The deep future

Foundations

The famous number is the wrong number

Everybody has heard that the Sun will swallow the Earth in about five billion years.

That is roughly right, and it is not the number that matters, because the biosphere ends about four billion years before the Sun gets here.

The mechanism is the one from lesson 4.7, running the other way.

The Sun brightens as it ages. Hydrogen fusion in the core gradually changes its composition, the core contracts and heats, and the star’s output rises. It is about thirty per cent brighter now than when the Earth formed. That rise continues.

Lesson 4.7 described the weathering thermostat: silicate rock reacts with carbon dioxide and water, the reaction goes faster when it is warmer, and the carbon ends up in ocean sediments. It is a negative feedback, and it is the reason Earth stayed habitable through a thirty per cent increase in solar output rather than boiling.

But a thermostat that works by removing carbon dioxide has a floor. As the Sun brightens further, the thermostat compensates by drawing carbon dioxide down. Eventually it reaches the level below which plants cannot photosynthesise.

Estimates put that on the order of a billion years away, with the exact figure depending on which photosynthetic pathways are considered and on assumptions about weathering rates. Loss of surface water follows, as higher temperatures drive evaporation and water vapour is broken up high in the atmosphere and the hydrogen escapes.

So the honest framing is unsettling in a way the popular version is not. Life on Earth has existed for something like 3.8 billion years, and has on the order of one billion left.

This planet’s habitable window is more than half over.

The same feedback that kept Earth alive through the faint young Sun problem of lesson 4.5 is the one that finishes it. It was never a permanent solution. It was a mechanism with a range, and we are well into the range.

And then the Sun does arrive

In roughly seven and a half billion years the Sun exhausts hydrogen in its core and expands as a red giant, reaching a radius larger than Earth’s current orbit.

There is a genuinely interesting subtlety here. A red giant loses mass in a strong stellar wind, and as the Sun loses mass its gravitational hold weakens, so the planets’ orbits expand. For a while it looked as though Earth might outrun the swelling surface.

Detailed modelling that includes tidal interaction between the bloated star and the planet concludes it does not. Earth is engulfed.

By then the surface has been sterile for billions of years, which is why the earlier number matters more.

The textbook fact that stopped being one

Now something that changed very recently, and it is a good example of why this course labels confidence.

Andromeda is approaching us. Measuring its motion across the sky — its proper motion, as opposed to its motion toward us — is extraordinarily difficult, because the galaxy is two and a half million light years away and the sideways motion is tiny.

It was measured with the Hubble Space Telescope, and in 2012 the conclusion was that the transverse motion is small enough that a merger with the Milky Way was essentially certain, in about four to five billion years. That result entered every popular account, this course’s own early drafts included, as a settled fact. Some accounts even named the merged galaxy.

In 2025 a new analysis revisited it with improved astrometry, updated mass estimates, and — importantly — the gravitational influence of the Large Magellanic Cloud, which is massive enough to matter and had been left out.

The probability of a merger within the next ten billion years came out close to even, rather than close to certain.

Notice what happened. A measurement improved, a neglected term was included, and a fact everybody repeated turned into a coin flip. Nothing was fraudulent, and nobody was foolish. The earlier result was the correct conclusion from the evidence available at the time.

This is the last chapter of the course, so it is worth saying explicitly: that is what a healthy fact looks like. Not a permanent truth, but the current best estimate, revisable when the measurements improve, and labelled honestly about which it is.

If the merger does happen, incidentally, essentially no stars collide. Stars are separated by distances tens of millions of times their own diameters. Two galaxies pass through each other and rearrange, and the individual stars sail past one another.

Past the point where words help

Now the timescales stop being intuitive and start being exponents. What follows is largely from a 1997 review that took known physics as far into the future as it will go, and it should be read as a careful extrapolation rather than a measurement, because that is what it is.

Around ten to the fourteen years. Galaxies run out of the gas needed to make new stars. The last, smallest, longest-lived stars burn out. Star formation ends.

The degenerate era. What remains is remnants: white dwarfs cooling toward the temperature of the surrounding universe, neutron stars, black holes. No new stars, no new planets. The universe is dark and consists mostly of objects held up by quantum mechanical pressure rather than by heat.

Then a genuine open question. Some theories predict that protons eventually decay. If they do, ordinary matter has a finite lifetime, and over immense timescales the white dwarfs and neutron stars evaporate into lighter particles. If they do not, matter persists.

Proton decay has never been observed. Large detectors have watched enormous volumes of water for decades and seen nothing, which sets a lower bound on the proton lifetime far beyond the current age of the universe. So this branch of the future is unresolved by experiment, and honestly labelled as such.

