320 | Solo: Complexity and the Universe
What this covers
Sean Carroll traces how structure and organization emerge between the universe's simple, hot beginning and its simple, cold end. The episode lays out the physics of complexogenesis — the stages by which complexity arises, peaks, and fades — without relying on new physical laws. The central insight is that subsystems exploit Available Information as Resource, the gap between maximum possible and actual entropy, to build increasingly sophisticated forms of order. Carroll demonstrates this progression through concrete examples: how cream mixing in coffee visualizes the rise and fall of complexity via image compression, why life and cognition are fundamentally ways of using low-entropy resources to maintain non-equilibrium stability, and how the emergence of the first eyes when fish moved onto land represents a leap in how organisms could extract and act on information about their world.
The conversation spans the foundational tensions that make complexity possible. Carroll argues that [Competition of Forces](concept:Competition of Forces) — gravity pulling inward balanced against pressure pushing outward — is essential; gravity alone cannot build genuinely complex structures. He contrasts his view with Stephen Wolfram's, explaining how complexity in the classical picture is encoded in initial conditions rather than generated by dynamical rules. A substantial portion examines how entropy and information relate differently in communication theory versus statistical mechanics, and why Kolmogorov Complexity remains uncomputable. Carroll revisits Erwin Schrodinger's insight about heredity requiring an "aperiodic crystal," the role of photons in enabling chemistry, and how living systems effectively invent future boundary conditions — goal states — that appear nowhere in the microscopic laws. The episode also addresses the thermodynamics of habitability, the timeline of cosmic star formation, and why the smooth early universe represented low entropy once gravity's role is understood.
Carroll argues that complexity in the universe (complexogenesis) arises in stages between a simple low-entropy beginning and a simple high-entropy end, driven not by new laws but by subsystems finding increasingly sophisticated ways to exploit 'available information' — the gap between maximum and actual entropy.
- Entropy increases monotonically while complexity rises then falls, peaking at intermediate entropy, as illustrated by cream mixing into coffee.
- Complexity grows via competing forces (e.g., gravity vs. pressure) and long-range coherent dynamics, not from a single attractive force.
- Life and cognition are increasingly sophisticated ways of using the available-information resource to maintain non-equilibrium stability and pursue future goals.
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The simple-minded version of complexity can be measured literally by image compression: a photo of a half-mixed cream-and-coffee configuration will have a larger saved file size than photos of the fully separated or fully mixed states, because the ordered and uniform states admit more efficient compression while the intermediate state does not.
“the image that you save on your phone of the medium entropy configuration where they're half mixed together will have a larger file size than the files of the simple configurations”
Computer scientists and physicists give opposite answers about the relation between entropy and information: in Shannon's communication theory, high entropy (uniform probability distribution) means high information because each symbol is maximally surprising, whereas in Boltzmann's statistical mechanics, low entropy means high information because specifying a low-entropy macrostate pins down the microstate far more tightly.
“the communication theorists or information theorists think that information and entropy are in the same direction. Physicists, statistical mechanics physicists anyway, thinking in Boltzmann's way, think that information and entropy are opposite to each other.”
The space of possible genomes is far too large to search comprehensively: even if all 10^88 particles in the observable universe were turned into DNA base pairs and reshuffled a billion times per second for the age of the universe, one could only exhaustively check strands of about 180 base pairs, whereas the human genome is three billion base pairs, which is why natural selection must proceed by random mutation and culling rather than comprehensive search.
“The answer is about 180, about 180 base pairs in a DNA molecule. We could, if we had the entire universe devoted to this program... The human genome is three billion base pairs long.”
The emergence of complex biological structures is fully compatible with the second law of thermodynamics because the Earth is not a closed system: it receives low-entropy visible photons from the sun and radiates back roughly 20 higher-entropy infrared photons, so local decreases in entropy are parasitic on a net global increase.
“For every one photon we get from the sun, which is typically a visible light wavelength photon, we give back 20 photons to the universe, 20 infrared wavelength light photons, and that's 20 times the entropy”
Schrodinger reasoned that heredity requires atoms arranged to store information stably: a gas or fluid is too random and a regular crystal carries no new information (each atom predicts the next), so genetic material must be an 'aperiodic crystal' where successive units are not predictable from the current one — a prediction realized by DNA.
