Escape From Model Land - Erica Thompson

 Escape From Model Land, by Dr Erica Thompson, is published on 24th November 2022.

Erica Thompson is a mathematician but this is a non-technical book with very few numbers and certainly no equations. Have no fear, it's easy to read, and at about 230 pages is not overlong, with every word and every sentence counting, no padding. Take it slowly, many of the sentences are worth reading twice. And there are jokes.

It's hard to categorize this book, what with it being the first of its kind, but put it on the shelf next to Nick Taleb's The Black Swan, because it deals with a subject of profound importance to everyone, but which has not been given anything like the attention it deserves, leaving us all exposed to misunderstandings and risks.

Mathematical models have become all pervasive, their outputs used by decision makers in all walks of life, affecting us all. Yet for the most part these decision makers do not have a good understanding of how models are constructed, how they operate, their limitations and how fit they are for the purpose assumed of them. Models can be invaluable, but inappropriately used can be dangerous. We need to know.

Erica Thompson explores how models have been used in three broad areas of public life, the financial services industries, health care, with particular reference to the covid pandemic, and climate science. She is at pains to point out the invaluable contribution that mathematical modelling has made in these and other fields, but the purpose of her book is to warn of their limitations and the dangers involved when decision makers use models with insufficient understanding. Her deep insights expose things which have been hidden in Model Land and she provides the tools and checklists needed to navigate the real world more safely. 

This is a book that should be read by all those involved in making decisions that are influenced by models, whether in business, science, or governance. And those of us not so directly involved, but subject to the decision-makers' decisions, would do well to read it too. That includes all of us.

*****

Here's what other others have said:

A wise, lucid and compelling guide to how mathematical modelling shapes our world. Dr Thompson teaches us how to go from being unthinking consumers of models to sophisticated users, combining a rich variety of vivid examples and case studies with deep conceptual expertise, presented in a lively and accessible way
Stian Westlake, CEO, Royal Statistical Society

Carefully researched and beautifully written, Dr Thompson's Escape from Model Land reveals how our progressively complex world is dominated by well-meaning experts' use and misuse of increasingly impenetrable models . . . For an open-minded reader keen to expose, understand and potentially reconstruct their own worldview, Escape from Model Land is, at the same time, an uncomfortable and uplifting read. It shines a gentle light on many of our own norms and beliefs
Kevin Anderson, Professor of Energy and Climate Change in the School of Mechanical, Aerospace and Civil Engineering, University of Manchester.

A brilliant account of how models are so often abused and of how they should be used.
How do mathematical models shape our world - and how can we harness their power for good?Models are at the centre of everything we do.
Whether we use them or are simply affected by them, they act as metaphors that help us better understand the increasingly complex problems facing us in the modern world.
Without models, we couldn't begin to tackle three of the major challenges facing modern society: regulation of the economy, climate change and the COVID-19 pandemic.
Yet in recent years, the validity of the models we use has been hotly debated and there has been renewed awareness of the disastrous consequences when the makers and interpreters of models get things wrong. Drawing on contemporary examples from finance, climate and health policy, Erica Thompson explores what models are, why we need them, how they work and what happens when they go wrong.
This is not a book that argues we should do away with models, but rather, that we need to properly understand how they are constructed - and how some of the assumptions that underlie the models we use can have significant unintended consequences.
Unexpectedly humorous, thought-provoking and passionate, this is essential reading for everyone.
John Kay

An eye-opening account of the limits and uses of mathematical models . . . Thompson offers a host of lessons, among them that every model depends upon value judgments to determine what's included in them, that models should be understood as "not an objective mathematical reality, but a social idea," and that models contain the biases of those who make them, so increased diversity among modelers is essential for "greater insight, improved decision-making capacities and better outcomes" . . . The result is a thoughtful, convincing look at how data works
Publisher's Weekly

Escape from Model Land demystifies the process of making the mathematical models that are increasingly used to make decisions about our lives, from the financial markets to the pandemic to climate change. A thought-provoking and helpful guide for data scientists and decision makers alike
Stephanie Hare, author of 'Technology Is Not Neutral'

The best place to buy the book is probably from Hive Books, who currently have it listed at £16.59 including postage. Just saying.

