Showing posts with label thermodynamics. Show all posts
Showing posts with label thermodynamics. Show all posts

The Strange Physics That Gave Birth to AI

Mike's Notes

Part of a series "Science, Promise and Peril in the Age of AI" from Quanta magazine in 2025. The series is excellent, explaining the science behind AI.

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Last Updated

12/01/2026

The Strange Physics That Gave Birth to AI

By: Elise Cutts
Quanta Magazine: 30/04/2025

Elise Cutts is one of those ex-researchers who realized that writing about science is much more fun than doing it herself. Previously a geobiologist, she now writes about physics, geoscience, and space research in Europe and beyond from her home in Graz, Austria.

Modern thinking machines owe their existence to insights from the physics of complex materials.

Spin glasses might turn out to be the most useful useless things ever discovered.

These materials — which are typically made of metal, not glass — exhibit puzzling behaviors that captivated a small community of physicists in the mid-20th century. Spin glasses themselves turned out to have no imaginable material application, but the theories devised to explain their strangeness would ultimately spark today’s revolution in artificial intelligence.

In 1982, a condensed matter physicist named John Hopfield borrowed the physics of spin glasses to construct simple networks that could learn and recall memories. In doing so, he reinvigorated the study of neural networks — tangled nets of digital neurons that had been largely abandoned by artificial intelligence researchers — and brought physics into a new domain: the study of minds, both biological and mechanical.

Hopfield reimagined memory as a classic problem from statistical mechanics, the physics of collectives: Given some ensemble of parts, how will the whole evolve? For any simple physical system, including a spin glass, the answer comes from thermodynamics: “toward lower energy.” Hopfield found a way to exploit that simple property of collectives to store and recall data using networks of digital neurons. In essence, he found a way to place memories at the bottoms of energetic slopes. To recall a memory, a Hopfield network, as such neural nets came to be known, doesn’t have to look anything up. It simply has to roll downhill.

The Hopfield network was a “conceptual breakthrough,” said Marc Mézard, a theoretical physicist at Bocconi University in Milan. By borrowing from the physics of spin glasses, later researchers working on AI could “use all these tools that have been developed for the physics of these old systems.”

In 2024, Hopfield and his fellow AI pioneer Geoffrey Hinton received the Nobel Prize in Physics for their work on the statistical physics of neural networks. The prize came as a surprise to many; there was grumbling that it appeared to be a win for research in AI, not physics. But the physics of spin glasses didn’t stop being physics when it helped model memory and build thinking machines. And today, some researchers believe that the same physics Hopfield used to make machines that could remember could be used to help them imagine, and to design neural networks that we can actually understand.

Emergent Memory


A black-and-white portrait of a man in a tweed jacket and tie with his arms crossed.

The American physicist John Hopfield, pictured in 1988, developed a model of a neural network that laid the foundation for modern AI. Caltech Archives and Special Collections

Hopfield started his career in the 1960s working out the physics of semiconductors. But by the end of the decade, “I had run out of problems in condensed matter physics to which my particular talents seemed useful,” he wrote in a 2018 essay(opens a new tab). So he went looking for something new. After a foray into biochemistry that produced a theory of how organisms “proofread(opens a new tab)” biochemical reactions, Hopfield settled on neuroscience.

“I was looking for a PROBLEM, not a problem,” he recalled in his essay, emphasizing the need to identify something truly important. “How mind emerges from brain is to me the deepest question posed by our humanity. Definitely a PROBLEM.”

Associative memory, Hopfield realized, was a part of that problem that his tool kit from condensed matter physics could solve.

In a normal computer, data is stored statically and accessed with an address. The address doesn’t have anything to do with the information that’s stored. It’s just an access code. So if you get the address even a little bit wrong, you’ll access the wrong data.

That’s not how humans seem to remember things. We often remember by association. Some cue or scrap of memory brings the full thing flooding back. It’s what happens when you smell lilacs and recall a childhood episode in your grandpa’s garden, or when you hear the first few lines of a song and find yourself belting out every word to a ballad you didn’t know you knew.

Hopfield spent years on understanding associative memory and translating it to a neural network. He tinkered with randomly wired neural networks and other potential models of memory. It wasn’t looking good until, eventually, Hopfield identified an unlikely key to the “PROBLEM.’’

Two smiling men in suits stand side by side.

Geoffrey Hinton (left) and John Hopfield accepted the 2024 Nobel Prize in Physics at a ceremony in Stockholm in December. The prize honored their pioneering work on the earliest neural network models, which were based on the physics of spin glasses. Wikimedia Commons

Spin Glasses

In the 1950s, scientists studying certain dilute alloys such as iron in gold realized that their samples were doing some strange things. Above a certain temperature, these alloys behave similarly to a normal material such as aluminum. They aren’t magnetic on their own, but they do interact weakly with external magnetic fields. For instance, you can use a very strong magnet to move an aluminum can, but aluminum itself can’t work as a magnet. Usually, materials such as aluminum lose their magnetization as soon as the external magnet disappears. But below a certain temperature, spin glasses do something different. Their transient magnetization sticks around, albeit at a lower value. (This isn’t the only weird thing that spin glasses do; their thermal properties are also puzzling.)

