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Our future, our universe, and other weighty topics

Saturday, December 21, 2019

Abiogenesis Would Be the Mother of All Improbability Explosions

"The mother of all" -- something regarded as the biggest, most impressive, or most important of (its kind).  
Collins Dictionary

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.

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.

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 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 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 1014.
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 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  should never occur even if they keep playing baseball games for a million 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 blocks of a living thing under experimental conditions realistically simulating the early earth.  The building blocks of visible organisms are cells, and the building blocks of a microorganism are proteins. Scientists have not been able to produce 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 blocks of the building blocks of microorganisms (amino acids) 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 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 hydrocloric 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-reproduced 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 abiogiogenesis (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. 

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