“it must have a configuration of atoms inside that contains information in a relatively stable form. So it can't be a real crystal because real crystals are just predictable and no information, but it also can't be a gas or a fluid. It has to be what Schrodinger called an aperiodic crystal”
In a closed system entropy increases monotonically while complexity starts low, rises to a peak at intermediate (medium-entropy) configurations, and then declines back to low complexity, because both the perfectly ordered and the perfectly mixed states have short macroscopic descriptions while intermediate states require much more information to specify.
“you start with low entropy and entropy simply increases, but you start simple and complexity can grow and then decrease”
Like entropy, complexity is a coarse-grained macroscopic phenomenon invisible to Laplace's demon: at the microstate level the information needed to specify the system is identical whether it is mixed or unmixed, so complexity only exists relative to a macroscopic coarse-graining that ignores microscopic specifics.
“Laplace's demon has complete information, so it doesn't need to talk that language. Complexity is a similar thing.”
Truly interesting complexity requires an interplay between an attractive force like gravity and a repulsive force like pressure; gravity alone (a 'dumb' long-range force that only accumulates matter) can raise apparent complexity slightly but cannot build genuinely complex structures, which only emerge when gravity's pull is balanced by forces such as material solidity or thermal/nuclear pressure.
“it's this interplay, this competition between two forces that allows complexity to really become interesting. If all you had in the world was gravity, you wouldn't make very, very complex, interesting structures”
Apparent complexity, defined via coarse-graining then compression, is low both for a perfectly ordered string (e.g., a billion zeros, trivially compressible) and for a truly random string (whose coarse-grained averages are uniform), but high for an intermediate string that has structure yet is not fully ordered, because only such structure survives coarse-graining while resisting full compression.
“The apparent complexity of a random number is low. The apparent complexity of a string of a billion zeros is low. The apparent complexity of an intermediate number that has some structure but is not completely random or completely ordered will be high.”
The smoothness of the early universe represents a low-entropy state rather than a high-entropy thermal equilibrium because gravity was strong, and when gravity is strong there is far more room to increase entropy by forming black holes and inhomogeneities than a smooth configuration uses.
“that smoothness of the early universe is actually low entropy because gravity was really strong. And there's much more room to make black holes and inhomogeneities in the configuration of matter when gravity is strong than when gravity is weak”
When fish moved onto land, the long attenuation length of light in air (versus meters in water) opened a new mode of information use: instead of merely seeing and reacting to nearby threats, land animals could see far-off things and plan, contemplating hypothetical future scenarios — a more sophisticated use of the information resource that costs energy but confers survival advantage.
“When you're a fish, the only evolutionarily useful mode of information processing is you see something and you react to it. When you're on land, you can see something and you can think about it. You can plan.”
In the classical approximation, the complexity that appears at late times is already inherent in the universe's initial conditions and is merely brought to life by deterministic laws of physics — a picture sharply different from Wolfram's cellular-automaton view in which complexity is generated by the dynamical update rule rather than the initial state.
“There the complexity was not inherent in the initial condition. It's inherent in the rules.”
A living being is distinguished from non-living matter by its ability to exploit its low-entropy, information-rich environment to persist — Schrodinger's quip that life keeps moving long after it should have stopped — and bacterial chemotaxis confirms this, since bacteria carry interior proteins holding mutual information with the external nutrient gradient rather than merely responding mindlessly to it.
“there are proteins inside the bacteria that basically keep track of the direction in which the nutrients are bigger”
Kolmogorov complexity — the length of the shortest program that outputs a given string — is formally uncomputable because cycling through candidate programs runs into Turing's halting problem (one cannot generally tell whether a long-running program will ever halt), though it remains estimable in practice via compression algorithms like gzip.
“Komolgorov complexity is uncomputable for cool computer science reasons that go back to the halting problem of Alan Turing”
In inflationary cosmology, wave-function branching via decoherence is necessary for complexity: the initial inflationary quantum state is essentially the featureless vacuum, and the density fluctuations that later seed galaxies arise as one particular branch when the universe effectively observes itself, making the cosmic microwave background map one realization of a random quantum process.
