The Probability Paradox: Darwinian Evolution’s Struggle with Combinatorial Inflation.
The combinatorial inflation problem, as outlined by Stephen Meyer in Darwin’s Doubt, is a fundamental critique of the ability of Darwinian evolution—particularly neo-Darwinism—to produce new biological information through random mutations and natural selection. At its core, this is a probabilistic argument grounded in information theory and molecular biology, challenging the idea that unguided evolutionary processes can generate the complex genetic instructions required for the emergence of new forms of life.
To provide some historical context, in the 1960s, Murray Eden, a professor of engineering and computer science at MIT, began questioning how the concept of specified information could be reconciled with the process of building functional biological organisms.
Eden was especially concerned with whether natural selection, acting on random mutations, could realistically generate the functional information necessary for life. His central worry revolved around the specificity of biological information.
He pointed out that if DNA were composed of a random sequence of nucleotide bases—where the exact order didn’t affect the function of the molecule—then random mutations would likely have little or no detrimental effect. However, we now know that the precise sequence of nucleotides is critical: even small changes can dramatically alter or destroy a molecule’s function. This dependence on highly specific arrangements means that most random changes will not lead to viable biological structures, making it extremely unlikely for useful sequences to emerge by chance.
A helpful and intuitive way to understand the combinatorial inflation problem is to consider the example of computer code and software, which are ubiquitous in today’s world. It’s obvious that the specificity of code matters. If you were to randomly jumble lines of Python code without following any particular syntax or structure, the software would no longer run. That’s because code must be precisely ordered to produce functional outcomes. Without specified functional information, software ceases to exist.
Murray Eden, a professor of engineering and computer science at MIT, recognized this parallel. He observed that in any system where sequence determines function—whether in computer programs or written language—random changes to that sequence tend to degrade rather than improve functionality.
Eden put it succinctly:
“No currently existing formal language can tolerate random changes in the symbol sequences which express its sentences. Meaning is almost invariably destroyed.”
This insight led him to question whether random mutations, the raw material of Darwinian evolution, could realistically generate the precise genetic sequences needed to form new functional proteins or genes. Given the necessity of specificity in DNA—just as in software—he found this highly improbable.
This concern raises a deeper mathematical question:
How likely is it that a blind, random process like mutation would stumble upon the highly specific sequences of DNA needed to produce new proteins and ultimately new forms of life?
Eden was not alone in raising these doubts. During a 1966 conference at the Wistar Institute, numerous scientists and mathematicians gathered to examine fundamental problems in evolutionary theory. One key issue they debated was whether mutation and selection—the mechanisms central to neo-Darwinism—were sufficient to account for the origin of biological information.
The discovery in the 1950s and '60s that genetic information is stored as a linear sequence of nucleotides in DNA was initially seen as a breakthrough. Mutations could, in theory, modify these sequences in the same way text can be edited—one letter at a time (point mutations) or by rearranging whole sections (insertions, deletions, recombinations, etc.).
Yet Eden and others at Wistar warned that, despite this range of mutational possibilities, random changes almost always degrade function when applied to meaningful sequences. For instance, take the phrase:
“One if by land and two if by sea.”
Randomly altering just a few characters might result in:
“Ine if bg lend and two ik bT Nea.”
The meaning is lost. Similarly, if you randomly alter a few characters in a software program, it crashes. French mathematician Marcel Schützenberger, a fellow Wistar participant, echoed this concern. He pointed out that even minimal random edits to a program often render it inoperable, concluding:
“We have no chance (i.e., less than 1 in 10¹⁰⁰⁰) even to see what the modified program would compute—it just jams.”
Eden argued that the same logic applied to DNA: if biological sequences operate like code, then random mutations are far more likely to destroy existing functionality than to create new genetic information.
Neo-Darwinism posits that mutation supplies the raw material for evolutionary change, while natural selection preserves beneficial mutations and eliminates harmful ones. But as Eden and others emphasized, natural selection cannot act until a functional variant already exists—it can’t guide the search, only edit what mutation produces.
As evolutionary biologists Jack King and Thomas Jukes noted in 1969:
“Natural selection is the editor, rather than the composer, of the genetic message.”
This distinction is crucial. Editing presumes there’s already a coherent draft. In the case of evolutionary biology, random mutation must write that draft from scratch, often in a combinatorial space so vast that the likelihood of success is astronomically low.
For every sequence of amino acids that produces a functional protein, there are an astronomical number of combinations that do not. And as the length of a protein increases, the number of possible combinations grows exponentially—a phenomenon known as combinatorial inflation. This makes the search for functional sequences via random mutation increasingly implausible.
The arrangement of bases in DNA is subject to this same combinatorial explosion. And it's precisely this insight that led the Wistar skeptics to question the creative power of the mutation-selection mechanism. They argued that far from being a reliable engine of innovation, random mutation is more likely to corrupt than compose—a major challenge to the plausibility of Darwinian evolution as an explanation for biological complexity.
The combinatorial inflation problem is not limited to chemical evolution; rather, it applies to both the origin of life and the evolution of biological complexity. While it plays a significant role in explaining the challenges faced by theories of chemical evolution, its implications extend well into neo-Darwinian evolution and the development of new genes, proteins, and body plans.
In the context of chemical evolution, the problem emerges when trying to explain how the first functional biological molecules—such as RNA or proteins—could have formed through purely random processes in a prebiotic environment. The challenge lies in the vast number of possible combinations of amino acids or nucleotides. Functional sequences represent only a tiny fraction of these possibilities, meaning that the chance of randomly assembling a sequence capable of carrying out a useful function (like self-replication or catalysis) is incredibly small. This creates a probabilistic hurdle that makes the undirected origin of life appear deeply implausible.