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Here are a couple of pictures of Erica caught at work, at the London Mathematical Laboratory.

Some copies have already found their way to the London Maths Lab library.

If you are in North America I'm afraid you will find the cover is not quite as pretty. What does that say about the publisher's view of the difference between American and European audiences? 

A review in The Economist: The Algorithm's Mercy

The problems with algorithmic formulae are tackled in depth in “Escape from Model Land” by Erica Thompson of the London School of Economics. These statistical models are the backbone of big data and ai: if data is the input, algorithms are the tool and models are the product. They are everywhere, from e-commerce tips to economic and climate-change forecasts.

Yet rather like the full-scale map of an empire imagined by the writer Jorge Luis Borges, a perfect model of the teeming world will always be beyond reach. The task is to ensure that the abstractions correspond to reality as far as is humanly possible. “All models are wrong,” runs a venerable saying. “Some are useful.”

Ms Thompson focuses on a challenge she calls the Hawkmoth Effect. In the better known Butterfly Effect, a serviceable model becomes less reliable over time because of the complexity of what it is simulating, or because of inaccuracies in the original data. In the case of climate change, say, this might lead to a prediction for rising temperatures being out by a fraction of a degree. In the Hawkmoth Effect, by contrast, the model itself is flawed; it might fail to take full account of the interplay between humidity, wind and temperature. This sort of mistake can be much more misleading, and much harder to rectify.

The author calls on data geeks to improve their solutions to real-world issues, not merely refine their formulae—in other words, to escape from model land. “We do not need to have the best possible answer,” she writes, “only a reasonable one.” Before there is a statistical model, she notes, there is a mental version. Data scientists need self-awareness and empathy as well as mathematical skill. Ms Thompson asks data scientists to be conscious of the choices and values in a model’s design. 

*****

Update 6th December 2022, publication day for North America.


Jeremy Williams writing for The Earthbound Report.

Mathematical models don’t often get a lot of attention from the general public. When they do, it’s rarely positive. Perhaps they have failed to predict a recession, or foretold pandemic doom scenarios that don’t materialise. All of a sudden it gets political, and everyone is talking about a science that they may or may not understand.

For those who do want to understand what models are and what they can do, Erica Thompson has written a very useful book: Escape from Model Land – How mathematical models can lead us astray and what we can do about it. She’s a data scientist and fellow at the London School of Economics, with a background in climate modelling. Her book is a clear and a surprisingly playful exploration of what models can and can’t do, when they’re useful and when they’re not.

Models are frameworks for thinking. They are how we form relationships between data, in order to understand the future. And while the focus is on mathematical models, Thompson takes a wide definition. We all use models all the time, even subconsciously. When we decide whether or not to take an umbrella with us as we leave the house, we assess the conditions outside against our past experience of weather and seasons. It’s a simple modelling exercise that will result in a best guess at chances of rain, and that will inform our decision.

Of course, the models the book is most concerned with are computerised and complicated, including the ones used by weather forecasters. Others are used to forecast election results, monitor volcanic activity, model consumer behaviour in order to advertise to us, manage the economy or coordinate disaster response. We can’t avoid models. All the more reason to understand them.

In the second half of the book there are specific chapters on economic, pandemic and climate modelling, but these are low on specifics and more concerned with the theory behind efforts to model such things. Overall, the book is quite philosophical in tone. It talks about how, in George Box’s famous phrase, “all models are wrong, but some are useful.” Thompson looks at models as metaphors, fictions, how they function culturally and politically. The national economy described as a household budget, for example, is a simplified model that politicians have used to justify their actions in what sound like common sense terms, but don’t reflect the money creating powers that governments have.

