Scale
Author: Geoffrey West Publisher: Penguin Press (2017) Pages: 481
Why Read This
Geoffrey West demonstrates that mice, elephants, New York City, and Fortune 500 companies all obey the same mathematical framework, derived from first principles. Over thirty years at the Santa Fe Institute, he studied eight million species of living organisms, hundreds of thousands of cities across five continents, and tens of thousands of public companies, arriving at a finding that all these systems are governed by power laws whose exponents are simple multiples of one-quarter.
This discovery reaches far beyond beautiful biological statistics. The quarter exponent carries a deep geometric origin: every complex organism relies on hierarchical branching distribution networks that fill three-dimensional space. The fractal character of these networks produces behavior as though each system operates in a fourth dimension. All biological exponents live there. From the heartbeat of a mouse to the evolutionary rate of a tree, the quarter-multiples stand as evidence that natural selection has optimized thousands of different systems in one shared mathematical language.
Scale is the argument that a single mathematical language suffices to explain why large cities produce more innovation per capita, why 90 percent of companies die within a few decades, why elephants outlive mice despite each of their cells working at a slower pace, and why our civilization moves toward a mathematical singularity that demands perpetually accelerating innovation. Biology, urban science, and organizational theory converge inside it into one framework.
There is one paradox that makes this book essential for leaders and decision-makers: cities and organisms follow the same law, yet with opposite signs. Organisms that grow larger become metabolically slower. Cities that grow larger accelerate every social process within them. The superlinear growth of cities generates innovation and prosperity, while also accelerating the spread of disease and crime at precisely the same rate. Companies, structured like organisms, cannot escape their own sublinear logic: they are subject to a constant mortality rate regardless of age or size.
The practical implications are concrete. From city population alone, West predicts average wages, patent counts, road length, and crime rates with 80-90 percent accuracy for hundreds of cities across multiple continents. In companies, the same logic explains why pressure for efficiency drives bureaucracy, bureaucracy narrows internal diversity, and narrowing diversity erodes resilience against external shocks. This logic operates beyond any individual leader; it is a law that holds across regions and industries.
Recommended for: Anyone who leads an organization, plans for growth, or wants to understand why large systems behave as they do. Business leaders will find a framework for recognizing when their companies move toward sublinear risk. Urban planners will see that metropolitan innovation flows as a mathematical consequence of size, well before any policy takes effect. Readers curious about civilizational trajectory will gain a tool for thinking about the approaching singularity. The book demands patience: 481 pages with some pedagogical repetition make it a weightier read, and the reward for that patience is a mental framework that permanently changes how one sees growth, organization, time, and sustainability.
Core Idea 1: Scaling and Power Laws
The Language Behind Complexity
When Geoffrey West plotted the metabolic rates of hundreds of mammal species against body mass on log-log paper, a single straight line appeared, stretching from a 30-gram shrew to a 150-ton blue whale. The range spans 27 orders of magnitude. A straight line on a log-log graph is the signature of a power law. Its slope is the exponent, a number that determines the character of the entire relationship.
"Almost miraculously, the data have lined up in approximately straight lines rather than being arbitrarily distributed across each of these graphs, as might have been anticipated given the unique historical and geographical contingency of each animal, city, or company."
Power laws differ fundamentally from linear relationships. A linear relationship says: double the size, double the quantity. A power law says: double the size, and the quantity changes by a factor of 2 raised to some exponent. When the exponent falls below one, the system is sublinear: it grows more slowly than its size, becoming more efficient as it scales. When the exponent exceeds one, the system is superlinear: its output grows faster than its size.
Galileo laid the foundation four centuries ago. Double an animal's size: its volume grows eightfold, while its bones' load-bearing strength grows only fourfold. The load per unit area of bone keeps rising as an animal enlarges. From this flows one consequence that ends the dream of monster films: a Godzilla standing 106 meters tall, built from ordinary flesh and bone, would collapse under its own weight before it could destroy any city.
The trap of linear thinking is literally lethal. In 1962, a group of researchers injected an elephant named Tusko with 297 milligrams of LSD, derived by linear scaling of a safe per-kilogram dose from cats. Tusko died one hour and forty minutes later.
"The problem, of course, is something we've already stressed several times, namely the seductive trap of linear thinking."