The black hole era. Black holes are predicted to radiate and slowly evaporate. The timescale for a supermassive black hole is around ten to the hundred years — a one followed by a hundred zeros.

To give that a handle: the universe is currently about ten to the ten years old. The exponent has to go up by ninety.

And after that, on standard assumptions, a cold, thin, expanding universe with no structure and no free energy to do anything with. The scenario is usually called heat death, and the name is misleading — it is cold. What dies is the temperature difference, and difference is what work requires.

Except that the ending is not settled either

Everything above assumes dark energy behaves as a cosmological constant: a fixed energy density that does not change as the universe expands.

That assumption is written as w equals minus one, where w is the ratio of pressure to energy density. If w is exactly minus one and stays there, the expansion accelerates forever and you get the picture above.

But w is measured, not derived. And recent large surveys of baryon acoustic oscillations — the frozen sound waves from lesson 1.4, used as a standard ruler — have been reported as showing a mild preference for dark energy that evolves rather than staying constant.

That result is not established. It depends on which datasets are combined and on how supernova samples are calibrated, and it is exactly the kind of marginal preference that has evaporated before.

But if it holds, the ending changes. Dark energy that weakens over time gives a different future from one that strengthens. The fate of the universe is currently an open observational question, and it may be settled within the working lifetime of anyone watching this.

Which is a remarkable thing to be able to say.

What this course was actually about

This is the last lesson, so let me say what the through-line has been.

Every structure in these fifty-nine preceding lessons is temporary, and maintained by a flow of energy through a system that is not in equilibrium.

A star is a temporary balance between gravity and radiation pressure, lesson 2.2. A planet is temporary. A cell is a structure that maintains itself by processing energy and falls apart the moment it stops, lesson 5.1. A civilisation is the same thing at a different scale, running on energy flows that lesson 8.3 traced to buried sunlight.

Complexity, in this course’s sense, is not a substance. It is a process that has to be paid for continuously, and everything that stops paying comes apart.

That sounds bleak stated flatly. I do not think it is, and here is why.

The universe had no obligation to contain arrangements of matter that could work out their own history. It contains at least one. On a planet whose habitable window is more than half spent, in a galaxy whose future was revised last year, a temporary structure made of elements forged in dead stars assembled a method for finding out what is true, and used it to measure the age of everything, the composition of the Sun, the temperature of the sky, the depth of time in the rock, and the sequence of its own genome.

That is what the fifty-nine lessons before this one were describing.

The one thing to keep

If you keep one thing from this course, do not make it a fact. Facts get revised — this lesson revised two of them.

Keep the procedure.

Ask what was measured, and by whom, and with what instrument. Ask who checked it, and whether they were in a position to disagree. Ask what would show it to be wrong, and whether anyone has looked. Notice the difference between a measurement, a model, and a guess, and refuse to let anyone blur them — including yourself, and including when the blurred version is more comfortable or more exciting.

That is the whole method. It is not difficult to state and it is difficult to practise, and it took four continents and a thousand years to assemble, as lesson 8.2 described.

Everything this course told you is provisional. That is not a weakness of the course. It is the only honest way to know anything, and it is the reason the parts that are solid are worth trusting.

Where to go now

Back to lesson 1.1, which said the Big Bang did not happen somewhere far away. It happened where you are sitting, because every point in space was part of it.

You now have thirteen point eight billion years of context for that sentence, and it should read differently than it did.

And then to lesson 1.7, on the open questions, which is the honest list of what this course does not know. That is the right place to leave a student: not with the answers, but with the current edge of the answers, and the tools to tell when it moves.

Deeper

How the biosphere lifespan estimate is made

The calculation couples a solar evolution model, giving luminosity against time, to a carbonate-silicate cycle model that computes the atmospheric carbon dioxide concentration required to balance the radiation budget at each luminosity. Falling below the compensation point for C3 photosynthesis terminates most plant life; C4 plants, which concentrate carbon dioxide internally, persist to lower concentrations and therefore later times. Caldeira and Kasting revised earlier and shorter estimates upward by treating the carbon cycle more carefully and allowing for C4 pathways. The result is a range rather than a date, and the uncertainties are in weathering kinetics, in how biological productivity responds near the limit, and in the solar model. What is robust is the direction and the order of magnitude: hundreds of millions to a couple of billion years, not tens of billions.