Another thing politicians do sometimes is claim to follow the science, and Thompson warns about this. It’s in the jump from the neatly defined parameters of the model back to the real world that things most often go astray, and why Thompson calls the book Escape from Model Land. Models cannot make decisions. Models are created by people and interpreted by people. The lines of accountability trace back to the creators of the model, their assumptions and their biases and blind spots. Inevitably, sophisticated mathematical models are created by highly educated people in well funded institutions, and that position of privilege affects what their models see and don’t see. Without acknowledging this, following the science can be a way of blurring responsibility. Ultimately it is up to human beings to bring in the values that models can’t help us with, and “meaningfully integrate concepts such as care, love, responsibility, stewardship and community.”

The book investigates all of this with metaphors and thought exercises, and Thompson has more fun with it than you might expect. There are birthday cakes, comparisons with astrology, the butterfly vs the hawkmoth effect, “the cat that looks most like a dog”. It’s full of creative ways of explaining things. It’s not technical, though readers with an interest in mathematics, computing and data will definitely get more from the book. And I finished it much better equipped to think about models and how we use them well, humbly, inclusively and with accountability, in our social decision making.

*****

Georgia Meyer (LSE Department of Management)

Escape from Model Land provides a blueprint for the kind of critical thinking required for us to more responsibly continue to co-create realities through models. Long ubiquitously deployed in finance, economics and climate forecasting, their increasing adoption across all aspects of economies and societies by virtue of the increasing sophistication of machine learning and predictive analytics demand a much more intentional and reflective scrutiny about their nature and impacts than what is oft the case. Dr Thompson does just that in Escape from Model Land by: (i) teasing apart the complicated enmeshment of models as translators of and / or producers of realities; (ii) reviewing models’ necessarily incomplete and changing quantification and qualification of uncertainties; (iii) considering their value in terms of transparency of decision-making processes and (iv), asking the important question of who gets to make the models in the first place (and with what ends in mind)?

Dr Thompson says that she ‘started thinking about these questions as a PhD student in Physics ten years ago’ when she ‘conducted a literature review on mathematical models of North Atlantic storms’. She realised that given the fact that all these peer-reviewed and published studies had ‘conflicting rather than overlapping uncertainty ranges’ an additionally important question (alongside figuring out how to predict the behaviour of North Atlantic storms) was ‘how we make inferences from models’. She sets up the ambition of the book as her effort to try and find a balance between two ‘unacceptable alternatives’: (i) taking models literally - not accounting for their misrepresentations of reality; or (ii) abandoning models and losing ‘lots of clearly valuable information’. The question she poses is: ‘how do we navigate the space between these extremes more effectively?’.

Following this set up in Chapter 1 Locating Model Land, Chapter 2 Thinking Inside the Box puts forward a case for how models articulate, and constrain, the boundaries of our imaginations. In making this case she first discusses a necessary and careful interplay between simplification and complexity as prerequisites for model explanatory power, citing Von Neumann’s parable about fitting an elephant with four parameters whilst a model with five parameters would make it 'wiggle his trunk'. Moving beyond the Ockham’s Razor principle (go with the simplest explanation) Dr Thompson expands the discussion on what is in and out of scope of models by introducing The Phillips-Newlyn Machine (or MONIAC, Monetary National Income Analogue Calculator) which ‘conceptualises and physically represents money as liquid…and circulated around the economy at rates depending on key model parameters’. Her discussion of the opportunities and limitations provided by MONIAC - including the way it expanded the consideration of relations between things not just the things themselves - notes how ‘each choice of representation lends itself to certain kinds of imaginative extension’. It is one of my favourite passages in the book (there are many).

Another chapter of the book, Models as Metaphors, riffs off a statement by Nobel Prize winning economist Peter Diamond’s Nobel lecture: ‘taking a model literally is not taking a model seriously’. Dr Thompson uses this starting point to set out how models have multi-dimensional purposes and applications depending on the phenomena at hand and the tacit acceptance of the nature of the stereotyping (reducing to simplicity) that is taking place in any given context within which a model is being deployed. In other words, she argues that we see models less as representations of reality and more as a companion to the version of reality that is acceptable in any given social context at any particular time. This is where questions of values - whose values - are at play when these ‘implicit value judgements are being made’ comes to the fore.

