Compound Interest Is at War with Physics
What happens when an Islamic finance professional discovers that a Nobel Prize-winning scientist reached the same conclusion about interest—from completely different starting points?
I've spent years studying Islamic finance. I can explain the difference between murābahah and mushārakah in my sleep. I've read the international standards, debated Sharīʿah compliance issues, and analyzed sukuk structures across multiple jurisdictions.
But I'd always treated the prohibition of ribā (interest) as primarily an ethical or theological matter. It was about justice, fairness, the exploitation of the poor. Important, yes. But ultimately a moral position.
Then I stumbled across Frederick Soddy.
Soddy won the Nobel Prize in Chemistry in 1921 for discovering isotopes—work that helped unlock the secrets of the atom. After World War I, this brilliant scientist turned his analytical mind to economics. And what he found disturbed him so deeply that he spent the rest of his life warning anyone who would listen.
His conclusion? Compound interest is at war with physics.
I'm not a physicist. But as I dug deeper into Soddy's work and the field of "biophysical economics," I realized something extraordinary: a Nobel-winning Western chemist and medieval Islamic jurists had independently identified the same fundamental problem with interest—from completely opposite starting points.
One used thermodynamics. The other used revelation. Both concluded that money cannot be allowed to grow on its own.
It's a structural observation about reality that two radically different intellectual traditions reached independently.
Let me explain.
The Tale of Two Curves
The best way to understand this is to visualize two lines on a graph racing toward the future.
The J-Curve: How Debt Grows
When you borrow money at compound interest, your debt follows what mathematicians call an "exponential" or "J-curve." It starts slowly, but accelerates relentlessly upward.
There's a simple rule finance professionals use called the Rule of 72: divide 72 by your interest rate, and you get the number of years until your debt doubles.
- At 5% interest, debt doubles every 14 years
- At 8% interest, debt doubles every 9 years
- At 10% interest, debt doubles every 7 years
Here's the thing: this doubling happens regardless of what occurs in the real world. Drought? Pandemic? Factory burns down? The mathematics of compound interest doesn't care. The debt keeps growing.
If you extend this math backward, you get absurd results. One penny invested at just 2% interest thousands of years ago would now be worth a ball of gold larger than the Earth. Obviously, this hasn't happened—which proves that compound interest has historically been "reset" through defaults, inflations, and financial crises.
But the expectation of the system remains exponential. The mathematics demands infinite growth.
The S-Curve: How Nature Grows
Now consider how things actually grow in the physical world.
When a farmer plants corn, it grows rapidly at first. But eventually, it stops. The soil runs out of nutrients. The rain doesn't fall. The plants crowd each other. Growth hits a ceiling—what biologists call "carrying capacity"—and plateaus.
This is the S-curve or "logistic growth." It's how populations expand, how forests mature, how oil wells deplete. Fast growth, then slowing, then stability (or collapse if the system overshoots its limits).
Trees don't grow to the moon. Bacteria colonies don't fill the ocean. Every physical system eventually hits constraints.
The Collision
Here's where Soddy got worried.
The financial system (J-curve) demands continuous exponential growth. The physical world (S-curve) can only deliver growth up to a point.
When debt grows at 5% but the real economy—the actual stuff we make and grow—can only expand at 2%, a gap opens up. The "claims" on wealth (the money owed) start exceeding the actual wealth available.
What happens then?
The system becomes predatory. To keep the J-curve going, we're forced to extract resources faster than nature can regenerate them. We overfish oceans, deplete aquifers, strip topsoil, and destabilize climates—not always because we need the resources, but because we need the cash to feed the debt.
This is what Soddy meant when he said compound interest is "at war with physics."
Money Is a Claim on Energy (Yes, Really)
This is where it gets interesting—and where I initially felt out of my depth as someone without a physics background.
Soddy argued that money isn't just paper or numbers on a screen. Money is a claim on energy.
Think about it: if you have $100, what can you actually do with it? You can buy gasoline (energy). You can pay someone to work for you (their caloric energy). You can purchase electricity. You can buy food (which is just stored solar energy captured by plants).
Every dollar in your wallet represents a right to demand that some amount of energy be expended on your behalf.