Around 1970, condensed matter physicists started to get a theoretical handle on these materials by tweaking physicists’ go-to model of collective magnetic behavior: the Ising model.

An Ising model looks like a simple grid of arrows, each of which can point up or down. Every arrow represents the intrinsic magnetic moment, or “spin,” of an atom. This is a simplification of a real atomic system, but by tweaking the rules by which nearby spins affect one another, the model can generate surprisingly complex behaviors.

In general, nearby arrows that point in the same direction have low energy, while arrows that point in opposite directions have high energy. If the spins are free to flip, the Ising model’s state will thus evolve towards a lower-energy state of alignment, like a ball rolling downhill. Magnetic materials such as iron end up settling into simple states with their spins aligned in either the all-up or all-down state.

In 1975, the physicists David Sherrington and Scott Kirkpatrick devised a model that could capture the more complicated behavior of spin glasses by modifying the rules of how spins interact. They randomly varied the interaction strengths between spin pairs and allowed each spin to interact with every other spin — not just its nearest neighbors. That change led to a rugged “landscape” of possible energy states. There were peaks and valleys corresponding to higher and lower energy configurations; depending on where the spin glass started off in this landscape, it would end up in a unique valley, or low-energy equilibrium state. That’s quite different from ferromagnets such as iron, which “freeze” into one of two orderly states with all spins aligned, and nonmagnets, whose spins fluctuate randomly and don’t settle down at all. In a spin glass, randomness gets frozen.

The Ising model is very much a toy model. Using it to try to predict anything about real materials is a bit like using a stick figure to plan a surgery. But remarkably, it often works. The Ising model is now a workhorse of statistical mechanics. Variations on its theme can be heard in just about every corner of the study of complex, collective phenomena — including, because of Hopfield, memory.

Spin Memory

A simple view of interacting neurons has a lot in common with an Ising model of magnetic spins. For one thing, neurons are often modeled as basically binary on-off switches; they either fire or they don’t. Spins, likewise, can point either up or down. In addition, a firing neuron can either encourage or discourage the firing of its neighbor. These variable interaction strengths between neurons recall the changeable interaction strengths between spins in a spin glass. “Mathematically, one can replace what were the spins or atoms,”  said Lenka Zdeborová, a physicist and computer scientist at the Swiss Federal Institute of Technology Lausanne. “Other systems can be described using the same toolbox.”

To make his network, Hopfield started with a web of artificial neurons that can be either “on” (firing) or “off” (resting). Each neuron influences every other neuron’s state, and these interactions can be adjusted. The network’s state at any given time is defined by which neurons are firing and which are at rest. You can code these two states in binary: A firing neuron is labeled with a 1 and a resting neuron with a 0. Write out the state of the entire network at any given moment, and you’ve got a string of bits. The network doesn’t “store” information, exactly. It is information.

A woman in a white sweater stands in front of a large architectural feature.

Lenka Zdeborová, a physicist and computer scientist at the Swiss Federal Institute of Technology Lausanne, studies how the physics of matter can help model the behavior of machine learning algorithms. Samuel Rubio for Quanta Magazine

To “teach” the network a pattern, Hopfield sculpted its energy landscape by modifying the strengths of interactions between neurons so that the desired pattern fell at a low-energy steady state. In such a state, the network stops evolving and stabilizes in just one pattern. He found a rule for doing this inspired by neuroscience’s classic “neurons that fire together wire together” rule. He would tune up interactions between neurons that both fire (or both rest) in the desired final state and dial down interactions between mismatched pairs. Once a network is taught a pattern this way, it can reach the pattern again simply by navigating downhill through the network’s energy landscape; it will naturally reach the pattern when it settles into an equilibrium state.

“Hopfield made the connection and said, ‘Look, if we can adapt, tune the exchange couplings in a spin glass, maybe we can shape the equilibrium points so that they can become memories,’” Mézard said.

Hopfield networks can remember multiple memories, each in its own little energy valley. Which valley the network falls into depends on where it begins in its energy landscape. In a network that stores a picture of a cat and a picture of a spaceship, for instance, a starting state that’s vaguely cat-shaped will roll down into the cat valley more often than not. Likewise, starting the network in a state that recalls the geometric forms of a spaceship will usually prompt it to evolve toward the spaceship. That’s what makes Hopfield networks a model of associative memory: Given a corrupted or incomplete version of a memory, a Hopfield network dynamically reconstructs the whole thing.

Old Model, New Ideas

From 1983 to 1985, Hinton and his colleagues built on Hopfield’s work. They found ways to inject randomness into Hopfield networks to create a new type of neural network called a Boltzmann machine. Rather than remember, these networks learn the statistical patterns in training data and spin up new data to match those patterns — an early kind of generative AI. In the 2000s, Hinton was able to use a pared-down version of the Boltzmann machine to finally crack the stubborn problem of training “deep’’ neural networks consisting of multiple layers of neurons.

