The claim: Most people think in straight lines. Reality compounds. The gap between straight-line intuition and compounding reality is where the biggest opportunities — and the biggest blind spots — live. Knowing where something sits on its curve tells you more about what happens next than any single data point does. This is a lens for asking that question, with the doubling times written down.
The core of it
- Exponential growth. A constant percentage increase per unit of time. It looks flat for a long while, then explodes — the "hockey stick." Most people notice only after the bend.
- The S-curve. Exponential growth that eventually runs out of room and levels off. Three phases: slow start (adoption), rapid growth (scaling), plateau (maturity). Every technology follows it. The question is always where on the curve we are.
- Doubling time. The most intuitive way to hold an exponential in your head. If something doubles every N months, after 10 doublings it is 1,024x where it started. The Rule of 72: divide 72 by the growth rate to get the doubling time.
How to use it
When evaluating any trend, investment, technology or decision, ask five things:
- Is it on an exponential curve? If it is, straight-line extrapolation will underestimate it.
- Where on the S-curve is it? Early is the chance to get in, mid is the ride, late means the gains are already priced in.
- What is the doubling period? Faster means more disruptive. Solar at 22 months is far faster than batteries at 8-10 years.
- What breaks the curve? Physical limits, regulation, social resistance, resource constraints.
- What does the curve enable downstream? Solar leads to cheap energy, which leads to cheap compute, which leads to cheap AI, which leads to postmodern agency.
Two things fall out of the lens. First, the picks-and-shovels idea: invest in the infrastructure of the exponential, not in the applications riding on top of it. Second, a warning about your own plans — a 7% portfolio return assumption is a straight line, and the question is whether AI exposure could instead ride an exponential. There is also a view from the inside: the organizational singularity, where the J-curve transition cost (output dips before it rises) is simply what an exponential feels like from inside a company that has to live through it.
Who argues it
- Peter Diamandis — the "6 D's of Exponentials": Digitization, Deception (it still looks flat), Disruption (suddenly it is everywhere), Demonetization (cost collapses), Dematerialization (physical becomes digital), Democratization (everyone gets access).
- Salim Ismail — exponential organizations. Companies built to ride these curves grow on them; linear organizations get disrupted by them.
- Benedict Evans — maps the curves onto market sizing. The total market isn't what it looks like at the start of the curve. It is what it becomes once the curve bends.
The evidence
Documented curves, with their doubling periods and where they currently sit.
Solar energy
- Doubling period: about 22 months, sustained for 40+ years and counting.
- Where it sits: still on the exponential part, not yet at the S-curve plateau.
- Why it matters: solar is following the same curve semiconductors did. Price per watt has fallen 99%+ since the 1970s. Most energy forecasts, from the IEA and others, have systematically underestimated solar because they projected in straight lines.
- Source: the Moonshot podcast, and also documented by Ramez Naam, Tony Seba, and the Oxford Martin School.
Semiconductors (Moore's Law)
- Doubling period: about 18-24 months for transistor density, running from 1965 to today — roughly 60 years.
- Where it sits: traditional silicon is approaching physical limits, but new architectures — 3D stacking, chiplets, new materials — keep the effective compute doubling going.
- Why it matters: it is the foundation everything else here is built on. AI compute spending ($37B, then $90B, then $219B across three years) is a downstream effect of it.
AI compute
- Doubling period: computing capacity is growing more than 200% per year — faster than spending, because the chips keep getting more efficient. Running from 2020 to now, and accelerating since GPT-3.
- Quality-adjusted output (counting capability gained, not just dollars spent): about 2,270% per year, per the UVA/Anthropic/Bank of Canada paper, 2026.
- Where it sits: early exponential. Enormous capital flowing in, returns not yet visible in GDP.
- Why it matters: at 2,270% annual growth this is the steepest documented exponential in economic history. As the paper puts it:
Conventional statistics show a sector growing slowly in nominal terms; our measures show one whose underlying capacity is more than doubling annually.
Genome sequencing
- Doubling period: faster than Moore's Law since about 2007.
- Cost trajectory: $100M in 2001, $1,000 in 2022, approaching $100 in 2026.
- Where it sits: the cost plateau is approaching, and the curve is shifting from "can we sequence it?" to "can we interpret it?"
- Why it matters: healthcare transformation. At $100, everyone gets sequenced, and the bottleneck moves to AI interpretation.
Battery energy density
- Doubling period: about 8-10 years — slower than solar or compute — improving consistently since lithium-ion was commercialized in 1991.
- Where it sits: mid-curve. Solid-state batteries could speed the doubling up.
- Why it matters: electric vehicles, grid storage and portable devices all ride this one. Slower than solar, but relentless.
Internet users
- Growth trajectory: 16M in 1995, 1B in 2005, 3.4B in 2016, 5.5B+ in 2026.
- Where it sits: approaching saturation — the S-curve plateau — in developed markets. Growth is now in developing economies.
- Why it matters: finishing this S-curve is what makes postmodern agency possible globally. AI access requires internet access, and internet access is now nearly universal.
Curves still on the list to document, not yet worked up: LEO satellite launches (SpaceX Starlink cadence), wind energy (follows solar, roughly 5 years behind), EV adoption by country (Norway as the leading indicator), robotics deployments (warehouse, surgical, agriculture), protein folding predictions (the AlphaFold accuracy curve), and LLM parameter count (GPT-2 to GPT-3 to GPT-4 to frontier models).
This is a living file. Add documented exponentials — with their doubling periods, durations and current position on the S-curve — as you come across them.
All theories · clickbridge.com · Rich Price · last reviewed September 2026 · People linked here have their own pages at people.clickbridge.com