Geoffrey West’s “Scale”: Book Review, Notes + Analysis

Poor Ash’s Almanack > Book Reviews > STEM > Mathematics

Overall Rating: ★★★★★★ (6/7) (standout for its category)

Learning Potential / Utility: ★★★★★★ (6/7)

Readability: ★★★★★★ (6/7)

Challenge Level: 4/5 (High) | ~450 pages ex-notes (496 official)

Blurb/Description: Theoretical physicist and former Santa Fe Institute President Geoffrey West provides an astonishingly accessible introduction to power laws and how they apply various across biological phenomena.

Summary: Terms like “complex adaptive systems,” “emergence,” and “ scaling laws” sound really intimidating (and, honestly, as my friend Josh put it, kind of douchebaggy, too.)  You might be forgiven, then, if it isn’t exactly at the top of your list to pick up a book about those topics by a theoretical physicist who used to head up the Santa Fe Institute.  I ordered it eagerly after an acquaintance recommended it… then it sat on my shelf for a while because, um, it’s big (you know how I feel about big books) and it sounded difficult.

But that was a mistake; I shouldn’t have been scared: this is, surprisingly, an extremely readable, engaging, accessible, and useful/interesting book (mostly).  Geoffrey West as a writer is neither dry, boring, and academic (a la Kahneman) nor intentionally obfuscatory and insulting (a la Gleick). West does a fantastic job, as he puts it, of translating complicated theory and mathematics into English that the rest of us can understand.

This book is a roughly a tale of two halves.  The first half deserves seven stars and may be one of the best science books I’ve ever read.  The second half, unfortunately, gets a bit discombobulated and (in my view) either spends a completely unnecessary number of words conveying a few really simple and obvious points that aren’t particularly useful or actionable… or it makes another point that is suddenly much more difficult to follow than the lead-ups.  

For a theoretical physicist, West is an engaging writer who explains things well to a lay audience. Image credit: YouTube (his Talk at Google)

Highlights: West does a really good job of making everything accessible; there were only one or two points in the book where I felt like it was going over my head.  The topics chosen to discuss are both educational and fascinating, answering a lot of questions I had and a lot I didn’t know I had.

This is a really thorough explanation of power laws that provides the mathematical basis for ideas like economies of scale.

Lowlights: As mentioned, the first half of the book is phenomenal and I have no criticisms there.  However, I do have three specific criticisms of the back half of the book.

First, the applications section to cities is, on the whole, not terribly helpful, albeit interesting to read to understand the methodology.  While some of the quantitative conclusions (like the scaling law) are fascinating, West explicitly mentions that analyzing the data in this way abstracts away much of what makes a city a city, and seems to spend more time investigating the easily quantifiable / more boring and predictable phenomena (economies of scale relative to the size of cities) than what makes the outliers the outliers.  

The applicable conclusions are unclear: cities are great because they’re efficient… I guess… but you’re not answering the humans vs. econs problem there; we’re not econs who only value global efficiency, and there are many of us who like being away from the noise and fast pace (one reason why the Santa Fe Institute is in Santa Fe as opposed to Manhattan.)

Moreover, and in my view more importantly, other than a passing mention at the end of the book which I’m not sure he gets right, West ignores one of the biggest paradigm shifts around: the increasing technologically-driven disintermediation of physical location as an important factor in maintaining either personal or professional links.  This renders the whole discussion backward-looking rather than forward-looking in many ways.

Second, the applications section to companies is functionally useless (so brutally so to the extent that I’d recommend skipping it): while West mentions issues like, for example, the confounding nature of M&A on discussions of company ‘death,’ there are no real useful takeaways here for consumers, businesspeople, or investors that aren’t already common knowledge (i.e., trees don’t grow to the sky).  Much more helpful discussions of this type of analysis are available elsewhere – for example, in Phil Rosenzweig’s The Halo Effect  ( Halo review + notes) – so don’t waste your time reading Chapter 9.

Third and finally, for all the fantastic science and thoughtful conveyance/explanation thereof, the conclusions section at the end is phenomenally weak: beyond the “obvious” points (i.e. that in the absence of technological debottlenecking, exponential growth necessarily meets a hard barrier in the form of finite resources, and also the importance of sustainability), there are no real applications/conclusions that readers can apply personally or immediately.

Building awareness of sustainability challenges is certainly an important goal, but surely West, with all his experience and focus on multidisciplinary thinking, could have gone one step further and translated his life’s research into takeaways us mere mortals could use to make the world a better place.

Mental Model / ART Thinking Pointsscalingnonlinearityinversionfeedbackn-order impacts,exponential growthcultureutilitynetwork effectscorrelation vs. causationtrait adaptivity,saliencevividness.

You should buy a copy of Scale if: you want an accessible introduction to power laws and an overview of some of complexity theory.

Reading Tips: Read the first half of the book really carefully.  Start skimming in chapter 8. Skip Chapter 9 entirely – it’s useless – better to use the time to read something else, or to go back over the highlights of the wonderful, wonderful first half of the book.  Skim the conclusions and afterword, which don’t say much that thoughtful readers won’t already have predicted, other than an intriguing bit about correlation vs. causation.

