Two faces have already appeared in this series. One is the marble bust of Aristotle in Rome, with the blank eyes I wrote about in the fifth essay. The other is James Clerk Maxwell, bearded, looking off to one side, from the second. This week I did something to them.

Any picture can be written as a sum of waves: broad, slow ones for the large shapes, fine, fast ones for the edges and the curls of a beard. Each wave carries two numbers. One is its amplitude, how strongly it is present. The other is its phase, where along the picture its crests fall. I took both portraits apart into their waves, kept every amplitude from Maxwell, and gave them Aristotle’s phases. Then I put the picture back together.

It is Aristotle. Grainy, washed over with a gray haze, but unmistakably the bust, down to the blank eyes. Do it the other way round, Aristotle’s amplitudes with Maxwell’s phases, and Maxwell comes back.

Where the crests fall

None of this is new. In 1981 Alan Oppenheim and Jae Lim, at MIT, published a long paper called “The Importance of Phase in Signals,” gathering a result their group had been demonstrating for a few years. In many situations, they wrote, keeping only the phase of a signal preserves many of its important features, and under some conditions, a signal of finite length among them, the phase alone is enough to rebuild it completely, up to a scale factor. A 1979 paper from the same group showed the other half. Keep only the amplitudes and you get “a small bright region near the origin” on a dark ground, with “no resemblance to the original image.”

The reason is easier to see than to say. An edge, the line of a nose against a background, is a place where many waves happen to crest together. The amplitudes say how much of each wave there is. The phases say where they agree. Move the agreements and the edges move with them, whatever the amounts.

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The hidden fitting

Hippolytus of Rome, writing against heresies in the early third century, quoted a sentence of Heraclitus as evidence that he praised the unseen and then, in turn, the seen. It is four words long:

ἁρμονίη ἀφανὴς φανερῆς κρείττων.

Charles Kahn translates it as “The hidden attunement is better than the obvious one.” Miroslav Marcovich has “Invisible connection is stronger than visible.” Edward Hussey goes furthest: “Latent structure is master of obvious structure.” The disagreement is about the first word. Before harmonia meant music, it was a craftsman’s word for the way pieces are fitted together, the joints Odysseus hammers into his raft in the Odyssey, and some scholars trace it back to Mycenaean Greek for a wheel held true by its spokes.

Heraclitus knew nothing about Fourier, and a fragment is not a theorem. But hold the line beside the figure. The amplitudes are what is obvious: there is this much fine detail, this much broad shading. The fitting is hidden in the phases, and the fitting decides whose face it is.

In the fifth essay I proposed that information is form in action, and I held it to a rule I had set earlier in the series: a reframing earns something only when it predicts what the old framing does not. I admitted it had not done so yet. Here is where I think it does.

How it would fail

In 2009 Niko Busch, Julien Dubois and Rufin VanRullen showed people flashes of light so faint that each person saw only about half of them, while recording their brain activity from the scalp. The flashes were identical. What differed was the brain: just before a flash, the phase of the slow rhythms already running in it, in the theta and alpha range, was different on the trials people saw from the trials they missed. Phase accounted for at least 16 percent of the variation. In 2019 Mireia Ruzzoli and colleagues set out to confirm effects of this kind with a design and a statistical power planned on the studies that had found them, and found that the amplitude of the alpha rhythm mattered but its phase did not. The question is open, and I would rather tell you that than pretend it is closed.

In September I published a paper with colleagues proposing that what a brain does with a rhythm depends on its phase structure more than on its power, because the membranes the rhythms run through act as interfaces where waves interfere. That is a hypothesis. The paper lists four ways to break it, and the one I care most about here is the simplest. In our words: “phase-scrambling with power preserved should abolish the predicted spectro-phase co-variation, a decisive negative control that fails if the co-variation persists.”

Phase scrambling is the portrait experiment run on a recording. You keep exactly how much of each rhythm there is and randomize where its crests fall. If information is something a signal contains, a quantity, then the pattern we predict should survive the scramble, because every quantity is untouched. If information is form in action, the pattern should vanish, because the arrangement was the form. If it survives, the proposal is wrong on its own terms, and I will have to say so here.

This is a test, not a result. Nobody should believe the idea because I have written down how it could fail. Writing it down is what makes it worth checking.

Go back to the figure. The face on the lower left is built entirely from Maxwell’s amounts, and still the blank eyes of the statue look out of it. Aristotle said an eye that cannot see is an eye only in name. This one cannot see either. But it is recognizable for one reason only: where the crests fall.

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Further reading:

Oppenheim, A. V., & Lim, J. S. (1981). The importance of phase in signals. Proceedings of the IEEE, 69(5), 529-541. https://doi.org/10.1109/PROC.1981.12022

Oppenheim, A. V., Lim, J. S., Kopec, G., & Pohlig, S. C. (1979). Phase in speech and pictures. ICASSP ‘79, IEEE.

Gabor, D. (1948). A new microscopic principle. Nature, 161, 777-778. https://doi.org/10.1038/161777a0

Busch, N. A., Dubois, J., & VanRullen, R. (2009). The phase of ongoing EEG oscillations predicts visual perception. Journal of Neuroscience, 29(24), 7869-7876. https://doi.org/10.1523/JNEUROSCI.0113-09.2009

Ruzzoli, M., Torralba, M., Morís Fernández, L., & Soto-Faraco, S. (2019). The relevance of alpha phase in human perception. Cortex, 120, 249-268. https://doi.org/10.1016/j.cortex.2019.05.012

Firaux, T., et al. (2026). Beyond representations: from active inference to active interference. Frontiers in Human Neuroscience, 20, 1925538. https://doi.org/10.3389/fnhum.2026.1925538

Heraclitus, DK 22 B54, in Hippolytus, Refutatio IX.9.5. Translations: C. H. Kahn, The Art and Thought of Heraclitus (1979); M. Marcovich, Heraclitus (2001); E. Hussey, The Presocratics (London, 1995), p. 35, as cited by Afonasina. On harmonia: A. Afonasina, “The birth of harmony out of the spirit of tekhne,” ΣΧΟΛΗ 6.1.

