The King’s Chessboard: The Inherent Absurdity of Compound Interest

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The King’s Chessboard (source unknown)

[A version of this article was first published as a comment at European Tribune in 2006, which explains why some of the references are a bit stale now. But the point being made is not, I think, invalidated by subsequent changes in the price of gold and other indices.]

erhaps what we call ‘capitalism’ today might better be called ‘interest-ism’ or more simply ‘usury’. Our financial system relies heavily on the magic of compound interest, a dangerously aphysical concept. Why aphysical? Because it cannot be reconciled with the realities of biotic systems or the energy or mineral budget of a planet. Why dangerous? To realise such unnatural rates of return, real capital (natural capital, the only kind there is) has to be liquidated — much as a business can be liquidated by selling off its premises and physical plant to reap a high return in a single year.

We maintain the fantasy of interest-ism only by liquidating real capital at an accelerating pace. This is otherwise known as a mass extinction event; as soil depletion; as persistent pollution; as deforestation; and of course, as climate cancer.

It has long seemed to me that compound interest is an inherently absurd premise. How about a thought experiment?

Let’s say that around the time of the Emperor Augustus we — you or I, who statistically speaking might most likely have been skilled-crafts slaves or artisans at the time — had invested a quadrans — call it a single copper penny — at 5 percent interest compounded annually, and that the world financial system had remained stable ever since — 2000 years for a nice round number.

…compound interest calculation

tcl>expr 1 * pow(1.05,2000)
2.39110220461e+42

After 2000 years we’d have… 2.39 times 10-to-the-42nd-power in pennies today. How big is that number?

A pre-1982 US penny (when they were still mostly copper) had a mass of 3.1 grams. Our Roman copper “penny” (a quarter of a silver denarius) however, was more like 2 grams. So, metal for metal, we would now in theory, be the proud owners of ummm… 4.782e+42 grams of copper.

A kilogram is about 2 lbs or about 1/1000th of a US short ton…. we or our lineal descendants would own 4.782e+39 kilos of theoretical copper penny here, or 4.782e+36 tons of copper. Do check me on the numbers — I did this on the fly, back-of-envelope stuff — but even if I’ve dropped an order or two of magnitude the grotesquerie of the calculation seems self-evident.

“Worldwide economic reserves of copper are stated to be 470 million tonnes by the USGS 2005 summary for copper. “ (ignore the rest of the article, this USGS quote is the relevant bit).

470 million tons is only 4.70e+8 — so compound interest, if applied literally to metals, would award us — after 2000 years at 5 percent — significantly (to say the least) more copper than the entire world currently owns or has at its disposal… by, what, 24 orders of magnitude?

But money is not metal, we argue — we went off the gold standard years ago and the world didn’t come to an end. It’s the notional money that was compounding, not the literal metal! So what we would really have is 2.39 times 10⁴² pennies — pennies worth far, far less in real purchasing power than the same weight of copper would have been in Roman times. Pennies aren’t even made of copper any more. OK, fair nuff.

So how many trillions of dollars is that? A trillion in the US is a one with 12 zeros or 1 times 10¹². 2.39e+42 pennies is a lot. Turn it into dollars, that’s 2.39e+40 dollars. Now, turn it into trillions… 2.39e+30 trillions. We would have some 30 orders of magnitude more than 2.39 trillion dollars. Dunno about you, but my brain sits down and sulks when it encounters numbers like this :-)

For perspective: in 1998 the World Bank claimed that the total GDP of all surveyed nations was 28.8 times 10⁶ millions of dollars, or about 2.9 times 10¹³ dollars. So our invested penny would have increased in value to something like 10²⁹ times the total world GDP…

How much purchasing power is that?

Gold is around $500/oz right now, or 2 oz for a grand. So we could buy, ummm, 2.39 times 2 times 10³⁹ ounces of gold.

“What is the mass of planet Earth?” The quick answer to that is: approximately 6000000000000000000000000 or 6e+24 kg — in other words, our Roman penny, after 2000 years of compound interest, would be worth a heckuva lot more gold than the total mass of planet Earth, at 2005 gold prices. Many times more. But heck, what’s a few orders of magnitude between friends, once we’re in the realm of fairyland already?

This is why it seems to me that there’s something inherently absurd about compound interest — it’s patently a fiction. Any system based on the idea that real wealth can accrue by usury, is going to need a devastating reset and devaluation every few years — let alone centuries — to overcome its own divorce from physical reality.

This is one reason why a copper penny today is not made of copper: the copper in the old penny is now worth more than a penny. The amount of copper in the world cannot possibly accrue as rapidly as notional money can compound, so something has to give.

Real wealth in the end comes down to material reality. We cannot have more clothes without using more fibre, dyes, and energy to produce them. We cannot have more cars (regardless of the power source for their traction engines) without using materials and energy to make them. We cannot have more people eating more food without the water, trace minerals, sunlight, land, and other inputs required to produce sufficiently nutritious food for them to eat. Not to mention the fuel and water to prepare it.

In fact, nothing in this world can accrue as rapidly as notional money does under compound interest: not crops, or herd animals, or wild animals, or water, or soil. If notional money grows exponentially, physical reality can’t keep up. You have more and more notional money chasing a relatively fixed amount of real stuff, real value. So compound interest forces a steady devaluation of money (as the money supply is growing faster than any possible physical value base), punctuated by severe crashes when that devaluation doesn’t happen fast enough.