Pairs Well With:

How Not To Be Wrong by Jordan Ellenberg (HNW review + notes).  Whereas West narrowly focuses on the idea of power laws with a lot of intellectual seriousness, Ellenberg more broadly focuses on other concepts from mathematics in a more lighthearted way.  Also, these two books will be forever linked in my mind because they were recommended by the same person.

The Landscape of History by John Lewis Gaddis ( LandH review + notes).  In a completely different context from West – i.e., that of how historians do (or should) think – Gaddis discusses complexity theory and many other topics.

Deep Survivalby Laurence Gonzales (DpSv review + notes).  Gonzales touches on complexity theory a lot, and provides some helpful explanations of emergent behavior like the sand pile bit.

Reread Value: 3/5 (medium)

More Detailed Notes + Analysis (SPOILERS BELOW):

IMPORTANT: the below commentary DOES NOT SUBSTITUTE for READING THE BOOK.  Full stop. This commentary is NOT a comprehensive summary of the lessons of the book, or intended to be comprehensive.  It was primarily created for my own personal reference.

Much of the below will be utterly incomprehensible if you have not read the book, or if you do not have the book on hand to reference.  Even if it was comprehensive, you would be depriving yourself of the vast majority of the learning opportunity by only reading the “Cliff Notes.”  Do so at your own peril.

I provide these notes and analysis for five use cases.  First, they may help you decide which books you should put on your shelf, based on a quick review of some of the ideas discussed.  

Second, as I discuss in the memory mental model, time-delayed re-encoding strengthens memory, and notes can also serve as a “cue” to enhance recall.  However, taking notes is a time consuming process that many busy students and professionals opt out of, so hopefully these notes can serve as a starting point to which you can append your own thoughts, marginalia, insights, etc.

Third, perhaps most importantly of all, I contextualize authors’ points with points from other books that either serve to strengthen, or weaken, the arguments made.  I also point out how specific examples tie in to specific mental models, which you are encouraged to read, thereby enriching your understanding and accelerating your learning.  Combining two and three, I recommend that you read these notes while the book’s still fresh in your mind – after a few days, perhaps.

Fourth, they will hopefully serve as a “discovery mechanism” for further related reading.

Fifth and finally, they will hopefully serve as an index for you to return to at a future point in time, to identify sections of the book worth rereading to help you better address current challenges and opportunities in your life – or to reinterpret and reimagine elements of the book in a light you didn’t see previously because you weren’t familiar with all the other models or books discussed in the third use case.

Pages 2 – 5: What is Scale about?  It’s about “systematic scaling laws” that govern how many measurable characteristics of things in our world ranging from plants to cities “scale” with size.

Page 8: One thing that’s particularly good about Scale is that West focuses on being decidedly nontechnical and pedagogical in spirit,” written for “the proverbial intelligent layperson,” by translating “mathematical or technical language into English.”

Page 9: West notes (he goes into it more later) that the seeming “speeding up” of life over time is actual real, in some senses.  

Meanwhile, he also notes that 200 years ago, merely 4% of the U.S. population lived in cities; that’s more than 80% today, and the world crossed the 50% threshold in 2006.

Page 11: West notes, intriguingly, that cities and biological organisms share many interesting characteristics, with a few notable differences: for example, while it’s easy to kill animals, it’s difficult to kill a city, even after you drop an atomic bomb on it.  

(See the end of Richard Rhodes’ The Making of the Atomic Bomb (TMAB review + notes), which provides… we’ll call them details.)

West also notes that the study of death:

 “tends to be suppressed and neglected, both socially and scientifically, relative to birth and life.”  

I had started reading Gawande’s Being Mortal a while ago but never finished it… on the list.

Page 13: West brings up the concept of “metabolic rates” – i.e., the amount of energy needed to sustain us.  He differentiates between the “biological” metabolic rate of 2,000 kilocalories per day, which is – astonishingly – equivalent to a 90-watt lightbulb, and our “social” metabolic rate, including all of our technology, which equates to 11,000 watts, or

“equivalent to the entire needs of about a dozen elephants.”  

West notes that energy is the building block for everything else; without energy, there are no ideas.  A nice example of  disaggregation.

Page 14: West brings up entropy and the Second Law of Thermodynamics… basically, he notes that waste heat is always a product.

Page 15: West on the definition of “scaling”:

“how a system responds when its size changes.”  

Pages 17 – 19: One of the consistent themes throughout the book is nonlinearity.

West notes that we often implicitly think linearly, which can make it difficult to recognize.  He cites the example of “GDP per capita,” which fails to account for the fact that GDP scales superlinearly; in other words, cities (or countries) with more people tend also to be richer (for reasons we’ll explore).

West differentiates between “superlinear” and “sublinear” scaling.  Intuitively, superlinear means you get more as you scale, and sublinear scaling means you get less as you scale.

It is worth noting, of course, that the two can be the same via inversion: for example, costs and capital intensity might scale “sublinearly” (relative to revenue or size) for a company, meaning profits scale “superlinearly” (the two statements are equivalent).

Metabolism, as we’ll see, scales sublinearly – larger animals are more efficient in their energy use than smaller ones.

Page 21: West provides a formal definition of complexity: it has nothing to do with being “simple” or “complicated,” but rather, a complex system has characteristics that:

“are usually not manifested in, nor could easily be predicted from, the properties of the individual components themselves.”  

