The dappled world
Speech given by
Andrew G Haldane, Chief Economist, Bank of England
GLS Shackle Biennial Memorial Lecture
10 November 2016
The views are not necessarily those of the Bank of England or the Monetary Policy Committee.
I would like to thank Arthur Turrell for his help in preparing the text and Rafa Baptista, Karen Braun-Munzinger,
Angelina Carvalho, Doyne Farmer, Jeremy Franklin, Marc Hinterschweiger, Andreas Joseph, Katie Low, Zijun Liu,
Matthew Manning, Rajan Patel, Paul Robinson, Daniel Tang, Ryland Thomas and Arzu Uluc for their comments and
contributions.
1
All speeches are available online at www.bankofengland.co.uk/publications/Pages/speeches/default.aspx
Introduction
I am delighted to be giving this year's Shackle Biennial Memorial Lecture.
The past few years have witnessed a jarring financial crisis as great as any have experienced since the
world wars, a crisis whose aftershocks are still being felt today. Against that dramatic backdrop, I thought I
would use this occasion to reflect on the state of economics, not least in helping us make sense of such
catastrophic phenomena.
This topic has risen in both prominence and urgency since the financial crisis (Coyle and Haldane (2015),
et al
Battiston (2016)). Indeed, it would probably not be an exaggeration to say the economic and financial
crisis has spawned a crisis in the economics and finance profession - and not for the first time. Much the
when economics was rethought under Keynes'
same occurred after the Great Depression of the 1930s
intellectual leadership (Keynes (1936)).
-
Although this crisis in economics is a threat for some, for others it is an opportunity an opportunity to make
a great leap forward, as Keynes did in the 1930s. For the students in this room, there is the chance to
rethink economics with as clean a sheet of paper as you are ever likely to find. That is perhaps why the
numbers of students applying to study economics has shot up over recent years. This is one of the silver
linings of the crisis. No discipline could ask for a better endowment.
But seizing this opportunity requires a re-examination of the contours of economics and an exploration of
some new pathways. That is what I wish to do in this lecture, drawing liberally on the work of
George Shackle. In the light of the crisis, there has been renewed interest in Shackle's work as economists
problems. Indeed, it was this quest that first brought Shackle's work
have sought new insights into age-old
to my own attention around five years ago.
In exploring new pathways, I will draw my inspiration from three features of economic systems which
underpinned Shackle's own work. First is the importance of recognising that these systems may often find
themselves in a state of near-continuous disequilibrium. Indeed, even the notion of an equilibrium, stationary
through time, may itself be misleading (Shackle (1972)). It was perhaps this feature of Shackle's work that
earned him his heterodox label.
Second is the importance of looking at economic systems through a cross-disciplinary lens. Drawing on
insights from a range of disciplines, natural as well as social sciences, can provide a different perspective on
dynamics. In Shackle's
individual behaviour and system-wide own work he drew liberally on a range of
economic schools of thought, from Keynesian to Austrian, as well as history, philosophy and psychology
(Shackle (1949, 1979)).
2
All speeches are available online at www.bankofengland.co.uk/publications/Pages/speeches/default.aspx
Third is the importance of radical uncertainty. Shackle saw uncertainty about the future as fundamental to
human decision-making and, thus, to the functioning of social systems (Shackle (1972)). Human imagination
was a crucial frame for social progress (Shackle (1979)). This meant social systems were inherently
unpredictable in their behaviour. Latterly, the importance of radical uncertainty in making sense of social
systems has gained new traction (Taleb (2014), King (2016)).
I wish to explore whether there are insights and techniques from other disciplines which better capture these
features of economic systems and which thus hold promise when moving the economics profession forward.
These approaches would still be considered heterodox in much of the profession even though, in many other
fields, they would be considered entirely standard.