By 2012, the success of deep neural networks developed by Hinton and other pioneers was impossible to ignore. “It became clear that this is actually working amazingly well and just transforming the whole tech industry,” Zdeborová said. The generative AI models many of us now interact with every day, including large language models such as ChatGPT and image-generation models such as Midjourney, are all deep neural networks. They can trace their success back to curious physicists in the 1970s who refused to let the “useless” properties of spin glasses go unexplained.

Hopfield networks aren’t just part of AI’s past, however. Thanks to new ideas, these old models could be making a comeback.

In 2016, Hopfield and Dmitry Krotov(opens a new tab) of IBM Research realized that Hopfield networks weren’t just one model, but a whole family of models with different memory storage capacities(opens a new tab). Then, in 2020, another team showed that a key part of the transformer architecture, the blueprint of most modern successful AI models, was a member of that extended Hopfield network family(opens a new tab).

Armed with that insight, Krotov and his colleagues recently developed a new deep learning architecture called the energy transformer(opens a new tab). Typical AI architectures are usually found by trial and error. But Krotov thinks energy transformers could be designed more intentionally with a specific energy landscape in mind, like a more complex take on a Hopfield network.

Though Hopfield networks were originally designed to remember, researchers are now exploring how they can be used to create. Image generators such as Midjourney are powered by “diffusion models,” which are themselves inspired by the physics of diffusion. To train them, researchers add noise to the training data — say, pictures of cats — and then teach the model to remove the noise. That’s a lot like what a Hopfield network does, except instead of always landing on the same cat picture, a diffusion model removes “non-cat” noise from a noisy, random starting state to produce a new cat.

A smiling man with crossed arms stands in front of a blackboard.

Dmitry Krotov, a computer scientist at IBM Research, has shown that some of the most advanced AI models in use today follow the same basic principle that Hopfield networks employed from the start. Kim Martineau

It turns out that diffusion models can be understood as a particular kind of modern Hopfield network(opens a new tab), according to Krotov and his colleagues, including Benjamin Hoover(opens a new tab), Yuchen Liang(opens a new tab) and Bao Pham(opens a new tab). And that approach can be used to predict aspects of these networks’ behavior. Their work suggests that feeding a modern Hopfield network more and more data doesn’t just saturate its memory. Instead, the model’s energy landscape gets so rugged that it is more likely to settle on a made-up memory than a real one. It becomes a diffusion model(opens a new tab).

That a simple change in quantity — in this case, the amount of training data — can trigger an unexpected change in quality isn’t anything new for physicists. As the condensed matter physicist Philip Anderson wrote back in 1972, “more is different(opens a new tab).” In collective systems, simply scaling up networks of interactions between parts can add up to surprising new behaviors. “The fact that [a neural network] works is an emergent property,” Mézard said.

Emergence in a deep learning architecture — or a brain — is as captivating as it is puzzling; there’s no universal theory of emergence. Perhaps statistical physics, which provided the first tools for understanding collective behavior, will be the key not just to using but also to understanding the inscrutable machine intelligences changing our world.

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Long live the aeonophiles!

Mike's Notes

Fascinating extreme example of thermodynamics of life pushing systems out of equilibrium.

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Last Updated

7/01/2026

Long live the aeonophiles!

By: Karen G Lloydis
Aeon: 18/12/2025

Karen G Lloydis a microbial biogeochemist, focused on discovering and describing life inside Earth’s crust. She is the Wrigley professor of earth sciences, and marine and environmental biology, at the University of Southern California, and the author of Intraterrestrials: Discovering the Strangest Life on Earth (2025)..

The discovery of organisms that have been alive for many thousands of years requires a revolution in how we understand life

Promethearchaeum syntrophicum, strain MK-D1, digitally coloured yellow, strain MK-D1. Courtesy Hiroyuki Imachi, Masaru K Nobu, and JAMSTEC

If you had to nominate the slowest, longest-living organisms on Earth, what would you picture? Among the vertebrates, some people might think of tortoises, whales or perhaps more obscure creatures like the Greenland shark, which can live for centuries. Others might imagine coral colonies, or perhaps an ancient tree: there are oaks in England that could be more than 1,000 years old, whereas in California, a few Bristlecone pines have been around for millennia, dating to around the formation of ancient Egypt.

But how about bacteria? Microbes, at the outset, may seem unsuitable candidates for the title of longest-living organism, since we’re so used to experiencing how they grow (and die) so quickly. If I wake up with a tickle in my throat, I get a feeling of dread because I know that, by the evening, I’m going to have a full-blown case of strep throat – the bacterial cells dividing like wildfire in my body. Some bacteria, like E coli, can double every 20 minutes. They can be killed off just as quickly, when faced with antibiotics or disinfectant.

However, E coli and other fast-replicating microbes don’t live in subsurface environments, where the conditions are ripe for a far more languid pace. In recent years, my fellow biologists and I have assembled evidence suggesting that the microbial world deep beneath the ground may be far slower than we think – perhaps remaining metabolically active for millions of years. I call these organisms aeonophiles – and by living as long as they do, they are rewriting the rules of biology itself. What are they doing down there? It turns out they might be waiting – waiting to return to the surface. But unlike cicadas or hibernating bears, these living things are holding on for events that might take centuries, millennia or even geological eras to arrive.