Core Idea 2: Kleiber's Law and the Number One-Quarter
One Hidden Optimal Design
Max Kleiber found in 1932 that the metabolic rate of all mammals follows a power law with an exponent of three-quarters against body mass. An elephant weighs 10,000 times more than a mouse but requires only 1,000 times as much energy. Each elephant cell works at one-tenth the intensity of a mouse cell. Cells that work more slowly degrade more slowly, and from this comes longevity.
The three-quarters exponent is one of more than fifty biological scaling laws, and every single one is a simple multiple of one number: one-quarter. Heart rate scales with an exponent of negative one-quarter (slower in larger animals). Lifespan scales with an exponent of positive one-quarter (longer in larger animals). Tree height, aorta cross-section, brain size, evolutionary rate: all resonate at one-quarter.
"Whales live in the ocean, elephants have trunks, giraffes have long necks, we walk on two legs, and dormice scurry around, yet despite these obvious differences, we are all, to a large degree, nonlinearly scaled versions of one another."
Where That Number Comes From
West, along with ecologists James Brown and Brian Enquist, spent nearly a year deriving the answer from first principles. Every complex organism is sustained by hierarchical branching distribution networks: the circulatory system, the respiratory system, the vascular network of a tree. These networks share three fundamental properties. First, they must fill the entire body volume, reaching every cell. Second, the terminal units of the network, such as capillaries, maintain nearly constant size across all species: a whale's capillary and a mouse's capillary are essentially the same diameter. Third, the energy used to pump blood or tree sap is minimized to its lowest possible value.
"Networks have evolved so that the energy needed to sustain an average individual's life and perform the mundane tasks of living is minimized in order to maximize the amount of energy available for sex, reproduction, and the raising of offspring."
From these three constraints emerges a decisive geometric fact: biological networks are fractals that fill three-dimensional space, and because of their fractal character they behave as though operating in dimension 3+1=4. That is the origin of the four in the denominator of all the exponents.
"The resulting magic number four emerges as an effective extension of the usual three dimensions of the volume serviced by the network by an additional dimension resulting from the fractal nature of the network."
The total length of blood vessels in the human body, if stretched end to end, reaches 100,000 kilometers, more than two and a half times the circumference of the Earth, all packed inside a body one and a half meters tall.
Core Idea 3: Growth, Aging, and Death
The Unavoidable Consequence
Organisms stop growing because of a mathematical conflict they cannot escape. The maintenance requirements of cells grow linearly with increasing mass: twice as many cells means twice the maintenance cost. The supply of metabolic energy grows sublinearly, with an exponent of three-quarters. As an organism enlarges, the energy margin available for growth keeps shrinking until it vanishes entirely.
"You stop growing because of the mismatch between the way maintenance and supply scale as size increases."
Aging is rooted in the same mechanism. The networks that sustain us also slowly wear us down. Blood flow through vessels produces physical erosion. ATP production in mitochondria generates free radicals, highly reactive molecules that damage DNA and vital cellular components. The damage spreads uniformly throughout the body because the network fills the body's entire volume uniformly.
"All the evidence points to the origins of aging and mortality as being the result of the 'wear and tear' processes that unavoidably arise simply from being alive... As we begin to lose the multiple localized battles against entropy we age, ultimately losing the war and succumbing to death. Entropy kills."
Two Astonishing Constants
The total number of heartbeats over a lifetime is nearly the same for all mammals: approximately 1.5 billion. A shrew beats its heart 1,500 times per minute and lives two years. An elephant beats at 30 times per minute and lives 75 years. Both spend roughly 1.5 billion heartbeats. The total energy used throughout a lifetime to sustain one gram of tissue is also nearly constant across all mammals: approximately 300 food calories per gram per lifetime.
Average human lifespan has risen steadily with advances in medicine. The upper tail of the survival curve has stayed fixed. All historical data from diverse populations converges on one consistent number:
"they all converge on about 125 years. This dramatically and convincingly illustrates the existence of a maximum biological life span."
