The Problem of Sequentialization

Our World as Sequences See It

In the beginning there were no sequences. The Earth of four billion years ago was devoid of one-dimensional patterns. Everything was predictable, humming along in accordance with the laws of nature. But then sequences appeared, and nothing was the same again.

The Earth we inhabit today is overrun with sequences and their products. First to emerge on our lifeless planet were the sequences of RNA, DNA, and protein that govern the function of living things. Later a certain kind of living thing, a social primate, developed sequences of speech and eventually of writing. Today all of these molecular and linguistic sequences are routinely transformed into one-dimensional patterns of zeros and ones that flow through wires and over the air. All day, every day, we swim in an ocean of sequences. And like the proverbial fish who does not know what water is, we are largely oblivious to their profound influences.

But on the sequence-free Earth of four billion years ago there was just the ordinary stuff of matter and energy, all obeying the predictable and inexorable laws of nature. Matter and energy are still with us and still obey the same laws but, thanks to sequences, they are much better organized across time and space, into liver cells and violins and universities. That’s a big change. How did it happen?

To appreciate how sequences achieved their hegemony, we must first understand how they differ from the ancient sequence-free physical world from which they arose. What are the properties of sequences—systems of sequences, really, because sequences never travel alone—that distinguish their behavior from that of ordinary matter governed by the laws of nature? Despite the long tenure of sequences on our planet, this is a relatively recent question, unasked before the modern age of molecular biology. This chapter will set out exactly why sequences are different and why they are worthy of study in their own right.

In the decade after Nobel laureates James Watson and Francis Crick figured out that the DNA molecule was in fact a sequence of smaller molecules,1 the field of molecular genetics struggled with the problem of what Crick calls sequentialization. “It is this problem, the problem of ‘sequentialization’, which is the crux of the matter,” he writes.2 DNA was known to be a sequence of nucleotides, as was its cousin RNA, and proteins were known to be sequences of amino acids. What was not known was how these sequences related to one another.

By the late 1960s, researchers had worked out a fundamental explanation of the genetic code, which shows how the one-dimensional patterns of nucleotides in DNA are mapped to the one-dimensional patterns of amino acids in proteins.3 That is what a code is, a mapping from one kind of sequence to another. In Morse Code, for example, unique sequences of dots and dashes map to the letters, numbers, and symbols of the alphabet. In the genetic code, three- letter sequences of DNA (codons) map uniquely to each of the 20 individual amino acids found in protein sequences.

But Crick’s problem of sequentialization can be viewed more broadly. How did Earth’s surface become sequentialized? How did systems of sequences emerge? How did they create and propagate their own complex world of coordinated matter and energy, a world that exhibits functional coherence and temporal endurance in ways that could never be predicted from the laws of nature, but which in no way contradict those laws? How did inanimate matter give rise to life and life in turn give rise to civilization?

But first things first. What is a sequence, anyway? In everyday usage, it is one thing following another: a sequence of steps to bake a pie or a sequence of stages in the development of an embryo or a sequence of floats and marching bands in a parade. Sequence is rooted in the Latin sequor (“to follow”), best known today for describing a lapse in logic: a non sequitur (“it does not follow”).

The steps required to bake a pie form an instructive sequence; the sequences of text in a recipe tell us what actions to perform and in what order. Navigational directions to a destination, the user manual for a kitchen appliance, instructions for erecting a tent, and lessons in how to tango are all examples of instructive sequences. They tell us how to behave, how to move in time and space; their one-dimensional arrangement specifies the order of steps to be performed in an activity.

The sequence of stages in embryonic development, however, is a descriptive sequence. We observe an event as it unfolds and, based on our perceptions, generate a one-dimensional pattern to record how it changes over time. Almost all observations of the natural world—most of science, from how stars form to how horses canter—take the form of descriptive sequences. The point is that descriptive sequences do not tell us how to behave; they result from our perception of how the world behaves.4

The sequences of human language can both describe and instruct. This may seem obvious, but it is also crucial. A single set of letters and words, and a single set of grammatical rules for combining them, can not only create a record of something that has happened in the world but also can guide worldly activities like baking a pie. We may not think twice about this, but try to envision a world that requires one language for instruction and a completely separate language for description. How cumbersome would that be? Imagine the instructions for assembling a bookcase where the text describing the parts is in Estonian and the text telling us how to put them together is in Hindi.

Instead, we have unitary languages in which instructive and descriptive sequences complement one another. We can receive instructions that guide our behavior: what to do, when to do it, how to do it, etc. We can also perceive the world and create a record of what we observe, what scientists call measurement. Since a single language can do both, the interplay between description and instruction gives systems of sequences extraordinary power to organize the world. See something, do something.