The steps that led to our discovery of this strange life can be traced back to advances in DNA technology in the 1980s. For the first time, biologists could sequence the DNA from microbes directly, in any environment, without first growing these microbes in a laboratory. In 1998, Philip Hugenholtz, Norman Pace and colleagues at the University of California, Berkeley used this new technology to discover 12 deep branches on the tree of life in a Yellowstone National Park hot spring. The next year, Costantino Vetriani and Anna-Louise Reysenbach at Rutgers University in New Jersey and colleagues discovered even more new groups in deep-sea mud. None of these organisms had parallels in the known world of microbiology; they were entirely new to science. This new DNA-sequencing technology took off like wildfire, and scientists around the world, including myself as a young researcher, started discovering new types of life all over the place.

What we’ve discovered since has changed our conception of what life is like on Earth. Before these discoveries, it was unknown whether life can exist inside Earth’s crust. We now know that there is life under our feet, way under our feet. These subsurface-dwelling single-celled organisms are collectively called intraterrestrials, due to their parallels with the mystery and novelty of extraterrestrials. But, unlike space aliens, we know for certain that intraterrestrials exist.

The author and research team drilling in Svalbard, northern Norway. Photo by Jon Leithe

Intraterrestrials comprise a vast still-mysterious ecosystem in Earth’s crust containing as many (or more) living microbial cells than are on Earth’s surface. We know this from scientists such as myself going out on scientific drilling ships that sample deep marine sediments or drilling deep into continental crust, laboriously counting the number of cells we find there, and extrapolating out to the rest of the world. The deepest we’ve found intraterrestrials thus far is about 5 km down. That’s deep enough for these intraterrestrials to never see the light of day, nor do they receive much food input from the surface world. Their world is mostly composed of tiny spaces between sediment grains or miniscule fractures in rocks. Rocks seem solid to us, but to very tiny life, rocks appear porous, with lots of places to live. From the few growing cultures that we have of these organisms, we know that many of them are tiny, and some have long appendages, such as the Asgard archaea and the Altiarchaeales, which may help them to hang on to their rock or sediment housing.

The intraterrestrial Lokiarchaeum ossiferum (‘skeleton-carrying’) is a member of the Asgard phylum, so named after Norse mythology because some of the first examples were found near the hydrothermal vent field Loki’s Castle in the Arctic Ocean. Its skeleton is probably a hallmark of Asgard archaea. Courtesy Rodrigues-Oliveira et al

Although deep geological sources of food and nutrition (often in the form of deep gases and hydrothermal fluids) can support life in some parts of the subsurface, thousands of years or longer might pass with little to no food inputs. This extreme scarcity has extraordinary implications for life. In much of this vast biosphere, there’s not enough energy to drive microbial cell division at anything like a normal rate. Before discovering these organisms, we had a narrower view of how much energy life requires and how long a single organism can stay alive.

But how long can a cell live like this? Theoretically, there’s no limit

The intraterrestrials are showing us that we were wrong; life can exist on orders of magnitude lower power and sustain their living cells for orders of magnitude more years than previously thought possible. This means that many of these living beings bump up against the energetic limits of life, and in the process seem to have cracked the code for near-immortality. These types of intraterrestrials have such extremely long lifespans that we need a new term to describe the type of extremophiles that they are. The word aeonophiles fits, since they like (-phile) long periods of time (aeon-). (If they could read, I’m sure they’d be die-hard subscribers to Aeon magazine too.)

Members of the Asgard archaea (left) were first collected from the Loki’s castle hydrothermal vent in the Arctic ocean in 2008. They include Lokiarchaeota, Thorarchaeia, Odinarchaeia and Heimdallarchaeia. Courtesy Wikipedia

Many of these aeonophile types of intraterrestrials survive on thousands of times lower power than the amount required to maintain a next-to-dead non-growing culture of normal bacteria. This means that even though the deep subseafloor is one of the largest ecosystems on Earth, hardly any of the microbes that live there are actually growing. They have 0.00001 per cent of the power that supports all other known types of cell growth on Earth, so even performing a single cell division is impossible.

Candidatus Altiarchaeum hamiconexum cells within their biofilm. Cells appear fluffy due to their extracellular polymeric matrix and cell-surface appendages (‘hami’). Courtesy Probst and Moissl-Eichinger

Aeonophiles funnel all the meagre power that’s available to them into replacing broken body parts, not dividing into two new daughter cells. So, long-term metabolically active dormancy is the only option. But how long can a cell live like this? Theoretically, there’s no limit if it slowly replaces its broken bits over time. This brings up a real conundrum. On the one hand, if anything like immortality were common, then we would be surrounded by beings that were born sometime around the origin of life, which is not the case. But on the other hand, these aeonophiles seem like they could live forever.

Luckily, there’s a lot of temporal real estate between a 20-minute doubling time and immortality. What if the aeonophiles live for 500,000 years or a million years? The oldest sediments that have not yet metamorphosed into rock are about 100 million years old, so this is an upper limit on the age of an individual cell in marine sediments. Older rocks could have older cells, as long as the rock has not been buried to sterilising temperatures over the course of its journey around our tectonically active planet.

