The innocent-sounding question, “Which came first, the chicken or the egg?”, when cracked open, contains much more than a yolk. Living things are replete with systems characterized by circular interdependencies that defy development from pathways of linear progression.

DNA codes for amino acids, which are assembled into proteins, but DNA cannot work in isolation. DNA requires an interdependent metropolis of molecular structures and mechanisms to fulfill its role as the instruction manual for life. And DNA itself can only be formed within a living cell. This leads to a “chicken and egg” problem: How can one component function or even be brought into existence without the other? 

Canceled Science, pp. 150-51

Von Neumann’s Self-Replicating Machine

Let’s examine this question further in the context of a general self-replicating mechanism. The great mathematician John von Neumann, in the mid 20th century, developed a model for a self-replicating machine.

Von Neumann recognised that a single ‘general constructive automaton’ might be able to construct ‘any’ machine…given a ‘description tape’ of that target machine.¹

In the context of evolution, three difficulties with this proposal immediately present themselves: 

1. How could something as complex as a “general constructive automaton” arise by undirected natural processes? 
2. Where does the vast amount of information resident in the “description tape” come from? (Especially considering that natural processes always destroy information with the passage of time).
3. How does the information required to construct the particular organism or mechanism come to reside within the “description tape” so that a functional outcome results? 

Embedded in these questions lies another “chicken and egg” paradox: Which came first, the constructive automaton or the instruction manual (“description tape”) the automaton requires to achieve self-reproduction? The automaton itself is no simple mechanism; the “description tape” is even more complex. Von Neumann thought that, for a complex self-replicating system, or automaton, such as a living organism,

…the automaton is simpler than a symbolic description of its behavior.²

According to von Neumann, “simple” self-replicating systems are a myth, undercutting any belief that such mechanisms could arise by undirected small steps.

He thought, for example, that below a certain level, complexity is degenerative, and self-reproduction is impossible.³

The miracle of life, then, shows itself in that reproduction happens at all — that a chicken can produce an egg, complete with a description of an egg-producing chicken, within a single cell.

For a Machine to Reproduce Itself

Research scientist Robert Gange cites von Neumann’s work to conclude that for a machine to reproduce itself, it minimally “would need to make about fifteen hundred correct decisions, one after the other without error.”⁴ Another way to express this is that the probability of actualizing a self-replicating machine is equivalent to one out of 2¹⁵⁰⁰ (or 10⁴⁵²) possibilities. Considering that there are only 10⁸⁰ elementary particles in the entire visible universe, undirected natural processes have absolutely no chance of producing any such mechanism.

One of the remarkable features of living things is how robust they are in terms of self-replication. By any measure, the mechanisms for constructing a new creature, and the means of storing, transferring, reading, and instantiating the vast amount of detailed information required for successful replication, involve complex and finely tuned processes. Contrarily, our uniform experience with artificial mechanisms that comprise complex processes is that they break down with time. 

I drive a 12-year old Buick that was somewhat of a luxury model when it was new. But when I bought it, it was already over ten years old and had about 175,000 miles on it. It has inconvenienced me more than once with breakdowns, not altogether unexpected for a vehicle with this much wear on it. 

I venture to say that the complexity involved in the reproducibility of even a single-cell organism, such as cyanobacteria, far exceeds that found in a Buick, or any man-made mechanism or device. And yet, such organisms have been reproducing successfully throughout most of Earth’s biological history:

The cyanobacteria have an extensive fossil record. The oldest known fossils, in fact, are cyanobacteria from Archaean rocks of western Australia, dated 3.5 billion years old.

Granville Sewell’s Vision

Professor of mathematics Granville Sewell has recently summarized the challenge of self-replication by imagining a sequence of increasingly complex versions of a classic car, the Model T. In Sewell’s vision, reproductive models U and V possess the capability, quite unlike my Buick, of producing the preexisting version. Model V’s can produce Model U’s that can produce Model T’s, each of which, like an old Buick, will work only until entropy gets the better of it. Professor Sewell cogently points out the impossibility of attaining ongoing self-replication in this manner.