Why the engulfment question was close

As the Sun ascends the red giant branch it loses a significant fraction of its mass in a wind. Angular momentum conservation expands the orbits of the surviving planets, and Earth’s orbital radius would grow substantially. Set against that is tidal interaction: the tidal bulge the planet raises on the slowly rotating giant lags, and the resulting torque transfers orbital angular momentum into the star, dragging the planet inward. Schröder and Connon Smith modelled both, together with the star’s maximum radius near the tip of the branch, and found the inward tidal drag wins. The result depends on the mass-loss prescription and on the tidal dissipation efficiency, both of which carry uncertainty, so this is a well-argued conclusion rather than a certainty.

What changed in the Andromeda calculation

Whether two galaxies merge depends on their relative transverse velocity, which sets the angular momentum of the encounter, and on their masses, which set the dynamical friction that removes energy from the orbit. Both are hard to measure. The transverse velocity of Andromeda is at the limit of what astrometry can do. The 2025 analysis used improved astrometric data and, critically, included the Large Magellanic Cloud, whose mass is large enough to displace the Milky Way’s centre of mass and perturb the orbit. Including it, and propagating realistic uncertainties through many simulations rather than adopting central values, produced a broad distribution of outcomes with merger and non-merger both common. The lesson is as much about propagating uncertainty properly as about the physics.

Why heat death is a statement about gradients

Work requires a difference: a hot reservoir and a cold one, a concentration gradient, a potential difference. The second law says isolated systems evolve toward states with fewer such differences. A universe expanding forever with no star formation and no bound structures approaches uniformity, and in that state no process can extract work regardless of how much energy is present. The energy does not disappear; it becomes unusable. This is the sense in which every structure in this course is temporary: each one is a local, temporary, paid-for departure from uniformity, and the account it draws on is finite.

Frontier

Whether dark energy evolves

Distinguishing a cosmological constant from slowly evolving dark energy requires precise distance and expansion-rate measurements across a wide range of redshift. Current hints depend on combining baryon acoustic oscillation measurements with supernova samples whose cross-calibration is difficult, and different supernova compilations shift the significance. Larger surveys now underway will either strengthen the preference or return it to consistency with a constant.

Proton decay

Experiments continue to push the lower limit on the proton lifetime upward. A detection would be one of the most important results in physics and would settle whether ordinary matter is permanent. A continued absence constrains grand unified theories without resolving the question, which is the frustrating asymmetry of null results.

Transcript and shot list

Target runtime about 13 minutes. The course closer. Built to correct the famous number, then zoom out by powers of ten until the exponents stop meaning anything, then come back to lesson 1.1. Shot types: ANIM is rendered from code with Manim, AI is a generated shot from Higgsfield with the shared style reference, REAL is agency imagery with credit, CAM is the narrator.

[00:00] S01 · CAM · Narrator direct to camera.

You have heard that the Sun will swallow the Earth in about five billion years. That is roughly right, and it is the wrong number to care about. Because the biosphere ends about four billion years before the Sun gets here.

[00:19] S02 · ANIM · Solar luminosity rising through the main sequence: core hydrogen converting, core contracting and heating, output climbing. Thirty per cent brighter now than at Earth’s formation, and still rising.

The Sun brightens as it ages. Fusion gradually changes the composition of the core, the core contracts and heats, and the star’s output rises. It is about thirty per cent brighter now than when the Earth formed, and that continues.

[00:37] S03 · ANIM · The weathering thermostat from lesson 4.7: silicate rock reacting with CO₂ and water, faster when warm, carbon ending in ocean sediments. Then the thermostat drawing CO₂ down as luminosity rises — and hitting a floor, below which photosynthesis fails.

Lesson 4.7 described the weathering thermostat. Silicate rock reacts with carbon dioxide and water, the reaction runs faster when it is warmer, and the carbon ends up in ocean sediments. A negative feedback, and the reason Earth stayed habitable through a thirty per cent increase in solar output instead of boiling. But a thermostat that works by removing carbon dioxide has a floor. As the Sun brightens further, the thermostat compensates by pulling carbon dioxide down, and eventually it reaches the level below which plants cannot photosynthesise. Estimates put that on the order of a billion years away. Loss of surface water follows, as higher temperatures drive evaporation and water vapour gets broken up high in the atmosphere and the hydrogen escapes.

[01:34] S04 · ANIM · Earth’s habitable span drawn as a bar: 3.8 billion years elapsed, about 1 billion remaining. The bar more than half filled.

So the honest framing is unsettling in a way the popular version is not. Life on Earth has existed for something like 3.8 billion years and has on the order of one billion left. This planet’s habitable window is more than half over. And the same feedback that kept Earth alive through the faint young Sun problem in lesson 4.5 is the one that ends it. It was never a permanent solution. It was a mechanism with a range, and we are well into the range.

