A New Law of Nature Attempts to Explain the Complexity of the Universe

The original version of this story appeared in Quanta Magazine.

In 1950 the Italian physicist Enrico Fermi was discussing the possibility of intelligent alien life with his colleagues. If alien civilizations exist, he said, some should surely have had enough time to expand throughout the cosmos. So where are they?

Many answers to Fermi’s “paradox” have been proposed: Maybe alien civilizations burn out or destroy themselves before they can become interstellar wanderers. But perhaps the simplest answer is that such civilizations don’t appear in the first place: Intelligent life is extremely unlikely, and we pose the question only because we are the supremely rare exception.

A new proposal by an interdisciplinary team of researchers challenges that bleak conclusion. They have proposed nothing less than a new law of nature, according to which the complexity of entities in the universe increases over time with an inexorability comparable to the second law of thermodynamics—the law that dictates an inevitable rise in entropy, a measure of disorder. If they’re right, complex and intelligent life should be widespread.

In this new view, biological evolution appears not as a unique process that gave rise to a qualitatively distinct form of matter—living organisms. Instead, evolution is a special (and perhaps inevitable) case of a more general principle that governs the universe. According to this principle, entities are selected because they are richer in a kind of information that enables them to perform some kind of function.

This hypothesis, formulated by the mineralogist Robert Hazen and the astrobiologist Michael Wong of the Carnegie Institution in Washington, DC, along with a team of others, has provoked intense debate. Some researchers have welcomed the idea as part of a grand narrative about fundamental laws of nature. They argue that the basic laws of physics are not “complete” in the sense of supplying all we need to comprehend natural phenomena; rather, evolution—biological or otherwise—introduces functions and novelties that could not even in principle be predicted from physics alone. “I’m so glad they’ve done what they’ve done,” said Stuart Kauffman, an emeritus complexity theorist at the University of Pennsylvania. “They’ve made these questions legitimate.”

Others argue that extending evolutionary ideas about function to non-living systems is an overreach. The quantitative value that measures information in this new approach is not only relative—it changes depending on context—it’s impossible to calculate. For this and other reasons, critics have charged that the new theory cannot be tested, and therefore is of little use.

The work taps into an expanding debate about how biological evolution fits within the normal framework of science. The theory of Darwinian evolution by natural selection helps us to understand how living things have changed in the past. But unlike most scientific theories, it can’t predict much about what is to come. Might embedding it within a meta-law of increasing complexity let us glimpse what the future holds?

The story begins in 2003, when the biologist Jack Szostak published a short article in Nature proposing the concept of functional information. Szostak—who six years later would get a Nobel Prize for unrelated work—wanted to quantify the amount of information or complexity that biological molecules like proteins or DNA strands embody. Classical information theory, developed by the telecommunications researcher Claude Shannon in the 1940s and later elaborated by the Russian mathematician Andrey Kolmogorov, offers one answer. Per Kolmogorov, the complexity of a string of symbols (such as binary 1s and 0s) depends on how concisely one can specify that sequence uniquely.

For example, consider DNA, which is a chain of four different building blocks called nucleotides. Α strand composed only of one nucleotide, repeating again and again, has much less complexity—and, by extension, encodes less information—than one composed of all four nucleotides in which the sequence seems random (as is more typical in the genome).

But Szostak pointed out that Kolmogorov’s measure of complexity neglects an issue crucial to biology: how biological molecules function.

In biology, sometimes many different molecules can do the same job. Consider RNA molecules, some of which have biochemical functions that can easily be defined and measured. (Like DNA, RNA is made up of sequences of nucleotides.) In particular, short strands of RNA called aptamers securely bind to other molecules.

Let’s say you want to find an RNA aptamer that binds to a particular target molecule. Can lots of aptamers do it, or just one? If only a single aptamer can do the job, then it’s unique, just as a long, seemingly random sequence of letters is unique. Szostak said that this aptamer would have a lot of what he called “functional information.”

If many different aptamers can perform the same task, the functional information is much smaller. So we can calculate the functional information of a molecule by asking how many other molecules of the same size can do the same task just as well.

Szostak went on to show that in a case like this, functional information can be measured experimentally. He made a bunch of RNA aptamers and used chemical methods to identify and isolate the ones that would bind to a chosen target molecule. He then mutated the winners a little to seek even better binders and repeated the process. The better an aptamer gets at binding, the less likely it is that another RNA molecule chosen at random will do just as well: The functional information of the winners in each round should rise. Szostak found that the functional information of the best-performing aptamers got ever closer to the maximum value predicted theoretically.