Core Idea 4: Cities as Social Reactors
Superlinearity and the 15 Percent Rule
Cities operate on a logic that runs counter to organisms. West's team at the Santa Fe Institute gathered data from cities across the United States, Europe, China, Brazil, and other countries. When physical infrastructure metrics, including road length, electrical cable, and water pipe, were plotted against population, the exponent that emerged was approximately 0.85: sublinear. Large cities are more infrastructure-efficient per capita, which is why a New York City resident generates a smaller per-capita carbon footprint than a resident of a small town, well before any policy intervenes.
Then came the finding that reframes everything:
"The larger the city, the higher the wages, the greater the GDP, the more crime, the more cases of AIDS and flu, the more restaurants, the more patents produced, and so on, all following the '15 percent rule' on a per capita basis in urban systems across the globe."
When city population doubles, all socioeconomic metrics rise by about 15 percent per capita, with an exponent of approximately 1.15: superlinear. Each additional resident contributes above-average output. This is increasing returns to scale.
The symmetry with infrastructure reveals the mechanism that unites them: infrastructure scales 15 percent below linear (0.85), socioeconomics 15 percent above linear (1.15). Both deviate from the value of one by exactly the same distance.
"To approximately the same degree as for the positive indicators, negative indicators of human social behavior also systematically increase with city size: doubling the size of a city not only increases wages, wealth, and innovation by approximately 15 percent per capita but also increases the amount of crime, pollution, and disease to the same degree. Apparently, the good, the bad, and the ugly come together hand in glove as an integrated, almost predictable package."
The Mechanism Behind the Number
The mechanistic explanation centers on social interaction. Larger cities expose each resident to more people, and interaction among individuals is the source of all socioeconomic output: innovation, commerce, crime, disease. The biological limits of the human social network, Dunbar's number of roughly 150 meaningful relationships per person, prevent the superlinear exponent from reaching its theoretical maximum. Mobile phone data from Portugal and the United Kingdom confirm this prediction: residents of Lisbon spend on average twice as much time in twice as many reciprocal calls as residents of the small town of Lixa.
From city population alone, prediction accuracy reaches 80 to 90 percent across dozens of metrics: average wages, patent counts, total road length, crime cases, restaurant counts, lawyer counts. Size accounts for the overwhelming majority of the variation, exceeding the influence of the mayor's personality, local history, or cultural distinctiveness.
"Consequently, to the same 15 percent degree, the bigger the city the more each person earns, creates, innovates, and interacts — and the more each person experiences crime, disease, entertainment, and opportunity — and all of this at a cost that requires less infrastructure and energy for each of them. This is the genius of the city."
Core Idea 5: Companies Resemble Organisms More Than Cities
Data from 28,853 Companies
Of 28,853 companies traded on American markets between 1950 and 2009, some 22,469 had already died when the data closed. Half of all companies that began trading in any given year had disappeared within 10.5 years. Fewer than 5 percent survived 30 years.
"Although there are significant differences, it's hard not to be struck by how similar the growth and death of companies and organisms are when viewed through the lens of scaling — and how dissimilar they both are to cities. Companies are surprisingly biological."
The survival curve of companies follows simple exponential decay: the probability of dying per year is constant, independent of age or size.
"The risk of a company's dying does not depend on its age or size."
Why Companies Scale Like Organisms
The difference between cities and companies is structural. Cities operate in a distributed fashion: power spreads among many actors without a single controlling hand, and from that apparent inefficiency emerges the wildness of social innovation. Companies work on the opposite logic: to improve efficiency and profits, they add layer upon layer of rules and bureaucracy at every level.
"To achieve greater efficiency in the pursuit of greater market share and increased profits, companies stereotypically add more rules, regulations, protocols, and procedures at increasingly finer levels of organization, resulting in the increased bureaucratic control that is typically needed to administer, manage, and oversee their execution. This is often accomplished at the expense of innovation and R&D."
A startup is born with energy flowing in many directions. Market pressure filters that energy, channeling it toward specialization. Surviving companies grow increasingly focused on one or two proven revenue sources. A city's dimensions of diversity keep expanding as it grows; a company's dimensions narrow.
"Most companies tend to be shortsighted, conservative, and not very supportive of innovative or risky ideas, happy to stay almost entirely with their major successes while the going is good... Consequently, they tend toward becoming more and more unidimensional. This reduction in diversity coupled with the predicament described earlier in which companies sit near a critical point is a classic indicator of reduced resilience and a recipe for eventual disaster."