One of the potential failings of the economics profession, I will argue, is that it may have borrowed too little
from other disciplines - a methodological mono-culture. In keeping with this spirit, the title of my lecture is
itself borrowed. In 1999 Professor Nancy Cartwright, a philosopher of science, published a book with the title
The Dappled World: A Study of the Boundaries of Science
(Cartwright (1999)). This quote captures its
essence:
"Science as we know it is apportioned into disciplines, apparently arbitrarily grown up; governing
different sets of properties at different levels of abstraction; pockets of great precision; large parcels
of qualitative maxims resisting precise formulation; erratic overlaps; here and there, once in a while,
corners line up but mostly ragged edges; and always the cover of law just loosely attracted to the
jumbled world of material things."
Cartwright was describing the natural sciences. She describes them as a patchwork of theory and evidence,
some of it precisely cut, most of it haphazardly shaped and pieced together irregularly. And there is, she
argues, no shame in that. To the contrary, it may be the best science can do, given limited knowledge and
limited time, in trying to make sense of an often-jumbled world.
Here is another way of putting Cartwright's point. Sometimes the popular perception of the natural sciences,
and physics in particular, is that it too is a methodological monoculture. The defining characteristics of this
great laws and unifying theories. For example, it is perhaps no accident that the world's
monoculture are
most famous equation is this one: E= MC2. Not only is this uniquely famous equation drawn from theoretical
physics; it defines a great law, a unifying theory.
Yet much of modern physics does not, in fact, deal in great laws and unifying theories. Instead it deals in
great unknowns and empiric regularities, in ragged edges and qualitative maxims (Buchanan (2014)).
Advances in physics these days often come courtesy of massive empirical fishing expeditions,
3
All speeches are available online at www.bankofengland.co.uk/publications/Pages/speeches/default.aspx
industrial-scale searches for needles in haystacks, often using large-scale computational techniques. The
large Hadron collider - in essence, a massive Monte Carlo machine - would be one prominent example of
these techniques in practice.
So even physics, for some the theoretical pinnacle of the natural sciences, is these days far from being a
precise science. Through its evolution, the intellectual bloodline of physics and the other natural sciences
has been mixed and re-mixed. What we have today is a methodological hybrid, an intellectual mongrel. This
has been not just a natural evolution, but an essential one in making sense of our dappled world.
From Natural to Social Sciences
While Cartwright's
Dappled World aims to dispel the notion that natural science is precise science, it goes
further in arguing that the self-same case can be made, just as forcefully, for the social sciences. It, too, is a
haphazard patchwork of theories and hunches, operating at different levels of abstraction, often loosely held
together. The economic and financial world is every bit as dappled as the natural world. And, as with the
natural sciences, there is real virtue in that eclectic approach.
Yet this view jars somewhat with the dominant methodological direction of travel in economics. That
The Logic of Scientific
methodological lead was provided by Karl Popper in the 1930s (Popper (1934)). In
Popper argued for a "deductive" approach to advancing
Discovery, knowledge. This involved, first,
specifying a clear set of assumptions or axioms. From those were deduced a set of logical propositions or
hypotheses. And then, and only then, were these hypotheses taken to the data to be validated or falsified.
This pursuit of empirically-falsifiable hypotheses had even-earlier antecedents. The use of dynamic
optimisation techniques goes back at least to Leon Walras (Walras (1874)). And he, in turn, drew on the
tools developed by mathematicians such as Leibniz, Lagrange and Euler. These techniques were used to
construct early "general equilibrium" models of the economy, models which where internally consistent when
looked at as a whole.
Newtonian physics was built on the same principle of internal consistency within systems, with energy within
that system always preserved. Those systems were subject to disturbances which could cause them to
oscillate dynamically. Ultimately, however, these systems typically had an equilibrium or steady-state to
As one of the simplest examples, Newton's pendulum exhibits damped harmonic
which they returned.
motion once displaced before returning to a state of rest.
Much of mainstream macro-economics and finance has essentially followed this intellectual lead. It typically
-
starts with a set of assumptions or axioms in economics often defining the preferences of consumers and
the technology facing firms. From those assumptions are derived equations of motion for the behaviour of
4
All speeches are available online at www.bankofengland.co.uk/publications/Pages/speeches/default.aspx
-
consumers and firms which, rather revealingly, are often called the Euler conditions. Then, and only then,
are these first-order conditions for behaviour taken to the data to be tested.