The Model V species will become extinct after two generations, because their children will be Model U’s, and their grandchildren will be infertile Model T’s. So back to work, and each time we add technology to this car, to move it closer to the goal of reproduction, we only move the goalposts, because now we have a more complicated car to reproduce. It seems that the new models would grow exponentially in complexity.

Applying his example to evolution exposes an unavoidable dead end to the supposition that self-replication arose from non-replicating precursors. And as we have already argued from von Neumann’s mathematical analysis of a general self-replicating automaton, the minimum complexity inherent in such a mechanism (or organism) defies natural explanations.

Professor Barry McMullin, in reviewing von Neumann’s work, similarly perceives the impasse that the development of self-replication presents to any evolutionary paradigm — the bootstrap fallacy (or trying to lay an egg without a chicken):

The evolutionary boot-strapping problem: in the von Neumann framework, at least, U₀ [a basic general constructive machine] is already a very complicated entity. It certainly seems implausible that it could occur spontaneously or by chance. Similarly, in real biology, the modern (self-consistent!) genetic system could not have plausibly arisen by chance (Cairns-Smith, 1982). It seems that we must therefore assume that something like U₀ (or a full-blown genetic system) must itself be the product of an extended evolutionary process. Of course, the problem with this —  and a major part of von Neumann’s own result — is that it seems that something like a genetic system is a pre-requisite to any such evolutionary process.⁵

Ratcheting Up the Complexity 

A further problem for any evolutionary self-replication system, obvious to von Neumann, is that evolutionary processes do not purport to “merely” function as static self-replicators, but to involve a scheme whereby the reproductive product gradually ratchets up in complexity, information content, and functionality. Von Neumann knew from his analysis of cellular automata that increasing complexity was just the opposite of what was to be expected from inevitable accumulated errors in the process.

It was well known even to von Neumann himself that his system would not in practice exhibit any evolutionary growth of complexity. The proximate reason is that, in his CA [cellular automata] framework, all automata of any significant scale are extremely fragile: that is, they are very easily disrupted even by minimal perturbation of the external environment….However, any serious claim to substantively model real biological organisms will inevitably have to confront their capacity for self-maintenance and repair in the face of continuous perturbation and material exchange with their environments.⁶

McMullen adds these thoughts on the problems of the counter-indicated model of evolution:

This deeper problem is what I call the evolutionary growth of complexity. More specifically, the problem of how, in a general and open-ended way, machines can manage to construct other machines more “complex” that themselves….Why is this growth of complexity a problem? Well, put simply, all our pragmatic experience of machines and engineering points in the opposite direction. In general, if we want to construct a machine of any given degree of complexity, we use even more complex machinery in its construction. While this is not definitive, it is surely suggestive of a difficulty.

The conclusion based on a mathematical analysis of self-replication is that asking which came first, the chicken or the egg, is getting way ahead of the game. The primary question to ask is how could either a “chicken” or an “egg” come into existence in the first place? No aspect of the theory of self-replication allows for the possibility of the gradual development of either — and yet the chicken still lays an egg. Intelligent design provides an answer for this paradox, and it looks like the yolk’s on evolution.

Notes

1. Barry McMullin, “John von Neumann and the Evolutionary Growth of Complexity: Looking Backwards, Looking Forwards…” (2000), https://www.eeng.dcu.ie/~alife/bmcm-2000-01/html-single/bmcm-2000-01.html#Burks:TSRA.
2. John von Neumann, “Theory of Self-Reproducing Automata,” edited and completed by Arthur W. Burks (Urbana: University of Illinois Press, 1966), p. 23.
3. Von Neumann, “Theory of Self-Reproducing Automata,” p. 23.
4. Robert Gange, Origins and Destiny (Dallas: Word Publishing, 1986), 95.
5. McMullin (2000).
6. McMullin (2000).