Core Idea 6: The Treadmill That Keeps Accelerating
The Acceleration of Social Time
The superlinear growth of cities produces one measurable consequence: the acceleration of social time. As a city grows, all socioeconomic processes unfold faster per capita. Disease spreads more quickly. Businesses are born and die more often. Transactions move faster. People even walk faster: from a small town of a few thousand residents to a city of over a million, average walking speed nearly doubles.
This is the precise inverse of biology. In organisms, greater size means a slower pace of life. In cities, greater size means a faster pace of life. Two systems following similar mathematical laws, with opposite signs.
"Rather than the pace of life systematically decreasing with size, the superlinear dynamics of social networks leads to a systematic increase in the pace of life: diseases spread faster, businesses are born and die more often, commerce is transacted more rapidly, and people even walk faster, all following the 15 percent rule."
The Finite-Time Singularity
When superexponential growth is entered into the equations, a more unsettling mathematical property appears. Ordinary exponential growth requires infinite time to reach infinity. Superexponential growth reaches infinity in finite time: there exists a date in the future at which the growth equation yields a value that is literally unbounded. Physical systems cannot execute that, so something must change.
"in the superlinear case, the general solution exhibits an unexpectedly curious property technically known as a finite time singularity, which is a signal of inevitable change, and possibly of potential trouble ahead."
Human history shows that each time a system approaches a singularity, a major innovation arrives and resets the clock. The steam engine, coal, the computer, the internet: each was a paradigm shift that pushed the singularity further away. The requirement is that each subsequent cycle must occur within a shrinking window of time.
"Not only does the general pace of life inevitably quicken, but we must innovate at a faster and faster rate!... We're not only living on an accelerating treadmill that's always getting faster and faster, but at some stage we have to jump onto another treadmill that is accelerating even faster."
The distance between the Stone Age, the Bronze Age, and the Iron Age was thousands of years. The distance between the Computer Age and the Digital Era was thirty years.
Core Idea 7: Data, Theory, and a Grand Unified Theory of Sustainability
When Data Without Theory Becomes Dangerous
West closes the book with a call that grows more urgent with each passing year. Science has approached sustainability in fragments: economists model the costs of climate change without incorporating the physics of energy; physicists study thermodynamic consequences without incorporating social dynamics; urban planners build without any quantitative framework for how cities actually work.
"We need a broad and more integrated scientific framework that encompasses a quantitative, predictive, mechanistic theory for understanding the relationship between human-engineered systems, both social and physical, and the 'natural' environment — a framework I call a grand unified theory of sustainability."
Our era generates data in volumes unimaginable two decades ago. Data without theory is an ocean without a compass.
"Data for data's sake, or the mindless gathering of big data, without any conceptual framework for organizing and understanding it, may actually be bad or even dangerous."
Particle physics supplies the strongest argument for this position. The LHC at CERN produces 600 million proton collisions per second. If all data were recorded, that would be 150 exabytes per day. The Higgs particle was discovered because decades of mature theory told physicists that of those 600 million collisions, only 100 were relevant. Theory is what turned an ocean of data into a single discovery.
Practical Application: Recognizing Scaling Dynamics in Your Organization
Three Questions for Leaders
1. Does your culture of innovation grow or shrink as the organization scales?
West found that large cities produce more patents per capita; large companies produce less R&D as a percentage of revenue. A useful diagnostic: as your team or organization grows, does the percentage of budget allocated to experimental projects or new technology rise or fall? A declining share signals movement toward a bureaucracy-burdened sublinear company. A stable or rising share means the organization is preserving the distributed, improvisational quality of a city.
2. Where is your organization's singularity point?
Superexponential growth reaches an unbounded value in finite time. There is a future date at which the system must either transition or collapse. For organizations: is the pace of your decision-making cycles consistently accelerating? Are your product cycles shortening? Is the volume of data your teams must process each day growing exponentially? Affirmative answers on all three signal that the organization is approaching a critical threshold where its existing architecture can no longer carry the new load. West found that every major innovation cycle in human history, from steam power to electricity to computing to the internet, has pushed that threshold further out. The pragmatic question: what paradigm-level innovation is your organization preparing for the next decade?