These models, so derived, predictably exhibit the same damped harmonic motion as Newton's pendulum.
Let me give a couple of examples of this approach in mainstream practice in economics and finance. The
most famous equation in finance is probably this one:
Figure 1: The Black-Scholes Formula
Source: Black and Scholes (1973).
This is the Black-Scholes options pricing formula (Black and Scholes (1973)). Under a (relatively) small set
of assumptions, it provides a (relatively) simple analytical description of how to price a financial option. It
cannot rival Einstein for its simplicity and aesthetic beauty. But it nonetheless has many of the trademark
characteristics of theoretical physics.
That should come as no surprise because this equation was itself drawn from theoretical physics. In seeking
a solution to their option-pricing problem, Fisher Black, Myron Scholes and Robert Merton drew an explicit
link between their contingent-claims pricing problem and the heat transfer equation in physics (Churchill
(1963)). If not quite a lift and shift from theoretical physics, the Black-Scholes formula was certainly a
genetic mutation.
Moving from finance to economics, the dominant approach over recent decades to modelling the
macro-economy has probably been the Dynamic Stochastic General Equilibrium (DSGE) model (Smets and
Wouters (2003)). In its plain-vanilla form, this comprises a set of representative, optimising households and
firms. This model gives rise to an equilibrium which is unique and stationary, and dynamics around that
equilibrium which are regular and oscillatory.
Various knobs and whistles have been added to this workhorse framework, often involving market frictions in
competition and credit provision. These add colour to the model's dynamics but, by and large,
price-setting,
-
leave intact its properties stable, stationary, oscillatory. It is not just among academics that this workhorse
5
All speeches are available online at www.bankofengland.co.uk/publications/Pages/speeches/default.aspx
framework has found favour. The majority of central banks also take the DSGE framework as their starting
point, including the Bank of England (Burgess et al (2013)).
The DSGE approach has many of the hallmarks of Newtonian physics. As every action has an equal and
The economy's
opposite reaction, every shock has an equal and proportional reaction in DSGE models.
dynamics exhibit the same damped harmonic motion as Newton's pendulum, or if a rocking horse were to be
hit with a stick. The rocking horse metaphor is apt, as it was first used by Swedish economist Knut Wicksell
almost a hundred years ago to describe the business cycle motion of an economy (Wicksell (1918)).1
Mainstream finance and macroeconomics has, then, followed firmly in the footsteps of giants, part
Popperian, part Newtonian. It has been heavily indebted, intellectually, to Classical physics. That has led
some to dub the dominant economic paradigm (Mirowski (1989)). Less kindly, some have
"econo-physics"
described economics as suffering from physics-envy.
Assessing the Pros and Cons
Despite recent criticism, which has come thick and fast, it is important not to overlook the benefits from
having followed this path. One benefit, shared with theoretical physics, is that economic theory has
foundations. There are fewer "free", or undefined, parameters floating
well-defined around the model. Nobel
Laureate Robert Lucas said "beware of economists bearing free parameters".2
He was right. A theory of
everything is a theory of nothing.
The advantages do not stop there. On the assumption agents' behaviour is representative -
it broadly
mirrors the average person's -
these models of micro-level behaviour can be simply-summed to replicate
macro-economic behaviour. The individual is, in effect, a shrunken replica of the economy as a whole.
-
These macro-economic models are, in the jargon, micro-founded that is, constructed bottom-up from
optimising, micro-economic foundations.
These advantages carry across into the policy sphere. If the assumptions underlying these models are valid,
then the behavioural rules from which they are derived will be unaffected by changes in the prevailing policy
for policy analysis. They are, in economists' jargon,
regime. These models are then a robust test-bed
explains these models'
immune to the Lucas critique (Lucas (1976)). This feature, above all others, probably
ubiquity in policy organisations.