This theme is expanded in various parts of the book to address the discrimination and dangerous stereotyping that arises when deeply flawed processes of constructing and applying models (and poor input data) are left unchecked, drawing on the polemical work of Cathy O’Neil, Emily Bender and Tinmit Gebru. What makes this chapter particularly interesting is the way Dr Thompson interrogates the value of model explainability across various contexts making the case that whilst in some (aforementioned e.g. discrimination) explainability is enmeshed with questions of accountability and fairness, in others (e.g. cyclone activity), the picture is less clear cut (if a model does more accurately predict cyclone activity but we don’t know how it was able to, is that a problem?). This is complex territory and the clarity and reflexivity that Dr Thompson deploys across this matrix of values, agency, context and decision-making reads like a ‘how-to’ for any researcher or practitioner working with models. Or, for that matter, for any human being with varied and changing levels of self-awareness about the internal working models we all use consciously and unconsciously to move through the world. 

These questions of how values intersect with science are addressed throughout the book in later chapters including one called The Accountability Gap. Here Dr Thompson draws on Birhane’s work mapping the territory of evaluative tools used in ML papers - noting how often the extent to which societal needs are met are absent from the discussion. In revisiting this theme the notion of objectivity in science is gently teased apart revealing the many constructed components that are inescapably bound up with processes of description, measurement and prediction. Where this thread leads is an instructive set of examples of various articulations of some kind of ‘social objectivity’ - which rests on multiple contributory accounts that are ultimately shared and agreed upon as a basis from which to move forward. Of course this is a notably different kind of treatment of scientific knowledge than that which has long held popularised dominance in many key areas of policy and common parlance.

Dr Thompson ends the book with five principles for responsible modelling, making a point about the human cognitive counterpart to navigating the world with models: that, ‘we must ourselves navigate the real-world territory and live up to the challenge of making the best of our imperfect knowledge to create a future worth living in.’. Amidst many important takeaways from the book (who’s values?; complexity vs simplicity trade-offs; explainability as virtue of accountability by context; obfuscation and misrepresentation via compression of variables in models and measurement), this point about human capacities feels critical. That ultimately, we cannot cede too much explanatory power to models - divorcing those who create and use them from the kind of transparency and humility to their imperfections. That we cannot sidestep our responsibilities to interrogate the decisions taken on the basis of models as new information or additional viewpoints come to light. Finally, what I take from this book, is that we ought regularly escape our own (internal) model lands that shape how we develop priorities, apply principles and evaluate our interactions with the world around us.

Publishers Weekly

Thompson, a senior policy fellow at the London School of Economics, debuts with an eye-opening account of the limits and uses of mathematical models. Thompson explains that models are metaphors for the real world, and that it’s crucial to avoid taking them too literally. “Force equals mass times acceleration is the ‘correct model’ to use to solve the question” of when a truck would reach 60 mph, for example, but real-world conditions contain variables that the model can’t account for. Thompson offers a host of lessons, among them that every model depends upon value judgments to determine what’s included in them, that models should be understood as “not an objective mathematical reality, but a social idea,” and that models contain the biases of those who make them, so increased diversity among modelers is essential for “greater insight, improved decision-making capacities and better outcomes.” Thompson wraps up with a list of principles for “responsible modelling,” including deciding “to what purpose(s)” models should be applied, and if “decisions informed by this model will influence other people or communities” who weren’t considered or consulted in the making of the model. The result is a thoughtful, convincing look at how data works.

Japanese readers may be interested in this review by @emigrl

かつては経済の分析に採用されることが主だったが近年あらゆる分野に応用され、政府によるさまざまな政策の根拠としても影響力を増している数理モデルについて、現実との乖離が生まれる理由やその倫理的な側面などについて解説する本。著者はロンドン・スクール・オブ・エコノミクスに所属するデータサイエンティスト。

******

Dr. David A. Shaywitz writes in the Wall Street Journal:

We live in an information age, as the cliché has it—really an age of information overload. But “measured quantities do not speak for themselves,” observes Erica Thompson, a statistician and a fellow at the London School of Economics. Data, she notes, are given meaning “only through the context and framing provided by models.”