Earlier in this thread

it’s science is for people who suspect that a living cell, a thinking brain and a quiet mind share a common root.

Every week, one idea from science, followed slowly: from something you can picture to the cell, the brain and the mind reading it. Around a thousand words, ten minutes with your coffee, no physics degree required.

Try one, right now

Stir a glass of muddy water and leave it alone. The grains sink, the water clears, and it looks as if order has come back by itself. It has not. Each grain that falls gives up its height to the water as a little warmth, and the glass slides toward the state with the most entropy it can reach. Once it gets there, nothing more happens. A living thing is exactly what does not do that.

Twenty seconds ago this was a glass of dirty water. Now it is a question about what keeps you alive. That is what these essays do.

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Start with these

Read in this order, they make one argument: what information is, what it costs to forget it, and what that means for a mind. Every essay is free.

How it works

One essay a week, usually on Thursday. Each one takes a single idea (a bit, an experiment, a formula) and follows it until it reaches life and mind, never further than the evidence goes. Where a claim is still a hypothesis, the essay says so.

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Who writes this

I’m Tommaso Firaux. I study how energy, mass and information weave together to produce living systems and, sometimes, minds that wonder about themselves. My research sits at the intersection of biophysics, neuroscience and complex systems. I write in English and Italian, depending on where the thought takes me.

it’s science publishes one essay a week on a single idea from physics, biology and neuroscience: information and entropy, energy and memory, cells, brains and contemplative states. Each essay starts from a concrete scene and follows the evidence no further than it goes. The science of life and mind, in ten minutes a week.

Questions

Do I need to know physics? No. Each essay starts from something you can picture and explains what it uses along the way.

Is it free? Yes. Every essay is free.

Can I write to you? Please do. Reply to any email, or leave a comment under an essay.

What happens when I subscribe? One email a week, usually on Thursday. No digests, no filler in between.

What if I want to leave? There is an unsubscribe link at the bottom of every email. No hard feelings; keep the glass of water.

By early summer a wheat field turns the same color everywhere at once. Every plant in it came up in the same season and flowered in the same few weeks, and each one will set its seed and die before the field is cut. Pick any grain from the harvest and ask how old the plant that made it was. You already know the answer, and it is the same for every grain.

At the western end of Crete, in the village of Ano Vouves, there is an olive tree you can see through. Its trunk has hollowed out from the inside, and the wood that might have kept count of its first years has gone with it, so where its beginning should be there is daylight, and nobody can say how old it is. Estimates of its age start at two thousand years and run past four thousand. It still bears olives.

Ask the same question among olive trees and the answer changes with every fruit. The tree that made this olive might be thirty years old. The one beside it might be three hundred.

A count with a clock in it

Last week ended with a question: what is entropy counting, when what it counts is not grains in a glass, but lives? The most exact answer I know belongs to Lloyd Demetrius, a mathematical biologist who has spent fifty years on it. In 1974 he introduced what he called the entropy of a population, and the version he later named evolutionary entropy measures the uncertainty in exactly that question: pick a newborn at random, and how old was its parent?

For the wheat, the uncertainty is zero. Demetrius uses the example himself: annual plants, which reproduce at a single stage of life, have zero entropy; perennials, which spread reproduction across many ages, have positive entropy. The measure belongs to a population and never to one plant, so the Vouves olive has none of its own. A population of wild olives has it. So does a town.

The mathematics is what keeps this from being a rename. Boltzmann’s entropy counts the ways a system can be arranged at an instant. Demetrius took his from ergodic theory instead, from the measure Kolmogorov and Sinai built in the 1950s for how unpredictable a trajectory is as it unfolds. His trajectory is a genealogy, a chain of parents running back through time, each at the age they were when the next was born. In his 2024 paper he puts the difference in two words. Thermodynamic entropy measures a “positional” ordering, evolutionary entropy a “temporal” one.

The glass counted where things are. The olive counts when.

Divide the same quantity by the generation time and it measures something the glass never had: how quickly a population finds its way back to its steady state after a small disturbance. On Demetrius’s mathematics, a population that puts all its births into one season scores zero on this measure, and one that spreads its births across decades finds its way back faster.

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Heat cannot pay for a cell

Why does life need a different entropy at all? His 2024 argument starts from something any engineer knows: heat does work only by flowing from hot to cold, and the most work you can get from it grows with the temperature difference. A cell has almost no temperature difference inside it, so heat can do almost no work there. Life pays in other currencies, energy held in chemical bonds, electrons handed from molecule to molecule, light caught by a pigment, concentrations held unequal across a membrane.

A measure built for heat moving through a gas is, he argues, the wrong ledger for a living thing.

Then comes the part he calls the Entropic Principle of Evolution. In its simplest form: where the source of energy is stable, mutation and selection push evolutionary entropy up; where it fluctuates, they push it down. Steady resources favor lives that spread themselves across time, and boom and bust favors lives that spend themselves at once. In his models this is a derived result. Whether real populations follow it is a question for data, and the cases he and colleagues have published are consistent with it, which is not the same as settling it.

In the same paper he goes further, onto softer ground. He argues that the second law of thermodynamics is a limiting case of his principle: let the parts vary only by chance fluctuation, close them off from any input of energy and matter, let their number grow without limit, and what remains is Boltzmann’s law. If that holds, and it is a large if, the second law is not the rule life breaks but a special case of the rule life follows.

It would be easy to stop there. The paper presents no new data; it is a theoretical reading of how the pieces fit. Directionality theory, as Demetrius calls the whole framework, has stayed outside the mainstream of evolutionary biology, where fitness is still mostly measured by how fast a population grows. I find the mathematics beautiful and the large claim unproven, and I want to hold both.

Long movement

Last week I ended on the second line of chapter fifteen of the Dao De Jing, and it is worth hearing again now: 孰能安以久動之徐生, who can take what is at rest and, by long movement, slowly bring it to life?