Not least in the light of the crisis, however, the potential pitfalls of these approaches have also become
clearer of late. Recently, these models have been subject to stinging critiques (Romer (2016)). One
1
"If you hit a rocking horse with a stick, the movement of the horse will be very different from that of the stick. The hits
are the cause of
but the system's own equilibrium laws condition the form of movement" (Wicksell (1918)).
the movement,
2
Attributed to Robert Lucas in Sargent (2001).
6
All speeches are available online at www.bankofengland.co.uk/publications/Pages/speeches/default.aspx
common complaint is that they may not do an especially good job of describing the real world, especially in
situations of economic stress. Exhibit one is that they offered a spectacularly poor guide to the economy's
dynamics around the time of the global financial crisis.
To illustrate, Chart 1 plots the range of forecasts for UK GDP growth from 2008 onwards produced by 27
economic forecasters (including the Bank) in 2007, the dawn of the financial crisis. Three features are
notable. First, pre-crisis forecasts were very tightly bunched in a range of one percentage point, perhaps
because they were drawn from similar models. The methodological mono-culture produced, unsurprisingly,
the same crop.
Second, these forecasts foresaw a continuation of the gentle undulations in the economy seen in the decade
prior to the crisis - the so-called Great Moderation (Bernanke (2004)). At the time, these damped oscillations
seemed to match well the damped harmonic motion of DSGE models. A good crop today foretold of an only
slightly less good crop tomorrow.
Third, most striking of all, every one of these forecasts was not just wrong but spectacularly so. Few
forecasters foresaw even a slight downturn in GDP in 2008 and none foresaw a recession. Yet we
witnessed not just a recession but the largest since the 1930s. The one-year-ahead forecast error in 2008
was 8 percentage points. The crop failed and the result was economic famine.
While forecasting performance has improved in the period since, there has a continued string of serially
correlated errors, with the speed of the recovery consistently over-estimated (Chart 2). The average forecast
error one-year-ahead has been consistently negative, averaging 0.5 percentage points per year. The
average error two years ahead has been over one percentage point per year.
At root, these were failures of models, methodologies and mono-cultures. It has been argued that these
more: "The charge
models were not designed to explain such extreme events. To quote Robert Lucas once
is that the [..] forecasting model failed to predict the events of September 2008. Yet the simulations were not
presented as assurance that no crisis would occur, but as a forecast of what could be expected conditional
on a crisis not occurring" (Lucas (2009)).
7
All speeches are available online at www.bankofengland.co.uk/publications/Pages/speeches/default.aspx
Chart 1: Range of GDP forecasts in 2007Q4 Chart 2: Forecasts for World Growth by the IMF since
2007
Apr-07 Oct-07 Apr-08
Latest vintage of GDP data Year on year growth
Percent year
Oct-08 Apr-09 Oct-09
4
on year
Apr-10 Oct-10 Apr-11
Oct-11 Apr-12 Oct-12 7
3
Apr-13 Oct-13 Apr-14
6
2
5
November 2007 IR
1
4
0
3
-1
2
-2
1
-3
0
-4
-1
-5
-2
2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
2000 2002 2004 2006 2008 2010 2012 2014 2016
Source: Bank of England November 2007 Inflation Report; Bank
Source: IMF World Economic Outlook.
of England Survey of Economic Forecasters.
For me, this is not really a defence. Economics is important because of the social costs of extreme events.
Economic policy matters precisely because of these events. If our models are silent about these events, this
jeopardises the very thing that makes economics interesting and economic policy important. It risks
squandering the human capital endowment the financial crisis has bestowed.
Even if some of the post-crisis criticism of workhorse macro-economic models is overdone, it still raises the
question of whether new modelling approaches might be explored which provide a different lens on the world
or which better match real-world dynamics. If, as Cartwright suggests, there is more methodologically that
links the natural and social sciences than divides them, there could be considerable scope for disciplinary
cross-pollination of ideas and models.
