The Money Machine - Modelling the Economy

In 1949, the economist Bill Phillips built a machine that modelled the British economy using water flows! This article tells its story from inception to the latest incarnation as a 3D virtual model.

Mar 05, 2025

Introduction.

Seeing the Forest for the Trees is not just the title of this substack but is the guiding principle for many of the articles I write. I firmly believe that presenting data visually makes information more accessible and easier to understand. Moreover, charts that allow readers to explore and interact with the data are even more powerful.

The same principles of presenting information visually and interactively also applies to mathematical models. Readers following my series of articles on How to Model a Pandemic, will have seen that the complex equations behind epidemiological models can be shown as simple ‘stock and flow’ diagrams, making the concepts much easier to understand. Furthermore, the ‘stock and flow’ models can be transformed in to computer models that anyone can interact with to learn about the dynamics of a pandemic.

This article shows how these same principles were applied some 75 years ago by Bill Phillips, an amazing engineer turned economist, who created one of the first physical models of an economy. Using salvaged parts from a World War Two Lancaster bomber and a whole lot of creativity he built a physical model of the economy based on water flows.

The article was inspired by a recent visit to London where I had the wonderful experience of ‘seeing’ and interacting with a 3-D virtual version of this hydraulic model at the FT Alphaville ‘Art of the Chart’ exhibition.

More about that experience at the end of the article, but let’s start the story with Bill Phillips - the engineering genius turned economics innovator.

The making of an amazing engineer.

Bill Phillips was a remarkable man who led a remarkable life. He was born in 1914 at a remote diary farm in Te Rehungao on the North Island of New Zealand. Like many farmers, his father was a keen amateur engineer who had adapted a water wheel to generate electricity for their farmhouse - the first in their area to do so. This environment clearly stimulated the young Bill’s interest in `things electric and mechanical' and he soon turned his hand to making crystal radio sets and adapting his bike so he could read books as he cycled to the local primary school. Such was his engineering skills that at just 14 years old he acquired a discarded truck, rebuilt and repaired it, and drove it to school every day, until the school authorities intervened.

Although a gifted student, the Great Depression meant his family could not afford to send him on to further education, so the 15 year old Bill got a job as an apprentice electrical engineer at New Zealand’s first government hydro-electricity generating station. Ever the entrepreneur, he supplemented his income by running an `Outdoor Cinema' in Te Rehungao and the back country, to which he travelled on a motorbike.

However, Bill Phillips was clearly a restless soul and in 1935 he left New Zealand to see the world. Travelling first to Australia he spent two years `carrying his swag' (and violin) across the country, doing a variety of casual jobs, including shooting crocodiles. From Australia he travelled to Japan where, for a short time, he was arrested on suspicion of spying. He then spent 12 months travelling across Russia, again taking what work was available, before arriving in London in 1937. Before and during the journey to Britain he had taken a correspondence course in Electrical Engineering, and soon obtained his formal qualification leading to a job with the London Electricity Supply Company.

When the Second World War came he joined the Royal Air Force and was sent to Singapore, only to be part of it’s evacuation to Java where he was captured by the Japanese. He spent the rest of the war in a POW camp suffering great deprivation. However, his engineering creativity was still put to great use and he built several miniature crystal radio sets which provided the latest news to his fellow prisoners, including the surrender of Japan in September 1945.

From engineer to economist

At the end of the Second World War Bill Phillips returned to England and registered for a degree at the London School of Economics to study Sociology, which included two compulsory courses in economics. Faced with compulsory economics, he quickly developed a great interest in the subject and became fascinated by what would eventually be called macro-economics. However, he found the concepts hard going. Fortunately, he was helped by an older student, Walter Newlyn, and his ability to translate economic concepts in to engineering diagrams. His important insight was that money stocks could be represented by tanks of water, and monetary flows by water circulating around pipes.