[02:13] S05 · ANIM · Seven and a half billion years on: core hydrogen exhausted, the Sun expanding past Earth’s current orbit. Mass loss in the stellar wind weakening its grip and orbits expanding; then tidal drag from the bulge on the slow-rotating giant pulling Earth back in. Engulfment.

Then the Sun does arrive. In roughly seven and a half billion years it exhausts core hydrogen and expands as a red giant, out past Earth’s present orbit. And there is a lovely subtlety here. A red giant loses mass in a strong wind, and as the Sun loses mass its gravitational grip weakens and the planets’ orbits expand. For a while it looked as though Earth might outrun the swelling surface. Detailed modelling that includes tidal interaction between the bloated star and the planet says it does not. Earth is engulfed. By then the surface has been sterile for billions of years, which is exactly why the earlier number matters more.

[03:05] S06 · ANIM · Andromeda two and a half million light years away; the transverse proper motion drawn as a tiny sideways arrow, at the limit of astrometry. Hubble measuring it; the 2012 conclusion of essentially certain merger in four to five billion years entering every popular account.

Now something that changed very recently, and it is a good example of why this course labels confidence. Andromeda is coming toward us. Measuring its motion across the sky, as opposed to toward us, is extraordinarily hard, because it is two and a half million light years away and the sideways motion is tiny. It was measured with Hubble, and in 2012 the conclusion was that the transverse motion is small enough that a merger was essentially certain, in about four to five billion years. That went into every popular account as settled fact. Some of them even named the merged galaxy.

[03:52] S07 · ANIM · The 2025 revision: improved astrometry, updated masses, and the Large Magellanic Cloud added — massive enough to shift the Milky Way’s centre of mass and perturb the orbit. Uncertainties propagated through many simulations rather than central values adopted. The outcome distribution coming out close to even.

In 2025 a new analysis revisited it with better astrometry, updated mass estimates, and — importantly — the gravitational influence of the Large Magellanic Cloud, which is massive enough to matter and had been left out. Propagating the uncertainties through many simulations instead of adopting central values, the probability of a merger within the next ten billion years came out close to even, rather than close to certain.

[04:24] S08 · CAM · Narrator direct to camera.

Notice what happened there. A measurement improved, a neglected term got included, and a fact everybody repeated became a coin flip. Nothing was fraudulent and nobody was foolish — the earlier result was the right conclusion from the evidence available then. This is the last video of the course, so let me say it plainly. That is what a healthy fact looks like. Not a permanent truth. The current best estimate, revisable when the measurements improve, labelled honestly about which it is. And if the merger does happen, essentially no stars collide. Stars are separated by tens of millions of times their own diameters. Two galaxies pass through each other and rearrange, and the stars sail past.

[05:18] S09 · ANIM · A logarithmic timeline beginning to run: 10^14 years, galaxies exhausting star-forming gas, the last small long-lived stars burning out. Then the degenerate era — white dwarfs cooling, neutron stars, black holes, no new stars or planets.

Now the timescales stop being intuitive and become exponents. What follows is largely from a 1997 review that took known physics as far into the future as it goes, and it should be read as careful extrapolation, because that is what it is. Around ten to the fourteen years, galaxies run out of the gas to make new stars, and the last, smallest, longest-lived stars burn out. Star formation ends. What is left is remnants. White dwarfs cooling toward the temperature of the universe around them, neutron stars, black holes. No new stars, no new planets, mostly objects held up by quantum mechanical pressure rather than by heat.

[06:07] S10 · ANIM · The proton decay branch: a predicted decay, never observed; huge detectors watching water for decades and seeing nothing; a lower bound far past the universe’s current age. Then the black hole era, supermassive holes evaporating at ~10^100 years, with the universe’s current age of ~10^10 marked and the exponent gap of ninety drawn explicitly.

Then a genuine open question. Some theories predict protons eventually decay. If they do, ordinary matter has a finite lifetime and over immense spans the white dwarfs and neutron stars evaporate into lighter particles. If they do not, matter persists. Proton decay has never been observed. Large detectors have watched enormous volumes of water for decades and seen nothing, which sets a lower bound on the proton lifetime far beyond the current age of the universe. So this branch of the future is unresolved by experiment, and I am labelling it that way. After that, the black hole era. Black holes are predicted to radiate and slowly evaporate, and for a supermassive one the timescale is around ten to the hundred years. A one followed by a hundred zeros. For a handle: the universe is currently about ten to the ten years old. The exponent has to go up by ninety.