However, the problem does not disappear once life begins. In biological evolution, especially within the framework of Neo-Darwinism, organisms must continually generate new genetic information to build novel proteins, structures, and body plans over time. This process also requires the discovery of new functional sequences within an exponentially expanding combinatorial space. For example, during the Cambrian Explosion - a period marked by the sudden appearance of numerous complex animal forms—entirely new gene regulatory networks and protein-coding sequences would have been required. Yet these too must be drawn from a vast sea of largely non-functional possibilities. As with chemical evolution, random mutation and natural selection face the same issue: the odds of hitting upon highly specific, functional sequences by chance are extraordinarily low.
In both stages—chemical and biological evolution—the fundamental challenge is the same: the number of potential sequences increases exponentially with length, while the number of functional sequences remains extremely rare. This vast discrepancy creates what is known as the combinatorial inflation problem, posing a serious obstacle to any theory that relies solely on unguided, random processes to generate the complex information found in living systems.
The central crux of this argument is that it questions the process of random variation or mutation can faciltiated specified functional biological information, also known as DNA and RNA. Biology, as it stands, cannot fully explain how the process of random variation or mutation can form functionally specified biological information or complex structures of any kind (Berlinski, 1996).
One central issue in Darwinian evolution is referred to as the combinatorial inflation argument (Meyer, 2014; Berlinski, 1996). The combinatorial inflation problem in evolution demonstrates the difficulty of explaining how complex, adaptive systems - such functional biological specified information - emerges from simpler, less organised components (Meyer, 2014; Berlinski, 1996). Functionally specified biological information refers to the specific sequences of nucleotides in DNA or amino acids in proteins that are necessary for life to function, also known as DNA & RNA (Meyer, 2014). Meyer argues that undirected processes like random mutation and natural selection cannot realistically account for the complexity and specificity of this information (Meyer, 2014). The problem stems from the vast number of possible combinations of sequences, coupled with the rarity of functional sequences within that immense space, which Meyer terms "combinatorial inflation" (Berlinski, 1996; Meyer, 2014).
It's worth examining the specifics of the combinatorial inflation problem in evolutionary theory. Proteins, which are essential for nearly all biological processes, are made up of chains of amino acids arranged in specific sequences (Meyer, 2014). For a protein with a length of 150 amino acids, the total number of possible sequences is 20 to the power of 150, since there are 20 standard amino acids (Berlinski, 1996). This number - approximately 10 to the power of 195 - represents the total "search space" of possible combinations (Meyer, 2014). To put this into perspective, the number of atoms in the observable universe is estimated to be around 10 to the power of 80 (Meyer, 2014). The sheer size of this combinatorial space poses a daunting problem for evolutionary theory, which posits that functional sequences arose through random mutations over time (Meyer, 2014; Denton, 1986). Meyer emphasises that exploring this vast search space to locate functional sequences is not feasible within the constraints of Earth's history (Eden, 1967). Even with billions of years of evolutionary time and countless organisms reproducing and mutating, the number of possible sequences far exceeds the number of trials nature could have conducted (Meyer, 2014; Denton, 1986). This mismatch between the size of the search space and the resources available for exploration highlights the improbability of finding functional biological molecules through random processes alone (Denton, 1986).
Without getting much further into the nuances pertaining to evolutionary theory, in straightforward terms, this issue apparent to Darwinism fundamentally highlights a significant gap in our understanding of how fundamental biological entities and information come together to generate biologically functional specified information (Denton and Scott 1986) Meyer uses the example of bike locks to illustrate this concept. A basic bike lock with just three dials, each containing 10 digits (0-9), has 1,000 possible combinations (10 × 10 × 10). If the number of dials is increased to four, the combinations rise to 10,000 (10 × 10 × 10 × 10). As the number of dials continues to grow, the number of possible combinations increases exponentially, making it progressively more difficult to guess the correct combination (Meyer, 2014). Thus far, my argument is this: in evolutionary theory, the combinatorial inflation problem highlights a key challenge—explaining how complex systems can emerge from simpler components through undirected processes (Meyer, 2014; Denton and Scott, 1986).
Thus, the central arguement being posed here is that the combinatorial inflation problem presents a significant challenge to the core assumptions of Darwinian and neo-Darwinian evolutionary theory. These frameworks rest on the idea that new biological forms arise through the gradual accumulation of random mutations, which are then filtered by natural selection. However, for this process to work, evolution must consistently produce functional genetic sequences—new genes, proteins, and regulatory elements—out of a vast space of possibilities, most of which are nonfunctional or harmful. The combinatorial inflation problem highlights the improbability of this happening by chance, especially as the complexity of organisms increases.
In essence, the problem suggests that as organisms evolve and become more complex, the amount of functional genetic information needed also increases. But with this increase comes an exponential growth in the number of possible combinations of genetic material—what we call “sequence space.” For every one sequence that performs a useful biological function, there may be trillions upon trillions that do not. Random mutations, being blind and unguided, have no way of targeting these rare functional islands in the vast sea of nonfunction. Natural selection can only preserve beneficial changes after they occur—it cannot guide mutations toward useful outcomes.
This raises serious doubts about the creative power of mutation and selection alone to generate the kind of complex, information-rich systems we observe in biology. The problem becomes especially acute in events like the Cambrian Explosion, where many new animal body plans appeared abruptly in the fossil record. These would have required large amounts of new genetic information in a relatively short period of time—an event that, under the constraints of combinatorial inflation, seems statistically implausible to have occurred through random mutation alone.