3. Is your organizational structure distributed (like a city) or centralized (like an organism)?
Large cities thrive because power is spread among many independent actors. Organizations that accumulate rules and bureaucratic controls at every level tend to narrow their focus and lose resilience. Diagnostic questions: how many approval layers does a new idea require before it can move? Are decisions routinely held up while waiting for central authorization? Do cross-functional teams working across silos have genuine autonomy? The most innovative organizations sustain a difficult balance: discipline toward the core mission, decentralization in execution.
Key Takeaways
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Power laws with quarter-multiple exponents hold universally across all biological life, a geometric consequence of fractal networks filling three-dimensional space. West and his team derived the one-quarter from first principles: three mathematical constraints on hierarchical distribution networks, filling the volume, maintaining constant-size terminal units, and minimizing energy, together produce exponents that behave as though the system operates in a fourth dimension. More than fifty biological laws, from the heart rate of a mouse to the evolutionary rate of a tree, follow this pattern without exception. The finding emerged from a long collaboration with biologists James Brown and Brian Enquist, and it places biology on the quantitative foundation that until then had belonged only to physics. This is the heart of the book, the point at which it departs furthest from an ordinary biological data survey.
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Cities scale superlinearly at an exponent of 1.15; organisms scale sublinearly at 0.75. Two systems move with opposite signs: organisms growing larger slow down metabolically, cities growing larger accelerate all their social processes. The symmetry is measurable and rooted in one shared mechanism, the optimization of distribution networks under selective pressure.
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Companies behave like organisms, subject to sublinear scaling and a scheduled mortality. Of 28,853 public American companies between 1950 and 2009, more than 22,000 had died when the data closed, with a constant mortality rate indifferent to age or size, and a half-life of approximately ten and a half years. The cause is structural: pressure for efficiency drives bureaucracy, bureaucracy narrows diversity, and narrowing diversity erodes resilience against shocks. For anyone building an organization, this is the sharpest warning in the book. It holds as a law, operating well beyond any individual leadership question.
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The 15 percent rule is testable in the field. From city population alone, West predicts wages, patents, road length, and crime with 80-90 percent accuracy across continents. Mobile phone data from Lisbon and Lixa confirm it directly.
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The finite-time singularity is a mathematical prediction with a calculable date. Ordinary exponential growth requires infinite time to reach infinity. Superexponential growth reaches it in finite time: there is a future critical point at which a system must leap to a new paradigm or collapse. Every major innovation cycle in history has pushed that point further out, while the intervals between cycles keep shortening, demanding each renewal arrive faster than the last.
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Big data without theory can mislead. At CERN, it was mature particle theory that filtered billions of collisions down to the handful that revealed the Higgs boson. Without a conceptual framework, data simply accumulates.
Critical Assessment
Strengths
1. Derived from first principles
The greatest strength of Scale is that West does not stop at empirical observation. He derives the quarter exponent from three mathematical constraints on hierarchical distribution networks, which means predictions can be made for systems that have never been observed. This separates the book from other "hidden patterns" books: there is a mechanism behind the pattern.
2. Willing to traverse scales freely
West writes as a physicist comfortable leaping from a mouse's heart rate to the rate of metropolitan innovation and then to civilizational sustainability. This willingness is what gives his argument its sense of coherence, and occasionally unsettles the reader in productive ways.
3. Honest about limits and variance
West repeatedly emphasizes that his predictions are zeroth-order approximations forecasting system averages, deliberately setting aside each individual case. Variance in company data is far larger than in biological data, and he explains why: market networks are two hundred years old, far younger than biological networks optimized over billions of years. This honesty strengthens the argument.
Limitations
1. The book is long and repetitive
At 481 pages, Scale runs longer than the core argument requires. West tends to explain the same point from several consecutive angles, a habit that feels pedagogical and can tire readers who have already followed the logic.
2. The company section is shallower than biology and cities
Company scaling data is sparser and noisier than biological or urban data. West acknowledges this; the company section feels less quantitatively convincing than the two preceding parts. His predictions about companies lean more qualitative.