To us, they look like they’re doing nothing. As an analogy, over a geological timescale, the California coastline is a constantly churning mass of rocks, but on our human timescale, it is stable enough to build a house on, which can be passed on to our grandchildren. These houses must be sound enough to withstand the occasional earthquake, but they will not survive the reorientations of land as they are spun, submerged, and exhumed over the course of a few million years. To think like an aeonophile, we have to grapple with some incomprehensible timescales.

How did these organisms evolve to stop growing for thousands of years? To answer this, first we might consider what they would experience in their lifetimes. They wouldn’t be concerned about the length of a day. They’re buried so deep that they can’t detect the Sun anyway. They probably wouldn’t even notice the seasons. However, they might care about other, and longer, geological rhythms: the opening and closing of oceanic basins through plate tectonics, the formation and subsidence of new island chains, or new fluid flows brought on by slow cracks opening in Earth’s crust. The biology I was taught in school considered these events to be evolutionary drivers for a species, not an individual. For instance, Charles Darwin’s finches evolved new beak shapes because they had been isolated on an archipelago.

We know that animals adapt to the daily or yearly rhythms of their environment, but it seems ridiculous to argue that any creature could anticipate tectonic cycles. It may, however, be reasonable for the aeonophiles. An individual that lives for a million years might be evolutionarily predisposed to count on something as slow as island subsidence in the same way that we are evolutionarily predisposed to wait for the Sun to rise tomorrow. To fully understand aeonophiles, we may have to rethink what qualifies as an evolutionary cue.

You may also wonder: how does evolution work for an organism that seemingly never produces offspring? According to Darwin’s theory of natural selection, these cells must grow and make new progeny to evolve. But how? I don’t think Darwin had nongrowth in mind when he described survival of the fittest. The answer to the question at the beginning of this paragraph lies in the word ‘seemingly’. They’re not producing offspring in the places that we normally look for them, but there has to be a place or time when they do make progeny.

We need to jailbreak our brains from our implicit assumptions about lifespan

Luckily, we have a good model in short-term seasonal dormancy, which various surface organisms enter for months before emerging to reproduce. Here dormancy during winter has an evolutionary advantage: by avoiding harsh, cold conditions, dormant organisms get the chance to have larger populations than non-dormant organisms in the spring. This provides a head start, allowing them to pass along their dormancy genes to a larger population of progeny. Textbook Darwinian natural selection.

To imagine dormancy that lasts for thousands of years, we have to think of an event that aeonophiles could possibly be waiting for. If we encounter a dormant microbe in soil in winter, we can presume that it’s holding out for summer. What is the equivalent situation for a deeply buried marine sediment organism waiting for thousands to millions of years?

Before we answer that question, let’s first consider a thought experiment to jailbreak our brains from our implicit assumptions about lifespan. Imagine human lives lasted only 24 hours. You’d be born at midnight, rebel against your parents at breakfast, settle down and have babies just before lunch, and pick up fishing as a retirement hobby around dinnertime. By midnight, your loved ones, who themselves were born only a few hours ago, would huddle close and hold your hand as you’d pass away peacefully at the ripe old age of a day. If everyone did that, hundreds of human generations would come and go within a single winter. Throughout that time span, which would represent a significant chunk of human history, the deciduous trees would remain brown and lifeless. The permanent deadness of trees would be taken as an undisputed fact, and scientists like me would probably apply for grants to understand whether or not trees are alive, given that they don’t seem to grow or make progeny. Of course, if you stretched back far enough, humans would have been present for the fall or even summer, but that might have been so many generations back that a stable form of writing had yet to be invented. We 100-year-lifespan humans know that trees are just waiting to take advantage of the summer sun. But the day-lifespan humans would be stumped.

When we think about life in the subsurface, are we like day-lifespan humans contemplating a tree? Are long-lived aeonophiles waiting for wake-up cues we don’t recognise because our lives are too short to see them? What is even the point of living for hundreds of thousands of years anyway? There must be some reason these aeonophiles stick around so long.

Seasonal cycles are way too fast. The only things slow enough are geological processes. For instance, island subsidence, floods or droughts often occur on 100- to 1,000-year cycles. Submarine landslides, earthquakes, tsunamis and volcanic eruptions might shift materials around on even longer timescales, exposing aeonophiles to new food sources that coax them out of dormancy after hundreds of thousands of years. It seems odd to say that a microbe is adapted to wait for something as infrequent as a volcanic eruption, but you can rely on them to happen, as long as you’ve got time to wait.

The author taking samples from a gassy deep subsurface spring. Photo by Jacopo Pasotti

If we really let our imagination run wild, individual microbes might be adapted to events with even longer periods, like interglacial cycles, which shift every 30,000 years or so. Or the slow movement of tectonic plates. As a new seafloor pops up in midocean ridges, the existing seafloor is constantly pushed from the middle of the ocean, until it eventually jams into a continent in the slowest-motion train wreck ever.

