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Tuesday, July 18, 2023

Alex Douglas On Arches And Money

Alex Douglas just published a post on arches and money which I quite liked. It is an easy read, and I will just offer my spin on one of his points. It also leaks into a discussion of engineering, which I will digress into at the end of this post.

He draws on an excellent book — J.E. Gordon’s The New Science of Strong Materials: or, Why You Don’t Fall Through the Floor. (I have sentimental attachment to this book since I won a copy of it and “Structures: Or Why Things Don’t Fall Down” from a provincial high school physics contest. Both books gave me a good introduction to the non-electrical parts of engineering — possibly more than my undergrad electrical engineering degree, since Canadian accreditation bodies do not allow much space for non-EE content in undergraduate programmes.) In the book, an arch is termed an “apparent impossibility.”

Douglas notes:

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.

The key to an arch is Newton’s Third Law of Motion: for every action, there is an equal an opposite reaction. You need to use scaffolding to erect an entire arch, but once complete, the voussoirs push back on the forces exerted by their neighbours, and gravity keeps the structure in one place.

The link to money (I cut out a couple sentences to keep the quote length down)?

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. […]

This is initially more puzzling than the arch. If banks can just magic money out of the air, how can money have any value? […]

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.

An alternative phrasing is to note that the usual way of stating the observation is that “banks create money (M1) by extending loans,” one could also state that “entities create money (M1) by borrowing from banks.” The first phrasing seems to have the implication that banks just magically snap their fingers and M1 appears — which generates never-ending controversy in online discussions. The second phrasing implies that money creation is a two-edged sword (the best kind of sword) — sure, the money (M1) is created, but the borrower is saddled with a loan.

If the objective of mainstream Economics 101 were to impart knowledge of how the world works, they would drop whatever means of teaching banking and money they use, and instead teach the basics of how banks work, and then “money creation” would just be understood as just one means of credit creation in a capitalist economy. Unfortunately, the objective of teaching is to push students into thinking about the economy as some kind of general equilibrium model, where “money” is a special entry in a vector of “endowments” that agents trade with each other on the way to creating optimal societal outcomes. In this scheme, money is not supposed to appear out of nowhere, it has to be traded for.

These problems show up in two ways in discussions.

  1. Discussion of any topic where money is created ends up being ludicrous.

  2. The strong belief that any form of money that is not purely an asset (as opposed to gold coins, or crypto currencies) is fake.

Appendix: Engineering Philosophy (?)

At the end of his article, Douglas states “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.”

Within control systems engineering, theoretical activity is typically divided into two areas, analysis and synthesis. Those are terms that I believe have a lot of theoretical baggage within philosophy, but are straightforward within control theory.

  • Analysis is the determination of how a given control system (both the system to be controlled, as well as a given controller) will behave, and its mathematical properties.

  • Synthesis is developing a framework to answer the question: given a system to be controlled, how to design a controller that has desired properties? (You need to be able to analysis to determine the properties, but a means of analysis does not imply the ability to design controls, as the design problem may be mathematically intractable. My thesis title — An Input-Output Analysis of Feedback Loops with Saturation Nonlinearities — was a nod to this reality.)

That is, analysis looks very similar to science (including mathematics): how do things behave? Synthesis is the design side of engineering, which relies on (hopefully) knowing how engineering systems will behave. It is relatively easy to draw a line between these areas in applied mathematics, but the division exists throughout engineering. In the hypothetical three-year Quebec electrical engineering undergraduate programme (I think faculties have accepted the programme requires four years, even though CEGEP covers courses that would be taught in first year undergraduate elsewhere in North America), the first two years are almost entirely
”analysis,” and only the last year has space to cover design. Nevertheless, the handful of class hours devoted to design is what separates science faculty graduates from engineering ones.

On the analysis side, there is not huge divide from engineering versus science faculties, and so one could argue that philosophy of science is applicable. However, engineering analysis can be messier, as pure sciences tend to focus on idealised circumstances in order to derive laws of nature, whereas engineers are stuck with having to deal with real-world objects of interest. As such, heuristics are viewed as more respectable within engineering.

The arch example falls under analysis, and can be viewed as being different than the usual preoccupations of pure science. The scientific laws of the arch components are straightforward, the issue is the “emergent property” of the arch structure. (I think there’s a move to include the study of “emergent properties” under science, although it was not a part of the curriculum I studied.)

As for synthesis, one might summarise it as “yay for Pareto Optimisation.” If you can design a new engineering system that is strictly better than an existing one, you do that. (Pareto optimality refers to a situation where you are attempting to maximise more than one objective function. If you cannot improve the level of one objective without reducing another, it is Pareto optimal.) However, real world engineering is built around trade-offs, and you typically end up with a menu of choices, and one needs to decide what objective to prioritise.

Trade-offs are also somewhat soft, since you have human beings interacting with systems. Take as an example safety systems. If you have safety features that block human operators from interacting with systems, inquests may then find out the hard way that operators might disengage those safety features since they are seen as too cumbersome.

To return to an example that I often discuss, optimal control theory ran into severe difficulties because people got excited about “optimal solutions,” and forgot about the trade-off side of engineering. The robust control (and classical control) response was to argue that we need to take into account our uncertainty about the system we are controlling versus the aggressiveness of our control inputs: the more certain we are we know how the system behaves, we can ramp up the aggression. A simplified version of the trade off is that one is trading off robustness against model error versus aggressiveness of control action.1

Engineering is an unusual faculty from the perspective of a “old school” university; a lot of the academic effort is in areas that are hard to disentangle from the pure sciences, while a lot of the value of the education comes from drumming into the skulls of undergraduates the importance of often vaguely-defined trade-offs that typically appear within an area of technology. If one wants to pursue a philosophy of engineering, this dual nature needs to be kept in mind.


Model uncertainty was best interpreted in the frequency domain. One typically has the best knowledge of a system’s behaviour at low frequencies. So your trade-off is thus dependent upon where you are in the frequency domain, and you thus need to shape your controller’s frequency response. 

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(c) Brian Romanchuk 2023

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