“branching of the wave function is 100% necessary for the story of complexity that we're telling right now”
We are past the peak of cosmic star formation: the peak star-formation rate occurred about four billion years after the Big Bang, and most stars that will ever form have already formed, placing us in a star-rich but slowing-down era.
“The peak star formation rate was about four billion years after the Big Bang. Most of the stars that will be ever formed in the history of our universe have already been formed.”
Szathmary and Maynard Smith's 'Major Evolutionary Transitions' identifies moments creating new modes of living (prokaryotes to eukaryotes, single-celled to multicellular, up to language), and the common thread uniting them is the use and transmission of information, even if the original identification was based on qualitative judgment rather than rigorous quantification.
“The common thread that they identified was the use of information. Really the transmission of information”
The entropy of our co-moving volume of the universe increases over time through identifiable stages: roughly 10^10 during inflation, ~10^88 after reheating into a gas of ~10^88 particles, ~10^103 once supermassive black holes form, and an estimated ~10^122 in the final de Sitter state set by the cosmological horizon area.
“the entropy goes up over time from 10 to the 10, to 10 to the 88, to 10 to the 103, to 10 to the 122”
Complexogenesis should be understood as subsystems finding increasingly sophisticated ways to use 'available information' — defined as the difference between the maximum possible entropy and the actual entropy — which is the information-theoretic generalization of free energy and is gradually used up as entropy rises toward equilibrium.
“let's define the available information as the difference between the maximum entropy the state could be in, in this Boltzmannian sense, and the actual entropy that it has right now”
The existence of photons (or something very much like them) is crucial to complexity because when atoms bond into molecules the collision is inelastic and does not conserve kinetic energy; massless photons can carry away any arbitrary amount of energy, enabling chemistry and thus the analog-to-digital transition in which freely-moving particles become ordered, information-storing polymers.
“photons, which are particles that can carry away any amount of energy you want, play an absolutely crucial role in this analog to digital transition”
The universe is governed by laws plus a past boundary condition (the low-entropy past hypothesis) with no future boundary condition, yet living systems effectively invent a future boundary condition for themselves — a goal state they work toward and adapt their behavior to reach — which appears nowhere in the microscopic laws and marks a key stage of complexogenesis.
“these individual subsystems of the universe invent a future boundary condition for themselves, some state in the future that they would like to reach. That is nowhere to be found in the microscopic laws of physics”
Whether complexity actually develops as a system moves from low to high entropy depends on the dynamics: in the coffee-automaton simulations, a nearest-neighbor swapping rule never produces complexity, whereas a 'tectonic' model with large-scale coherent block motions does, suggesting that long-range forces or long-range coherence (like gravity in the universe) are necessary for complexity to arise.
“The tectonic model, where there are these coherent motions, large-scale agreement between different pixels about what they're doing, that's when you get complexity.”
One can construct a tongue-in-cheek anthropic argument that gauge symmetry must exist: intelligent observers are complex information-processing systems that can only form by dissipating energy, which requires low-mass particles that nonetheless interact strongly enough to carry energy away; the only such particles are gauge bosons (like photons), whose masslessness is permitted by gauge symmetry, so the existence of observers presupposes gauge symmetry.
“the only low mass particles that interact noticeably with other particles are gauge bosons... And therefore, the existence of intelligent observers relies on the existence of gauge symmetries.”
Planets and stars are both long-lived but for fundamentally different reasons: a planet is mechanically stable and uses no resource, while a star is metastable, maintaining a non-equilibrium steady state by consuming nuclear fuel — an early and unsophisticated example of using the available-information resource to persist.
“The planet is not using up any resource. It's just mechanically stable... The star is using a resource. It's stable because it has fuel inside”
The universe is currently about 10^10 years old and will reach maximum entropy — a cold, dark, empty thermal-equilibrium state — roughly 10^100 years from now, after the last supermassive black holes evaporate, but the rate at which interesting things happen slows down over time.
“about 10 to the 100 years from now, we will reach maximum entropy, a thermal equilibrium state of the universe”
Podcasting, like the subject of the episode, is a complex system where many things happen and you cannot always know what is going on.
“Podcasting, like the subject of today's episode, is a complex system. Many things happen. You cannot always know what is going on.”