Capítulo 1
The Measure of All Things: How Size Shapes Our World
Ever wondered why we're so obsessed with size? From the tallest skyscrapers to the tiniest microchips, from the vastness of galaxies to the minuteness of atoms-size fundamentally shapes how we perceive and interact with our world. In "Size," renowned polymath Vaclav Smil takes readers on an intellectual journey through this universal attribute that affects everything from biology to architecture to economics. Bill Gates calls Smil "my favorite author" and has praised this book as "a masterful exploration of scale." With his characteristic interdisciplinary approach, Smil challenges our assumptions about size relationships while revealing the mathematical principles that govern them. This book arrives at a perfect moment, as our society grapples with questions of sustainable scale in everything from city planning to energy systems to personal consumption. What makes this exploration so compelling is how it connects abstract principles to everyday experiences-showing us that understanding size is ultimately about understanding ourselves.
Capítulo 2
Between Large and Small: Our Fascination with Extremes
Size has captivated human imagination since our earliest days. Ancient epics like Gilgamesh featured terrifying giants like Humbaba, while Greek mythology gave us the one-eyed Polyphemus. These fictional creatures persist through history-from biblical Goliath to Grimm's fairy tales to Swift's Gulliver and Carroll's Alice. Our fascination with size extremes isn't just literary; it manifests in our built environment too. Throughout history, humans have constructed impressively large structures-from Stonehenge and Egyptian pyramids to Gothic cathedrals and modern skyscrapers-demonstrating our persistent preference for grandeur.
This fascination begins early. Children naturally draw figures they like larger than those they dislike, a tendency that continues into adulthood as we seek larger salaries, homes, and possessions. While miniatures can certainly impress us with their craftsmanship, only truly large sizes inspire genuine awe. This relates to our visual perception, which allows us to appreciate enormity far more readily than minuteness.
Interestingly, our perception of size can sometimes become distorted. Some people experience Alice in Wonderland syndrome, a neurological condition where they perceive their body parts as disproportionately large or small. This rare disorder reminds us that size perception isn't just physical-it's processed through our neurological systems.
Modern technology has created a fascinating paradox. The miniaturization of electronics-perhaps our most impressive technical achievement-has actually enabled our quest for ever-larger artifacts and structures. Without miniaturized components, we couldn't build today's massive cruise ships, skyscrapers, or space stations. The very small has become the enabler of the very large, creating a curious relationship between opposite ends of the size spectrum.
Our size obsession reflects something fundamental about human nature-we're constantly measuring, comparing, and seeking to understand our place in the physical world. Whether marveling at the enormity of the universe or peering through microscopes at the subatomic world, we define ourselves partly through our relationship to things larger and smaller than ourselves.
Capítulo 3
Modernity's Size Obsession: Bigger, Heavier, More
Our modern infatuation with larger sizes reflects unprecedented prosperity and technical capability. Today's vehicles exemplify this trend perfectly-contemporary SUVs weigh two to three times more than popular European cars from the 1950s. This growth extends beyond transportation to homes, appliances, and electronics, fueled by extraordinary post-WWII economic expansion that increased US GDP tenfold since 1945.
While evolution shows a general trend toward larger organisms-from microbes to blue whales spanning 22 orders of magnitude in biovolume-our artificial world has seen far more dramatic growth. Since 1900, hydroelectric stations have grown 600-fold in capacity, skyscrapers nine times in height, and cities 11-fold in population. Information storage capacity has increased perhaps 3,000-fold in just a few generations.
This supersizing extends beyond necessity to become a form of status display. American houses have grown 2.5 times larger since WWII despite shrinking family sizes. Refrigerators have tripled in volume while TV screen areas expanded 15-fold. Yet surveys consistently show no corresponding increase in happiness or life satisfaction, suggesting we're approaching physical and practical limits to these excesses.
Notably, large size can be counterproductive in critical cases. Childhood obesity rates have reached alarming levels in developed nations, creating health challenges that may reverse longevity gains. Similarly, larger nations often struggle with greater economic disparities and regional conflicts than smaller, more cohesive countries.