Now here's the critical insight: We can create unlimited money, but we cannot create energy.
Central banks can print trillions of dollars with keystrokes. Banks can create credit by making loans. But no one can print oil, grow electricity, or manufacture sunlight.
When the money supply (claims on energy) grows faster than the energy supply (actual energy available), one of two things must happen:
- Inflation: The value of each dollar drops to match reality
- Default: Debts that can't be paid won't be paid
It's arithmetic meeting physics.
Entropy: Why Time Works Against Wealth
Here's the concept that really made everything click for me.
In physics, entropy is a measure of disorder. The Second Law of Thermodynamics states that everything naturally tends toward disorder over time. Iron rusts. Food rots. Buildings crumble. Machines break down.
Keeping things organized costs energy.
If you own a barn, nature is constantly trying to destroy it—through weather, decay, termites, rot. To maintain that barn, you must continuously invest energy (your labor, materials, repairs). Left alone, the barn will eventually collapse into a pile of rubble.
Now consider how the financial system treats assets.
A $1 million loan doesn't rust. It doesn't decay. Instead, through interest, it grows to $1.05 million next year—without any physical work being done. While real assets are fighting entropy (losing value unless maintained), financial assets are gaining value automatically.
This is the fundamental disconnect.
In the physical world, time subtracts value. In the financial world, time adds value. These two systems are pulling in opposite directions.
Soddy called this the attempt to convert "Real Wealth" (which decays) into "Virtual Wealth" (which grows). He argued this was a rebellion against the laws of physics—an attempt to escape entropy through accounting tricks.
Why Interest Rates Have Collapsed (And Won't Come Back)
Here's where modern data confirms Soddy's nearly century-old theory.
Biophysical economists use a metric called EROI: Energy Return on Investment. It measures how much energy we get back for every unit of energy we invest in extraction.
- 1930s (conventional oil): We invested 1 barrel of energy and got back 100 barrels. EROI = 100:1. Massive surplus. This funded the building of modern civilization.
- Today (fracking, deep sea, tar sands): We invest 1 barrel and get back maybe 10-15 barrels. EROI = 10:1. The surplus has shrunk dramatically.
This declining EROI explains something that puzzles many economists: why have global interest rates trended toward zero for decades?
It's not just central bank policy. It's physics.
When the "energy profit" of civilization was high (100:1), the economy could easily grow at 5-7% annually. Paying 5% interest was easy because real growth exceeded it.
Now, with energy getting harder and more expensive to extract, real growth struggles to hit 2%. The physical economy simply cannot generate the surplus needed to pay high interest rates.
Central banks have been forced to push rates to near-zero not as a temporary emergency measure, but because the biophysical reality has changed. Demanding 5% returns in a world that can only deliver 2% growth is demanding the impossible.
What Medieval Scholars Understood
Now we arrive at the convergence that still astonishes me.
Islamic prohibited ribā—the charging of interest—over 1,400 years ago.
But look at what the prohibition actually does from a physics perspective:
Risk-Sharing vs. Risk-Transfer
In a conventional loan, the bank transfers risk to the borrower. If you borrow $1 million to build a factory and the factory burns down, you still owe $1 million plus interest. The debt grows independently of physical reality.
In the Islamic model of mushārakah (partnership), the financier shares the risk. They provide capital in exchange for a share of actual profits. If the factory burns down, they lose their investment. If it succeeds, they share the gains.
The physics of this are profound:
- In risk-sharing, financial returns are tied 1:1 to physical output
- If the harvest fails (entropy wins), financial returns are zero
- Financial claims cannot grow faster than physical reality
- There's no "gap" between the J-curve and S-curve—because there is no J-curve
This is what Soddy was calling for without knowing it existed: a system where money is coupled to reality rather than divorced from it.
Asset-Backing
Islamic finance requires transactions to be backed by tangible assets. You can't make money purely from money. Every financial transaction must correspond to something real—a house, a commodity, a service.
This puts a "speed limit" on money creation. The financial system can only expand as fast as the real economy because it's tethered to actual things.
