How the Engineering of Arches Explains Money

Update: Brian Romanchuk has written an excellent response to my post here.

J.E. Gordon’s excellent old book, The Science of Strong Materials: Or Why You Don’t Fall Through the Floor, calls an arch “an apparent impossibility”.

Why does an arch seem impossible? Imagine building an arch from one side. Each wedge-shaped stone (or “voussoir” as it’s technically called) is held in place by the one above it. But this means that each voussoir you try to lay (besides the first, or maybe the first two) must fall. You can put another on to hold it in place, but then there will be nothing to hold up this new voussoir.

Of course you can’t build the arch like this. You have to lay all the voussoirs on a curved scaffolding, then remove the scaffolding and marvel at how the arch stays up. Still, something seems fishy. If no incomplete section of the arch can hold itself up, how come the whole arch can?

I think what makes this counterintuitive is our tendency to think of forces going in only one direction. Each voussoir in the arch seems to be held in place by the one above it. But nothing is above the keystone right at the middle of the arch.

What we forget is that when a stone is pressed upon by another, it also presses back. This follows from Newton’s Third Law. Thus the keystone is held in place because it is squeezed on either side by its neighbours; meanwhile it pushes out against them so that they too are squeezed on both sides.

The arch is held up by these compressive forces running in both directions, each voussoir always being “in compression”, as engineers say. The voussoirs at the ends—the “springers”—are squeezed by the voussoirs above them on one side and by whatever the arch is resting on (for that also pushes back) on the other. When the force of these compressions matches the force of gravity, the arch stays up.

In a lovely passage from her book Built, Roma Agrawal finds this meaning in the Arabic saying “Arches never sleep”: “They never sleep because their components are continuously in compression, resisting the weight they bear with endless patience.”

According to the Wall Street sequel, money also never sleeps. Our problems with understanding money also come from thinking of forces unidirectionally. An equivalent to the seeming impossibility of arches is the bizarre ability of banks to create money. A bank loans me £1000 and the money magically appears in my account. Where did it come from? Not from anyone’s savings—after all, no accounts were debited. The bank created the deposit for me out of thin air: a process from which, as J.K. Galbraith put it, “the intellect recoils”.

This is initially more puzzling than the arch. If banks can just magic money out of the air, how can money have any value? Or why doesn’t the owner of the bank just create trillions in her own deposit?

The answer is that just as a stone, when pushed, pushes back, so when you get a loan, the loan also gets you. Your deposit is really a promise by the bank to make payments on your behalf, up to £1000 (each time it makes a payment for you, it deducts that amount from your deposit). But you have also made a promise to the bank, to repay the £1000. When the bank created your deposit, it added to the supply of bank deposits, but it added equally to the demand: you have a new need for £1000 to repay the loan (plus interest, but that’s too complex to go into here).

If the bank supplied deposits by crediting accounts without demanding deposits in loans, deposits would soon lose all value. But because the forces go in both directions—borrowers pull deposits out of the bank in loans and the bank pulls them back in in repayments—the system holds itself up like the arch. The force of the money’s yearning to return to its origin, balanced against our urge to hold onto it, is what sustains its value.

Classical Econophysics, by Paul Cockshott et al, calls money “a projection, in the strict relational sense, of an information structure”. The full information structure reflects what is pushed out by banks into people’s accounts and what is pulled back in as debt repayments. But “money” counts only the pushes. One way of measuring what is called the “money supply” is to count up all the deposits in customers’ accounts, leaving out all the debts to the banks that run in the opposite direction.

Cockshott et al apply the point to currency. Currency is issued by the state and handed out to people (or banks), but then why does it have value? Because here too there is a reciprocal force pulling money back into the state: taxation. On this “chartalist” theory, every portion of currency represents an unpaid tax debt somewhere in the system. If a government consistently issues more currency than it takes back in taxes, the currency starts to lose value and we have inflation. But, again, when we measure the money supply as the sum of all currency holdings, we project only half the information structure. Or, in my metaphor, we measure only half the forces.

Cockshott et all put it thus: “holdings of coin by the public constitute one column of a relation between subjects and the state. The other column holds individual tax debts. This column is ‘hidden’ in the sense that it takes the form of covert records held by the exchequer.”

Thinking in terms of money is falling victim to the sort of unidirectional thinking that makes arches seem impossible. No wonder people think that money “isn’t real”, that it’s all a big sham. Money is real, but it’s only half of the story.

An engineering perspective can help us see through seeming impossibility to the real story, which is about reciprocal forces in balance. Daniel Dennett writes somewhere that it’s a shame there is philosophy of physics, philosophy of biology, even philosophy of economics, but no philosophy of engineering. There isn’t quite no philosophy of engineering. But more would be nice.