While the notion of representing the flow of money in an economy by the flow of water was not new, he was encouraged by Walter Newlyn to write a draft paper outlining how a physical device could actually be built based on these principles. At the heart of such a machine would be the hydraulic system illustrated in the following image of Bill Phillips’s hand written sketch from that unpublished paper.

Here, the upper pipe represents the flow of money to the market, while the lower pipe represents the flow from the market, thus altering the level of the stocks tank. The openings of the two valves are determined by the supply and demand curves.

The draft paper was completed while Bill Phillips was still an undergraduate studying for his degree in Sociology. His passion for economics must have taken up all of his time as he only graduated with a Pass degree, the lowest possible class. However, the draft paper had inspired his friend and mentor, Walter Newlyn, who had just taken up a post in the Economics Department at Leeds University. Amazingly, Newlyn managed to persuade his new department to pay an advance of £100 to Bill Phillips for materials to build a hydro-mechanical model of an economy.

Building the ‘Phillips Money Machine’.

With his degree finished and funds available, Bill Phillips turned to building a working machine during the summer of 1949. An improvised workshop was created in his landladies garage on the outskirts of London, war surplus parts were obtained (famously from a retired Lancaster bomber), Perspex tubing bought and fishing line borrowed. Fuelled by nicotine, he was an inveterate smoker, and his undoubted genius at solving engineering problems the machine started to take shape.

To illustrate the ingenuity of his design it is worthwhile looking at one of the physical problems he had to overcome. The problem is that water flows out of a small hole in a tank at a rate proportional to the square root of the height of the water above the hole. This means that as water levels in the tank fall, the rate at which it drains slows down, and vice versa. A model of the economy needs to carefully control the rate of flow from one stock (tank) to another so Bill Phillips had to overcome this ‘physics’ problem to make his hydraulic model faithfully represented the desired ‘economic’ flow rates.

The following annotated diagram, taken from his published paper (chapter 10) describing the machine, shows how his design overcame this ‘physics’ problem for one component of the economic model.

In the model, the production flow of a commodity is represented by the flow of water into a tank called Stocks w. This flow is controlled by a valve, consisting of a flat plate sliding horizontally over a narrow parallel slot. Importantly, the head of water over the valve is kept constant by an overflow weir at a fixed height above it, so that the rate of flow of water through the valve is proportional to the width of slot uncovered. The consumption flow of the commodity is represented by the flow of water out of the tank water which is also controlled by a sliding flat plate.

Price is represented by the volume of liquid in the tank and is inversely proportional to the height of water in the tank. The tank is rectangular except for one end, the shape and position of which determines the demand curve for stocks of the commodity so as to reproduce on the machine the relationship between the stock level and the price of the commodity. This end of the tank slides freely when the hand-wheel is turned, enabling a shift in the demand curve for stocks to be introduced.

Finally, attached to a float on the tank is a bar which moves vertically between guides, and carrying two graphs, a production and a consumption curve, which move in front of their respective valves. Each graph is made by cutting a narrow slot in a thin sheet of plastic; a pin projecting from the end of the valve engages in this slot so that when the float moves the graph vertically, the graph moves the valves horizontally, opening or closing them according to the shape of the curve.

In this way the production and consumption flows are adjusted by the price of the stock which is represented by the height of the water in the tank. As the water level rises the price decreases and the production and consumption flows automatically adjust according to the shape of the slots cut in the plastic graphs. By replacing the plastic graphs with different shaped slots the machine can be ‘programmed’ to represent different production or consumption curves.

Demonstrating the ‘Phillips Money Machine’.

Having spent the summer and early autumn building his ‘money machine’, Bill Phillips now needed to persuade the economics world that it was a serious instrument. Nicholas Barr in an article on the ‘Phillips Machine’ writes that:

‘There are rumours of learned professors and dignitaries of the Royal Economic Society, as they walked from the entrance of the London School of Economics toward the lift, being interrupted by a wild man from New Zealand waving blue prints in one hand and pieces of Perspex in the other.’