When we want to know how rapidly a new infectious virus is likely to spread, we turn to mathematical models. Models are used by climate scientists to project global warming; by options traders to price contracts; by the Congressional Budget Office to forecast the economic effects of legislation; by meteorologists to warn of approaching storms. Without models, Ms. Thompson says, data “would be only a meaningless stream of numbers.”

Ubiquitous and persuasive, models also drive decisions—one reason why, in Ms. Thompson’s view, they require our urgent attention. She tells us that, as a graduate student studying North Atlantic storms, she noticed how different models predicted different overall effects and produced contradictory results. She started to reflect on the role of models—as metaphors, as tools for understanding, as expressions of sociopolitical power. “Escape From Model Land” offers a contemplative, densely encapsulated summary of her reflection and research.

Models seek to represent the real world, but they live outside it. Indeed, they exist in their own “wonderful place,” what Ms. Thompson dubs “Model Land.” In Model Land, the assumptions of a model are considered “literally true,” enabling expansive exploration and ambitious predictions. The problem is that Model Land is easy to enter but difficult to escape. Having built “a beautiful internally consistent model,” Ms. Thompson writes, it can be “emotionally difficult to acknowledge that the initial assumptions on which the whole thing is built are literally not true.”

There are all sorts of ways that models can lead us astray. A small measurement error on an input can lead to wildly inaccurate forecasts—a phenomenon known as the Butterfly Effect. Fortunately, this type of uncertainty is often manageable. Far more problematic are what Ms. Thompson calls “unquantifiable unknowns”—things that are left out of a model’s calculation because they can’t be anticipated, such as the unexpected arrival of a transformative technology or the abrupt collapse of a robust market. It is not always true, she observes, that the data we have now will be relevant to the future—as traders discovered in the stock-market crash of 1987, when their models catastrophically failed.

Beyond the inherent inability of models to account for the unaccountable, models also reflect the biases of their creators. We may be inclined to regard models as objective expressions of truth, yet they are deliberately constructed interpretations, imbued with the values and viewpoints of the modelers—primarily, as Ms. Thompson notes, well-educated, middle-class individuals. During the pandemic, models “took more account of harms to some groups of people than others,” resulting in a “moral case” for lockdowns that was “partial and biased.” Modelers who worked from home—while others maintained the supply chain—often overlooked “all of the possible harms” of the actions their models were suggesting. And even when models try to describe the effects of different courses of action, it’s human beings who must ultimately weigh the benefits and harms. “Science cannot tell us how to value things,” Ms. Thompson says. “The idea of ‘following the science’ is meaningless.”

The promise and peril of models, Ms. Thompson recognizes, has deep resonance in biomedicine, where so-called model organisms, like yeast and zebrafish, have led to foundational insights and accelerated the development of therapeutics. At the same time, treatments that work brilliantly in Model Land often fail in people, devastating patients and disappointing drug developers. The search for improved disease models can be complicated when proponents of one model suppress research into alternative approaches, as the late journalist Sharon Begley documented in a powerful 2019 report. Ms. Thompson perceptively critiques the adoption of singular “gold standard” models, noting that the “solidification” of one set of assumptions can lock us into one way of thinking and close off other important avenues of inquiry.

The statistician George Box once observed that “all models are wrong, but some are useful.” For Ms. Thompson, the real utility of models is as a tool for exploration rather than a mechanism to divine the truth or predict the future. “The process of generating a model changes the way that we think about a situation,” she writes; it “strengthens some concepts and weakens others.” Recalling President Eisenhower’s legendary maxim—that “plans are useless, but planning is indispensable”—she argues that relying on models solely for their output misses the indispensable value of the process of model development: a deeper understanding of trade-offs, and the agility to adapt if foundational assumptions unexpectedly change.

While acknowledging our “overenthusiasm for mathematical solutions,” Ms. Thompson emphatically counsels not abstinence but discipline and humility. Clarity about the purpose of the model matters, she says: An epidemiological model may inform us about viral transmission and hospital pressure but not about the economic effects of closing businesses. Modelers should acknowledge the value judgments implicit in their models, explain what makes a model “good” and describe relevant limitations. But it’s up to us to learn from models without being drawn in by their seductive elegance, and to ensure that the lessons from Model Land find substantive expression where it actually matters: in our messy, material, magnificent world.

