Notes

Please note that some of the links referenced in this work are no longer active.

PROLOGUE

Dimensions of an oxygen atom: The atomic radius of oxygen is 60 picometers or 60 × 10−12 m (Slater, 1964), and a reasonable estimate for the radius of an oxygen nucleus is 3 femtometers or 3 × 10−15 m, with the radius of a proton being about 0.84 femtometers (Pohl et al., 2010). Inflating the nucleus to the size of a raspberry with a radius of 1 centimeter would be to increase its size by roughly 3.3 × 1012 times, so the radius of the whole atom would then be (3.3 × 1012) × (60 × 10−12 m) or about 200 m. The volume of the spherical atom would then be about 33.5 million m3 or 43.6 million cubic yards. The volume of MetLife Stadium is said to be 1.8 million m3, roughly 1/18 of the volume of the inflated atom.

Mass of fingertip made of pure nuclei: Most sources put the density of an atomic nucleus on the order of 1017 kg/m3 (for example, the HyperPhysics Web site at http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/nucuni.html. The volume of a fingertip is roughly one cubic centimeter, or a millionth of a cubic meter. The mass of a fingertip’s worth of nuclei would therefore weigh roughly 1017 × 10−6 = 1011 kg. At 2.2 pounds per kilogram, that converts to 220 billion pounds or 110 million U.S. tons.

CHAPTER 1: FIRES OF LIFE

Calculations for the journey of an oxygen atom down your arm: The atomic radius of oxygen is 60 picometers (60 × 10−12 m; Slater, 1964), so an oxygen atom is 120 picometers or 120 × 10−12 m wide. If the atom’s diameter were to inflate 1010 times, its diameter would be 1.2 m. For ease of calculations, let that be the height of a (short) person so the scaling factor to use on you will be 1010 times. If we also take the approximate length of a typical adult arm to be 0.6 m, it would convert to an equivalent distance of 0.6 × 1010 m, or 60 million km. At 0.62 miles per km, that would be 37 million miles, and to travel that distance in one second would require you to move much faster than the speed of light, which is “only” 186,282 miles per second. Einstein’s work on relativity showed this to be impossible.

Dimensions of components of a cell that has been magnified 10 million times to the size of a 300 foot hill: The diameter of a human cell is on the order of 10 microns or 10−5 m (Daniels et al., 1979), so magnifying it 10 million times (107 times) would inflate it to about 100 m in height (roughly 300 feet). The diameters of structural microfilaments in cells are roughly 6–10 nanometers or 6–10 × 10−9 m (Fuchs and Cleveland, 1998). Magnified 107 times, they would be 6–10 cm or roughly 2–4 inches thick. Mitochondria typically range in length between 0.5 and 10 micrometers or 5 × 10−7 to 10−5 m (e.g., Krauss, 2001), converting to 5–100 m, consistent with the size of a tractor-trailer truck in this example.

CHAPTER 2: THE DANCE OF THE ATOMS

Online calculator for molecular speeds and collision rates (HyperPhysics, Department of Physics and Astronomy, Georgia State University): http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html#c3.

IBM Web site for “A Boy and His Atom”: http://www.research.ibm.com/articles/madewithatoms.shtml#fbid=yfOjFKDc8us.

Diffusion time calculator on PhysiologyWeb: http://www.physiologyweb.com/calculators/diffusion_time_calculator.html.

CHAPTER 4: CARBON CHAINS

For USEPA information on mercury emissions 1990–2005: http://www.epa.gov/mats/powerplants.html.

For USEPA information on mercury exposure in women and children: http://www.epa.gov/hg/exposure.htm.

For USFDA information on mercury concentrations in fish: http://www.fda.gov/Food/FoodborneIllnessContaminants/Metals/ucm115644.htm.

CHAPTER 5: TEARS FROM THE EARTH

Gluphisia moth vs. human statistics (after Smedley and Eisner, 1996): The male moths weigh about 80 mg and can pump 10–50 ml of water at a sitting. Taking the volume of a moth’s emission as 40 ml, the mass of that amount of water is 40,000 mg, which is 500 times larger than 80 mg. Therefore the moths can pump about 500 times their body weight at a sitting. If you weigh 150 pounds, you would therefore pump 75,000 pounds of water (500 × 150). A gallon of water weighs 8.3 pounds, so this would represent about 9,000 gallons of waste water. A Gluphisia moth’s body is roughly 1 cm long, and it can pump a jet of waste fluid 40 cm, or 40 body lengths. If you stand 1.8 m tall, 40 of your body lengths would be 72 m, or 236 feet. A Gluphisia moth can collect 17 micrograms of sodium at a sitting, and a male moth’s total body sodium is normally about 19 micrograms. A moth can therefore collect the equivalent of most of its body sodium supply at a sitting. Adult human body sodium content is roughly 3.4 ounces (Freitas, 1998), so a reasonable estimate of puddled sodium would be 3 ounces.