These periodic devaluations have important consequences. When the value of the “coin of the realm” (whether that be metal discs or plastic tokens) falls, the people who have lots of capital invested at compound interest are keeping up (after a fashion). Their dollars or zlotys may be losing real-world value, but they are still multiplying in interest-bearing accounts. The wage labourer who has little or no savings, however, does not keep up. Wages never rise to keep pace with the devaluation of money; they get adjusted in widely-spaced fits and starts.

Even when a crash comes, the very wealthy weather the storm (and sometimes expand their holdings by acquiring bankrupted businesses and distress-sale properties). If you start out on the high side of the crash with a hundred million dollars, and two weeks later your worth is only ten million dollars, you’re still very well off compared to the person who started out with no savings at all and ended up jobless and homeless.

In the real physical world, interest does not compound, or compounds for a strictly limited time and then stabilises at a fixed return rate. Fibonacci and other geometric sequences can be approximated by animal or plant populations fed by a nutrient bonanza or deprived of an effective predator, but they quickly outstrip the baseline “return rate” of solar energy, photosynthesis, and water recycling… and suffer a population crash and reset.

Creatures living in a sustainable ecological niche survive by squandering some of their reproductive potential to predators and mishaps (thus preventing a geometric population growth) and by consuming the yearly “rate of return” of the foodstuffs available in their niche. Not all manage to do so. Some populations show K selection and others R selection, that is, R-selected species reproduce rapidly and go through a boom/crash cycle, and K-selected species demonstrate a levelling-off effect where their population stabilises fairly close to the resource limits of their habitat.

Consumer capitalism presupposes that even where populations may level off, consumption is theoretically infinite; one person in the US now routinely consumes something like 17 Bangladeshis’-worth of energy and raw materials per annum. (The population density of Bangladesh is about 30 times that of the USA.) There is no obvious ceiling on the desire for material possessions and conveniences; and lest that desire accidentally approach satiation, it is relentlessly provoked and cultivated by the marketeers, driven by their own necessities.

This furnace of material consumption has to be stoked because the fantasy of compound interest requires infinite growth, (accelerating too) to repay the ballooning burden of debt on usurious loans and to return liquidationist rates of return to stockholders. (Another system that has to grow exponentially to survive is the pyramid or Ponzi scheme, and it similarly tends to bankrupt those on the lower tiers when it hits its growth ceiling.)

So I agree with the Guardian article [that was under discussion when I wrote this piece in 2006], except for the caveat that what we call “capitalism” today is actually more like rentier-isme, or “finance capitalism” or “the usury state.” It’s an absurd ideology that requires us to liquidate real capital to produce unsustainably high short-term returns.

I feel I should emphasise again that compound interest vastly favours the larger fortune, so that those who have accrued in the past see ever-accelerating rates of accrual, and wealth gaps widen more and more rapidly over any stable investment period; wealthy families (especially with the repeal of estate taxes) and corporations act as long-lived “super-individuals” who are positioned to exploit the long-term absurdity of compound interest and accrue grotesque sums of theoretical wealth. So interest-ism also facilitates the accretion of vast wealth around smaller and smaller elites.

More than just the technology has to change, to bring us to a genuine “capital”-ism rather than a breakneck casino “interest”-ism.

A long time ago my father — not the most progressive of thinkers by any means — told me that any rate of return higher than 3 or 4 percent (annual, not compound) on an investment was an indicator of shady dealings and/or high risk. His words strike me today as far more Delphic (and frightening) than he ever intended. The risks of our present model are unimaginably high.

One way to deal with the structural usury problem (the problem that keeps not just US college graduates, but most of the third world, buried under a mountain of compounding debt that can never be repaid) is the ancient Hebrew concept of the Jubilee Year. Instead of waiting for a crash-reset, every N years (I think it was 49?) all bad debts are written off and everyone starts over. So usurious interest cannot compound to planet-crushing levels.

Another option is simply to outlaw usury — prohibit compound interest entirely and fix reasonable rates of simple return, proportionate with biotic return rates. And so on.

The more I think about it, the more it seems to me that as long as compound interest is the mainspring of our systems of finance, investment, and profit, we are in irreconcilable conflict with the biological and physical envelope of our own existence… and Nature bats last.

[Note: the King’s Chessboard is a famous anecdotal illustration of an exponential or geometric progression. Once upon a time, a clever man did a great service for a king. He wanted no reward; but the king couldn’t bear owing anyone a favour, and insisted he must name any reward he pleased. Possibly somewhat annoyed, the clever man said that he “only” wanted the king to grant him some wheat. Pointing to the king’s chessboard, he asked that each day the king should give him some wheat, for as many days as there were squares on the board. But the amount would increase with each square: one grain of wheat for the first square, two for the second, four for the third, eight for the fourth, sixteen for the fifth… in other words, a series of powers of two.

The king, who was apparently not much of a mathematician, happily agreed. But the reader who is paying attention will have realised that the last square of the chessboard will be worth 9.223372e+18 grains of wheat, or 2 to the 63rd power. A grain of modern wheat weighs anywhere from 30 to 50 mg depending on variety, so let’s call it 40 mg. So that last pile of wheat is 4 grams times 9.223372e+15, or 4 kilograms times 9.223372e+12, or 4 metric tons times 9.223372e+9, which would be about 36 billion metric tons of wheat. Worldwide wheat production averages around 750 million metric tons per annum, for reference. I hope the king learned his lesson, but I wonder if we will learn ours in time!]

Retired; ex-software engineer. Paleo-feminist. Sailor. Arduino tinkerer. Enviro. Libertarian Socialist (Anarcho-Syndicalist, kinda). Writer. Altermondialiste.

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