*****

Felix Martin writes in The Guardian:

Escape from Model Land by Erica Thompson review – the power and pitfalls of prediction

From financial forecasts to the climate crisis, a constructive and nuanced critique of mathematical modelling from a data scientist

The only function of economic forecasting,” wrote the great American economist John Kenneth Galbraith, “is to make astrology look respectable.” It is characteristic of Erica Thompson’s sprightly and highly original new book on the uses and abuses of mathematical modelling that she dares to turn Galbraith’s verdict on its head. The medieval practice of casting horoscopes, she shows in one typically engaging section that embodies her most important themes, has a surprising amount to teach us about the modern practice of using models to guide policy.

The topic is an exceptionally important and timely one. The Covid-19 pandemic, the climate crisis, and turbulence in financial markets are just three examples of how fundamental mathematical modelling has become to decision-making in many areas of modern life.

Thompson’s argument is not, of course, that scientific forecasting has made no progress over the past half-millennium. Today’s researchers benefit from a world awash with data on natural phenomena and human behaviour, making the raw material for model-building vastly richer than it once was. Mathematical and statistical techniques are far more sophisticated – and we have modern computing power to help us crunch the numbers. These differences make the artificial worlds which modern economists, meteorologists and epidemiologists build dramatically more hi-res than anything the benighted court astrologer could come up with.

But just like their medieval counterparts, today’s “Model Lands” – the hypothetical worlds we construct in order to explore the future – have no practical value until their analyses and predictions are applied in real life. It is in this all-important step – the escape of Thompson’s title – that the parallels between astrology and mathematical modelling become particularly relevant. The central common challenge is working out how much of what we learn in pristine but artificial models remains valid in messy but concrete real life.

One way of figuring this out is quantitative: you compare the predictions of the model against new, incoming data. A critical obstacle here is that predictions based on modern mathematical models, no less than those based on medieval horoscopes, usually depend on an extensive hinterland of assumptions. That makes testing the validity of their forecasts intrinsically difficult: were the assumptions wrong, or was it just that not enough assumptions were included?

Another problem is that the fresh, real-world data needed to test the results is often not even available. It will flood in quickly and easily for day-ahead weather forecasts, for example – but might arrive centuries too late to discriminate between today’s long-term climate models.

That’s why, Thompson explains, a second, qualitative way of determining the success of predictions is much more common: reliance on expert judgment. The pitfalls of this route were also well known to the medieval courts. Only those versed in the most cutting-edge mathematical knowledge were skilled enough to interpret medieval horoscopes. As such, it was in practice impossible for the client to come to their own conclusions. The result was that an exclusive guild, whose true competence remained unknown, ended up marking their own homework. The same could be said today.

Another hazard stalking ancient and modern modellers alike is that they fall in love with the sheer beauty and complexity of their own constructions. Having eaten the lotuses of Model Land, they can’t bring themselves to escape. Scenarios and predictions are simply accepted as if the model actually is real life.

“Such naive Model Land realism,” Thompson warns, “can have catastrophic effects because it invariably results in an underestimation of uncertainties and exposure to greater-than-expected risk.” Anyone who remembers Goldman Sachs’s chief financial officer blaming the global credit crunch of 2007 on the occurrence of “twenty-five standard deviation events, several days in a row” knows what Thompson is getting at. If it couldn’t happen in the model, it just wasn’t meant to happen in real life.

It’s not all bad news. Thompson is a data scientist and mathematical modeller herself, and her book is far from an exercise in model-bashing. It is instead a nuanced and constructive critique of what remains an invaluable analytical method – just not necessarily for the reasons you might expect.

For example, even though the astrologers’ models of natural forces and human behaviour were wrong, the practice of casting horoscopes could still be a useful aid to policymaking. They brought systematic thinkers into the orbit of otherwise impulsive rulers; it allowed the discussion of important, otherwise taboo subjects in the safe context of interpreting the stars; and it could give decision-makers the public narrative they needed in order to act.