Some marine sediments – and the aeonophiles that live in them – will get dragged down on the subducting plate and destroyed. Even for extremophiles, the mantle is an evolutionary dead end. However, some seafloor sediments survive these collisions – rather than subducting, they are scraped off and shoved onto a continental plate. Could all this piling up, faulting and burbling up to the surface be what the aeonophiles are waiting for? Is this an aeonophiles’ version of summer?

Living on human timescales, it’s hard to say for certain. However, we do know that the aeonophiles are showing us that some Earthlings can live for many thousands of years or longer. In my opinion, these are fundamental discoveries about the nature of life on Earth. In fact, I believe that the discovery of ultra-long-lived creatures is up there with the discovery of hyperthermophiles, microbes that thrive at temperatures above the boiling point of water. When hyperthermophiles were discovered in the 1960s, it blew open our understanding of where life might exist in the Universe. I foresee a similar seismic shift from the discovery of aeonophiles.

The existence of such organisms greatly expands the window of time during which we can look for biomarkers in the cosmos. In fact, they raise the troubling possibility that, if life on other planets is extremely slow, it might also be nearly impossible to detect. As we examine other planetary bodies, we look for changes that might signify that something is alive and doing work on that planet. But if that life is extremely slow, we may not realise we’re looking at it because it doesn’t change much while we’re observing it. It is not impossible that beneath the surface of Mars or Europa, things are alive and functioning much more slowly than the life that we’re used to.

By living as slow as they do, aeonophiles prompt us to consider how we define life and non-life. How can we scientifically distinguish between the two? For answers, I believe we need to think of life, in its most basic function, as an energetic phenomenon. And to do that, it’s necessary to look at it through the lens of thermodynamics.

In their book Into the Cool (2005), the scientist Eric Schneider and the writer Dorion Sagan suggest that life and non-life exist in a continuous line. At one end of the spectrum are non-living systems at energetic equilibrium; and at the other end are living systems continuously creating further energetic potential to make sure they stay well out of equilibrium. So, one way to define life would be that it is good at creating energetic opportunities to push things far out of equilibrium.

If we’re talking about energy, we have to talk about the second law of thermodynamics, which is driving it all. The law says that, in a closed system, entropy – roughly the number of ways a system can be arranged – tends to increase overall. As entropy rises, less of a system’s energy can be used to do work. We’ve long known that life is good at producing entropy; just look at the heat radiating from our bodies and even whole cities. Non-life can produce entropy too, though, so how does this help us tell the difference?

Aeonophiles show us that life has more creative ways of producing entropy than we thought possible

According to non-equilibrium thermodynamics, it is life’s propensity for continually pushing systems back out of equilibrium that sets it apart from non-life. Once things are well out of equilibrium, entropy can be produced in the race to regain equilibrium. Crucially, life seems to be better than non-life at creating new systems in which entropy can be produced. An eddy in a stream is not alive, but for a short amount of time, the water molecules become a whirlpool to maximise entropy production through energy dissipation from the system. Life does this too, but it’s more sophisticated and effective in its approach. Non-life makes whirlpools, but life dams the river to go whitewater rafting on those whirlpools. Non-living asphalt heats up when sunlight hits it, creating a bit of entropy, but a rainforest places leaves at different levels capturing every last photon of light and turning it into biomass that will support an entire ecosystem of animals and fungi that produce more entropy per ray of light than asphalt ever could.

What the aeonophiles do for us is to show us that life has more creative ways of producing entropy than we previously thought possible. If the point of life is to create more entropy by spreading out its production over increasingly large scales of space and time, then this task seems tailor-made for aeonophiles. Simply by living for aeons, they may stretch out entropy production for longer timescales, maximising its final tally for the second law. Finding such an outlandish new way to create opportunities for entropy production supports the idea that this opportunity for entropy creation is, itself, the why of life. In short, life happens because the second law of thermodynamics demands it. And the aeonophiles, by their very long-lived existence, drive that point home for us.

Even though they may seem extraordinary to us, individuals that live for thousands of years or longer may be ordinary on Earth. In addition to showing us that life is far more diverse than we thought, and can use energy and time in ways we would never have dreamed up on our own, aeonophiles might be key to understanding why life exists. They’re showing us new ways for life to conduct its delicate dance with energy and entropy. As we continue to learn more about these strange intraterrestrials, and the aeonophiles among them, I believe we will continue smashing our preconceived notions of how life itself is supposed to work, one barely breathing cell at a time.

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What is Thermodynamic Computing and how does it help AI development?!

Mike's Notes

The reasoning behind this chip is the same as behind Pipi 9. Pipi 9 runs on noise.

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17/06/2025

What is Thermodynamic Computing and how does it help AI development?!

By: Laszlo Fazekas
Medium: 05/04/2024

The foundation of modern computing is the transistor, a miniature electronic switch from which logic gates can be constructed, creating complex digital circuits like CPUs or GPUs. With the advancement of technology, transistors have become progressively smaller. According to Moore’s Law, the number of transistors in integrated circuits approximately doubles every 2 years. This exponential growth has enabled the exponential development of computing technology. However, there is a limit to how much the size of transistors can be reduced; we will soon reach a threshold below which transistors cannot function. Moreover, the advancement of AI has made the need for increased computational capacity more critical than ever before.


