Solar Ceilings and Compounding Dreams

It is fashionable to wave away physical constraints with vague references to solar abundance and human ingenuity. Yet every balance sheet eventually meets a balance of energy. Solar photons may shower Earth with roughly 170,000 terawatts, but financial markets expect growth that compounds on top of itself forever. The math linking those stories rarely appears in the same paragraph—so let’s put them together.

Setting the Stage

I keep coming back to Tom Murphy’s dialogue in Exponential Economist Meets Finite Physicist. In Act One, Murphy plots U.S. energy use from 1650 onward and it traces a remarkably straight exponential line at ~3% per year. Economists in the conversation shrug; after all, 2–3% feels modest. But compounding at that pace means energy demand multiplies by ten every century. Our economic models implicitly assume something even more optimistic : 8–10% returns in equity markets, pension targets, and venture decks; without asking what energy supply function supports that.

Thermodynamic Guardrails

Murphy distills the second law of thermodynamics into plain language:

“At a 2.3% growth rate (conveniently chosen to represent a 10× increase every century), we would reach boiling temperature in about 400 years… Even if we don’t have a name for the energy source yet, as long as it obeys thermodynamics, we cook ourselves with perpetual energy increase.”

That thought experiment matters less for the literal 400-year timer and more because it shows energy growth must decelerate to avoid turning Earth into a heat engine. Solar panels, fusion, space mirrors … pick your technology. The waste heat still has to radiate away. We cannot spreadsheet, app and AI our way around Stefan–Boltzmann and Black Body radiation.

Solar Arithmetic vs Demand Curves

Let’s grant the optimists a heroic build-out: cover 5% of Earth’s land area with 20%-efficient photovoltaic arrays, assume a generous 200 W/m² average output, and we net roughly 20 TW—about the entire human primary energy demand today. That is fantastic news for decarbonization, but it is not a blank check for compounding GDP. If demand keeps growing at 3%, we would need 20 TW × (1.03)ⁿ in perpetuity. Within 250 years we’d be trying to harvest thousands of terawatts—orders of magnitude more land, materials, storage, and transmission than our initial miracle project. Solar abundance is real; solar infinity is fiction.

Finance Is an Energy IOU

Money is a claim on future work, and work requires energy. When pensions assume 7–8% annual returns, when startups pledge 10× growth, and when national budgets bake in permanent productivity gains, they are effectively promising that future societies will deliver 2–3 doublings of net energy per century. If we instead hit a solar plateau—because land, materials, or social license cap expansion—those financial promises become unmoored. We can pretend that virtual goods, algorithmic trading, or luxury desserts (to borrow Murphy’s Act Four anecdote) deliver infinite utility without added energy, but the chefs, coders, and data centers still eat, commute, and cool their CPU’s , GPU’s and Tensor processors. The intangible economy rides on a very tangible energy base.

Rewriting the Business Plan

Accepting a solar ceiling does not doom us to stagnation. It just forces different design constraints:

• grow quality, not quantity—prioritize outcomes per unit energy … do proof of useful work rather that roll the dice and gamble.
• align finance with expected energy supply rather than mythical exponentials … and I am not talking of wasting energy on crypto.
• treat efficiency gains as buying time, not as a perpetual motion machine … if you learnt enough physics in high school to reject the perpetual motion machine, but have been lulled into perpetual 8% returns from the finance markets, there is a serious schizophrenia issue.
• embed thermodynamic literacy in economic education so debates start from the same math.

Murphy ends his essay noting that growth is not a “good quantum number.” It is not conserved. Our job is to craft institutions, portfolios, and narratives that can thrive when net energy flattens, because physics already told us that day will arrive long before our spreadsheets hit overflow errors.