The same applies today. As Thompson shows, mathematical model-building can still be a constructive tool, even if the models themselves are flawed. As Dwight D Eisenhower said: “Plans are useless, but planning is indispensable”.

*****

Here's Mike Jakeman's review for Stragegy+Business

The limitations of mathematical modeling
A new book demonstrates the danger of the perfect model.

The single most famous weather forecast in British history is also one of the worst. In October 1987, a meteorologist working for the British Broadcasting Corporation reassured a concerned viewer that rumors of an approaching hurricane were unfounded. Hours later, 22 people had been killed and billions of pounds of damage done by highly unusual hurricane-force winds. Although the erroneous forecast owed to a lack of data in parts of the North Atlantic, it was the meteorologist, Michael Fish, who became a synonym for flawed prediction models. The work of everyone who uses such mathematical models to produce explanations of how complicated things work is the subject of a new book by Erica Thompson, an academic at the London School of Economics. Her contention is that too many of us have become ensconced in a comfortable but ultimately unhelpful place, which she dubs Model Land.

Thompson believes Model Land is a great place for theorists—economists, climatologists, financiers, political scientists—because models are entirely controllable. Experimenters can set the parameters, run their tests, and write with confidence about their results. There are no messy or uncomplicated factors. “Whole careers can be spent in Model Land,” Thompson writes, “doing difficult and exciting things.” Except these things are not real. Or rather, they do not apply to the real world. It is this delusion that has led governments and businesses that are unquestioning of model results into trouble—and prompted Thompson to write her redress, Escape from Model Land.

In the late 1940s, one of Thompson’s predecessors at LSE, an undergraduate named Bill Phillips, and his colleague Walter Newlyn, built a physical model of the UK economy out of water tanks, pipes, and pumps to demonstrate how something very complicated works in a simplified, visual way. The water represented the flow of money through the economy and was held in tanks, representing banks and the government, while the pump represented taxation. The aim, as Thompson interprets, was to set the pumps and valves at a level “that allows for a closed loop that prevents all of the water ending up in one place and the other tanks running dry.”

But to Thompson, Phillips’s work is a product of Model Land. “The only way that the Phillips–Newlyn machine can represent economic failure, for example, is by the running-dry of the taxation pumps; there is no concept of political failure by…failing to provide adequate public services. And the only success is a continued flow of money.” In other words, the land of Phillips’s model is a creative and admirable approximation of how real economies work, but it has edges and limits to its scope that do not apply to the real world.

And when we let these models dictate behavior in the real world, we flirt with disaster. Thompson writes an excellent section on financial crises to illustrate her point. The classic mistake made by banks, hedge funds, and other investors is “assuming the data we have are relevant for the future we expect.” During times of stability, this approach can be profitable. But when events that models believe are very unlikely suddenly materialize, as the collapse of Southeast Asian currencies did in 1997–98 or the unravelling of the US mortgage market a decade later, model-guided investors can be caught out.

Thompson believes these failures are often owing to misaligned incentives: “Those who correctly estimate significant tail risks [i.e., deviations from the normal distribution in a statistical model] may not be recognized or rewarded for doing so. Before the event, tail risks are unknown anyway if they can only be estimated from past data,” and “after the event, there are other things to worry about.” In short, it was in investors’ interest to design a model that characterized unlikely risks as infinitesimally so, and regulators weren’t paying attention.

So why should we bother with models at all? Occasionally, Thompson believes, they do get it right. Her preferred example concerns research by two chemists, F. Sherwood Rowland and Mario Molina, who in the 1970s modeled the potential impact on the ozone layer of the continued release of chlorofluorocarbons, or CFCs. Within 15 years of their research, an international agreement, the Montreal Protocol, had been signed to limit CFC use, and it is now possible that the ozone layer could recover to its 1980 level by 2050. “The acceptability of the model was a function of the relatively simple context and the low costs of action,” Thompson explains, before warning, “this is in direct contrast with the situation for climate change.”