Laozi was not doing demography, and nothing in Demetrius depends on him; a resemblance is not evidence. Still, set the line beside the two plants and the words Demetrius’s measure would underline are the slow ones. Long. Slowly. The wheat gives everything once. The olive keeps giving, year after year, from a body that has lost its own beginning.

Go back to Vouves. The tree has outlived its heartwood, the part that would have told us when it started, and kept the part that keeps it going. Someone picking olives there this autumn will hold this year’s fruit from a tree nobody can date

Further reading

Demetrius, L. A. (2024). Directionality theory and the origin of life. Royal Society Open Science, 11, 230623. https://doi.org/10.1098/rsos.230623

Demetrius, L. (1997). Directionality principles in thermodynamics and evolution. Proceedings of the National Academy of Sciences, 94(8), 3491-3498. https://doi.org/10.1073/pnas.94.8.3491

Demetrius, L. (1974). Demographic parameters and natural selection. Proceedings of the National Academy of Sciences, 71(12), 4645-4647. https://doi.org/10.1073/pnas.71.12.4645

Dao De Jing, chapter 15, in the received text of Wang Bi (226-249).

Earlier in this thread:

It is three in the morning and your mind will not settle. The afternoon’s conversation plays again, with better lines this time, and behind it come the email you forgot to send and a number that still does not add up. Nothing arrives in order. It all comes up at once, like silt kicked up from the bottom of a glass, and hangs there in the dark.

We have a word for this now, and it is a physicist’s word. My head is pure entropy. The relationship slowly turned into entropy. We use it for anything that has come apart and will not go back together.

More than two thousand years ago, a Chinese text traditionally attributed to Laozi gave different advice for the same condition. Chapter fifteen of the Dao De Jing asks: 孰能濁以靜之徐清, who can take what is muddy and, by stillness, slowly make it clear?

What I got wrong about a deck of cards

I have used the word loosely here too. Three essays ago, explaining Boltzmann’s equation, I wrote that a system drifts toward the descriptions there are more of “for the same reason a shuffled deck comes out disordered.” The counting in that sentence was right. The word was wrong.

Shuffling a deck changes nothing a thermometer could register. What Boltzmann counted was the number of ways the energy and the molecules of a system can be arranged while it stays, to our coarse eyes, the same system, and tidiness never came into it. Disorder is a picture we lay over that count, and most of the time it fits well enough to be useful.

The glass of muddy water is where the picture stops fitting. Leave it alone and the grains sink and the water clears, which looks like entropy running backward, mess turning into order with nobody tidying. What happens is the reverse. Each grain that falls gives up its height to the water as a little warmth, spread among more molecules than anyone could count, and the total number of ways goes up. The glass is obeying the second law the whole time.

The clarity is in what you can see. The entropy is in what you cannot.

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Two entropies in one head

The slide from entropy to disorder is so easy that serious science makes it too. In 2014 Robin Carhart-Harris and his colleagues proposed what they called the entropic brain, and their abstract opens by noting that entropy can “imply physical qualities, where high entropy is synonymous with high disorder.”

What they measure is something else, and more interesting: entropy in Shannon’s sense, how varied and unpredictable the brain’s spontaneous activity is, how large the repertoire of patterns it moves through. On their proposal, that repertoire widens under psychedelics, and ordinary waking consciousness is a state in which it is held in check, kept just short of the point where order gives way. It is a hypothesis, and it is argued over, but the measure is clear.

Gustavo Deco and his colleagues come at it from the thermodynamic side. A system at equilibrium looks the same whether you run its film forward or backward; a system far from equilibrium has an arrow of time, and physicists measure that arrow as the rate at which it produces entropy. That rate is hard to get from brain signals, so Deco’s group uses a simpler stand-in: how easily you could tell a recording of brain activity from the same recording played backward. In 2022, using electrodes on the surface of the brain in monkeys, they found that arrow sharper in wakefulness than in deep sleep or under most anesthetics, and sharpening again as the animals came back.

So one word reaches into the skull as two measures, answering different questions. One asks how many different states the brain visits, the other how far its flow is from coming to rest. By the first, set against the psychedelic state, waking is the constrained one. By the second, set against sleep and anesthesia, waking is the one furthest from still.

Three weeks ago I said that a shared form is not evidence of a shared thing until it predicts something. A shared name is weaker still, and here we can watch it split in two.

Still water is not a quiet mind

The settled glass is equilibrium. Film it, play the film backward, and nobody could tell you which way it ran. No one would put a glass of water on Deco's scale, but in principle it belongs at the zero point, below deep sleep and anesthesia, where there is no arrow at all. Whatever Laozi meant by clarity, it cannot be that.

Last week I proposed that information is not simply something that is, but something that is done. A thinking brain keeps doing it, holding itself away from equilibrium and paying for that all the time, even at three in the morning. I do not know what these measures show in a meditating brain, and I will not pretend to. But if Laozi’s stillness is anything real, it has to be a kind of movement.

The chapter seems to know this. Straight after the muddy water it asks the opposite question: 孰能安以久動之徐生, who can take what is at rest and, by long movement, slowly bring it to life?

Stillness makes clear. Movement makes alive.

The glass settles, and then nothing more happens; the count has gone as high as it can go. A living thing is exactly what does not do that. Which leaves the question the next essay is for: what is entropy counting, when what it counts is not grains in a glass, but lives?

A developed hologram is a disappointing thing to look at. Vittorio and I wrote about one this week, the plate Dennis Gabor dreamed up in 1947 while waiting for a tennis court, and what we did not dwell on is how little there is to see once it comes out of the developer. A sheet of glass gone grey, like breath on a window. Nothing you would think to frame.

Now put it in a drawer.

Where is the picture?

It is not in the glass, not in any sense you could point to. The plate recorded only the quarrel between two beams of light, one that bounced off the object and one that did not, and a quarrel does not look like either party. The picture stands up again only when the clean beam is sent back through, and then it stands in the air behind the plate, exactly where nothing is. In the essay we put it this way: information “is not carried from place to place but takes shape where it is.”