West uses the example of how our cells are more than the sum of the molecules they’re comprised of, and how we are more than the sum of our cells.

West also notes that each “level” of the system has its own rules and interactions that may function independently of the other, yet they integrate.

Emergence.  See also Laurence Gonzales in Deep Survival ( DpSv review + notes).

On the sand pile experiment, Gonzales notes:

“nothing in the physics of silicon dioxide that could predict the behavior of the sand pile.”  

This is translated to powerful nonlinear forces like avalanches, undertow currents, etc that can easily kill unsuspecting city slickers like you and me.

Page 22: West notes that ant colonies, and other seemingly complex behavior, can be simulated given a small number of rules in an algorithm, so complexity doesn’t have to “come from” anywhere.

Page 23: West defines emergent behavior as an outcome in which a system:

“manifests significantly different characteristics from those resulting from simply adding up all of the contributions of its individual constituent parts.”  

West also here notes “self-organization” – in which constituents agglomerate to form the emergent whole,” like ant rafts or book clubs – and the idea of complex adaptive systems, which, simply, are complex systems that adapt to their environment.

Page 24: West here touches on the idea of feedback and n-order impacts.  He notes that systems can’t always be analyzed in terms of their component parts, the same way the sand pile can’t be understood via the physics and chemistry of silicon dioxide…

He also notes that while we might not be able to predict the specific outcomes of specific systems, we can analyze the ways in which systems are similar to others… for example, we might not be able to predict one human’s lifespan, but we can predict the average lifespan of humans.

Page 26: West introduces the idea of power laws and logarithmic graphs – on a logarithmic graph, the slope of the graph is the exponent of the power law.  A power law refers to the amount a given quantity increases relative to every doubling of the X-axis…

… so if an animal’s metabolic consumption increases 75% rather than 100% for every doubling in size, the exponent of the power law is three-fourths, or 0.75.  Many biological quantities scale with a power law with a denominator of 4, call “Kleiber’s law.”

Page 31: West brings up the idea of a “finite time singularity,” which basically means thatexponential growth cannot continue forever without infinite resources or a “paradigm shift” that makes use of resources more efficient.

He also notes that thanks to the nature of exponential growth, such discoveries “must occur at an increasingly accelerating pace.”  He notes that thousands of years passed between the Stone Age and the Bronze Age, whereas mere decades passed between the “Computer Age” and “Digital Age.”

Pages 41 – 43: Scaling laws underlie many of the physical phenomena around us.  For example, surface area increases as the square of length, while volume increases as the cube; this makes it harder for large buildings, and large animals, to be cooled.

Strength also increases relative to cross-sectional areas, while weight increases relative to volume… so strength displays “sublinear” scaling relative to size: this is why ants are so strong relative to their size.  West notes that if strength scaled linearly, we’d be able to lift about a ton, or ten other people, rather than just one other person…

Pages 45 – 47: West brings up the idea of “orders of magnitude” here – basically, another zero, or the exponent of something expressed as a power of 10.  He notes that volumes increase by 3/2 orders of magnitude relative to area, whereas strength increases by ⅔ orders of magnitude relative to weight.

Scales such as the Richter scale operate in terms of orders of magnitude, otherwise everything would be bunched up to the left.

The Richter scale actually measures amplitude of shaking; energy actually scales een faster (3/2), such that a 3.0 earthquake releases 1,000x the energy as a 1.0 earthquake.

One pound of TNT is about a 1 magnitude on the Richter scale; the Hiroshima “Little Boy” bomb was about 15 kilotons of TNT, roughly equivalent to a 6.5 earthquake.  The 2005 Sumatra earthquake could have fueled New York City for a year.

Pages 53 – 55: How much LSD should you give an elephant (and how much Tylenol should you give your infant?)  Poor Tusko.  That latter one is a super important question, as I discuss in my own nonlinearity mental model, because acetaminophen can really blank up your liver.

Anyway, West notes that dosage of drugs scales sublinearly (⅔ exponent) because drugs are typically absorbed relative to surface area rather than weight.

Pages 58 – 59: West points out that many common metrics – in this case, BMI – fail to account for scaling laws.

Pages 60 – 61: West notes that the one thing that can disrupt scaling laws are new designs, materials, or technologies; he cites the tensile strength of wood and bridges made of stone, iron, and steel.  Of course, when you start using new materials, you run into a bit of a culture problem because what worked with the old material doesn’t always work with the new.

Henry Petroski’s “To Engineer is Human” (TEIH review + notes) provides some great historical examples relating to iron bridges and how, at first, they suffered a lot of collapses (see pages 68 – 69 of To Engineer Is Human).

Page 66: Here’s a nice example of inversion: Isambard Brunel realized that cargo ships’ capacity scales with volume, whereas the drag force scales with the square of its dimensions (a 3/2 power law).  So, the required engine capacity scales sublinearly relative to size… or, inversely, bigger ships are more efficient.

Page 70: West cites the aforementioned culture argument here, with a slightly different perspective:

“there was no need for a deep scientific understanding of why something worked the way it did because the long succession of previous successful vessels effectively ensured that most of the problems to be addressed had already been solved.”  