Fortunately, this unorthodox approach brought success when he was introduced to Professor James Meade, a future Nobel prize winner for economics and fellow ‘gadget freak’. James Meade immediately saw the potential of what was becoming known as the Phillips Machine and agreed that Bill Phillips could demonstrate his hydraulic model at an upcoming seminar.

On the 29 November 1949, the Phillips Machine was wheeled in to the seminar room and Bill Phillips proceeded to demonstrate his hydraulic model to a sceptical audience. As the machine pumped water around the system he adjusted the flows governing interest rates and showed the economic impact on charts drawn at the top of the machine.

The following image shows Bill Phillips demonstrating the prototype version of his hydraulic simulator.

The impact was instant. He had created a machine which simplified and made visible many of the the key concepts in macro-economics. Furthermore, the machine was interactive and could be used to explore the dynamics of an economy as changes were made to monetary levers.

This was no accident, Bill Phillips intuitively understood the value of visualisation and interactivity for communication and learning. He writes in his 1950 paper describing the machine that:

Fundamentally, the problem is to design and build a machine the operations of which can be described by a particular system of equations which it may be found useful to set up as the hypotheses of a mathematical model, in other words, a calculating machine for solving differential equations. Since, however, the machines are intended for exposition rather than accurate calculation, a second requirement is that the whole of the operations should be clearly visible and comprehensible to an onlooker. For this reason hydraulic methods have been used in preference to electronic ones which may have given greater accuracy and flexibility, the machines being made of transparent plastic (`Perspex') tanks and tubes, through which is pumped coloured water.

Although intended primarily as a teaching aid, the Phillips Machine was remarkably accurate. Overall the completed machine simultaneously solves a nine differential equation system within 2% accuracy. It also plotted the path an economy would take over time as it moved from one stable equilibrium to another. A task way beyond the capacity of any economist at the time.

From prototype to international acclaim.

Following the presentation of the first prototype the London School of Economics (LSE) appointed Bill Phillips as an assistant lecturer in Economics. A considerable achievement for a recent graduate with a 3rd class degree in Sociology. The rest, as they say, is history. He obtained his doctorate in January 1954, Reader in 1954, and was appointed Tooke Professor of Economic Science and Statistics in 1958.

The LSE also commissioned him to build updated versions of the Phillips Machine and the ‘Type 2’ version became a regular feature of lectures at the LSE. As the machines reputation spread, there was growing interest from other institutions and several were made for universities in Britain. In the early 1950s, a former LSE student returning home to the USA, christened it the MONIAC (Monetary National Income Analogue Computer), and sold several more.

In all, about a dozen machines were built, ultimately ending up not only in British universities but also as far afield as Melbourne, Australia; Roosevelt College, Harvard; the Ford Motor Company; and the Central Bank of Guatemala!

By the late 1970s, the machines had fallen into disuse as other computation and simulation methods became available. However, such was its appeal that two machines have been repaired to full working order. One was restored by Allan McRobie, an engineering professor at Cambridge University, and the other is appropriately in the Reserve Bank of New Zealand museum.

This means that we are still able to experience the full impact of seeing the flow of money through an economy as the following short video shows.

If the video doesn’t play in Substack then it is available at this link.

I hope that you will agree with the economists who observed:

Seeing the machine working is different from pictures of it, as those who have seen the Phillips machine working readily attest. Spectators could not only see the red water streaming through the pipes, but also hear the bubbling and splashing as it ran through the machine. They were able to see not just a 2-D picture or systems of equations, or even a static 3-D representation, but the kind of interrelated and dynamic cause effect changes over time that economists suppose to happen in the circular flow of the aggregate economy. The working machine was a 4-D representation.

Bringing the ‘Phillips Money Machine’ in to the 21st century.

The Phillips Money Machine not only inspired economists but also captured the imagination of others who see the machine as a powerful metaphor of the economy.