In the end, Thompson comes back to experts. Michael Fish interpreted his data correctly, but the data itself was not sufficient. The real mistake made by the Met Office, the UK’s national weather service, was putting too much faith in its model. She recounts the Challenger disaster in 1986. Previous missions had revealed several faults in the space shuttle’s O-rings, which sealed its rocket boosters. Some engineers had calculated that the likelihood of a major disaster was high. Others saw it differently: the fact that Challenger had been able to complete the previous flights provided a data set that underlined its strength. “On the face of it, and with reference to the data,” Thompson argues, “either scenario is feasible.” It is only when the modeling is supplemented with expert judgment that we stand a chance of escaping from Model Land and finding ourselves with information that can be applied in the real world.

*****

Anthony Sadar has written a good review in the Washington Times:

In the early days of my career in meteorology, which included determining the impact of air pollution emissions using mathematical models, one of my bosses, concerned about the outcome of a computer model I was using to assess a contentious industrial operation, asked me: “What will the model show?” I replied facetiously: “Well, what do you want it to show?”

In no way was I going to manipulate a model to get the results I or anyone else wanted. But the point is that models can produce results intentionally or unintentionally skewed by the modelers. Intentional tampering is akin to the adage “Figures don’t lie, but liars figure,” while unintentional bias can manifest itself in almost innumerable ways.

In “Escape From Model Land: How Mathematical Models Can Lead Us Astray and What We Can Do About It,” Erica Thompson provides a thorough, thoughtful treatment of the whys and wherefores of modeling and how to improve the practice, avoiding unintentional bias. Ms. Thompson is “a senior policy fellow at the London School of Economics’ Data Science Institute and a fellow of the London Mathematical Laboratory” with a doctorate from Imperial College and many years of modeling experience. As such, she is well qualified to expound and comment on the world of modeling.

“Escape From Model Land” contains 10 well-written, accessible, relatable chapters that seamlessly incorporate engaging pertinent vignettes. The book progresses from defining the idealized locale of Model Land in Chapter 1 to showing with honed insight and practical guidance how to escape from Model Land in Chapter 10. The five principles for responsible modeling spelled out in Chapter 10 are especially helpful for improving modeling and the modeler.

The journey between Chapters 1 and 10 includes many stops that frequently prompt reflection on the personal bias of modelers, the role of expert opinion in model construction, expanding perspective to improve model applicability and reality, and the like. One chapter addresses a topic that the author is especially well versed in and is appropriately titled “The Atmosphere Is Complicated.” Other chapters adeptly focus on financial and pandemic modeling.

“Escape From Model Land” rightly reminds the reader of the ubiquitous paramount importance of knowing the assumptions and limitations of any model. For instance, the book notes that “there is a responsibility for misunderstandings or failures to communicate the limitations of models and the pitfalls inherent in using them to inform public policy-making. If modeling is to be taken seriously as an input to decision-making, we need to be clearer on this front, and part of that is acknowledging the social element of modeling rather than taking it to be a simple prediction tool that can be either right or wrong.”

Along this same vein, but in the wider context of science practice and public perception, “Escape From Model Land” observes: “If we are serious about addressing lack of confidence in science, it is necessary for those who currently make their living from and have built their reputation on their models to stop trying to push their version of reality on others.”

I frequently train professionals on the fundamentals of air pollution dispersion modeling. And regarding the reliability of model output, I remind my students that besides remembering the adage that “computers help you make mistakes at the speed of light,” once you get a result, ask yourself, “Does the answer make sense?”

Furthermore, relative to the essentials and uses of modeling, in my experience, a model is a tentative representation of an observation based on the interpretation of available information, a tool used to simulate real-world conditions. Yet among other things, “Escape From Model Land” shows that models are also “metaphors that facilitate communication, frame narratives and include value judgments with scientific information.”

Physicist Richard Feynman once observed: “It doesn’t matter how beautiful your theory is, it doesn’t matter how smart you are. If it doesn’t agree with experiment, it’s wrong.” By extension, if your model does not sufficiently represent reality, it’s wrong, or at least a large dose of humble rethinking of your model inputs is necessary. “Escape From Model Land” is a book that can help with that rethink and get you from Model Land to Realityville.

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