Of course, this only works to a certain point; back to Petroski, consider his example about houses on a desert island.

Pages 71 – 72: West cites Navier-Stokes fluid dynamics equations as an example of the difficulty of modeling complex systems subject to feedback (note that there are other approaches – I used to follow Exa when it was publicly traded).

Page 73!: West offers one of the few sensible explanations for supporting research with no immediate/practical utility: he notes that

“many of us recognize [… dismissive rhetoric] aimed at scholarly or academic research [… that is] out of touch with the ‘real world.’  Well, no doubt, much of it is. But much of it isn’t, and more to the point, it is very often difficult to perceive in the moment the potential impact of some piece of seemingly arcane research.  Much of our entire technologically driven society and extraordinary quality of life that many of us are privileged to enjoy is the result of such research.”

In other words, it’s a local vs. global optimization problem.  What is useful today is hill-climbing, but sometimes arcane research can shift us to another hill.  Credit where credit’s due.

Similar views, by the way, were expressed by Benjamin Franklin.  One of the (few) worthwhile portions of Walter Isaacson’s (terrible) “Benjamin Franklin: An American Life” ( BFAAL review + notes) was Franklin’s views on science and the  utility thereof.

Franklin’s beliefs on science and the utility thereof, per Isaacson:

“science should be pursued initially for pure fascination and curiosity, and then practical uses would eventually flow from what was discovered.”  

On balloons: while he saw no immediate purpose, he thought they might

“pave the way to some discoveries in natural philosophy of which at present we have no conception… important consequences that no one can foresee.”  

Another quote:

“what is the use of a newborn baby?”


“It does not seem to me a good reason to decline prosecuting a new experiment which apparently increases the power of man over matter until we can see to what use that power may be applied.  

When we have learned to manage it, we may hope some time or other to find uses for it, as men have done for magnetism or electricity, of which the first experiments were mere matters of amusement.”

Still, I do think it’s possible to at least probabilistically determine whether or not a field of inquiry is likely to be useful… even Jordan Ellenberg notes in How Not To Be Wrong (HNW review + notes), as do some mathematicians I’ve met that much of their work is completely pointless and divorced from reality.

Ellenberg did a good job on a lot of things, but didn’t manage to make me feel that any of the current research on prime numbers is beautiful or interesting or useful… I am aware that they are useful in cryptography, for example, but it’s difficult to understand the point of a lot of number theory problems.)

This is obviously a critical question for individuals and businesses trying to achieve something… and it’s one that is frequently ignored.

Page 75: Intriguing, if offbeat, example of n-order impactsWest notes that car designs used to be more unique/interesting before automakers started running Navier-Stokes simulations to figure out aerodynamics… which is why all modern cars are the same shape.

Page 76: West brings up the idea of “dimensionless” units.  My height is not dimensionless, because it has a dimension (feet/inches, centimeters) attached to it.  Pi and e are dimensionless.

Page 84: How could physics help biology?  By addressing the “death vacuum” West referenced earlier, as well as finding answers to things like “where does the human lifespan come from?”

Page 86: West cites an old book (1917) by Sir D’Arcy Wentworth Thompson, On Growth and Form… Wikipedia notes that it is really long (over 1,000 pages) and “less often read than it is cited.”  I’d be willing to wager the same goes for a lot of books today…

Unsurprisingly, West is citing Thompson to sort of defend (not entirely) the standard, questionable“physics envy” view that unless it involves complicated mathematics, it’s not a real science.   

Page 88: Interesting example of disaggregation: to answer the question of how/why people die, West viewed us as “metaphorical machines” and tried to understand the processes that keep us alive, and the consequences of those processes.  We’re back to metabolic rate now.

Pages 91 – 93: West here notes again that many biological qualities follow scaling laws with exponents that have denominators of 4.

He brings up the concept of “scale invariance” and “self-similarity” – related, as we’ll see, to fractals – which means that at any scale and any factor, the scaling law holds… that is, it doesn’t change over time… it’s a constant function.  So you can go from 1 to 100 using the same logic as 1,000 to 100,000.

Again, logarithmic scales are necessary so everything doesn’t bunch up to the left (West notes that a non-logarithmic piece of paper would have to be a kilometer wide, or even 100 kilometers wide.)

Pages 97 – 99: West here notes the idea of “allometric scaling,” i.e., that different features scale at different rates… this is not anything new.  He does note that the universality of certain laws suggests a physical underpinning (ex. that bigger things need to be stockier thanks to the way weight scales).

Pages 99 – 100: West provides a brief reference to ATP and mitchondria… the powerhouses of the cell… (I was a biochem undergrad, I remember that much, but not much more.)  He notes that our bodies contain only about half a pound of ATP, but that we manufacture 175 pounds of it per day.

I don’t really like the way he phrased this, because it sort of implies we’re regenerating that many molecules each day… which we’re not.  As he notes, ATP is essentially like a little battery; we cleave off one phosphate group to release energy, and put it back together using new energy.  So it’s a bit like snapping a lego brick onto and off of another lego brick hundreds of times… with a finite supply of bricks you can come up with really big numbers.

Pages 103 – 104: he brings up the idea of networks transporting information, energy, etc… biological systems can be viewed as physical networks, and it is from these that scaling laws emerge.