So just how interdisciplinary is economics? The short answer appears, regrettably, to be "not very". Table 1
different social sciences to the proposition
looks at responses by professionals in "inter-disciplinary
knowledge is better than knowledge obtained by a single discipline" (Fourcade, Ollion and Algan (2015)). A
majority, often a large majority, of other social sciences agree with this statement. Only in economics do a
majority disagree.
8
All speeches are available online at www.bankofengland.co.uk/publications/Pages/speeches/default.aspx
Table 1: Responses to the question - Interdisciplinary knowledge is better than knowledge obtained by a
single discipline?
Source: Fourcade, Ollion and Algan (2015). Notes: Table shows responses as a percentage of professors in each discipline.
Economists' words are matched by their actions. The science periodical Nature recently published
interdisciplinary indices, measuring the number of references made to outside disciplines by a subject area
and the number of citations made outside the discipline to that subject area. Over the period 1950-2014,
economics sat in the bottom left-hand quadrant (Chart 3). Alongside theoretical physics, economics was at
the bottom of the inter-disciplinary league table (van Noordan (2015)).
Chart 3: Citations and references to outside Chart 4: Citations and references to outside
disciplines disciplines over time
Source: van Noordan (2015). Source: van Noordan (2015).
Looking at these patterns over time paints a somewhat more optimistic picture (Chart 4). There is clear
evidence of economics having become more cross-disciplinary during the course of this century. Once
finance is taken out of these estimates, however, economics continues to lag. And alternative metrics, such
as the degree of rigidity in hierarchies and gender diversity, paint economics in a less favourable light
(Fourcade, Ollion and Algan (2015)). Despite progress, it is difficult to escape the conclusion that economics
remains an insular, self-referential discipline.
9
All speeches are available online at www.bankofengland.co.uk/publications/Pages/speeches/default.aspx
The economics profession's intellectual bloodline is purer than in most other disciplines. In some respects, it
is a source of strength that the workhorse economic model is a thoroughbred. That quest for purity also
contributed importantly, however, to this workhorse falling at the first meaningful fence put in its path. This
suggests it is probably as good a time as any to consider mixing the intellectual bloodline, just as physics
and other of the natural sciences have done.
Agent-Based Models (ABMs)
Against this backdrop, what other disciplines and approaches might be productive alternative lines of
enquiry? One potentially promising strand is so-called agent-based modelling. Agent-based models (ABMs)
are interconnected systems of individual "agents" who follow
well-defined behavioural rules of thumb.
What makes these models interesting is that these agents are heterogeneous and interactive. In other
words, these models relax one of the key assumptions of the standard model - a single, representative
agent. For social systems, this does not sound too implausible. Humans are social animals. Indeed, the
feature which set humans apart from other
Chart 5: The most highly cited articles on agent-based
animals is their degree of social interaction
modelling across disciplines
(Harari (2015)).
This, on the face of it, modest adaptation
gives rise to some fundamental changes in
model dynamics. Linear, proportional
responses to shocks become the exception;
complex, non-linear responses the rule.
Single, stationary equilibria become the
exception; multiple, evolutionary equilibria the
rule. I discuss these differences in the next
section.
Before doing so, I want to bring to life some of
Source: Google scholar; Bank calculations. Notes: This was found by
performing a Google Scholar search of the relevant term for
the uses of ABMs. These models have found
"agentbased modelling" in each field and then using the citation count of the
most highly cited paper which could be fairly and solely attributed to each
widespread application across a broad array
distinct field. When searching for "Monte Carlo" only papers
modelling
of disciplines in both the natural and social distinct subsystems were considered and not those using the technique
of random number generation more generally.
sciences. They have been used to address a
massive array of problems, big and small: from segregating nuts to segregating races, from simulating the
fate of the universe to simulating the fate of a human cell, from military planning to family planning, from
flocking birds to herding (fat) cats.
