Cellular Automata, the Universal Ancestor, and the Tree of Life

The most important meditation

Discovering the Universal Ancestor

I was watching the Netflix series, Life on Our Planet, a vastly spanning documentary featuring Morgan Freeman’s narration and state-of-the-art CG animation to transport you back through the millions and billions of years of history. Right from the start of the series, I was struck by a recent scientific discovery– recent, that is, compared to when I’d first learned about Evolutionary Biology at school in the 80’s. The series explains that everything began with a universal ancestor, a singular cell that became the progenitor of all life on Earth. It was quite a revelation to me. Previously, I’d understood life as emerging from a ‘primordial soup’, consisting of random proto-cellular entities emerging to form the seeds of life, akin to pasta bubbling in minestrone. However, science has moved on from the days of Members Only jackets and kids spiking their hair with glue. Current scientific consensus points towards a singular origin, though it allows for some ambiguity, considering phenomena like horizontal gene transfer (HGT) – nonetheless, if you trace the evolutionary family tree back to the beginning, you get a single point.

The concept of all life having evolved from a common ancestor is both not profound, meaning it’s something that we’ve been told from our early school days, but it is also the most profound truth you could hope to truly internalize in your view of life and the role of your existence in the world. While grasping the entire history of life is a feat beyond human cognition, this series at least helped our imagination by compressing a few billion years down to several hours. Still, even saying ‘billion’ or ‘million’ is an abstraction we cannot truly understand as a tangible quantity.

From Cells to Cellular Automata

To explore this concept further, I find it helpful to draw parallels with the language of computer programming. This perspective is not new– Richard Feynman, in his 1959 talk, "There’s Plenty of Room at the Bottom," spoke about biological machines, and I found this fun presentation by Jacob Martin relating cell structures to computer hardware and software called, “Cell Analogy to a Computer.”

Let’s distill the complexity of a biological cell down further, for our purposes, to a mathematical function f_c, describing the state of a ‘cell’ over time.  So at any given point in time t, f_c(t) is the state of a cell. If we view cells as state machines, changing from moment to moment (t₁ to t₂), we can see that the ‘entity’ nature of the cell is defined by the function f_c – not by the cell’s current state at a point in time.

That is to say, we call a particular white blood cell, that white blood cell there – not because of what it is doing at a given point in time.  The white blood cell is an entity of its own, not related to its biological function over time.  It is continuous over time, despite changing its internal state.  In our computer programming analogy – the white blood cell is a function.  The function does not change, while its input, and the state, or result of the function, does change over time.

The crux of my argument lies in the concept of continuity. Let’s imagine an entire organism as a cellular automation function. A process function describing the set of the cells (also functions) that it contains.  Given this definition, we can imagine a process to describe the development of an organism from a single fertilized cell to a complete being, which we can describe, pseudo-mathematically, as a process evolving over time. 

So now we have a cellular automation function C_a which results in, over time, a set of cells.  So that: 

C_a(t) = {f_c1(t), f_c2(t) … f_cn(t)}  

At the start, t=1, we have a function that describes a single cell. 

C_a(1) = {f_c1(1)}

But the cell’s function can include adding a new cell to set by spawning a new cell (e.g. cell mitosis).

C_a(t) = {f_c1(t), f_c2(t)}

Through this lens we see an organism growing out from a single cell, or maybe we imagine this set as a colony of single cell organisms, but somewhere along the evolutionary path we decide to put a demarcation around certain sets of cells which are specialized and interdependent enough to call the set a single organism separate from other organisms.  So we might have:

C_a(t) = Organism X:{f_cx1(t), f_cx2(t) … f_cxn(t)} + Organism Y:{f_cy1(t), f_cy2(t) … f_cyn(t)} 

However, looking at it in this way, our definition of ‘Organism’ seems rather arbitrary.

The Tree of Life through Spacetime

Now if we imagine not just a single slice of time, but the series of time from t=1 when the Universal Ancestor was spawned into existence to t = present day, and we put that time series into our process function C_a(t₁…t_present) – we get the union of all cells of all life. 

Again our designation of what makes a group of cells distinct as an organism seem arbitrary when we look at things pseudo-mathematically, also makes past and present delineation of organisms past and organisms present seem equally arbitrary.

Einstein made the concept of spacetime an essential concept in Physics. That is, to look at the 3-dimensions of motion through space as linked to the 4th dimension of time as a single coordinate system that can define the ‘shape’ of spacetime.

I’d like us to look at Evolutionary Biology too, through the perspective of spacetime. Given the rationale I’ve sketched above, surely looking at life on earth in this way would not yield disparate organisms, but a single organism, much like a Tree of Life, spanning across the world and through time.