I want to take that sentence further than a hologram, because I think it is what this whole series has been circling.

A somewhat heady draught

In March 1956 Claude Shannon published a single page in the journal of his own field. It is called “The Bandwagon,” and it reads like a host asking the party to turn the music down.

Eight years after his paper, information theory was everywhere. Biologists, psychologists and economists were all applying it, and Shannon wrote, dryly, that the field was “partaking of a somewhat heady draught of general popularity.” Then the warning. It would be all too easy, he wrote, for the whole thing to collapse “when it is realized that the use of a few exciting words like information, entropy, redundancy, do not solve all our problems.” Applying the theory elsewhere was “not a trivial matter of translating words to a new domain.”

Warren Weaver had warned in 1949 that information “must not be confused with meaning.” We confused it anyway, and the confusion I care about is quieter than that one. Somewhere between the telephone wire and the present, information became a substance. We talk about it the way we talk about grain: it is stored, shipped, leaked, owned, and it sits inside things waiting to be taken out.

Read back through the last four essays and notice that it never once behaved that way.

Shannon’s bit was a measure of choice, how much an answer narrows down what it could have been, which means it needs someone, or something, for whom the alternatives exist. Maxwell’s demon, in Szilard’s hands, turned out to have a knower inside the second law, and when Landauer and Bennett finished the accounting, the bill fell not on the knowing but on the forgetting: an event, two possible pasts becoming one present, measured on a bead in Lyon. Landauer’s slogan was that information is physical, which is not the same as saying it is a thing.

A physicist working today has pushed the same way. In 1996 Carlo Rovelli proposed reading quantum mechanics as a theory that describes “only the information that systems have about each other.” Twenty years later he went back to Shannon and argued that the purely physical notion of information in that work would be better called correlation: “downright crude physical correlation.” Relational quantum mechanics is one contested interpretation among several, but on his reading information is never inside a system. It is between two.

And every time it turned up in this series, it was doing something.

The eye of a statue

On a January evening in 1970, the anthropologist Gregory Bateson gave a lecture in memory of Alfred Korzybski and borrowed a piece of chalk from Kant. Around and within it, he said, there is an infinite number of differences; “of this infinitude, we select a very limited number, which become information.” Then the definition everyone quotes, rarely in full. Information is “a difference which makes a difference,” and it is able to make one, he went on, because the pathways it travels along “are themselves provided with energy.”

That last clause usually gets dropped. It is the part I need.

It sends me back much further, to a word Aristotle put at the center of his philosophy. Energeia, built on ergon, work. The translator Joe Sachs renders it, deliberately literally, as being-at-work. It is the word for a thing being what it is by doing it, and it is the root, two thousand years later, of our word energy.

Aristotle’s clearest example is in the second book of On the Soul. Suppose, he says, that the eye were an animal. Then sight would be its soul. And when the seeing is taken away, the eye “is no longer an eye, except in name,” no more a real eye than the eye of a statue.

The plate in the drawer is the eye of a statue.

In the first essay of this series I went back to the Latin under our word: informare, to give form, the way a hand shapes clay. Put that beside energeia and you have the phrase I have been working toward since then without writing it down.

Form in action.

I want to propose that this is what information is: not a shape stored in a medium, but a shape at work in something it changes. Rovelli puts information between two things. What I would add is the verb.

A proposal, then, and I should hold it to the rule I set in this series two weeks ago: a reframing earns something only when it predicts what the old framing does not. This one has not done that yet. For now it is a way of standing in front of the evidence that fits four essays better than information as grain. Whether it tells you where to look is work still ahead of it, and you are entitled to ask me for it.

The third word

The first essay in this series ended by naming where it was going, four essays on: Energy, Mass, Information. This is the fourth since.

Energy comes from Aristotle’s being-at-work. Information comes from the Latin for giving form. And in the same chapter of On the Soul, Aristotle reaches for a seal pressed into wax: asking whether soul and body are one, he says, is as pointless as asking it of the wax and the shape the stamp gives it. The wax is the third term: matter. Not yet mass, which had to wait for Newton to define it as the quantity of matter.

The model that Jack Tuszynski, Marco Cavaglià and I published this year proposes reading the mind as a network of interactions among the three: energetic oscillations, material substrates, informational patterns. It is a framework, stated as one. This essay was for the drawer.

The plate is still in there. The picture is not anywhere at all. It is waiting for the light.

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Earlier in this thread:

In a laboratory in Lyon, in 2012, a group of physicists built the smallest memory anyone had ever built, and then measured what it costs to wipe it.

The memory was a single glass bead two micrometers across, suspended in water and held by a laser. By flicking the laser between two nearby points fast enough, they made a landscape with two valleys and a hill between them. The bead sits in one valley or the other. Left or right. That is the entire device: one bit, made of one bead.

Then they erased it. They lowered the hill, tilted the landscape so that the bead ended up on the left whichever side it had started on, and put the hill back. Whatever had been written was gone. And because the bead was in water and they could watch it, they could add up the heat that went into the water while it happened.

The number they were looking for is about three thousandths of a billionth of a billionth of a joule. Small enough that nothing in ordinary life would ever notice it. Not zero, which is the whole point.

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The bill nobody was looking for

That number came from a paper written fifty years earlier by a man at IBM who wanted to know whether computing has a physical floor.

In 1961 Rolf Landauer published “Irreversibility and heat generation in the computing process.” The question was not whether better engineering could reduce the power a computer draws. It was whether the manipulation of information has any minimum cost at all, in principle, that no cleverness could get under.

His answer was that most of it does not. You can add, copy, and route, in principle, for nothing. But one operation is different, and it is the one nobody thinks about.

Erasing.

Almost every operation in a computer can be run backwards. Told the output of a copy, you know the input. Erasure cannot. “Set this bit to zero” takes a one and returns zero, and takes a zero and returns zero. Two different pasts, one present. Told that the answer is zero, you cannot say what was there before.