Pages 107 – 108: West notes an interesting contrast between biology and physics: in physics, the problems are known and the work is calculation; in biology, the calculation is usually trivial and it’s the problem that is the hard part.  Biology, clearly, is much more like real life than physics (which is one reason I tend to be skeptical of physics envy.)

More interestingly, West brings up the idea of “scale dependence” – “what was irrelevant at one scale can become dominant at another.”  Back to the sand-pile problem and the  dose-dependency  of disaggregation  for emergent behavior. 

Pages 109 – 110: Using examples like molecules as billiard balls and temperature as kinetic energy, West brings up the idea of a “zeroth order” approximation: the simplest-to-work-with assumption (for example, the zeroth order approximation of Chicago’s population is ~10 million).  West set out to find zeroth-order approximations of biological systems.   Precision vs. accuracy.

Pages 112 – 115: A nice example of a form of hindsight bias here: West notes that developing the “set of general network principles” took months and was a major challenge.  After the fact, it seemed obvious (as it does in his book).

What are these principles?  One is “space filling” – the idea that networks, whether in our bodies or in cities, need to service all of the space they contain.

Another is “the invariance of terminal units” – that is to say, the central parts of the network might get bigger and bigger, but the endpoints stay the same.  Mitochondria are not meaningfully different size between elephants and mice; similarly, the faucets and electrical outlets in the Empire State Building aren’t that different sized than those in our houses.  Of course, the water mains in NYC are probably bigger than in Lufkin, TX…

Third and finally is optimization, related to trait adaptivity – different systems could have evolved, but the ones that have evolved are the ones that are most efficient.

Pages 116 – 117: It is worth noting that the terminal unit invariance is a zeroth-order approximation – West isn’t literally saying that all trees have leaves of the same size, but rather that leaf size varies very little with respect to tree size.  

West is examining the “average idealized organism.” This is a very useful approach for understanding the physical networks, of course, but not cities/companies (as we’ll get to), or even animals on a grand scale, because it leaves out all the interesting parts.  

Knowing how the metabolic rate of a tiger relates to that of a human doesn’t really tell you much interesting about the difference between us.

Pages 119 – 122: There’s a lot of fascinating and counterintuitive stuff here.  West provides the example of terminal invariance – blue whales have massive aortas but relatively approachable capillaries – and goes on to note that most of the energy in a distribution system is used to push blood through the tiniest end vessels, rather than the big arteries… a little bit like how water flows easily through a big hole, but not through a fine-mesh paper filter.  

The “optimized,” energy-conserving design of a cardiovascular system therefore requires more central stuff and limited capillaries.

Additionally, waves/reflection/feedback/turbulence can occur at branch points… you don’t want the heart pumping against itself.  (This is a big deal when it comes to pipelines, too.)

For reasons that are mathematically complicated, reflections are minimized/eliminated at branch points if the cross-sectional areas of branches are equivalent to the main tube… so the radii decrease by a constant factor of the square root of two.

West compares this to the electrical concept of “impedance matching.”

Page 125: Blood moves way more slowly in capillaries than it does in arteries… which gives the blood time to diffuse and deliver oxygen.  This is why scratches and scrapes aren’t dangerous, but cutting a major artera is bad.

Blood pressure is also the same across mammals.

Page 126: Before introducing fractals, West references the book The Last Man Who Knew Everything: Thomas Young.  (Amazon, by the way, turns up another biography with the same title, except it’s for Enrico Fermi.)

Pages 127 – 130: West introduces the ideas of fractals and goes back to self-similarity with a different angle: while some things look very different under a microscope, things that are self-similar look similar at different resolutions.

Meanwhile, back to blood, in the nonpulsatile portion of the circulatory system, viscous forces dominate and thus the system shifts to following a cube root factor of two rather than a square root factor.  Additionally, length requires a cube root factor of two.

West goes into the idea of “fractal dimensions” later, but the point of it is that, counterintuitively, organisms operate as if they are four rather than three-dimensional.  Fractals basically add a dimension.

Pages 133 – 134: Human murder (from individual murder to war) follows a power law.  West notes that “no general theory has yet been advanced for understanding these regularities.”  The zeroth-order approximation, then, is that “a large war is just a scaled-up version of a small conflict.”

Again, it’s important to remember that this zeroth-order approximation leaves out a lot of important stuff.

Pages 135 – 137, 139:The “how long is a coastline” question has been addressed elsewhere – by John Lewis Gaddis in “The Landscape of History” (LandH review + notes), for example – but I think West does the best job.  The surprising, counterintuitive conclusion is that the length of a coastline depends on your scale of measurement; increasingly fine units of measurement will result in increasingly long coastlines.

Borders are fractal-like, although not uniformly (South Africa has a very smooth coast; fjordy Norway is very unsmooth.)

Page 140: The idea of a “fractal dimension” is something’s exponent of the power law plus one; this sort of approximates how it scales.

Page 142: In terms of self-similarity, West notes that fluctuations in the stock market are the same for a day, a month, a year, or a decade… you can’t tell the difference.

Page 143: West uses the fractal nature of EKGs as an example of trait adaptivity: more “spiky” EKGs actually indicate health whereas smooth ones don’t; he notes that flexibility allows systems to withstand shocks.   Margin of safety.