Transistor count per year from https://en.wikipedia.org/wiki/Moore%27s_law

The fundamental issue is that nature is stochastic (unpredictable). And here, I’m not just referring to quantum mechanical effects. Environmental influences, thermal noise, and other disruptive factors must be considered when designing a circuit. For a transistor, the expectation is that it operates deterministically (predictably). If I run an algorithm 100 times in succession, I must get the same result every time. Currently, transistors are large enough that these factors do not interfere with their operation, but as their size is reduced, these issues will become increasingly relevant. So, what direction can technology take from here? The “usual” answer: quantum computers.

An image of a quantum computer from https://www.flickr.com/photos/ibm_research_zurich/50252942522

In fact, with quantum computers, we encounter the same issue: the need to eliminate environmental effects and thermal noise. This is why quantum computers must be cooled to temperatures near absolute zero. These extreme conditions preclude quantum processors from replacing today’s CPUs. But what could be the solution? It appears that to move forward, we must abandon our deterministic computers and embrace the stochastic nature of the world. This idea is not new. It’s several billion years old.

Educational videos often depict the functioning of cells as little factories, where everything operates with the precision of clockwork. Enzymes, like tiny robots, cut up DNA, to which amino acids attach, leading to the production of proteins. These proteins neatly interlock and, during cell division, separate from the old cell to form a new one. However, this is a highly simplified model. In reality, particles move entirely at random, and when the right components happen to come together, they bind. While human-made structures operate under strict rules, here processes form spontaneously under the compelling influence of physical and chemical laws. Of course, from a bird’s-eye view, the system might appear to function with the precision of a clockwork.

DNA replication from https://en.wikipedia.org/wiki/DNA

A very simple example is when we mix cold water with hot water. It would be impossible to track the random motion of each particle. Some particles move faster, while others move slower. Occasionally, particles collide and exchange energy. The system is entirely chaotic, requiring immense computational capacity to simulate. Despite this, we can accurately predict that after a short period, the water will reach a uniform temperature. This is also a simple self-organizing system that is very complex at the particle level, yet entirely predictable due to the laws of physics and the rules of statistics. Similarly, cell division becomes predictable as a result of complex chemical processes and random motion. Of course, errors can occur. The DNA may not copy correctly, mutations may develop, or other errors may occur. That’s why the system is highly redundant. Several processes will destroy the cell in case of an error (apoptosis), thus preventing faulty units from causing problems (or only very rarely, which is how diseases like cancer can develop).

The energy consumption of a transistor can be comparable to the energy consumption of a cell, even though a cell is orders of magnitude more complex. Imagine the complex calculations we could perform with such low consumption if we carried them out in an analog manner, exploiting the laws of nature.

In biology, thermal noise is not only not a problem, but it is necessary. Below certain temperatures, biological systems are incapable of functioning. It is the random motion induced by heat that powers them.

The foundation of thermodynamic computing is similar. Instead of trying to eliminate the stochastic nature of physical processes, we utilize it. But what can be done with a computer whose operation is non-deterministic?

In fact, in the field of machine learning, there are many random components. For example, in the case of a neural network, the initial weights are randomly initialized. The dropout layer, which eliminates overfitting, also randomly discards inputs. But at a higher level, for instance, diffusion models also use random noise for their operation. In the case of Midjourney, for example, the model was trained to generate images from random noise, taking into account the given instructions.

Here, a bit of noise is added to the image at every step until the entire image becomes noise. The neural network is then trained to reverse this process, that is, to generate an image from noise based on the given text. If the system is trained with enough images and text, it will be capable of generating images from random noise based on text. This is how Midjourney operates.


Steps of Stable Diffusion from https://en.wikipedia.org/wiki/Stable_Diffusion

In current systems, we eliminate the random thermal noise to obtain deterministic transistors, and then on these deterministic transistors, we simulate randomness, which is necessary for the operation of neural networks. Instead of simulation, why not leverage nature’s randomness? The idea is similar to that of any analog computer. Instead of digitally simulating a given process, we should utilize the opportunities provided by nature and run it in an analog manner.

The startup Extrophic is working on the development of such a chip. Like Google, the company was founded by two guys: Guillaume Verdon and Trevor McCourt. Both worked in the field of quantum computing before founding the company, and their chip lies somewhere halfway between traditional integrated circuits and quantum computers.

Extropic’s circuit works in an analog manner. The starting state is completely random, normally distributed thermal noise. Through programming the circuit, this noise can be modified within each component. Instead of transistors, analog weights take their place, which are noisy, but the outcome can be determined through statistical analysis of the output. The guys call this probabilistic computing.

Microscope image of an Extropic chip from https://www.extropic.ai/future

These analog circuits are much faster and consume much less energy, and since the thermal noise is not only non-disruptive but an essential component of the operation, they do not require the special conditions needed by quantum computers. The chips can be manufactured with existing production technology, so they could enter the commercial market within a few years.