Our understanding of cosmic size extremes took millennia to develop, with accelerated progress in the last 150 years. Size fundamentally shapes our universe-Earth's perfectly sized gravity enables life while being small enough to allow escape velocity for space exploration. Ancient knowledge began with Eratosthenes calculating Earth's circumference in the 3rd century BCE, while early universe models placed Earth at the center with fixed stars relatively nearby.
The true astronomical breakthrough came in the 19th century when astronomers measured distances to nearby stars, revealing they were trillions of kilometers away. By 1924, Edwin Hubble proved Andromeda was a separate galaxy. Modern observations have expanded our known universe to 93 billion light-years across-an expansion of 15 orders of magnitude in our cosmic understanding since 1600.
Microscopic exploration began seriously in the 17th century. Robert Hooke's 1665 Micrographia revealed cells and microorganisms at 50x magnification, while van Leeuwenhoek's 250x microscopes discovered bacteria. Technological advances eventually enabled electron microscopes (1939) and scanning tunneling microscopes (1981) to resolve objects down to 0.01 nanometers-allowing us to see individual atoms. This incredible journey spans nearly 35 orders of magnitude, from hydrogen atoms to the observable universe.
Capítulo 4
Perceptions and Illusions: How We Experience Size
Our perception of size has evolved dramatically with modern technology. Until the late 19th century, even the largest Renaissance frescoes showed figures only 40-60% larger than life. The arrival of the Lumiere cinematograph in 1895-1896 revolutionized our visual experience, with the first American movie screens measuring 6.1 x 3.7 meters-large enough to display humans at twice their actual height.
This "Gulliverization" of visual media has reached extraordinary extremes. Movie screens expanded from 6.1 x 7.6 meters in 1905 to modern IMAX theaters with screens 24.4 x 19.9 meters, showing people ten times their actual height. Building projections have displayed endangered animals 33 stories tall and fashion models 42 stories tall-approaching Jules Verne's 1889 science fiction vision of advertisements projected onto clouds.
Simultaneously, screens have shrunk to unprecedented smallness, from television to wrist-mounted devices like the 38.6 x 33.3 millimeter Apple watch. The modern screen range spans from 4 centimeters to 150 meters-a 3,750-fold difference that far exceeds Swift's 140-fold difference between Lilliputians and Brobdingnagians. With nearly 15 billion portable screens globally by 2020, many people now spend more time with miniaturized or virtual humans than with actual people, fundamentally altering our perception of size and reality.
Our perception of size is remarkably fallible, with society increasingly normalizing unhealthy body sizes. Studies show people consistently miscategorize overweight male bodies as normal weight while perceiving underweight female bodies as normal-revealing a concerning gender bias in our perception standards. Parents frequently underestimate their children's body size, placing them in healthier BMI categories than appropriate, which makes addressing childhood obesity more difficult.
Media-driven body image distortions have led to dangerous conditions like anorexia nervosa (affecting 0.3-1% of young women) and body dysmorphic disorder (affecting 0.7-2.4% of the population). These psychiatric disorders involve distorted perceptions of physical appearance, with sufferers seeing nonexistent flaws or perceiving emaciated bodies as "fat." Both conditions involve abnormal brain activation in visual processing systems.
Even food portion perception is distorted. Restaurant plates have increased from 25cm to 30cm diameter (a 44% area increase), with American restaurants serving enormous portions like 64-ounce steaks. While some studies suggest smaller plates might reduce consumption (Chinese buffet diners with large plates served themselves 52% more food), meta-analyses show plate size may have only marginal effects on actual intake.
Capítulo 5
The Advantages of Height: Size as Social Currency
Height measurements reveal fascinating global patterns and social implications. A century-long study of nearly 20 million people born between 1896-1996 shows women gained 8.3cm and men 8.8cm on average, with remarkable variations: South Korean women gained 20.2cm, Iranian men 16.5cm, while sub-Saharan Africa and South Asia saw minimal increases. Today, Dutch men (183.8cm) are the world's tallest, followed closely by Montenegrins, Estonians, and Danes, while the shortest populations live in Timor-Leste, Yemen, and parts of Africa.