Pages 151 – 154: West notes that optimization has led to fractals, because they maximize surface area in limited space… he cites how long our capillaries are and how much surface area our lungs have; compare to how much DNA we have in our bodies, etc.  Fractal geometry allows us to fill space maximally.

Pages 155 – 158: West here discusses the idea of constraints… he notes, interestingly, that most mammals have roughly fifteen nonpulsatile branching levels (where viscosity dominates).  The difference is among the pulsatile levels – one or two for a shrew, 7-8 for us, and 16-17 for a blue whale.

It doesn’t make sense to have a beating heart without vessels that can support it, so that’s why there are no mammals smaller than a shrew…

Pages 158 – 160: … and on the other end, spacing scales with a 1/12 power law, which explains why blue whale capillaries aren’t that far apart relative to shrews, but at some point you just can’t distribute enough blood.

Pages 165 – 173: Why do we stop growing?  Again, it’s power laws: our ability to generate and distribute energy scales at a 3/4th exponent, so at some point we have to devote all of our energy to maintenance.

Pages 173 – 177: West points out the large impact a small change in temperature can have on metabolism rates.

Pages 182 – 188: West provides an interesting discussion of aging: a lot of the increase in life expectancy (though certainly not all of it) is due to lower infant mortality… driven by better availability of health services and better technology.

He also makes an argument vaguely analogous to the Peter Thiel X | Y framework (see disaggregation)… when we think about extending our lives, there are two separate questions to be answered: the maximum achievable lifespan of a human, and whether that can be extended (probably not), and our ability to get to that maximum (which probably can, and this is where our gains have come from).

West also discusses the difference between lifespan and quality of life, with the usual scientist’s focus on quality rather than quantity.

Pages 190 – 193: This bit on “survivorship curves” is fascinating.  Most animals have (nonintuitively) a constant mortality rate in exponential terms, meaning that their likelihood of dying is relatively constant over time.  We’ve obviously managed to flatten the curve quite meaningfully.

West’s conclusion is that the estimated gain in life expectancy for major diseases is actually surprisingly small, and it’s usually damage – rather than infectious disease or accidents – that gets us.

Pages 194 – 199: West here starts with a somewhat similar trait adaptivity argument to that of Peter Godfrey-Smith in the wonderful Other Minds (OthM rview + notes).  Godfrey-Smith hypothesizes on pages 162 – 169 of OM that since animals only need to live long enough to reproduce to pass on their genes, bad genes that don’t crop up until after the age of reproduction are not selected against.

West takes a similar tack, although he points out that we are “overengineered” – i.e. there’s a margin of safety – to make sure we get to reproductive age and beyond.

Unlike a car, however, we can’t just swap out parts… West notes, interestingly, that pretty much all animals have about the same number of heartbeats in a lifetime (1.5 billion).  (We are an exception – 2.5 billion heartbeats – thanks to modern medicine.)

Death is also not sudden in the sense that aging is a gradient; West demonstrates that organ function steadily declines from roughly age 20 onward.

Pages 199 – 203: West notes that aging seems likely to be a process of a combination of simple wear and tear combined with oxidative damage.

Pages 203 – 207: West here notes n-order impacts: lower temperatures are correlated with slower metabolism and therefore longer lifespan, but he notes that artificially lowering our body temperature by 1 degree C (1.8 degrees F) might have many other deleterious, potentially life-threatening outcomes.”  (Thing to investigate: resting heart rate and exercise as a proxy for lower stresses on the cardiovascular system?)

West also discusses the idea of caloric restriction,

Pages 209 – 211: The Industrial Revolution was a major “paradigm shift” – West calls it “the socioeconomic equivalent of the Big Bang.”  He uses the term “Anthropocene” to refer to the past 10,000 years.

Pages 214 – 215: He uses the term “Urbanocene” to refer to the rise of cities.  He notes – again, thanks to power laws – that cities drive wealth creation and innovation, but also crime, disease, pollution, and other negatives.  (It is worth noting that cities would seem, as he discusses later, to be more rather than less environmentally efficient due to sublinear scaling of network infrastructure.  But anyway.)

West’s point here is that:

 “it is in the very nature of an exponential that the future becomes the present at an increasingly rapid pace, so much so that by the time a problem has arisen it’s often too late to address it successfully.”

 West fights back against the techno-utopian view that technology will solve everything, but he doesn’t really empirically back this up to my satisfaction… in the sense that if everything is a power law and ideas are a function of energy, then they should scale faster than our energy consumption, since energy consumption is being depressed by new technology, right?

Pages 216 – 222: West provides an overview here of exponential growth, which contains the usual suspects: the chessboard story, the “at what time will the colony of bacteria be half its final size” question, etc.  His takeaway is that one of the challenges of exponential growth is that the “wall” can seem to be hit very suddenly.

Pages 229 – 232: West here discusses the Malthusian question: will we run out of resources?  Economists say no (thanks to the laws of innovation); physicists say yes (thanks to the laws of physics).

Pages 233 – 235: West reviews some of the staggering statistics on how rapidly our energy use has skyrocketed…

Pages 236 – 244!: How much power does the sun generate?  West notes that the Sun delivers more energy to Earth in one hour than we use in a year.  (He reviews the difference between closed systems and open systems and highlights entropy.)