[07:17] S11 · ANIM · A cold, thin, expanding universe with no structure. The label “heat death” shown and corrected — it is cold; what dies is the temperature difference, and difference is what work requires.

And after that, on standard assumptions, a cold thin expanding universe with no structure and no free energy to do anything with. It gets called heat death, which is a misleading name, because it is cold. What dies is the temperature difference. And difference is what work requires.

[07:39] S12 · ANIM · The cosmological constant assumption written as w = −1. Then baryon acoustic oscillations from lesson 1.4 used as a standard ruler; recent surveys reported as mildly preferring evolving dark energy; the dependence on dataset combination and supernova calibration flagged; the result marked not established.

Except the ending is not settled either. All of that assumes dark energy behaves as a cosmological constant: a fixed energy density that does not change as the universe expands. That is written as w equals minus one, w being the ratio of pressure to energy density. If it is exactly minus one and stays there, expansion accelerates forever and you get the picture I just described. But w is measured, not derived. And recent large surveys of baryon acoustic oscillations — the frozen sound waves from lesson 1.4, used as a standard ruler — have been reported as mildly preferring dark energy that evolves rather than staying constant. That is not established. It depends which datasets you combine and how the supernova samples are calibrated, and it is exactly the sort of marginal preference that has evaporated before. But if it holds, the ending changes. So the fate of the universe is currently an open observational question, and it might be settled within the working lifetime of anybody watching this. Which is a remarkable thing to be able to say.

[09:03] S13 · ANIM · Structures assembled and then dissolving in sequence: a star as a temporary balance of gravity and radiation pressure; a planet; a cell maintaining itself by processing energy; a civilisation running on buried sunlight. Each labelled temporary, each paid for by an energy flow.

This is the last lesson, so let me say what the through-line has been. Every structure in the fifty-nine lessons before this one is temporary, and maintained by a flow of energy through a system that is not in equilibrium. A star is a temporary balance between gravity and radiation pressure. A planet is temporary. A cell is a structure that holds itself together by processing energy and falls apart the moment it stops. A civilisation is the same thing at a different scale, running on the buried sunlight of lesson 8.3. Complexity, in this course’s sense, is not a substance. It is a process that has to be paid for continuously, and everything that stops paying comes apart.

[09:58] S14 · CAM · Narrator direct to camera.

Stated flatly that sounds bleak. I do not think it is. The universe had no obligation to contain arrangements of matter that could work out their own history. It contains at least one. On a planet whose habitable window is more than half spent, in a galaxy whose future got revised last year, a temporary structure made of elements forged in dead stars assembled a method for finding out what is true — and used it to measure the age of everything, the composition of the Sun, the temperature of the sky, the depth of time in the rock, and the sequence of its own genome. That is what the fifty-nine lessons before this one were describing.

[10:52] S15 · ANIM · The method restated as four questions: what was measured and with what instrument; who checked it and could they disagree; what would show it wrong and has anyone looked; is this a measurement, a model or a guess. Then the three categories held apart and refusing to blur.

So if you keep one thing from this course, do not make it a fact. Facts get revised — this video revised two of them. Keep the procedure. Ask what was measured, and by whom, and with what instrument. Ask who checked it, and whether they were in a position to disagree. Ask what would show it to be wrong, and whether anybody has looked. And notice the difference between a measurement, a model and a guess, and refuse to let anyone blur them — including yourself, and especially when the blurred version is more comfortable or more exciting. That is the whole method. Easy to state, hard to practise, and it took four continents and a thousand years to put together.

[11:48] S16 · ANIM · The cosmic calendar running all the way back to the first frame of lesson 1.1: the Big Bang happening at every point in space, including this one. Then a pointer forward to lesson 1.7, the open questions.

Everything this course told you is provisional. That is not a weakness. It is the only honest way to know anything, and it is exactly why the parts that are solid are worth trusting. Go back to lesson 1.1, which said the Big Bang did not happen somewhere far away. It happened where you are sitting, because every point in space was part of it. You now have thirteen point eight billion years of context for that sentence, and it should read differently than it did. And then go to lesson 1.7, the open questions, which is the honest list of what this course does not know. That is the right place to leave you. Not with the answers. With the current edge of the answers, and the tools to notice when it moves.

Shot list

Zero AI shots, thirteen code-rendered shots, three narrator shots. The final shot reuses the opening scene of lesson 1.1 deliberately, run in reverse, so the course closes on the frame it opened with.