Hazen came across Szostak’s idea while thinking about the origin of life—an issue that drew him in as a mineralogist, because chemical reactions taking place on minerals have long been suspected to have played a key role in getting life started. “I concluded that talking about life versus nonlife is a false dichotomy,” Hazen said. “I felt there had to be some kind of continuum—there has to be something that’s driving this process from simpler to more complex systems.” Functional information, he thought, promised a way to get at the “increasing complexity of all kinds of evolving systems.”

In 2007 Hazen collaborated with Szostak to write a computer simulation involving algorithms that evolve via mutations. Their function, in this case, was not to bind to a target molecule, but to carry out computations. Again they found that the functional information increased spontaneously over time as the system evolved.

There the idea languished for years. Hazen could not see how to take it any further until Wong accepted a fellowship at the Carnegie Institution in 2021. Wong had a background in planetary atmospheres, but he and Hazen discovered they were thinking about the same questions. “From the very first moment that we sat down and talked about ideas, it was unbelievable,” Hazen said.

“I had got disillusioned with the state of the art of looking for life on other worlds,” Wong said. “I thought it was too narrowly constrained to life as we know it here on Earth, but life elsewhere may take a completely different evolutionary trajectory. So how do we abstract far enough away from life on Earth that we’d be able to notice life elsewhere even if it had different chemical specifics, but not so far that we’d be including all kinds of self-organizing structures like hurricanes?”

The pair soon realized that they needed expertise from a whole other set of disciplines. “We needed people who came at this problem from very different points of view, so that we all had checks and balances on each other’s prejudices,” Hazen said. “This is not a mineralogical problem; it’s not a physics problem, or a philosophical problem. It’s all of those things.”

They suspected that functional information was the key to understanding how complex systems like living organisms arise through evolutionary processes happening over time. “We all assumed the second law of thermodynamics supplies the arrow of time,” Hazen said. “But it seems like there’s a much more idiosyncratic pathway that the universe takes. We think it’s because of selection for function—a very orderly process that leads to ordered states. That’s not part of the second law, although it’s not inconsistent with it either.”

Looked at this way, the concept of functional information allowed the team to think about the development of complex systems that don’t seem related to life at all.

At first glance, it doesn’t seem a promising idea. In biology, function makes sense. But what does “function” mean for a rock?

All it really implies, Hazen said, is that some selective process favors one entity over lots of other potential combinations. A huge number of different minerals can form from silicon, oxygen, aluminum, calcium, and so on. But only a few are found in any given environment. The most stable minerals turn out to be the most common. But sometimes less stable minerals persist because there isn’t enough energy available to convert them to more stable phases.

This might seem trivial, like saying that some objects exist while other ones don’t, even if they could in theory. But Hazen and Wong have shown that, even for minerals, functional information has increased over the course of Earth’s history. Minerals evolve toward greater complexity (though not in the Darwinian sense). Hazen and colleagues speculate that complex forms of carbon such as graphene might form in the hydrocarbon-rich environment of Saturn’s moon Titan—another example of an increase in functional information that doesn’t involve life.

It’s the same with chemical elements. The first moments after the Big Bang were filled with undifferentiated energy. As things cooled, quarks formed and then condensed into protons and neutrons. These gathered into the nuclei of hydrogen, helium, and lithium atoms. Only once stars formed and nuclear fusion happened within them did more complex elements like carbon and oxygen form. And only when some stars had exhausted their fusion fuel did their collapse and explosion in supernovas create heavier elements such as heavy metals. Steadily, the elements increased in nuclear complexity.

Wong said their work implies three main conclusions.

First, biology is just one example of evolution. “There is a more universal description that drives the evolution of complex systems.”

Second, he said, there might be “an arrow in time that describes this increasing complexity,” similar to the way the second law of thermodynamics, which describes the increase in entropy, is thought to create a preferred direction of time.

Finally, Wong said, “information itself might be a vital parameter of the cosmos, similar to mass, charge and energy.”