That compression is not an inconvenience, it is a physical event. The system had two possible states and now has one. Phase space does not simply lose volume: something has to expand to compensate, and what expands is the surroundings, warmed by at least kT ln 2 per bit destroyed.

The correction

Two essays ago I left Leo Szilard in 1929, concluding that the demon survives the second law because its measurement must cost something. Knowing, he said, cannot be free.

He was right that the books balance. He was wrong about where.

In 1982 Charles Bennett showed that measurement can be made thermodynamically reversible. The demon can look at a molecule, register which side it is on, and pay nothing in principle. For half a century physicists had been guarding the wrong door.

The trick is that looking, done carefully, adds no information to the world. It correlates two things that were already there. If the demon’s memory starts in a known blank state and ends up matching the molecule, nothing has been destroyed: run the interaction backwards and the memory returns to blank, the molecule to wherever it was. Nothing about that is forbidden. It is bookkeeping, not creation.

What the demon cannot do is keep looking forever. Every observation writes something into its memory, and no memory is infinite. Sooner or later, to carry on working at all, it has to clear the record and begin again.

That is when the bill arrives. Not at the seeing. At the forgetting.

I find this the strangest result in the whole sequence, and I have been sitting with it for a long time without getting used to it. The universe does not charge you for looking. It charges you for letting go.

What the number licenses

Last week I set a criterion, and it applies here first. A shared form is evidence that two things are one thing only when treating them as one predicts something that treating them as two does not.

This is that case. If thermodynamic entropy and information entropy were genuinely separate quantities that happen to share a formula, then erasing one bit of memory would carry no particular thermodynamic price, and the heat measured in Lyon could have come out at any value at all. Treating them as one quantity predicts a specific floor. The heat settled onto that floor as the erasure was performed more and more slowly, exactly as the theory requires.

So the identity earns something here. Not a metaphor, not a coincidence of notation. At one point at least, an informational fact about a system predicted a thermodynamic measurement, and the measurement agreed.

Now the part where I would rather be careful in front of you than caught out later. What was established is a lower bound on the heat released by a logically irreversible operation in a system at thermal equilibrium. It is not a theory of mind. It does not show that thinking is computing. It says nothing about whether your brain is paying Landauer’s bill in any way that matters, and anyone who tells you otherwise has skipped several steps that have not been taken.

What it does establish is smaller, firmer, and enough to be going on with.

Forgetting has a price. The price is in joules. Somebody has measured it.

There is a cemetery in Vienna where the composers draw visitors all year. Beethoven, Brahms, Schubert, a Strauss or two. A short walk from them, in a quieter row, stands a headstone with a bust on top and something carved beneath it that nobody puts on a grave.

An equation.

S = k log W

The man under it is Ludwig Boltzmann, who died in 1906. The popular version of his story has him taking his own life because the scientific world refused to believe in atoms. Historians of science mostly do not accept that account, and the chronology does not help it: Einstein had published on Brownian motion the year before, and the question was closing rather than hardening. What actually happened is simpler and sadder and belongs to him rather than to physics.

The equation is his in substance: he established the relation in a paper of 1877. But the compact form carved on the stone, constant and all, is Planck’s, and it was Planck who named that constant after him.

What the equation says

Take a room full of air. There is a description of it you can fit in a sentence: temperature, pressure, volume. And there is a description of the same room listing where every molecule is and how fast it is going, a number so large it is of no use to anyone.

W is how many of the second kind of description are compatible with one of the first. How many arrangements of the invisible parts would give you exactly this visible room.

S is the logarithm of that count, times a constant.

Which means entropy is not a fluid, a force, or a tendency. It is a number of ways. When a physicist says entropy increases, the claim is that a system drifts toward the descriptions there are more of, for the same reason a shuffled deck comes out disordered. There are vastly more disordered arrangements than ordered ones and nothing is steering.

Now notice what the equation needs in order to mean anything at all. To count arrangements you must have things to arrange. Boltzmann wrote this while the existence of atoms was still being argued about, which makes the carving on the headstone less a tribute than a verdict.

Eighty years later, from a telephone wire

In 1948 Claude Shannon, at Bell Labs, was working on a problem with nothing to do with gases: how much channel you need to carry a message. He arrived at a quantity measuring how much a message narrows down what it could have been, and called it H.

Put the two side by side.

The same function. Not similar, not analogous in spirit. The same mathematics, reached twice, by two people who were not looking at the same thing and one of whom was not born when the other died.

Shannon did not choose the name himself. He told the story to Myron Tribus in April 1961, and Tribus printed it in Scientific American ten years after that. He had thought of calling the quantity information and rejected the word as overused. He settled on uncertainty. Then he mentioned it to John von Neumann, who told him to call it entropy for two reasons: the function already had that name in statistical mechanics, and, more usefully, nobody knows what entropy really is, so in a debate he would always have the advantage.

The story gets repeated as though someone had minuted it. It is a recollection at two removes, printed a decade after the conversation that recalled it. It is probably true. It is not documented the way its circulation implies, and that matters more here than it usually would, because this anecdote is load-bearing: it is the origin of the word that made everyone assume the two quantities were one thing.

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When is a resemblance an identity?

That the two expressions are formally identical is disputed by nobody. What follows from it has been argued for seventy years.

E. T. Jaynes argued from 1957 that the resemblance is not a coincidence at all. On his account, statistical mechanics is properly understood as a form of inference, and thermodynamic entropy is an information measure applied to a physical system. The two entropies are one thing wearing two names, and physicists were doing information theory before it existed.

The opposing view is that a shared form is mathematics doing what mathematics does. The same function turns up in ecology, in population genetics, in linguistics, and nobody concludes from this that a forest is a message.

I have no settlement to offer and would distrust anyone who did. What I want to name is what this essay is actually about, because it is something I keep doing here and have never examined.