Also, West gives a nice example of salience / vividness bias here, as well as schema bottlenecks and what I view as an example of hedonic adaptation (contrast bias):

“We are surprisingly tolerant of death and destruction arising from ‘unnatural, man-made’ causes when they occur on a continual and regular basis, but are extremely intolerant when they occur suddenly as discrete events even though the numbers involved are much smaller.  

For instance, each year more than a million and a quarter people die from car accidents worldwide, which is comparable to the number who die from lung cancer, the most common cause of cancer death. Nevertheless, the fear and anxiety about dying from cancer seems to be far greater than the concern about being killed in an automobile accident, and this is reflected in the large discrepancy in the resources we devote to addressing each of these problems.”

Pages 253 – 255: West calls cities “emergent complex adaptive social network systems.”  He cites another old-ish book, The Death and Life of Great American Cities by Jane Jacobs (1961); to say she doesn’t like urban planning would be putting it mildly.

West briefly discusses the idea of a “garden city” (which is directionally … suburbia?) and notes that Singapore is one of the few examples of a garden city at scale.  Lee Kuan Yew’s From Third World To First: The Singapore Story is on my shelf thanks to a recommendation from the contest, but I haven’t read it yet because it’s really long and not terribly high up the interest spectrum.

Page 260: West cites Robert Moses in New York… an acquaintance sent me a copy of The Power Broker by Robert Caro, and another friend has told me it’s good, but again, due to length and seeming density, I haven’t read it yet.

Pages 272 – 273: If you want to impress your MBB interviewer when they ask you how many gas stations are in the United States, just memorize pages 272 – 273 (including the chart) of Scale

West has studied this in some depth and concludes that gas stations scale sublinearly with population, i.e. fewer are needed to support more people, which isn’t surprising.  (The exponent is about 0.85.)

Page 275: West notes that cities are more efficient per-capita in terms of energy use thanks to the sublinear scaling of infrastructure.  He also notes that wages, professionals, patents, crime, and so on demonstrate scaling behavior.

Page 278: Unlike infrastructure, however, things that depend on interactions between people – ranging from crime to disease to GDP growth – scale superlinearly.

Pages 282 – 283: One of West’s pluses is that he doesn’t seem to really buy the “humans are just animals” argument, which, obviously not.  Look around.

Pages 284 – 288: West discusses how there’s more disparity in cities’ data than there is in biological organisms.  He questions whether cities are optimizing for anything; his answer is “social interaction” – directionally, anyway.

Pages 297 – 298: West discusses network effects here: he cites Milgram on something that isn’tauthority bias, i.e. “six degrees of separations.”  He also discusses the idea of “cliques” with “high connectivity” where “almost any two nodes are connected” – i.e. small groups… recall this pops up in a lot of other contexts.

Pages 299 – 300: A bridge failure example that includes feedback.  Most engineers apparently focused only on vertical, not horizontal motions.

Pages 303 – 304: West, to his credit, notes that cities aren’t perfect: there is actually evidence (thanks to Milgram) that people in cities are less friendly, and have higher stress/fear and less trust/civility.

Pages 305 – 309: The visual depiction of “Dunbar numbers” is really interesting; West also notes that memory and other human factors make it hard for individuals to keep track of more than 150 people.  See all the entrepreneur stories about what happens when you scale a company beyond everyone knowing everyone’s name…

Pages 310 – 315: West discusses Zipf’s law and the Pareto principle, sort of; the size of cities follows a power law too (negative exponent).  West notes that this makes Gaussian/normal distributions inapplicable in some situations.  So, for example, the distribution of words in books is non-Gaussian because some mean more than others.

Pages 317 – 318: West provides the underlying mathematics of network effects: he uses the simple formula:

(N) x (N-1) ÷ 2

Which, it should be pointed out, is the same as n C 2 (n choose 2), for those who have some background in probability.  The logic is that you’re trying to count the number of handshakes in a group of N people – you start with N people, and multiply that by (N – 1) people they can shake hands with (you can’t shake hands with yourself… at least, not if you don’t want people to look at you weirdly.)  

But then you have to divide by two, because order doesn’t matter, and Harry-Sally is the same as Sally-Harry. (West also notes, intriguingly, that if you want a dinner party to be intimate, it’s hard to have more than six people, otherwise the group splinters.)

How does this relate to scaling?  West provides a hilarious analogy about frenzied churning of raisins in cake dough, but the point is that relationships don’t quite scale this way because people don’t interact with each other all the time, and of course the cap on how many people we can keep track of.

West notes that in a city of 200K people there are theoretically 20 billion relationships, but that’s implausible because that would allow for only one minute spent per relationship, with no time for anything else.

Pages 319 – 320XXX: For all his brilliance, West gets these pages very, very, very wrong.  He says on 319 – 320:

“An obvious though subtle fundamental constraint is that all of our interactions and relationships necessarily take place in a physical setting […] no matter how you communicate with other people, even if it’s […] on the Internet, you have to be somewhere […]

I emphasize this obvious fact because the development of the Internet and the rapidly evolving field of network science have spawned an unfortunate and misleading impression that social networks are somehow suspended in space as if no longer bound by the constraints of gravity and the nasty encumbrances of the physical world.