CHAPTER 6: LIFE, DEATH, AND BREAD FROM THE AIR

User-friendly Web sites on scattering and colors of the sky:

Dietrich Zawischa. “Scattering: The colours of the sky.” http://www.itp.uni-hannover.de/~zawischa/ITP/scattering.html; NOAA National Weather Service, JetStream—Online School for Weather. “The Color of Clouds”; http://www.srh.noaa.gov/jetstream/clouds/color.htm.

Atmospheric Optics. “Why is the sky blue?” http://www.atoptics.co.uk/atoptics/blsky.htm.

CHAPTER 8: LIMITS TO GROWTH

Length of total human DNA strung together: A recent estimate of a total human cell count is 37 trillion (Bianconi et al., 2013). However, red blood cells contain no DNA, and they are abundant in your body. A typical adult carries about 5 liters of blood (you can use the blood-volume calculator at easycalculation.com to adjust for sex, weight, and height), and a typical liter of human blood contains about 5 trillion red blood cells (about 5 million per microliter; Mayo Clinic staff, 2011), which could leave you with about 12 trillion DNA-bearing cells. According to most sources, a human cell contains roughly 2 m of DNA on average, as estimated from the length of two sets of 3 billion human genome base pairs per cell (Annunziato, 2008). Multiplying 12 trillion by 2 m yields a length of 24 billion km (2.4 × 1013 m), or about 15 billion miles. Pluto lies between 4 and 8 billion km away from us, so your combined DNA strand could cover the trip several times.

Sand grains in a swimming pool: If a typical long-course Olympic-size pool measures 50 m × 25 m × 3 m, then its volume is 3.750 m3. If a cube-shaped sand grain has a diameter of 1 mm, then it has a volume of 1 mm3. There are a billion mm3 in a m3. Multiply 3,750 by a billion to get 3.75 trillion such sand grains in such a pool. If you have 7,000 trillion trillion atoms in your body (Freitas, 2008), you could therefore fill about 2 trillion pools with that number of sand grains. If the pools measured 50 × 25 m apiece, they would cover roughly (1,250 m2) × (2 trillion) = 25 × 1014 m2 or 25 × 108 km2. Earth’s surface area is about 5 × 108 km2, which is about 5 times too small to fit so many pools.

Spending 7,000 trillion trillion dollars: There are 86,400 seconds in a day, and 31.5 million seconds in a year. If you could spend a million dollars per second, you could end up spending 31.5 trillion dollars in a year. Then it would take another 222 trillion years to spend the rest. The current hydrogen-burning, star-producing Stelliferous era of the universe is thought to have an expected duration on the order of 100 trillion years (Adams and Laughlin, 1997).

Amount of potential human carbon in the atmosphere: Trenberth and Smith (2005) put the mass of the atmosphere at 5.1 × 1018 kg, and an atmospheric carbon dioxide concentration of 400 ppm as of 2013 amounts to roughly 2 × 1015 kg of CO2, with a quarter of that mass due to carbon alone, or roughly 50 × 1013 kg (500 billion metric tons). Freitas (1998) lists an adult’s human carbon content as roughly 16 kg, so the carbon content of the atmosphere could supply the carbon budgets of 3.1 × 1013 adult human bodies (31 trillion people).

CHAPTER 9: FLEETING FLESH

Airborne carbon atoms after cremation: A typical adult carries about 8 × 1026 (800 trillion trillion) carbon atoms in his or her body (Freitas, 1998). If they are all converted to CO2 during cremation and mixed evenly through the atmosphere of the Northern Hemisphere (ca 98 million square miles of land area), there should be (rounding 8 × 1026 atoms to 1027 and dividing by 108 square miles) on the order of 1019 carbon atoms (10 million trillion) over every square mile. There are 27,878,400 square feet in a square mile, so there would be 3.6 × 1011 carbon atoms over a square-foot sector of the Northern Hemisphere, or 360 billion.