The independent convergence here is remarkable. A 20th-century Nobel chemist and 7th-century jurists, working from entirely different premises, reached the same structural conclusion: separating money from physical reality creates systemic instability.
The Uncomfortable Truth I Can't Ignore
Now I need to be honest about something that troubles me professionally.
Modern Islamic banking has largely failed to implement this physics-compliant model.
The data is clear:
- True profit-and-loss sharing (mushārakah and mudārabah) represents less than 6% of Islamic banking assets globally
- The dominant product is murābahah (cost-plus financing)—which creates fixed debt obligations nearly identical to conventional loans
- Islamic bank returns are typically benchmarked to LIBOR, SOFR, or local interest rates
- Studies find "few significant differences" between Islamic and conventional banks in practice
In other words, the industry has largely mimicked conventional finance with Arabic terminology. We've taken the form of Islamic finance without the substance that would make it thermodynamically different.
This is painful to acknowledge. But intellectual honesty requires it.
The theoretical framework of Islamic finance offers a genuine solution to Soddy's problem. The current practice mostly doesn't.
Why This Matters Now
You might be wondering: why does any of this matter? Interest-based banking has existed for centuries. The world hasn't ended.
Three reasons:
1. We're Hitting Real Limits
For most of industrial history, the S-curve was still in its steep upward phase. There was always more land to farm, more oil to drill, more fish to catch. The J-curve of debt could chase an expanding physical economy.
Now we're approaching (or have passed) numerous planetary boundaries: climate stability, biodiversity, freshwater availability, nitrogen cycles. The S-curve is flattening. But the J-curve of global debt continues to spike.
2. The Gap Is Widening
Global debt has reached approximately $300 trillion—over 350% of global GDP. This represents claims on future production that may not be physically possible to deliver.
When the gap between financial claims and physical capacity gets too wide, it doesn't close gradually. It closes suddenly and painfully through defaults, inflation, or collapse.
3. There's a Real Alternative (In Theory)
Soddy spent decades calling for monetary reform but had no working model to point to. We do. The principles of risk-sharing and asset-backing in Islamic finance offer a template for a financial system that doesn't require infinite growth.
What I've Learned
This journey from Islamic finance specialist to amateur biophysical economist has changed how I see my field.
I used to view ribā prohibition primarily through the lens of social justice—protecting borrowers from exploitation. That remains important.
But now I see a deeper dimension: structural stability.
Compound interest creates a mathematical demand for infinite growth. Islamic finance (in its ideal form) creates a financial system that can exist in equilibrium with physical limits. One is at war with entropy; the other acknowledges it.
A Nobel chemist and medieval scholars converged on this understanding from opposite directions. That convergence suggests they were both responding to something real—not just cultural preferences, but a genuine structural feature of reality.
The prohibition of ribā isn't just ethical. It's ecological. It's thermodynamic. It's a recognition that you cannot pit abstract mathematics against the laws of physics and expect it to work forever.
Where Do We Go From Here?
I don't have all the answers. But here's what I believe:
For Islamic finance professionals: We need to take the theoretical foundations of our field more seriously. The dominance of murābahah and debt-mimicking structures has hollowed out the transformative potential of Islamic finance. True risk-sharing isn't just Sharīʿah-compliant—it's physics-compliant.
For sustainability advocates: The Islamic finance tradition offers conceptual resources that secular steady-state economics lacks. The convergence between Soddy's critique and ribā prohibition deserves serious academic attention.
For everyone: The fantasy isn't critiquing compound interest. The fantasy is believing that 3% compound growth can continue forever on a finite planet. Whether we address this through Islamic finance reform, monetary restructuring, or something else entirely—address it we must.
The math of compound interest is colliding with the physics of a finite world. Two very different traditions saw this clearly. Perhaps it's time we started listening.
What do you think? Have you encountered other traditions that recognize the tension between exponential finance and physical limits? I'd love to hear your thoughts in the comments.
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Disclaimer: The views expressed in this blog are not necessarily those of the blog writer and his affiliations and are for informational purposes only.
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Tags: Islamic Finance, Sustainable Finance, Compound Interest, Riba, Frederick Soddy, Biophysical Economics, Green Sukuk, Steady State Economics, EROI, Thermodynamics