BY THE NUMBERS

The world behind the numbers.

A closer look at AI’s physical footprint. Every chart keeps its units, dates, scope, and source attached.

Test an idea.

Scaling, in motion

Find the balance between model and data.

Move the model-size slider. With a fixed training budget, a larger model gets fewer training tokens.

Assumptions: a historical Chinchilla loss fit and C ≈ 6ND. Data quality and architecture stay fixed; lower loss does not measure intelligence.

Make a prediction

At the original budget, double the model from 70B to 140B parameters. What happens to fitted loss?

LowerHigherThe same

Your model Fit’s minimumDashed curve: original budget

Model size 70B

8.75B280B

Training budget 1.00×

¼× compute4× compute

Model parameters70B

Training tokens1.40T

Fitted loss1.937

At this budget, the equation’s minimum is around 32.5B parameters and 3.02T tokens.

Historical fit, extrapolated here—not measured scores or a forecast for today’s models. Hoffmann et al., 2022.

The equation and assumptions

Appendix D.2 fits L = 1.69 + 406.4/N⁰·³⁴ + 410.7/D⁰·²⁸, using raw parameter and token counts. We approximate training compute as C = 6ND; the reference budget is 5.88 × 10²³ FLOPs. This is one fit from the paper, not a universal optimal recipe. Loss measures prediction on the study’s text distribution, not intelligence. Architecture, data quality, inference expense, and modern training changes are outside this illustration.

Read the scaling-laws guide

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GLOBAL DATA-CENTER INVESTMENT$500bn

Estimated investment in 2024.
All data centers, not AI alone.

IEA · Energy and AI (2025)

SHARE OF GLOBAL ELECTRICITY1.5%

Data centers’ estimated share in 2024.
Concentrated local demand matters too.

IEA · Energy and AI (2025)

GLOBAL DATA-CENTER ELECTRICITY DEMAND

A growing appetite for power.

TWh / year

2024

415

Estimate

2030

945

Projection

IEA’s 2025 base-case outlook. The 2030 value is a projection, not an observed result. These totals include AI and other data-center workloads.

Source: International Energy Agency, 2025

A useful distinction.

Company-wide capital expenditure, data-center investment, and AI-specific spending measure different things. We don’t add them together or call them interchangeable.