost no one ever uses), schools do a poor job of teaching simple mathematics that are useful in real life (such as financial mathematics), and simple mathematics that are useful in evaluating the credibility of claims such as claims of accidental biological origins.  Our intellectual ruling class does not want you to know the relevant mathematical principles, because if you understand them well, you would not believe the biology dogmas they want you to believe. 

In a previous post I stated one of those principles, what I called the first rule of accidental construction:

The first rule of accidental construction: the credibility of any claim that an impressively organized final result was accidentally achieved is inversely proportional to the number of parts that had to be well-arranged to achieve such a result, and the amount of organization needed to achieve such a result.

Additional consideration of the complexity of living things and the improbability of them arising from accidental combinations will lead the thorough thinker to some firm conclusions:

(1) There are combinatorial explosions and improbability explosions everywhere in the progression from one-celled life to multicellular organisms such as mammals. 

(2) The appearance of organisms as complex and highly organized as humans requires stratospheric heights of engineering and the most special arrangement of interdependent components, things that are utterly beyond the reach of blind chance. 

(3) Organisms such as humans require the most precise engineering all over the place, and such engineering is utterly beyond the reach of random unguided processes. 

In general, Darwinist professors ignore the mountainous improbability of parts fitting together to make complex innovations. Our Darwinist experts typically speak as if having the parts for something is about as good as  having that thing, ignoring the reality that the more complex something is, the more improbable that parts would accidentally fit together to make that thing, even if all the parts were present.  How often have we heard SETI enthusiasts speaking as if having "the building blocks of life" in space (by which they mean mere amino acids) was almost as good as having a living thing (which requires  a fantastically improbable special arrangement of such building components utterly beyond the reach of chance)? 

Roughly speaking, we can say that the improbability of a complex innovation appearing accidentally usually rises exponentially and geometrically as the number of parts needed for that innovation undergoes a simple linear increase, in most cases when a special arrangement of the parts is required. Similarly, the improbability of you throwing a handful of cards into the air and having them all form into a house of cards will rise exponentially and geometrically as the number of cards in your hand undergoes a simple linear increase.  Getting a two-card house of cards by accident isn't too hard, by having two cards lean together diagonally. But if all the humans in the world spent their whole lives throwing a deck of cards into the air, none of these random throws would ever produce a triangular 26-card three-level house of cards by accident. 

In his interesting book Cosmological Koans, which has some nice flourishes of literary style, the physicist Anthony Aquirre tells us about just how complex biological life is. He states the following on page 338:

"On the physical level, biological creatures are so much more complex in a functional way than current artifacts of our technology that there's almost no comparison. The most elaborate and sophisticated human-designed machines, while quite impressive, are utter child's play compared with the workings of a cell: a cell contains on the order of 100 trillion atoms, and probably billions of quite complex molecules working with amazing precision. The most complex engineered machines -- modern jet aircraft, for example -- have several million parts. Thus, perhaps all the jetliners in the world (without people in them, of course) could compete in functional complexity with a lowly bacterium."

What is the chance of you getting such wonders of engineering by unguided processes? Zero or negligible. 

Below we see one of the "molecular machines" that appear constantly in human bodies, by some means that we do not understand. It is an example of what is called a protein complex, a special team of different types of proteins, well-arranged to achieve some functional purpose. DNA and its genes do not specify the structure of protein complexes, but merely specify lower-level information such as which amino acids make up particular proteins.  More than 7000 types of useful protein complexes have been identified. The origin of protein complexes is an unsolved mystery of biology. As two scientists confessed in 2019, "A general theoretical framework to understand protein complex formation and usage is still lacking."  The problem is not one of merely explaining how proteins could bind together to become protein complexes.  The problem is explaining how protein molecules act so consistently and so rapidly to produce well-engineered protein complexes (often called "molecular machines") that are so useful and vitally necessary for organisms such as humans to exist, with there occurring so abundantly throughout the body a fine-tuned and purposeful organization of protein molecules into functional and beneficial teams of different types of proteins that we would expect chance to never (or only very, very rarely) produce.