Height correlates strongly with numerous advantages. Taller people are perceived as healthier, smarter, more confident, and better educated-qualities that translate into higher incomes and greater influence. While height is highly polygenic (up to 90% of variation attributable to genetic factors), it also reflects childhood environment and nutrition. Studies consistently show taller children come from families with educated parents and higher incomes, with better cognitive function and mental health outcomes.
The height-income gradient is particularly steep at low incomes but persists even at executive levels, where Swedish CEOs of larger companies averaged 3cm taller than those managing smaller firms. In China, each centimeter of height increases Communist Party membership probability by 0.05%, though market-based height premiums exceed political advantages.
The few downsides to height include shorter lifespans (0.5-0.7 fewer years per additional centimeter) and increased cancer risk (approximately 10% higher risk per 10cm of height), likely because more cells provide more targets for cancer-causing mutations. Truly excessive growth from conditions like gigantism or Marfan syndrome significantly reduces life expectancy, though medical advances have improved outcomes.
Height's social advantages reflect our deep-seated tendency to equate physical stature with capability and dominance-a pattern observed across cultures and throughout history. Even in our supposedly meritocratic modern society, these unconscious biases persist, influencing everything from hiring decisions to leadership perceptions to romantic choices.
Capítulo 6
Proportions and Symmetry: The Mathematics of Beauty
Proportion-how parts relate to each other or to the whole-shapes our perception of beauty and function in both nature and design. The waist-to-hip ratio (WHR) has deteriorated globally with rising obesity rates, exceeding WHO's recommended maximums of 0.85 for women and 0.9 for men, with even slight increases posing health risks. German conscripts demonstrate how bodies shifted from growing taller (plateauing since the 1990s) to growing wider, with notable regional height variations.
The index-to-ring-finger ratio (2D:4D) gained scientific attention as a potential indicator of prenatal hormone exposure, with men typically having longer ring fingers (ratio 0.98) compared to women's equal digits (ratio 1.0). Despite thousands of studies linking this ratio to various conditions and abilities, many scientists question its validity due to small differences between sexes, inconsistent results across populations, and replication failures.
In art, proportions evolved from strict realism to deliberate distortion, as seen in El Greco's elongated figures and Modigliani's distinctive style. Analysis of nearly 15,000 Western paintings reveals a shift from horizontal-vertical compositions before 1850 to horizontal-horizontal designs afterward. Famous paintings vary widely in their dimensions and proportions, from the small upright Mona Lisa to landscape-oriented rectangles like Guernica to near-squares like Klimt's Kiss.
Facial symmetry is widely considered attractive as a signal of social acceptability and genetic quality. Studies confirm that more symmetrical faces receive higher ratings of attractiveness, health, and positive personality attributes like sociability and intelligence. We're remarkably adept at detecting even minor asymmetries-identifying changes as small as 1.5mm in eye size-though experiments suggest bilateral symmetry may not be the principal factor in facial beauty assessment. Other factors include facial averageness, skin health, and proportions, with modern beauty standards showing cross-cultural similarities but differing from classical ideals.
Symmetry in human design has ancient origins, dating back to Acheulean hand axes 1.5 million years ago. Architecture provides the most impressive expressions of symmetry-from Mesopotamian ziggurats and Egyptian pyramids to classical Greek and Roman monuments, medieval Islamic structures like the Alhambra and Taj Mahal, and Renaissance buildings inspired by classical forms. Medieval castles represent rare examples of deliberately asymmetric large structures. While symmetry dominated architecture until the 20th century, asymmetric designs became more common after 1920 through Bauhaus architects and Frank Lloyd Wright, with recent extremes in the sculptural buildings of Frank Gehry and Zaha Hadid.
Capítulo 7
The Golden Ratio Myth: Beauty Beyond Numbers
Examining the golden ratio reveals contradictions between enthusiasts and skeptics. While many designers promote it as essential for creating "gorgeous graphic designs," others dismiss it as "design's biggest myth." The ratio has been claimed to appear in works ranging from the Parthenon to paintings by Botticelli, da Vinci, Raphael, Seurat, and Dali. However, mathematician George Markowsky systematically debunked these claims, finding no evidence of golden ratio use in the Great Pyramid, Parthenon, UN building, or famous paintings. Keith Devlin from Stanford concluded people simply "WANT there to be numbers with mystical properties."