[…] It is surprising that despite the enormous amount of recent research on the structure, organization, and mathematics of social networks, almost none acknowledge, let alone embrace, their direct and necessary coupling to the grungy reality of the physical world.  And that physical world is primarily that of the urban environment.

[…] People in cities cannot be static; their mobility is essential for its viability and vitality.  We are persistently on the move from one place to another whether going to an office or factory for work, returning home to sleep and eat, going to a store to buy food, or going to a theater for entertainment.”

This is a truly delusional view of the world; technology has not fully disintermediated relationships from time and location, but it’s done a pretty gosh-darn good job of moving us in that direction.

Let’s use me as a test case.  Here is my nucleus of 5 closest people excluding direct family.  (The fifth person is now a former friend forever in the doghouse, but we’ll pretend he’s still in the list for the sake of the discussion.)

So, of my 5 most meaningful relationships, three were relationships started over the internet, of which one ended up being local (and that likely drove the relationship to what it is today).  Of the two others, neither would ever be a local relationship. The other two were started at school, but both parties moved away; one is coming back at some point and one may or may not ever come back.  

And then let’s look at the professional context: other than Investor 1, most of my professional investor network lives elsewhere, ranging from Tennessee to New York to London.  Only a handful of clients, representing ~10 – 15% of AUM, actually live in the D/FW area (and one of those clients is moving to another state).

Most of the rest of my clients are remote and, you guessed it, I met them over the internet.  Most of my service providers (custodian/prime, fund administrator, auditor) are located in different states. Compliance and lawyer are located locally, and I don’t have to be here to work with them. In fact, I don’t have to be anywhere – as long as I have an internet connection, I can run my business.  

Nor do I physically go anywhere most days (other than the gym) – I work from home.

It is clear that the vast majority of my business interactions, now and in the future, will be in no physical location – “suspended in space.”  With my personal interactions beyond the top 5, it is more of an open question; there will certainly be a higher weighting toward local vs. virtual, but at the very least, “virtual” interactions will make up a substantial minority.

So, West gets it brutally wrong: social networks can, in fact, be “suspended in space.”  They will never be fully that way because of our natural, deep-seated desire to have face-to-face interaction with each other, but they are certainly moving that direction, and that radically undermines a lot of his assumptions about cities.  

Pages 322 – 323: Again, here, West’s conclusions ring hollow: he calls New York, London, and Rio “truly hot” cities… he notes that cities have a “genius” of scaling returns.

But this doesn’t explain outliers like Silicon Valley, nor does it account for the fact that really big cities can often stifle innovation in some senses by encouraging groupthink / social proof – this is why a lot of investors don’t like New York and actively avoid it…

Pages 331 – 332: West notes that predictions that technology will save us time never come true thanks to n-order impacts: we reinest that time!

Pages 333 – 334: West goes into more detail regarding commute times by different modalities… people tolerate a certain amount of transportation per day, and when there’s not enough, cities expand.  Old city walls were determined by walking limits!

Page 335: Data confirms that walking speeds do increase: from ~2 mph in small towns to ~4 mph in big cities.

Pages 347 – 348, 351: There’s also a power law for the distance traveled multiplied by the frequency of visits to any location, with a negative exponent… an interesting example of things being unpredictable on the micro but predictable in aggregate.

Page 354: There are of course outliers, like the airport.

Page 357: measured by patents, NYC isn’t very innovative…

Pages 360 – 361: West shares my frustration with lawns.  (I’m not even an environmentalist… I just think that watering lawns is wasteful.)

Pages 368 – 369: West here discusses the idea of “preferential attachment.”

Page 404: West’s discussion of survival rate counts mergers as deaths, which doesn’t… make a lot of sense.  This chapter is useless and something like Rosenzweig’s “The Halo Effect” (Halo review + notes) is much more thoughtful on the topic.

Pages 424 – 425: setting aside the (not-very-well-fleshed-out) discussion of the need to innovate more rapidly (which one would assume, based on the data presented, is scaling as fast as population), West does note an interesting discrepancy between this generation and previous generations:

“A typical human being now lives significantly longer than the time between major innovations […] nowadays young people entering the workforce can expect to see several major changes during their lifetime that will very likely disrupt the continuity of their careers.”

Pages 441 – 446: West makes some interesting comments here on correlation vs. causation and notes that “neither science nor data are democratic.  Science is meritocratic and not all data are equal.”  His skepticism here of the only-correlations-matter big data approach is in line with, for example, that of Nate Silver in The Signal and the Noise (SigN review + notes).  As Silver notes there,

“Numbers have no way of speaking for themselves.  We speak for them. We imbue them with meaning.

[…] It is when we deny our role in the process that the odds of failure rise.  Before we demand more of our data, we need to demand more of ourselves.

Page 447: To West’s credit, he does admit that the phenomenon I talk about in relation to 319 – 320 is beginning to happen “on a small scale.”  He just underestimates the scale, ironically.


First Read: spring 2018

Last Read: spring 2018

Number of Times Read: 1

Planning to reread?  Maybe


Review Date: spring 2018

Notes Date: spring 2018