Every few weeks in this newsletter I put two things next to each other and notice that they rhyme. An etymology that lines up too well with a piece of engineering. A Sanskrit term for sustained attention that behaves suspiciously like a thermodynamic operation. Each time there is a sentence somewhere saying that the resemblance is not the argument.

Here is the strongest resemblance available anywhere in science. Not a likeness of theme, not a similarity of shape. The same function, arrived at independently, eighty years and an ocean apart, by people with no common problem.

And even that does not settle itself.

What would settle it

So here is a criterion, and it applies to my resemblances at least as much as to this one.

A shared form is not evidence that two things are one thing. It becomes evidence when treating them as one lets you predict something that treating them as two does not.

That is a demand rather than a mood. It says: show me the case where the identity does work. Where assuming that the entropy of a gas and the entropy of a message are the same quantity produces a number you could not otherwise have got, and then go and measure the number.

Jaynes believed he had that case. Whether he did is worth its own essay.

In the meantime, the test I am setting myself, and handing you to hold me to. When I put two things side by side here and they rhyme, ask me what the identity would predict that the separation would not. If I cannot answer, then I have shown you a coincidence and called it a finding, and you should say so.

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Earlier in this thread:

On the eleventh of December 1867, James Clerk Maxwell sat down to write to his friend Peter Guthrie Tait. He was thirty six. What he wanted, he told Tait, was to pick a hole in the second law of thermodynamics.

The hole he proposed had a caretaker.

Imagine two chambers of gas at exactly the same temperature, and a door between them. Now imagine something standing at that door, watching the molecules come. Molecules in a gas do not all move at one speed; they move at a spread of speeds, and temperature is only the average. So the being waits, and opens the door for a fast molecule heading left and a slow one heading right, and keeps it shut for everything else.

Wait long enough and one side is hot and the other is cold. Nothing has been pushed, lifted, burned, or spent. A difference has appeared out of a room that had none.

A very observant and neat fingered being

That phrase is Maxwell’s, and not the one that survived. Writing to Tait he summarized what his creature had achieved: “The hot system has got hotter and the cold colder and yet no work has been done, only the intelligence of a very observant and neat fingered being has been employed.”

Neat fingered. Observant. Intelligent. Those are the whole toolkit.

When he made the argument public in Theory of Heat in 1871, he was careful in a way that later readers were not. “But if we conceive a being whose faculties are so sharpened that he can follow every molecule in its course,” he wrote, “such a being, whose attributes are still as essentially finite as our own, would be able to do what is at present impossible to us.”

Read that middle clause again. As essentially finite as our own. Maxwell insists, in the same breath that introduces the thing, that it is not supernatural. It is not a god and not a devil. It is a creature exactly as limited as we are, only faster and more careful, able to see one molecule where we see millions at once.

The word demon was not his. William Thomson introduced it in 1874, in Nature, in a paper on the dissipation of energy, and it stuck so hard that Maxwell’s careful finite creature was buried under it. The Greek daimon was an intermediary spirit rather than a devil, closer to what Maxwell meant than the word’s later career suggests. He never used it himself.

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The sentence everyone walked past

Here is what usually gets lost. Maxwell was not trying to prove the second law false. He was trying to show it was a different kind of law than anyone had assumed.

He was still saying so a decade later, in an encyclopaedia article on diffusion, in one of the strangest sentences a Victorian physicist ever committed to print: “The idea of dissipation of energy depends on the extent of our knowledge.”

It is a claim that one of the central quantities in physics is not a property of the gas alone. Entropy, on this reading, belongs to the gas together with what can be known about it. The molecules do not change. The demon does not touch them, or heat them, or push them. It sees them individually rather than in bulk, and that alone is enough to move a quantity thermodynamics treats as real.

Change the knower, and you change the number.

That is a strange thing to find in nineteenth century physics. Stranger still is what happened next, which is nothing. For sixty years the demon was passed around, argued over, and left where it was.

One molecule, one bit, one number

Then in 1929 a Hungarian physicist named Leo Szilard published a paper whose title shows how far the problem had traveled from the gas: “On the decrease of entropy in a thermodynamic system by the intervention of intelligent beings.”

Szilard did the thing that turns a puzzle into physics. He made it smaller. One box, one molecule, one partition. The molecule is on the left or on the right. That is the entire state of the world, and knowing it is one yes-or-no question answered, which is to say one bit.

And from that single bit, Szilard showed, you can extract work. A specific, calculable amount: at most kT ln 2, where T is the temperature and k is Boltzmann’s constant.

One molecule. One thing known about it. One quantity of usable energy at the end.

Szilard’s conclusion was that the second law survives, and survives because the demon’s measurement cannot be free. The knowing has to carry an entropic price at least as large as what it buys, or the books do not balance.

Whether entropy and information are therefore the same quantity wearing two names is a harder question, and still open. Some hold the informational reading is essential. Others, John Norton and Orly Shenker among them, argue it is a relabelling that adds nothing you did not already have. I am not going to settle that here, and I would be suspicious of anyone who claimed to.

What is not in dispute is smaller and stranger and enough: a thought about a gas turned out to have a price. Szilard’s answer, as it happens, was right about the conclusion and wrong about where the cost sits, and correcting it took another fifty years. That is not this essay.

What the hole let through

The demon’s only power is attention. No strength, no leverage, nothing to heat anything or push anything with. All it does is watch a great many things, one at a time, and act at the right moment. Everything it achieves comes from noticing.

There is a line that circulates in modern spiritual writing: where attention goes, energy flows. The phrasing is recent and usually sold as older than it is. But it compresses something with a much longer pedigree. Patanjali gives sustained attention a technical name, samyama, defined at the opening of the third chapter of the Yoga Sutras as concentration, meditation and absorption held together on a single object. What follows is a catalogue: hold samyama on this, and you obtain that. Attention there is not a state you rest in. It is an operation, and it yields.

Now set that beside what Szilard proved. A being that knows which half of a box its molecule is in can turn that knowing into kT ln 2 of work. Knowledge on one side, joules on the other, convertible at a fixed rate.