3. The sustainability closing feels disconnected
The final chapters on a grand unified theory of sustainability read more like a personal manifesto; their connection to the technical arguments in earlier sections is less seamless. The link between scaling laws and sustainability policy is not resolved with the same rigor as the link between fractals and the quarter exponent.
Conclusion
Scale ranks among the boldest works of popular science published in the last decade. It offers a genuinely new quantitative framework for understanding organisms, cities, and companies, derived from first principles and tested against large-scale data. Readers who stay with it through the slower sections will find that their way of seeing growth and time has changed permanently. Rating: 5 out of 5.
Related Reading
Complementary Books
- The Origins of Order by Stuart Kauffman (1993). The theoretical foundations of biological complexity from a statistical physics perspective.
- Complexity: A Guided Tour by Melanie Mitchell (2009). A more accessible introduction to complexity science, from a fellow Santa Fe Institute researcher.
- The Death and Life of Great American Cities by Jane Jacobs (1961). A classic argument for urban vitality through observational urban perspective, an illuminating contrast to West's quantitative approach.
- On the Origin of Species by Charles Darwin (1859). The mechanism of natural selection that West uses as the foundation for explaining why biological networks are optimized.
- The Nature of Cities by Lewis Mumford (1961). History and theory of urban development, complementing West's physics perspective.
- Poor Charlie's Almanack by Charlie Munger. Mental models on interconnected systems, relevant for understanding the decision-making implications of scaling.
Note: Also explore this site for articles on complexity, fractals, and organizational dynamics that extend West's core ideas.
FAQ
Q: Do I need a mathematics background to follow this book? A: No. West writes for a general audience and explains mathematical concepts such as logarithms and power laws from scratch. Some of the technical sections in the biology chapters can be skimmed without losing the main argument. More important than mathematics is reading patience: the book is long and sometimes repetitive.
Q: Have West's predictions about cities held up outside the United States and Europe? A: Yes. West's team gathered data from cities in China, Brazil, South Africa, India, and several other developing nations. The 15 percent rule appeared consistently across all urban systems studied, though the precise exponent value varies slightly by context. This is one of the book's strongest claims: universality across systems that differ enormously in cultural and historical character.
Q: If cities are superlinear and companies sublinear, can a company behave more like a city? A: West does not offer a prescription. He offers one clue from his comparison: a city's resilience comes from the imperfect distribution of power, from many actors moving with their own agendas. Companies that deliberately maintain distributed structures and cultivate internal diversity move in that direction, though market pressure always pushes toward centralization and specialization.
Q: Is West's finding of a 125-year maximum human lifespan accepted by the scientific community? A: Active debate continues. The finding rests on patterns in historical data from diverse populations, all converging near 125 years. Some gerontology researchers challenge the statistical methodology. The scientific community has not yet reached full consensus; empirical data from the longest-lived person on record, Jeanne Calment at 122 years, is consistent with West's estimate.
Q: How can I view my business growth through the lens of scaling? A: Several useful questions: is your growth absolute, or measured relative to market growth? Is your R&D spending as a percentage of revenue rising or falling as the company scales? Is your decision-making structure becoming more centralized? West found that "falling" and "more centralized" are nearly universal answers for growing companies, and both are early indicators of a sigmoid curve approaching its plateau.
Q: The book was published in 2017. Have subsequent findings updated or challenged its arguments? A: The core argument on biological scaling with quarter exponents remains robust. The urban argument has been reinforced by subsequent research using digital mobility data from smartphones. The company section remains the most contested because of its lower data quality. West himself remains active at the Santa Fe Institute and continues to publish follow-on research.
Q: A physicist writing about biology and economics. Is the approach too reductive? A: This is the most common critique. West acknowledges that his models are zeroth-order approximations forecasting averages, deliberately setting individual detail aside. Some biologists feel the quarter exponent is overstated given the variance present in real data. The value of the physicist's approach lies precisely in its simplicity: it finds a signal amid the noise, and that signal is strong enough to produce testable predictions.
Q: After reading Scale, what should I read next? A: The answer depends on where your interest leads. For depth in complexity theory, Complexity: A Guided Tour by Melanie Mitchell is the natural continuation, more technical and still readable. For the concrete implications on cities, The Death and Life of Great American Cities by Jane Jacobs offers a perspective that nearly inverts West's and, in doing so, illuminates both.