Futures

The world of 2126 depends, above all, on two decisions: how much we regulate and cooperate (peace) and how fast we let AI advance (the frontier). Crossing them gives four futures. None is a prediction, and the atlas does not advocate any of them.

How the model works

A small model simulates the century year by year. It takes two numbers between 0 and 1, peace and frontier, and computes twelve indicators: AI capability, robots, work, inequality, population, pace of science, energy, warming, power concentration and risk. It runs 200 times with parameters drawn at random within their ranges; that is why every chart shows a band, not a single line.

Each future’s page starts at its corner of the matrix, but you can move the controls and watch the numbers change.

Equations

AI capability

$$L(t+1)=L(t)+g(t)(1-\frac{L(t)}{L_{max}}),g(t)=[g_{min}+(g_{max}-g_{min})f](1-\phi \mathrm{crisis}(t))$$

L is the logarithm of compute relative to 2026. It grows with the frontier f, slows near its ceiling and during crises.

Automatable tasks

$$A(t)=A_0+(A_{max}-A_0)\frac{L{(t)}^n}{L{(t)}^n+L_{50}^n}$$

An S-curve: few tasks at first, half of them once capability reaches L₅₀.

Employment

$$E(t)=E_0(1-(A(t)-A_0)(1-\kappa )),\kappa ={\kappa }_{min}+({\kappa }_{max}-{\kappa }_{min})p$$

Peace p increases the share of displacement offset by new tasks and policies (κ).

Inequality

$$G(t)=G_0+a(A(t)-A_0)(1-p)-b(A(t)-A_0)p$$

Automation without rules raises it; redistribution lowers it.

Robots

$$R(t+1)=R(t)+rR(t)(1-\frac{R(t)}{\max (R(t),R_{sat}A(t))}),r=r_{min}+(r_{max}-r_{min})f$$

An S-curve whose ceiling rises with automation.

Pace of science

$$S(t)=1+\sigma L(t)(\frac{3}{5}+\frac{2}{5}p)$$

Each order of magnitude of AI speeds up science; cooperation (open science) amplifies it.

AI electricity

$$E_{IA}(t)=E_{IA,0}{10}^{\epsilon L(t)}{(1-\eta )}^t$$

It grows with capability and is tempered by efficiency.

Clean energy

$$Q(t+1)=Q(t)+q_0(\frac{1}{2}+p)(1+\lambda {\log }_{10}S(t))Q(t)(1-Q(t))$$

An S-curve accelerated by cooperation and science.

Warming

$$T(t)=T_0+\mathrm{TCRE}\cdot \frac{{\sum }_{\tau <t}Em(\tau )}{1000},Em(t)=E{m}_0\frac{TE(t)}{T{E}_0}\frac{1-Q(t)}{1-Q_0}+U_0{(1-\upsilon )}^t$$

The IPCC TCRE relationship: warming is proportional to cumulative CO₂. Energy demand TE grows faster with more frontier.

Population

$$P(t)=P_{ONU}(t)(1+\frac{z_{ONU}t}{740})(1+\mu {\log }_{10}S(t))$$

The UN medium variant, shifted within its interval and adjusted for health advances.

Power concentration

$$\mathrm{\Pi }(t)={\mathrm{\Pi }}_0+cL(t){(1-p)}^2-dp$$

An illustrative index: more AI without peace concentrates power.

Cumulative risk of catastrophe

$$h(t)=h_{nat}+h_{IA}\frac{\mathrm{\Delta }L(t)}{g_{max}}{(1-p)}^2+h_{conf}\frac{\mathrm{\Pi }(t)}{100}(1-p),\mathrm{riesgo}(t)=1-e^{-{\sum }_{\tau \le t}h(\tau )}$$

Probability of a catastrophe killing ≥ 10% of humanity: a baseline risk plus that of fast progress without peace and that of power concentration.

Crises

$$\chi (t)=(1-p)(\frac{1}{2}+\frac{\mathrm{\Pi }(t)}{100}),\mathrm{crisis}(t)=1⟺\chi (t)>\theta$$

When tension χ exceeds θ a crisis of D years breaks out; it cannot repeat within 15 years (the last one was the 2020 pandemic).

Parameters

Every parameter has a central value, a range and a source. When there is no direct source, we mark it as an assumption.

Calibration

Before publishing, the model is checked against official figures. These are the targets and whether they are met:

• MetPeaceful frontier temperature 2081–2100, within SSP1-2.6Model value: 2.04 °C
• MetPause temperature 2081–2100, between SSP1-2.6 and SSP2-4.5Model value: 1.97 °C
• MetMatrix-center temperature 2081–2100, within SSP2-4.5Model value: 2.19 °C
• MetRace temperature 2081–2100, between SSP2-4.5 and SSP5-8.5Model value: 2.61 °C
• MetFracture temperature 2081–2100, between SSP2-4.5 and SSP5-8.5Model value: 2.36 °C
• MetRace and Fracture end warmer than Peaceful frontier (difference in °C)Model value: 0.32 °C
• MetCatastrophe risk by 2100 at the center, between superforecasters (9%) and experts (20%)Model value: 17%
• MetCatastrophe risk by 2100 in Pause, below 9%Model value: 7.9%
• MetCatastrophe risk by 2100 in Race, above 20%Model value: 32.8%
• MetData-center electricity in 2030 at the center, ±30% of the IEA base case (945 TWh)Model value: 1,008.48 TWh
• MetYear half of all tasks are automated (center), between 2047 and 2116Model value: 2049
• MetPopulation in 2100 (center) within the UN intervalModel value: 10.28
• MetRobots 2016→2023 at the historical pace, ±15% of IFR’s 4.28 MModel value: 4.03
• MetCompute growth in the first year at full frontier, between ×4 and ×5Model value: 4.5

The risk thresholds (Pause below 9%, Race above 20%) are an editorial choice, anchored in the estimates of superforecasters and experts in the XPT tournament.

Limits of the model

• It does not predict: it links assumptions to consequences.
• Temperature only counts CO₂ and does not model carbon removal, so it never falls; at most, it levels off.
• Population does not react to catastrophes: risk is shown as a probability; the event itself is not simulated.
• The power and inequality indices are illustrative.
• The UN projects to 2100; after that we extend its last rate.
• The relationships between variables are simple on purpose, so they can be read and debated.