In previous articles, I have explored the research of Richard Sternberg and others who argue that standard algorithms cannot fully explain biology. Sternberg’s thought is the subject of a new book, Plato’s Revenge: The New Science of the Immaterial Genome, by science writer David Klinghoffer. According to Sternberg’s argument, biological processes are guided by cognition — the capacity to make authentic choices and exhibit creative behavior — and life’s control center is immaterial (here, here). Here, I will offer a few back-of-the-envelope calculations to illustrate why many have reached these conclusions. While not a formal defense, the analysis aims to give readers an intuitive grasp of the reasoning behind this perspective.

Defining the Problem

The non-algorithmic nature of life is well illustrated in development — the process of a fertilized egg developing into an infant. If embryological development were controlled algorithmically (i.e., solely through physical mechanisms), the fertilized egg, or other starting point, would contain the required information to direct the entire developmental process. The following analysis will test this “preformationist” assumption for humans. 

The first step is estimating the amount of information in a human fertilized egg (zygote). The information in human DNA is around 10 billion bits (10¹⁰) — each of the 3 billion loci could contain any 1 of the 4 nucleotides, and each nucleotide corresponds to 2 bits. The largest amount of information that could be contained in a zygote is likely less than the number of proteins, DNA, RNA, lipids, and carbohydrates (here, here, here), a value less than 1,000,000,000,000,000 (10¹⁵) bits. 

Determining whether these values fall below the required information for development starts by dividing embryology into distinct regions and stages. I will estimate the number of distinct regions based on the average distance between capillaries and the range of many chemical signals, which is on the order of 1 mm (here, here), yielding 1,000,000 regions containing several thousand cells. I will estimate the number of stages in development based on the time between distinct cell states related to transcription, cellular organization, motion, and signaling (here, here, here). A lower-bound estimate is 1,000 distinct stages in human development, approximately 7 hours in duration. The total number of transitions between stages in distinct regions is the product of the two numbers, which is 1,000,000,000 (10⁹). 

If the zygote contained all the information necessary to guide development, it would need to encode instructions for each of the estimated 10⁹ distinct developmental transitions. However, the amount of information in the genome that could be allocated per transition is limited. Using an upper bound of 10¹⁰ bits in the genome yields only about 10 bits per transition — barely enough to encode a few binary choices. Even if we assume the maximum theoretical information capacity of the cell is closer to 10¹⁵ bits, this upper-bound estimate still provides only about 1,000,000 bits per transition.

Calculating the Required Information 

Whole-cell computation models can provide insight into the minimal informational requirements for developmental algorithms. Karr et al. (2012) modeled the life cycle of Mycoplasma genitalium, including its components and molecular interactions. Their simulation modeled 28 cellular processes using around 1,000 equations and 2,000 variables. The simulation software package is 500 million bits in size. Even this simulation of one of the simplest known cells is above the threshold for the zygote to contain the required information for development. 

Yet the complexity of transforming one region of a human fetus into the next stage in development is an immensely more challenging problem. Each region corresponds to thousands of cells. The minimal list of relevant variables for just one cell includes the following:

• 10,000 gene states
• 10,000 epigenetic states
• 100 signaling molecule states
• 100 extracellular matrix and mechanical states

Additional variables correspond to cell types and shapes, movement, and microenvironments. 

Any algorithm involved in directing development would need to operate across a vast set of variables, including both internal cellular states and signaling variables shared among neighboring cells, and often between cells in distant regions. Certain cell types, such as osteoblasts, migrate substantial distances while executing complex functions, interacting dynamically with multiple cell types and tissue environments. As a result, the total number of variables and their interdependencies during development far exceeds the number in whole-cell simulations.

In addition, whole-cell models employ well-defined algorithms to solve systems of equations. In contrast, embryos can respond creatively to challenges using non-standard cellular mechanisms in a non-algorithmic manner (here, here). They often find optimal solutions to problems never encountered before very quickly. These differences from whole-cell models indicate that the information associated with any set of algorithms that could direct just one of the 10⁹ transitions should be far larger than 500 million bits. Moreover, the information stored in the zygote must correspond to the software and the hardware to run the developmental algorithms. The zygote is not capable of storing all the required information. 

Even if the zygote could contain the algorithmic information, the required number of computations poses an equally daunting problem. The open-ended nature of the challenges faced during development implies that directing the cells from one stage to the next represents a non-algorithmic problem (see my article, “Recent Article Calls for a Philosophical Revolution in Biology by Placing Mind Over Matter”). Such problems require more operations than NP-hard problems, which scale exponentially with the number of variables. 

Consequently, the number of computations for one developmental transition should exceed 10⁹ to the power of 10, which is 10⁹⁰ (1 with 90 zeroes behind it). Whole-cell models can simulate a cell cycle in 10⁹ operations, and the exponent is multiplied by 10 since developmental transitions involve more than 10 times the number of variables. This number of computations could not be performed on the fastest possible computer, the Earth’s size, in the universe’s entire history; it is trans-computational.

Another illustration of development’s trans-computational nature is the number of possible gene state changes. If just 30 of the approximately 10,000 genes involved in development are altered, the number of combinations approaches 10⁹⁰. By comparison, thousands of gene state changes can occur during one stage of development, so responding to developmental disturbances throughout development can require altering more than 30 genes. The number of possible responses — and the computations needed to evaluate them — vastly exceeds 10⁹⁰.

Assessing the Implications

If the zygote cannot contain the information directing development, then that information must reside in a logical and mathematical structure that stems from or is tantamount to a Platonic form, as Sternberg has inferred and as Plato’s Revenge describes. If one does not wish to embrace such a radical conclusion, one must accept that developmental algorithms display an efficiency and ingenuity that vastly surpass human knowledge. They could only have arisen from a mind far superior to our own.  

In addition, any undirected evolutionary framework must be abandoned. Every fetal region employs a set of operations that include a map of subsequent stages in development and the instructions to direct the current stage to the next. They must also possess contingency plans for countless perturbed starting states. Any major evolutionary transition would need to simultaneously alter the algorithms in every region at every stage instantly. If mutations only redirected a few regions at a few stages toward a new organism, the subsequent stages would return the fetal trajectory back toward the original target. If the redirection efforts failed, the individual would experience deformations or death. Only a designer could simultaneously alter every algorithm to guide development toward a new outcome coherently. 

Image source: Discovery Institute Press.