None of which means Patanjali anticipated thermodynamics. He did not, he was not trying to, and a resemblance is not evidence of anything. What I notice is narrower and harder to shake. Two systems that share no vocabulary, no method, and no century both refuse to let attention be free. One says it costs the attender and returns something. The other says it costs the demon and returns joules. Both put a price on noticing.

Attention is not free. Somebody pays.

Maxwell wanted to pick a hole in the second law. He found one, and it held. What came through it was not a broken law. It was the discovery that the law had a knower inside it the whole time, and that nobody had thought to look.

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On a Saturday evening in February 1946, a new program went out on the Mutual Broadcasting System from a theater on West 48th Street in New York. Four panelists. One hidden object, mailed in by a listener. Twenty questions, each answerable only yes or no. The show was called Twenty Questions, and it ran, in one format or another, for the better part of a decade. The object listeners sent in more often than any other, according to the show’s own historians, was Winston Churchill’s cigar.

Nobody playing along at home thought they were doing mathematics. They were guessing. Is it alive. Is it larger than a person. Is it in this room right now. Every answer threw half the world away and kept the other half, and nobody mourned the half that went, because the game was only ever interested in what was left.

Two years later, an engineer at Bell Labs named Claude Shannon published a paper that never mentions the radio show. He was not trying to explain a parlor game. He was trying to explain a telephone wire: how much of it you actually need, and how to know when you have used enough. It turned out to be the same problem, and solving it meant throwing something away as well.

The Word Nobody Meant to Coin

What Shannon threw away was meaning, and he did it on the first page, without apology. Messages frequently have meaning, he granted. They refer to things, they correlate with physical or conceptual entities. And then: “These semantic aspects of communication are irrelevant to the engineering problem.”

Irrelevant is a strong word to use about the thing most people would say communication is for. But it bought him something no one had been able to get any other way. Once meaning is out of the account, a message is no longer judged by what it says. It is judged only by how much it narrows down what it could have said, and that is a quantity you can put a number on.

The smallest such number has a name. If there are two equally likely possibilities and one question settles which is true, that question is worth exactly one bit. A fair coin flip is the cleanest bit there is: heads or tails, nothing else it could have been, one question, one answer, done.

Shannon did not coin the word. The same page hands it to a colleague, in a single sentence:

If the base 2 is used the resulting units may be called binary digits, or more briefly bits, a word suggested by J. W. Tukey.

It is a strange kind of monument, a paper that reshaped the twentieth century, giving away its most famous word in a subordinate clause.

The word was small, but what it measured was not. Twenty good questions can sort among more than a million possibilities, because each one halves what remains: one question leaves two candidates, two leave four, three leave eight, and by the twentieth the field has been cut in half twenty times over. That is enough to land on almost anything a listener could put in an envelope. What the panel was spending, all along, was bits.

Shannon never described it as a guessing game. His own words for the quantity were choice and uncertainty: a measure, as he put it, of how much choice is involved in selecting an event, or how uncertain we are of its outcome. Not what the outcome means. How much of the world it rules out.

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The Word Before the Word

So the theory works, and it works precisely because meaning was removed from it. That is worth sitting with, because the removal was not a discovery about information. It was a decision about what to stop counting, made by someone with a wire to build. And the word he was making that decision about had been in English for six hundred years already, meaning something else.

Inform entered the language in the early fourteenth century, from Old French, from the Latin informare: in, into, plus formare, to shape. To inform something, in the oldest sense, was to give it form. The first English use was to train or instruct, to shape a mind the way a hand shapes clay. The sense we reach for now without thinking, to report facts, to pass along data, is not recorded until decades later. It is the younger, narrower branch of the same word.

This is a resemblance, not evidence. A word’s history is not an argument. But the older sense describes something Shannon’s does not, and the difference is not decorative: one of them involves two parties and a change, and the other involves a count.

What Twenty Questions Could Not Hold

The next time a hidden object survives all twenty questions, that is not a failure of the game. It means the object carried more bits than the panel had questions left to spend.

Shannon’s stripped down bit was strong enough to build every wire, disc, and screen standing between this sentence and you, and it is tempting to stop there, with meaning subtracted and the problem solved. But subtracting something is not the same as showing it was never there.

A quieter tradition disagrees. The philosopher Gilbert Simondon argued that information is not a property a message carries in itself at all. It arises from the tension between two orders that are not yet in phase with each other, and it exists only in that relation, never in one of the terms alone. Follow that thought one step further, which he did not do in these words, and to inform stops meaning to transmit and starts meaning something closer to its Latin root: to change the form of the other, so that the two of you are no longer out of phase.

Whether that survives contact with two people instead of two circuits is a question this series will keep returning to, without settling it here. What the panel spent, in the end, was twenty bits. What the game was actually made of was two parties, and the distance between them, and the slow work of closing it. Four essays from now, that asking already has a name: Energy, Mass, Information, three quantities this publication’s own model holds together, and the reason it exists at all.

Earlier in this thread:

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A woman crying in a parking lot. Engine off, hands still on the wheel. The kind of crying that has no audience.

A long table, open bottles, the meal long finished. Someone laughing so hard they go silent, mouth open, no sound, tears forming for a completely different reason than the woman in the parking lot.

A runner at the fortieth kilometer. The body has crossed a threshold it did not know existed. Something else has taken over.

Seventy thousand people singing the same word at the same moment. None of them decided to. It simply happened, like a wave that no single water molecule chose to become.

What do they have in common?

The obvious answer: emotions. The brain. Human experience in its most intense form.

But there is another answer. One that does not contradict the first.

They are physics.

The 20% engine

The brain weighs about 1.4 kilograms. It accounts for roughly 2% of body mass. Yet it consumes nearly 20% of the body’s total energy, and it never fully switches off. Even at rest, it burns through glucose at a rate that would exhaust most tissues within minutes.