As we have seen from the above, Extropic’s technology is very promising. However, what personally piqued my interest is that it is more biologically plausible. Of course, I don’t think that the neurons in artificial neural networks have anything to do with human brain neurons. These are two very different systems. However, the human brain does not learn through gradient descent. Biological learning is something entirely different, and randomness certainly plays a significant role in it.

As I mentioned, in biology and nature, everything operates randomly. What we see as deterministic at a high level is just what statistically stands out from many random events. This is how, for example, many living beings (including us humans) came to be through completely random evolution yet are built with almost engineering precision. I suspect that the human brain operates in a similar way to evolution. A multitude of random events within a suitably directed system, which we perceive from the outside as consistent thinking. This is why genetic algorithms were so intriguing to me, and now I see the same principle in Extropic’s chip.

If you are interested, check the company homepage or this interview with the founder guys.

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Thermodynamics in plain sight

Mike's Notes

I figured out how to use thermodynamics to describe Pipi's state. The solution was hiding in plain sight. I credit Terrence Deacon's work and James "Jim" Miller for introducing me to Terrence's writings.

I also had to add a small process/state engine I built in 2018 and integrate some Markov.

The root Pipi system (sys) has now been updated.

And yes, there are feedback loops.

As part of refactoring Pipi 8 to Pipi 9, I had to run many systems manually to test them. To get ready for production, I'm slowly checking and finishing them to switch them over to complete automation.

The main problems I have discovered are;

  • Silly minor typos and inconsistent naming of variables.
  • Manual overrides of automated results, requiring tweaked parameters.
  • The odd thing that was never finished and forgotten about, like the problem just solved.
I should have a 48U rack cabinet to house Pipi in about a week.

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15/04/2025

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Thermodynamics at the root of Pipi

Mike's Notes

This week, I had a hunch that I needed to use thermodynamics to describe the state of Pipi. You can read about this adventure in this latest blog post. Instead of answers, I have lots of questions. There will be experiments. So it's off into the deep end again.

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12/04/2025

Thermodynamics at the root of Pipi

By: Mike Peters
On a Sandy Beach: 12/03/2025

Mike is the inventor and architect of Pipi and the founder of Ajabbi.

The root system of Pipi (sys) gives each copy of Pipi a unique name. The names are taken from a list of the old gods of early human history. Loki, Zeus, etc. Each name stays with that Pipi regardless of version numbering. The System deals with the growth, replication and death of each Pipi. It will also enable the Pipis to talk to each other.

Each unique Pipi system consists of hundreds of multiple nested subsystems, which can be combined in various combinations to give different emergent properties.

It is said that the whole is more than the sum of the parts. Prof. Terrence Deacon believes that with life, the whole is less than the sum of the parts due to constraints (I think Terrence is correct about many things). That is the version I am playing with here.

So far, I am figuring out at a high level which bits constrain others and clarifying the self-organisation that occurs where and when—basically, I am building a working data model.

I suspect I will get deeply into Shannon information theory and Boltzmann entropy.

Will this act as a feedback loop? Probably.

Hopefully, I won't end up in some rabbit hole.

I discovered this issue a few days ago while methodically checking, testing and tidying up a long list of systems. Most of them were good to go, but I found something I had missed entirely.

It's a bit of a brain teaser, and I am making many drawings on paper. I want to understand the problem more clearly and then find a solution.

Time for more coffee.

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Why Everything in the Universe Turns More Complex

Mike's Notes

Philip Ball has written another article for Quanta Magazine that suggests complexity increases over time.

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07/04/2025

Why Everything in the Universe Turns More Complex

By: Philip Ball
Quanta Magazine: 2/04/2025

Philip Ball is a science writer and author based in London who contributes frequently to Nature, New Scientist, Prospect, Nautilus and The Atlantic, among other publications. His books include Bright Earth, Invisible and most recently, The Water Kingdom.

A new suggestion that complexity increases over time, not just in living organisms but in the nonliving world, promises to rewrite notions of time and evolution.

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(opens a new tab), formulated by the mineralogist Robert Hazen and the astrobiologist Michael Wong of the Carnegie Institution in Washington, D.C., 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.”


Michael Wong, an astrobiologist at the Carnegie Institution in Washington, D.C.

Katherine Cain/Carnegie Science

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?

Making Meaning

The story begins in 2003, when the biologist Jack Szostak published a short article(opens a new tab) 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).

Jack Szostak proposed a way to quantify information in biological systems.

HHMI

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.

Selected for Function

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(opens a new tab) 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.


Robert Hazen, a mineralogist at the Carnegie Institution in Washington, D.C.

Courtesy of Robert Hazen

“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.

Information itself might be a vital parameter of the cosmos, similar to mass, charge and energy.

Michael Wong, Carnegie Institution

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(opens a new tab) 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 Biosphere Creates Its Own Possibilities

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.”

An increase in complexity provides the future potential to find new strategies unavailable to simpler organisms.

Marcus Heisler, University of Sydney

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(opens a new tab) 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.

Back to the Bench

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(opens a new tab) 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(opens a new tab) 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.

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