In the work Hazen and Szostak conducted on evolution using artificial-life algorithms, the increase in functional information was not always gradual. Sometimes it would happen in sudden jumps. That echoes what is seen in biological evolution. Biologists have long recognized transitions where the complexity of organisms increases abruptly. One such transition was the appearance of organisms with cellular nuclei (around 1.8 billion to 2.7 billion years ago). Then there was the transition to multicellular organisms (around 2 billion to 1.6 billion years ago), the abrupt diversification of body forms in the Cambrian explosion (540 million years ago), and the appearance of central nervous systems (around 600 million to 520 million years ago). The arrival of humans was arguably another major and rapid evolutionary transition.

Evolutionary biologists have tended to view each of these transitions as a contingent event. But within the functional-information framework, it seems possible that such jumps in evolutionary processes (whether biological or not) are inevitable.

In these jumps, Wong pictures the evolving objects as accessing an entirely new landscape of possibilities and ways to become organized, as if penetrating to the “next floor up.” Crucially, what matters—the criteria for selection, on which continued evolution depends—also changes, plotting a wholly novel course. On the next floor up, possibilities await that could not have been guessed before you reached it.

For example, during the origin of life it might initially have mattered that proto-biological molecules would persist for a long time—that they’d be stable. But once such molecules became organized into groups that could catalyze one another’s formation—what Kauffman has called autocatalytic cycles—the molecules themselves could be short-lived, so long as the cycles persisted. Now it was dynamical, not thermodynamic, stability that mattered. Ricard Solé of the Santa Fe Institute thinks such jumps might be equivalent to phase transitions in physics, such as the freezing of water or the magnetization of iron: They are collective processes with universal features, and they mean that everything changes, everywhere, all at once. In other words, in this view there’s a kind of physics of evolution—and it’s a kind of physics we know about already.

The tricky thing about functional information is that, unlike a measure such as size or mass, it is contextual: It depends on what we want the object to do, and what environment it is in. For instance, the functional information for an RNA aptamer binding to a particular molecule will generally be quite different from the information for binding to a different molecule.

Yet finding new uses for existing components is precisely what evolution does. Feathers did not evolve for flight, for example. This repurposing reflects how biological evolution is jerry-rigged, making use of what’s available.

Kauffman argues that biological evolution is thus constantly creating not just new types of organisms but new possibilities for organisms, ones that not only did not exist at an earlier stage of evolution but could not possibly have existed. From the soup of single-celled organisms that constituted life on Earth 3 billion years ago, no elephant could have suddenly emerged—this required a whole host of preceding, contingent but specific innovations.

However, there is no theoretical limit to the number of uses an object has. This means that the appearance of new functions in evolution can’t be predicted—and yet some new functions can dictate the very rules of how the system evolves subsequently. “The biosphere is creating its own possibilities,” Kauffman said. “Not only do we not know what will happen, we don’t even know what can happen.” Photosynthesis was such a profound development; so were eukaryotes, nervous systems and language. As the microbiologist Carl Woese and the physicist Nigel Goldenfeld put it in 2011, “We need an additional set of rules describing the evolution of the original rules. But this upper level of rules itself needs to evolve. Thus, we end up with an infinite hierarchy.”

The physicist Paul Davies of Arizona State University agrees that biological evolution “generates its own extended possibility space which cannot be reliably predicted or captured via any deterministic process from prior states. So life evolves partly into the unknown.”

Mathematically, a “phase space” is a way of describing all possible configurations of a physical system, whether it’s as comparatively simple as an idealized pendulum or as complicated as all the atoms comprising the Earth. Davies and his co-workers have recently suggested that evolution in an expanding accessible phase space might be formally equivalent to the “incompleteness theorems” devised by the mathematician Kurt Gödel. Gödel showed that any system of axioms in mathematics permits the formulation of statements that can’t be shown to be true or false. We can only decide such statements by adding new axioms.

Davies and colleagues say that, as with Gödel’s theorem, the key factor that makes biological evolution open-ended and prevents us from being able to express it in a self-contained and all-encompassing phase space is that it is self-referential: The appearance of new actors in the space feeds back on those already there to create new possibilities for action. This isn’t the case for physical systems, which, even if they have, say, millions of stars in a galaxy, are not self-referential.

“An increase in complexity provides the future potential to find new strategies unavailable to simpler organisms,” said Marcus Heisler, a plant developmental biologist at the University of Sydney and co-author of the incompleteness paper. This connection between biological evolution and the issue of noncomputability, Davies said, “goes right to the heart of what makes life so magical.”