The term "golden ratio" dates only to the 19th century, gaining prominence when German psychologist Adolf Zeising claimed it as a "universal law" governing beauty in nature and art. Despite Theodor Fechner's more measured assessment finding limited applications, the notion persisted. Recent examples of golden ratio infatuation include Turkish physicians claiming heart rhythms follow the "God ratio" and attempts to find it in everything from sperm heads to concrete cracks.
Studies of human faces consistently fail to support golden ratio claims. Research on Malaysian students found only 17% of facial proportions conformed to the ratio. Similarly, studies of Miss Universe winners showed statistically significant deviations from golden ratio proportions. Mathematician Roger Herz-Fischler concluded that without documentary evidence, measurements alone cannot prove artists used the golden ratio.
Despite overwhelming evidence against its importance, the infatuation persists, exemplified by Dubai's $60 million "Dubai Frame" built to golden ratio proportions-what Smil calls "a hideous demonstration of having money to waste." While the search for golden ratios may be misplaced, proper sizing and proportions in design remain genuinely important.
Our persistent belief in the golden ratio despite contrary evidence reveals something deeper about human nature-our desire to find mathematical order in beauty. We want to believe aesthetic appeal can be reduced to formulas, that there's an objective standard we can measure and reproduce. The golden ratio myth persists not because of its mathematical validity but because it satisfies our psychological need to quantify the unquantifiable. Perhaps beauty's true nature lies precisely in its resistance to such simple formulations.
Capítulo 8
The Science of Scaling: Why Size Changes Everything
Jonathan Swift's "Gulliver's Travels" contains fundamental errors about scaling that Galileo Galilei had actually addressed nearly a century earlier. Swift's first mistake was assuming body mass scales as the cube of height (M ~ L3), which would be true for simple geometric shapes but not complex organisms. With proper scaling (M ~ L2), Gulliver at 175cm and 67kg would mean Lilliputians weighing about 500 grams (like squirrels) rather than 39 grams, and Brobdingnagians weighing nearly 10 tons (like large elephants) rather than 116 tons.
Swift's second critical error was assuming identical behavior across drastically different sizes. Small creatures like Lilliputians would lose body heat much faster due to their higher surface-to-volume ratio, requiring frequent eating beyond the three daily meals Swift described. They would also suffer from water clinging proportionally more to their bodies after rain-up to 15% of body weight.
Brobdingnagians would face opposite challenges: interior overheating and impossible biomechanics. At 21 meters tall, their bones couldn't support their weight while walking upright, as calcium apatite (the mineral in all vertebrate bones) has inherent strength limits. The giant horses Swift described would weigh 70-75 tons-comparable to Argentinosaurus-and would break their legs with each step.
Even Swift's imagined plants couldn't escape scaling laws. Wheat in Brobdingnag would need to reach 15 meters tall-impossible for annual grain plants whose stems naturally dry after one growing season. Such plants would require completely different structures, more like bamboo than wheat stalks. The plant density would also be impossible-standard wheat has about 350 plants per square meter, but bamboo-like giant wheat would allow only about 400 clumps per hectare due to self-thinning.
Despite these scientific errors, Swift's work provides both entertainment and valuable lessons about the inescapable consequences of scaling in organisms. As Galilei had explained in 1638, "For every machine and structure, whether artificial or natural, there is set a necessary limit beyond which neither art nor nature can pass." Size cannot change alone-everything else must change too.
The systematic study of how structural and functional properties scale with size began in late 19th century Germany. In 1879, physician Karl Meeh pioneered measuring body surface area as a function of mass, developing a formula (where surface area grows as weight raised to power 2/3) still used nearly 150 years later despite his limited sample of just 16 subjects.