The laws of thermodynamics apply here without exception. Energy is neither created nor destroyed, it changes form. Heat, work, dissipation. The brain is a system that takes in energy and continuously transforms it, maintaining itself far from equilibrium.

But a heat engine does not cry in a parking lot. It does not synchronize with seventy thousand strangers. It does not feel the fortieth kilometer as something other than damage.

The physics is real and it is not enough. Or rather: maybe it is pointing toward something deeper than we usually allow it to.

Think of two violins. Same note, same frequency. The wood is different, the age is different, the history of the instrument is different. The resonance is different.

The material is not incidental to the sound, the material is the sound.

The brain has a material too. And that material changes everything.

Where does the physics end?

Energy does not disappear inside the brain. It changes form, continuously. Mitochondria convert glucose into electrical activity. Electrical activity propagates across membranes. Membranes generate fields. Fields couple to other fields.

Nothing is lost. Everything is transformed.

But here is what classical physics missed for a long time: a living system is not a closed engine running down toward equilibrium. It is an open system that maintains itself precisely because it dissipates. The brain is not alive despite the constant flow of energy through it, it is alive because of it. Order sustained by throughput. Structure built from flux.

This changes what we mean by stability.

Imagine a spinning top. It does not stand still, it oscillates, it wobbles, it traces small circles around a center it never quite reaches. It stays upright not through rigidity but through movement. The stability is dynamic, not static.

The brain works the same way. Researchers studying whole-brain dynamics have found that the optimal condition for cognition is not order and not chaos, it is the edge between them. A state of perpetual near-transition, where the system is always ready to shift configuration without ever collapsing into noise. Metastability: the technical name for a system that lives in the tension between settling and dissolving.

Think of attractors as valleys in a landscape. The system rolls toward them naturally, but the landscape itself is alive, shifting, redrawn by every experience. There is no fixed bottom. There is only the current shape of the terrain.

A flame, not an engine

A hundred years ago, in a short text he never published, Sigmund Freud tried to derive a Newtonian mechanics of the brain. He called the governing principle neuronal inertia. He had trained in the school of Helmholtz and Brücke, physicists who believed that living organisms obeyed the same laws as everything else in nature. He took that seriously.

The intuition was correct. He lacked the instruments to measure what we are only now beginning to see.

What Freud was missing was the thermodynamics of open systems, the understanding that life does not minimize energy, it organizes it. He treated the mind like a closed engine, pressure building until it found release. But a living system is not a closed engine. It is a flame, it does not wind down, it sustains itself through continuous flow.

The top does not stop spinning. It learns to spin differently.

The science caught up with the intuition. It just took another century.

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The patterns do not stop at the skull

In the research we are developing with Marco Cavaglià and Jack Tuszynski, the membrane is not a wall.

Think of skin. Skin is not where the body ends, it is where the body meets the world. A surface that breathes, senses, regulates, remembers contact. A boundary that does not separate so much as translate.

The membranes inside the brain do the same thing, at a different scale. They are where information becomes body. They write and read. They store and retrieve. Everything the system can say passes through them.

Now picture something else entirely.

Two stones dropped into a still lake.

Each creates its own pattern of waves, expanding rings, crests and troughs radiating outward. When the two patterns meet, they do not simply add together. They interfere. Where crests align, the water rises higher. Where crest meets trough, they cancel. What emerges is not the sum of two separate patterns, it is something new, a structure that belongs to neither stone alone.

Two people in a room are not isolated systems exchanging signals. They are oscillating fields coupling at their boundaries, membranes responding to membranes, rhythms entraining rhythms, phase patterns writing themselves onto phase patterns. The interference is physical. It happens whether or not either person is aware of it.

Energy, mass, and information form a continuous loop across scales. What begins as molecular oscillation at the membrane interface propagates upward, through electrical fields, through the body’s geometry, through the space between bodies. The loop extends itself out of the skull.

This is measurable, at least at small scales. When two people engage in genuine interaction, conversation, collaboration, shared attention, their neural oscillations synchronize in ways that exceed chance. Electroencephalography can record it. The coupling is real, it is directional, and it scales with the quality of the interaction.

Whether the same physics scales up to seventy thousand people in a stadium is a question the data has not yet answered. But if it does, the concert is not just an image. It is a phase transition, a collective configuration that none of them could produce alone, that exists only in the interference between them.

The physics did not end. It was just larger than we thought.

A woman crying in a parking lot. A standing wave in a body that looks still.

A long table, open bottles, someone laughing so hard they go silent. Interference at the edge of dissolution.

A runner at the fortieth kilometer, the body past itself. Energy finding a configuration it had not known.

Seventy thousand voices, one word, one moment. A phase no single throat can produce.

Not four human experiences. Four physical configurations in relation. Four sets of interference patterns writing and reading each other across the boundaries between systems.

The energy was always there. The mass was always there. The information was always there, not just inside any one of them, but between them, in the structure that emerged from their relations.

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Further reading

• Cavaglià, M., & Tuszynski, J.A. (2026). A Unified Holographic Framework for neural computation and consciousness: From lipid membranes to the Schumann resonance. BioSystems, 259, 105669. https://doi.org/10.1016/j.biosystems.2025.105669

• Firaux, T., Tuszynski, J.A., & Cavaglià, M. (2026). EMI model: A scale free biophysical framework for human consciousness, cognition and behaviour. BioSystems, 259, 105674. https://doi.org/10.1016/j.biosystems.2025.105674

• Deco, G., & Kringelbach, M.L. Whole-Brain Modelling: Cartography of the Dynamics of Mind. Oxford University Press. https://academic.oup.com/book/62453

• Cieri, F. (a cura di). (2022). Neuroscienze Psicodinamiche. Verso il superamento di una mindless neuroscience e di una brainless psychoanalysis. Milano: FrancoAngeli.

• Freud, S. (1950 [1895]). Project for a Scientific Psychology. In The Standard Edition of the Complete Psychological Works of Sigmund Freud, Vol. 1, pp. 283-397. London: Hogarth Press.