For example, an art installation based on the ‘Phillips Machine’ is presently on display in the Museum of Modern Art in New York. Appropriately created by the New Zealand artist Michael Stephenson it is called the ‘Fountain of Prosperity’ and Michael tells his story here.

Also, the Terry Pratchett novel Making Money contains a device based on the Phillips Machine as a major plot line. However, after the device is fully perfected, it magically becomes directly coupled to the economy it was intended to simulate, with the result that the machine cannot then be adjusted without causing a change in the actual economy!

On a more practical level, members of the Financial Times (FT) Alphaville data journalist team were also inspired by the Phillips Machine. Motivated by a desire to make the historic machine more accessible and to provide students with the opportunity to learn basic economic lessons they have developed a virtual version of the 75-year-old hydraulic computer. You can read their full story here.

In November last year, the FT team visited Cambridge University and used the latest scanning technology to produce a milli-meter perfect 3-D computer model of their Phillips Machine. The model was then loaded into a gaming engine where the Phillips Machine was brought to life. The next stage was to replicate the mechanisms controlling the water flow which was helped by a paper that described a System Dynamics view of the Phillips Machine. Finally, the completed model was ported to run on the mixed-reality environment of the Apple Vision Pro — a high-tech mixed reality headset that seamlessly blends digital content with your real-world surroundings, allowing you to interact using your eyes, hands, and voice.

Last week I had the opportunity to experience the virtual Phillips machine at the FT Alphaville ‘Art of the Chart’ exhibition held in Saint Bartholomew’s Church in the City of London. After a few moments training the headset to recognise my eye and hand movements, I ‘pinched’ the virtual white square I could see on the Church floor, and the Phillips Machine magically appeared. It was as if a ghost of the machine had materialised in front of me! A ghost that I could walk around and almost touch while still seeing the Church and the other visitors to the exhibition.

Indeed, I could 'touch' the virtual machine and, by pinching the power switch, set the water circulating in the hydraulic model of the economy. Soon, I was moving the levers of the economy, raising and lowering taxes in a manner that Chancellors of the Exchequer could only dream of — and, hopefully, will never do!

While a static image can never fully capture the real experience, the following image from a recent FT article provides an idea of what it looks like when wearing the headset.

We will never know what Bill Phillips would have made of the enduring interest in the hydraulic economic model he created over 75 years ago as he was a shy and modest man. However, as an exceptional engineer, I am sure he would have approved of this 21st century version of his iconic machine.

Concluding thoughts

If you have made it to this section then you most likely share my interest in this amazing story. I hope that you have enjoyed reading it as much as I enjoyed researching and writing it.

Bill Phillips was undoubtable an exceptional man who made an immense contribution to economics. But for me it was his ability to see the big picture and understand how the behaviour of complex systems can be made visible through visual models that makes him stand out.

Bill Phillips was indeed someone who could ‘See the Forest for the Trees.’

Sources

The mains source for this article comes from a series of articles published under the title of A. W. H. Phillips: Collected Works in Contemporary Perspective.

The articles can be found at the following link.

http://pombo.free.fr/leesonphillips2000.pdf

Links to other sources are as follows:

Historical perspectives - A Hydromechanical Analog Computer of the 1950s

https://scispace.com/pdf/historical-perspectives-the-moniac-a-hydromechanical-analog-5dr35k8g8j.pdf

Fortune Article from the 1950s: The MONIAC - ‘Economics in 30 fascinating minutes’

https://www.fulltable.com/vts/f/fortune/n/m03.jpg

The FT Money Machine: how we transformed an iconic invention for virtual reality

https://www.ft.com/content/547a3fea-378d-45ec-a2cb-cb157ea7a9b4

Short YouTube video demonstration of the Phillips Machine Type 2 (4 mins)

Live demonstration of the only working Phillips Machine in the Southern Hemisphere

Long YouTube video demonstration of the Phillips Machine Type 2 (45 mins)