The human brain's extraordinary size-averaging 1,407 grams in adult males versus under 200 grams for pigs and 450 grams for chimps-represents our evolutionary pinnacle alongside bipedalism and dexterity. With over 80 billion neurons (10 times more than chimps) and 100 trillion synaptic connections, our brains enable unparalleled cognitive capabilities. However, brain size alone doesn't determine intelligence-equid brains tripled during the same period as human brains without comparable behavioral advances. Our exceptional brain-to-body ratio likely resulted from digestive tract reduction enabled by cooked, processed foods.
Capítulo 9
Metabolic Scaling: The Energy of Size
Metabolic scaling follows a 3/4 power law rather than being directly proportional to mass. This means larger animals need proportionally less food than smaller ones. Kleiber established in 1932 that metabolic rates scale as M^0.75 across species from mice to elephants. This relationship reveals that a mouse needs 20 times more energy per unit weight than an elephant. For humans, basal metabolism equals approximately 70M^0.75 kilocalories daily (about 80 watts for an average adult), with actual daily requirements 1.55-1.78 times higher depending on activity level.
Why should power laws and 3/4 scaling appear so frequently in organisms across many orders of magnitude? Despite nearly half a century of efforts, there's still no universally accepted explanation. West, Brown, and Enquist proposed a sweeping theory based on networks of tubes (blood vessels, plant xylem) that distribute resources throughout organisms, mathematically deriving the 3/4 power scaling. However, this "universal scaling law" faces significant challenges. Recent studies show considerable variation: plant studies found no support for 3/4 scaling; analysis of 600+ mammalian species yielded an exponent of 0.675 (confirming Rubner's original 2/3 calculation); and exponents for individual mammalian orders range from 0.58 for insectivores to 0.77 for carnivores.
Field metabolic rates (FMR) measured with isotope techniques reveal even greater diversity, with exponents ranging from 0.59 for marsupials to 0.92 for lizards. Even animals of identical weight show dramatic differences-an Arctic fox's metabolic rate is 2.1 times higher than a sloth of the same weight. A comprehensive study of 3,006 species spanning 20 orders of magnitude in mass conclusively rejected any universal scaling law, though metabolic rates remarkably fall within a relatively narrow 30-fold range.
Examining the 2.5 billion gasoline and diesel engines worldwide reveals remarkable scaling patterns. From tiny 5-watt model plane engines to massive 84-megawatt marine diesels, these machines span seven orders of magnitude in power-comparable to the body mass range in mammals. Studies confirm that engine power scales nearly isometrically with mass (exponent ~0.95), meaning doubling an engine's power requires roughly doubling its mass.
Most fascinating is James Marden and Lee Allen's discovery that across ten orders of magnitude-from flying insects to jet engines-the maximum force output of all complex "motors" scales at an almost perfectly isometric rate. This creates a remarkable constant: 1 kilogram of "motor" mass consistently produces 43-71 newtons of force, whether in birds, bats, mammals, or turbofans. This physical reality imposes clear size limits on our machines, just as it does on organisms.
Capítulo 10
Normal Distributions and Their Exceptions
The elegant bell-shaped curve tracing symmetrical continuous probability distributions appears throughout scientific disciplines. However, many curves conforming to normal distribution formulas aren't actually bell-shaped-some are narrower and tighter like tongues, while others form gentle mounds rather than pronounced bells. The term "normal" misleadingly implies other distributions are abnormal, though many sizes are asymmetrically distributed.
This terminology emerged from a nearly 300-year history beginning with astronomers like Tycho Brahe and Galileo who sought to improve observational accuracy. Abraham de Moivre published the first mathematical treatment in 1733, though Pierre-Simon Laplace and Carl Friedrich Gauss later became synonymous with the distribution. Adolphe Quetelet applied these principles to human measurements, introducing the concept of "average man" through studies of Scottish soldiers' chest measurements and French conscripts' heights.
While many size distributions can be approximated as normal curves, real-world data rarely fits perfectly. A normal distribution is defined by just two parameters: the mean () and standard deviation (). The mean represents both the most common value and the median, while standard deviation determines the curve's spread-smaller deviations create taller, peakier curves while larger ones produce more mound-shaped distributions. In a perfect normal distribution, 68.27% of values fall within one standard deviation of the mean, 95.45% within two, and 99.74% within three. This 68-95-99.7 rule provides a powerful tool for assessing how ordinary or exceptional observed sizes are.