10
All speeches are available online at www.bankofengland.co.uk/publications/Pages/speeches/default.aspx
Yet in economics, ABMs have been used relatively less (Battiston et al (2016)). Chart 5 shows the number
of citations that the most-cited article on agent-based modelling has in different fields. Economics has been
a late and slow-adopter of ABM techniques. In other words, ABMs may be another example of the lack of
cross-disciplinary perspective in economics.
To be clear, ABMs are no panacea for the modelling ills of economics. In discussing them here, the
implication is not that they should replace DSGE models, lock, stock and barrel. Rather, their value comes
from providing a different, complementary, lens through which to make sense of our dappled economic and
financial world, a lens which other disciplines have found useful when understanding their worlds or when
devising policies to improve it.
(a) Early Origins
ABMs grew out of some of the earliest applications of computing at Los Alamos National Laboratory in the
-
United States (Metropolis (1987)). In 1945, it was this lab that developed the first-ever nuclear weapon
the fission bomb. The chain-reactions used in these weapons are based on the fissioning of large atoms by
neutrons. Neutron transport involves high-dimension, discrete collisions, with each step probabilistic. This
quickly gives rise to a vast probability tree of possible outcomes.
Enrico Fermi had experimented with a method to solve these sorts of high-dimensional problems in the
1930s, using a small mechanical adding machine. The technique involved generating random numbers and
comparing them with probabilities derived from theory. By doing this for a large number of possible neutron
paths, he painstakingly painted a picture of the transport of neutrons. Fermi had, by hand, constructed the
first agent-based model.
These models were about to get a machine which could do these large-scale computations for them.
Assembled at Los Alamos during World War II was a dream team of the great and good in science, including
John von Neumann, Richard Feynman, Niels Bohr and Robert Oppenheimer. Von Neumann himself offered
use of one of the first-ever computers to perform neutron calculations. That exercise culminated in the
hydrogen bomb. ABMs had found their first real-world application.
11
All speeches are available online at www.bankofengland.co.uk/publications/Pages/speeches/default.aspx
Figure 2: John von Neumann Figure 3: The hydrogen bomb
Source: LANL (public domain). John von Source: The Official CTBTO Photostream (CC-BY-2.0). An atmospheric nuclear test
Neumann in the 1940s (image available here). conducted by the U.S. at Enewetak Atoll on 1 November 1952 (image available
here).
(b) Military Planning
-
By 1947, the use of random numbers in computation had a name which reflected its probabilistic nature
Monte Carlo, home of the casino.3 In a lecture in 1948, von Neumann described the idea of cellular
automata - artificial systems of cells exhibiting life-like behaviour which evolved according to simple rules of
behaviour (von Neumann et al (1966), Sarkar (2000)). Perhaps the best-known example of cellular
automata came several years later: Conway's "Game of Life" (Conway (1970)).
In 1949, the emerging technique of Monte Carlo analysis was beginning to gain traction. A symposium
- -
organised and sponsored by the RAND Corporation a spin-off of the US War Department was the
springboard for developing some of the first military applications of ABMs. What had once been simple
board-and-dice based war games switched to computational ABMs during the 1960s, borrowing heavily on
cellular automata (Woodcock
von Neumann's et al (1988)).
These models have since been used to provide insights in a range of real-world military operations, past and
present. They have been used to understand the dynamics of past battles, such as the operation of German
U-boat battles (Champagne (2003)), Hill et al (2004)). And they have been used, typically secretly, to plan
3
See Metropolis and Ulam (1949). Metropolis reports that he came up with the name, but it was inspired by Ulam's uncle asking for
money by claiming he "just had to go to Monte Carlo''. By 1949, they had written a paper together outlining the potential uses of this
method including a chain-reaction with particles as Monte Carlo agents.
12
All speeches are available online at www.bankofengland.co.uk/publications/Pages/speeches/default.aspx
military strategies for current conflicts, with organisations such as the US Naval Research Laboratory and the
US Air Force investing in ABM technology (Manheimer et al (1997)).
