I'm at the University of Cambridge.
That is the world's only working
water powered model of the British economy.
And by moving this graph
we'll find out what happens when you divide it by zero.
For the sake of this week's prime minister,
please don't try this at home.
Huge thanks to NordVPN for sponsoring this episode.
The device is known as a Bill Phillips machine.
And as you might expect,
it was invented by a man named Bill Phillips.
He was born in New Zealand in 1914,
dropped out of school to become a hydroelectric engineer,
moved to Australia to become a crocodile hunter,
and then spent some time during World War II
working on airplanes.
He was eventually captured as a POW
where he made tea for his fellow inmates,
boiling water by dunking mains voltage
directly into a bucket of water.
After the war he studied at the London School of Economics
where he noticed a striking resemblance
between the fluid flow equations of hydrodynamics
and the money flow equations covered in his classes.
Living in a time before digital computers,
he decided to simulate these equations
using a custom built water computer
constructed of old airplane parts.
This impressed so many people
that he was eventually commissioned
to build another 14 machines,
one of which is today housed at the University of Cambridge.
This is the Phillips machine.
You can think of it like a zoomed out map of the economy,
where a bottle of water is worth 500 million dollars cash,
or roughly the same price as it is at Wembley Stadium.
(machine clicking)
(machine whirring)
Water is pumped to the top as income.
Some is taxed, go into the government,
some is saved to the banking sector, and the rest is spent.
Governments pay for projects, banks invest funds,
and our flows recombine.
Some of this expenditure is on imports
and money goes out the economy.
Some extra funds trickle in from exports,
and everything meets at the bottom as transaction balances.
The cycle begins anew.
We won't be running the foreign section today
because after Brexit it's mostly broken.
When it comes to it, the Phillips machine
is a way of doing lots and lots of integration calculations
using water rather than maths.
This relies on a couple of key mechanisms.
Now I did ask Cambridge if I could pull apart their machine
to show you these in action,
but they weren't particularly pleased with it.
So instead, I've built some of my own.
Full disclosure, I constructed these in my bedroom,
so they're not particularly leak proof.
According to the Quantity Theory of Money,
the more cash we have in an economy,
represented here by water in the tank,
the higher the level of income.
Water coming out the tank through the hole.
According to the theory, the two are directly proportional,
but when we try it out with water
things aren't quite so simple.
To fix this we use a special sort of hole
known as a Sutro Weir,
thin at the top, thicker at the bottom.
As the height of the water changes
so does the effective area of our hole.
In such a way so as to linearize the relationship
between height and water flowing out.
Let me introduce to you another law of economics,
that of supply and demand.
If we have a farmer selling eggs
and people trying to buy them,
then the invisible hand of the market
is able to juggle the price of eggs
to most obviously allocate eggs to people stomachs,
and cash into the farmers wallet.
If the farmer has lots of eggs
then the price of eggs is low.
Chances are if eggs being sold for a dollar a dozen
then I'll be eating a lot of omelets.
On the other hand, if the farmer doesn't have many eggs
then the price of eggs gets really high.
I will no longer be eating omelets
but my wealthy next door neighbor who loves quiche
is still probably going to be buying a pack.
So how does that translate to water?
This is the basic mechanism.
Supply is in this bucket
and then the amount of consumption,
people actually buying and eating eggs,
is given by the water flowing out of it.
The relationship between supply and demand
through the medium of price is embedded in this graph.
Height to the tank is measured using a rubber duck
floating at the surface.
Using this string
it will then either lower or raise the board.
A pin through the slot
converts the up down movement of the board
to the left right movement of a wooden beam,
opening or closing a hole at the bottom of the tank.
Just like the theory says,
more supply of eggs means a lower price.
A hole opens and people buy more eggs.
The benefit of using this contraption
rather than just drilling another hole,
is that we can experiment with different relationships
between supply and demand.
For the moment, our slot is at 60 degrees.
If we want to see what happens
if people are more sensitive to price,
they would make it shallower.
Less sensitive, steeper.
When we started up at the machine
I had to sand back some copper oxide residue
which had formed on this exposed wire.
Originally this would be dumping
two 40 volt mains electricity directly into a water stream
to measure the spending flow intensity.
Bill probably used something similar
in his POW days to make tea,
but nowadays we're a little more afraid of dying,
so have stepped it down
to a safer but less reliable 20 volts.
As digital computers didn't exist,
Bill used this contraption to convert its reading
into the raising and lowering of certain slots.
With a whole bunch of tinkering Bill got his model
to within four percent of the equations,
which in 1950 were believed to govern the economy.
As far as I can tell,
no one's used it to make actual policy decisions,
but governments, banks, and tons of students,
have messed about with its various settings
to get an intuitive understanding
of how the economy should work.
A particularly cool demonstration
was to have two Phillips machines tied together,
with one representing the U.S. and the other the UK.
Even if the UK started out strong and stable
in the totally hypothetical scenario
where the U.S. does something very dumb,
then both economies would fall apart.
Now that we've seen how this water calculator works,
and what it's meant to be used for,
let's do the only logical thing,
and see if it has a divide by zero button.
Quick introduction to some relevant theory.
If I give you 100 dollars
and you spent 20 of it on eggs and pocket the rest,
then you'd have a propensity to consume of point two,
and a propensity to save of point eight.
Marginal propensity to save is defined mathematically
as the portion of each additional dollar of income
that is saved rather than spent.
However, if we do something sneaky and flip that round
we get change in income equals the change in savings
over marginal propensity to save.
We're actually have this propensity
as a feature of the entire economy as a user defined input,
a slider like the one we made earlier.
It's written here as propensity to consume,
but remember, the two are basically the same thing.
We start out with a normal propensity to consume graph.
People are saving some money and spending the rest.
Now if we move our slider to 45 degrees,
this is a propensity to consume of 100%,
and importantly a propensity to save of zero.
This graph shows income.
It's steady at the moment,
but if I kick in a bit of investment savings,
then mathematically we have just
divided something by nothing.
And now, oh yeah, it's going up.
Apparently something divided by nothing is infinity,
and yeah, after a bit of time,
water is spilling out the machine.
Surprisingly, this does actually have
some economic validity.
Now the 20 dollars you spent on eggs goes to the farmer,
who used it to buy tickets
to a pirate metal rock concert,
who use it to buy a Hurdy-gurdy.
The same cash is being used by more and more people,
faster and faster,
increasing income of the overall economy
with every transaction.
So we've done it,
divided by zero and made infinite money.
All we have to do is just spend everything
as soon as we earn it.
Now that doesn't quite work
if it's just me spending all my money on omelets.
There are billionaires out there
who earn loads and spend very very little.
If they were actually going to spend all that money
then maybe everyone's favorite metaphor
of trickle down economics would actually work.
But they don't, and it doesn't.
We might as well tax them.
And as protest, I'm gonna go eat some omelet.
After the success of his water model,
Bill Phillips keeps inventing, teaching, and chain smoking.
Foreseeing the rise of digital economics in the 1960's
he helps to pioneer that field as well.
(light music)
At age 54, probably brought about from all that smoking,
he suffers a stroke and ends up retiring,
dying just a couple of years later.
The Phillips machine lives on, both as a touchstone
in the history of computational economics,
but also for the lessons that it can still share with us,
particularly when you divide by zero.
Until next time, this has been James Dingley
from Atomic Frontier.
Keep looking up.
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