In everyday life, we typically prefer values near the mean-whether in precipitation, medical test results, or clothing sizes-while extremes can be problematic. Politicians target "average" voters, and parents generally prefer babies born at full term with average birth weight rather than premature or underweight infants.
Normal distributions have practical applications beyond health metrics. For everyday life, understanding height distributions can enhance self-esteem or provide reality checks. In the Netherlands, 180cm is slightly below average for men, with 11% exceeding 190cm. Contrast this with Filipino men, where only one in 13,116 reaches 190cm. Only 2% of American women exceed the average American male height, while twice as many men fall below the average female height.
Industrial applications of normal distributions are particularly valuable. The Six Sigma methodology, pioneered by Motorola in the 1980s, aims for extraordinary reliability-just 0.002 defects per million opportunities. In practice, accounting for performance drift, the standard is 4.5 (3.4 defects per million). For companies producing billions of units annually like Coca-Cola (1.9 billion servings daily in 2020), this precision is crucial.
Capítulo 11
When Asymmetry Rules: Power Laws in Nature and Society
Just before World War II, Czech statistician Jaromir Korcak identified "two fundamental types of statistical distribution." Centered distributions dominate nature-in plants, animals, and humans-appearing in whole organisms, their organs, and functions (impala brain sizes, Turkish wheat grains, elite athletes' heart rates). Conversely, asymmetric distributions prevail where physical forces dominate-in tectonic, geomorphic, and atmospheric phenomena.
This natural dichotomy extends beyond statistics to understanding both the natural world and human endeavors. Korcak attributed asymmetric distributions to external factors and symmetrical ordering to internal effects. His lectures in the 1960s emphasized how planetary features almost universally follow asymmetric distributions-European islands, lakes, watersheds, river lengths, and lake depths all demonstrate this pattern.
The Amazon River exemplifies this asymmetry, discharging five times more water than the Congo, while only two other rivers (Ganges and Orinoco) approach the Congo's flow. Depending on classification criteria, there are potentially hundreds of millions of smaller streams worldwide. This extreme size asymmetry also characterizes geotectonic processes like earthquakes and volcanic eruptions, as well as cosmic phenomena including solar flares and celestial impacts.
Since the 1940s, numerous researchers have identified power-law distributions across diverse domains. Geoscientists applied them to lakes, islands, watersheds, rivers, and earthquake intensities. Kiyoo Wadati first recognized power-law distribution for earthquake energy in the 1930s, followed by Ishimoto and Iida's application to earthquake amplitudes, and Gutenberg and Richter's relation of earthquake numbers to magnitude. Lewis Richardson suggested power laws link the frequency of fatal conflicts with their magnitude.
George Kingsley Zipf made the most consequential contribution, building on Estoup's linguistic observations. He found that word frequency in English is almost inversely proportional to rank, with "the" accounting for 7% of occurrences, about twice as frequent as "of" at 3.5%. His 1949 book revealed that the largest city is roughly twice the second-largest city's size and three times the third-largest-expressed as x = r^-1 where x is city size and r is rank.
Real-world data rarely conforms perfectly to simple inverse power-law equations. Richard Perline distinguishes between "strong inverse power laws" (rare) and weak or false ones, where the expected straight-line distribution on double-log graphs applies only to segments of data. Global wealth distribution exemplifies stark asymmetry: 55% of adults own just 1.3% of global wealth, while 1.1% of adults control 45%. In the US, the poorest half owns merely 1% of the country's wealth, with many in debt. The fortunes of America's wealthiest individuals exceed average net worth by six orders of magnitude.
Size, in all its manifestations, remains the fundamental measure through which we understand our world. From the microscopic to the cosmic, from the personal to the planetary, size relationships shape everything from our bodies to our cities to our understanding of the universe itself. While we may never develop a single unified theory of size, appreciating its complexities enriches our perception of reality and helps us design better systems, structures, and societies that work within natural constraints rather than against them.