Is biology special, then, among evolutionary processes in having an open-endedness generated by self-reference? Hazen thinks that in fact once complex cognition is added to the mix—once the components of the system can reason, choose, and run experiments “in their heads”—the potential for macro-micro feedback and open-ended growth is even greater. “Technological applications take us way beyond Darwinism,” he said. A watch gets made faster if the watchmaker is not blind.

If Hazen and colleagues are right that evolution involving any kind of selection inevitably increases functional information—in effect, complexity—does this mean that life itself, and perhaps consciousness and higher intelligence, is inevitable in the universe? That would run counter to what some biologists have thought. The eminent evolutionary biologist Ernst Mayr believed that the search for extraterrestrial intelligence was doomed because the appearance of humanlike intelligence is “utterly improbable.” After all, he said, if intelligence at a level that leads to cultures and civilizations were so adaptively useful in Darwinian evolution, how come it only arose once across the entire tree of life?

Mayr’s evolutionary point possibly vanishes in the jump to humanlike complexity and intelligence, whereupon the whole playing field is utterly transformed. Humans attained planetary dominance so rapidly (for better or worse) that the question of when it will happen again becomes moot.

But what about the chances of such a jump happening in the first place? If the new “law of increasing functional information” is right, it looks as though life, once it exists, is bound to get more complex by leaps and bounds. It doesn’t have to rely on some highly improbable chance event.

What’s more, such an increase in complexity seems to imply the appearance of new causal laws in nature that, while not incompatible with the fundamental laws of physics governing the smallest component parts, effectively take over from them in determining what happens next. Arguably we see this already in biology: Galileo’s (apocryphal) experiment of dropping two masses from the Leaning Tower of Pisa no longer has predictive power when the masses are not cannonballs but living birds.

Together with the chemist Lee Cronin of the University of Glasgow, Sara Walker of Arizona State University has devised an alternative set of ideas to describe how complexity arises, called assembly theory. In place of functional information, assembly theory relies on a number called the assembly index, which measures the minimum number of steps required to make an object from its constituent ingredients.

“Laws for living systems must be somewhat different than what we have in physics now,” Walker said, “but that does not mean that there are no laws.” But she doubts that the putative law of functional information can be rigorously tested in the lab. “I am not sure how one could say [the theory] is right or wrong, since there is no way to test it objectively,” she said. “What would the experiment look for? How would it be controlled? I would love to see an example, but I remain skeptical until some metrology is done in this area.”

Hazen acknowledges that, for most physical objects, it is impossible to calculate functional information even in principle. Even for a single living cell, he admits, there’s no way of quantifying it. But he argues that this is not a sticking point, because we can still understand it conceptually and get an approximate quantitative sense of it. Similarly, we can’t calculate the exact dynamics of the asteroid belt because the gravitational problem is too complicated—but we can still describe it approximately enough to navigate spacecraft through it.

Wong sees a potential application of their ideas in astrobiology. One of the curious aspects of living organisms on Earth is that they tend to make a far smaller subset of organic molecules than they could make given the basic ingredients. That’s because natural selection has picked out some favored compounds. There’s much more glucose in living cells, for example, than you’d expect if molecules were simply being made either randomly or according to their thermodynamic stability. So one potential signature of lifelike entities on other worlds might be similar signs of selection outside what chemical thermodynamics or kinetics alone would generate. (Assembly theory similarly predicts complexity-based biosignatures.)

There might be other ways of putting the ideas to the test. Wong said there is more work still to be done on mineral evolution, and they hope to look at nucleosynthesis and computational “artificial life.” Hazen also sees possible applications in oncology, soil science and language evolution. For example, the evolutionary biologist Frédéric Thomas of the University of Montpellier in France and colleagues have argued that the selective principles governing the way cancer cells change over time in tumors are not like those of Darwinian evolution, in which the selection criterion is fitness, but more closely resemble the idea of selection for function from Hazen and colleagues.

Hazen’s team has been fielding queries from researchers ranging from economists to neuroscientists, who are keen to see if the approach can help. “People are approaching us because they are desperate to find a model to explain their system,” Hazen said.

But whether or not functional information turns out to be the right tool for thinking about these questions, many researchers seem to be converging on similar questions about complexity, information, evolution (both biological and cosmic), function and purpose, and the directionality of time. It’s hard not to suspect that something big is afoot. There are echoes of the early days of thermodynamics, which began with humble questions about how machines work and ended up speaking to the arrow of time, the peculiarities of living matter, and the fate of the universe.

Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.