Figure 4: WW2 U-Boat Campaigns Figure 5: War Games
Source: IWM Collections (public domain). Torpedo fired on a merchant ship Source: GSC Game World (GNU FDL) (Image from
'Cosacks: European Wars' (image available
(image available here). here).
The US Air Force has an agent-based model known as Systems Effectiveness Analysis Simulation (SEAS).
The SEAS package models the entire surface of the earth and its satellites. Each agent has a specific
longitude and latitude to a resolution of one millimetre. In order to allow interaction, SEAS agents are
equipped with sensors, communications, and weapons allowing co-operative or competitive behaviour
(Brooks et al (2004)).
Most recently, the work on ABMs in a military context has taken on a new direction. As autonomous vehicles
such as drones are used in war, they add a new dimension to ABM simulations. In a world of human agents,
ABMs could only approximate agent behaviours. In a world of military automata, these simulations come
closer to replicating real-world warfare (Sanchez and Lucas (2002)).
A more benign military application of ABMs has been in the context of war games. Military ABMs were a
forerunner of many of today's
computer war games: Eve Online, World of Warcraft and Command and
Conquer are all popular, sophisticated ABM-based games which mix computer and human controlled agents.
(c) Physical Sciences
As the Large Hadron Collider illustrates, modern physics is heavily computational in certain fields. This
arises in part because even simple systems can quickly exhibit complex behaviours. In general, a system
- the
comprising three bodies undergoing motion via a force cannot be solved analytically "three-body
problem". And there are many problems in physics which involve the interaction of "particles" in ways which
are complex and non-deterministic.
13
All speeches are available online at www.bankofengland.co.uk/publications/Pages/speeches/default.aspx
These features have resulted in ABMs being extremely widely used in the physical sciences, at various
different levels of resolution. At the micro scale, some of the earliest applications of ABMs were to study
plasmas -
charged particles which constantly interact. Plasmas are the fourth state of matter after solids,
liquids and gases. They are prime ABM candidates because they exhibit rich, non-linear, complex
behaviour.
In 1966, Edward Teller wrote a paper which described how to build a plasma ABM with 32 interacting
(1966)). Even with "only" 32 interacting agents, this was a formidable
particles (Brush, Sahlin and Teller
computational challenge. But the advent of parallel and high performance computing since the 1990s has
changed the scale of plasma particle simulations. Simulations today regularly use as many as 109
et al
computational agents (Turrell (2015)).
These plasma ABMs have found widespread application, micro and macro. At the micro level, they have
been used to help identify and kill cancer cells with pinpoint accuracy, while leaving healthy surrounding cells
et al
unharmed (Bulanov (2002)). At the macro level, they have been used to simulate and reproduce the
way stars produce energy, using a nuclear fusion reactor here on Earth, an approach that has the potential
to provide clean energy for billions of years (Turrell (2013)).
Simulating the processes powering stars is modest by comparison with ABMs which aim to model the entire
universe. In 1985, one of the first comprehensive computational models of the universe was published, with
over 32,000 particles representing known matter (Davis et al (1985)). As estimates put the number of
protons and neutrons in the Universe at 1080, this ABM was impressively parsimonious (Penrose (1999)).
These models have generated important insights, including the role of "dark matter" in the
evolution of
galaxies.
Not all applications of ABMs are, however, large in scale and universal in application. A 1987 paper called
"Why the Brazil Nuts Are on Top" used an ABM with agents of different physical sizes to explain how mixed
nuts segregate over time when shaken, with Brazil nuts generally rising to the surface (Rosato et al (1987)).
This research was not as nuts as it sounds. It has since found real-world applications in industries such as
pharmaceuticals and manufacturing.
14
All speeches are available online at www.bankofengland.co.uk/publications/Pages/speeches/default.aspx
Figure 6: Segregation of nuts Figure 7: The universe
Source: Sae Rpss (CC-BY-SA-3.0). Nuts (image available here).
Source: NASA Headquarters - Greatest Images of NASA
(NASA-HQ-GRIN) (public domain). Spiral galaxy in the
constellation Coma Berenices (image available here).
(d)