The Calculus Diaries: How Math Can Help You Lose Weight, Win in Vegas, and Survive a Zombie Apocalypse

by Jennifer Ouellette

  He found that burning a pound of coal in a steam engine produced five times as much work (then known as duty) as a pound of zinc consumed in an early electric battery. His brewery was better off with the steam engines.

  Food is another energy-dense substance, typically measured in calories. A calorie is the amount of heat energy produced when food is burned to ashes under carefully controlled laboratory conditions. It is not something that is “in” food per se. Another way to define a calorie is the amount of energy (heat) required to raise the temperature of one gram of water 1 degree Celsius (1.8 degrees Fahrenheit). The exact amount of energy required to do so is 4.18 joules. Unlike nutritionists, physicists almost never refer to energy in terms of calories. They prefer joules or watts—the derivative of joules, since watts measure the rate of energy (watts=joules per second). The “calories” in food are actually kilocalories: 1,000 calories equal 1 kilocalorie. So if I run four miles, I might burn 400 food calories (kilocalories); it sounds much more impressive when transposed into 400,000 regular calories. And that Power Bar I consume post-workout contains 270 food calories, or 27,000 regular calories—over one million joules, the unit of energy named after James Joule.

  Let’s see how this all applies to our intrepid Wheelman, Steve Gilmore. His body is burning food (and stored fat, assuming he has any left) for energy. But all that energy is not being harnessed for any useful purpose, other than keeping him slim and incredibly fit. He also loses a fair amount of energy as heat, radiating away a good 100 watts (8.5 million joules) every day when he’s not riding up and down Fargo Street, and far more than that on a strenuous bike ride. His system is increasing in entropy as he is burning fuel (his breakfast). Entropy is a way to determine how much energy can be harnessed to produce useful “work.” The lower the entropy, the more orderly things are, and the more useful work can be harvested as entropy increases over time. (It is a hard-and-fast law of thermodynamics that entropy always increases in a closed system.)

  How much work can we get out of the system by letting entropy increase? We can determine this by taking an integral of temperature as the entropy increases over time. Gilmore’s body gains potential energy as he chugs up the hill because he increases his distance from the earth’s center of gravity, but he loses potential energy as he descends, while his kinetic energy increases. (Entropy also increases as he radiates away more heat with his exertions.) The two cancel each other out, and the amount of work produced is zero—unless the Wheelmen could find some way to harness the kinetic energy. For instance, Gilmore could carry a small package to the top of the hill and then work would have been done: The package has more energy as a result of his exertions. It has gained potential energy with the increase in altitude, which can be converted into kinetic energy should Gilmore then decide to toss it down the hill.

  SPIN CYCLE

  In the late 1980s, Henry Works founder Mike Taggett built his first retrofitted exercise bike with a car generator. He described it as a “Gilligan’s Island human-powered blender” and used it to mix margaritas without an electrical outlet. Twenty years later, the same concept underlies his new retrofitted machine that makes use of both the arms and legs to maximize calories burned and watts created. It looks like your typical stationary bike, except there is a hand crank in place of the handlebars that one can spin while pedaling. All that effort turns the eighteen-inch flywheel, which in turn is connected to a generator.

  Boesel started with three of Taggett’s retrofitted spin bikes for his Green Microgym, and then collaborated with Henry Works to build a system of four linked Team Dynamo stationary bikes outfitted with a small motor connected to a bank of batteries. As users pedal, the motor charges the batteries, which then power the TV and stereo system. A single exerciser might only generate 50 to 100 watts of electricity—100 watts would power a small TV—but all four bikes working together can generate about four times that much, depending on how hard each person is working.

  But are Green Microgyms practical? Just how much energy do all those überfit exercisers produce? Certainly Boesel’s gym members are expending a great deal of effort during their workouts, but when it comes to harnessing that effort for a practical purpose, we must contend with the grim realities of thermodynamics. Boesel found that, as energy passes through the battery, some gets lost in the conversion process (entropy). So in practice, the battery pack option was less efficient in generating useful energy than a machine retrofitted with a grid-tie inverter, which sends the generated energy directly back into the power grid.

  Taggett’s company obliged with its FireWheel InterGrid (FIG) system. Boesel plugs the machine into a wall socket as if it were a common household appliance. The inverter is a clever device commonly used in conjunction with solar panels, enabling those who install the panels to literally spin the meter backward and sell extra power back to their local power company. In this case, the system harvests some of the ambient heat normally emitted by exercise machines (due to friction) while in operation. The battery-based Human Dynamo system uses less than 50 percent of the current coming out of the machine, while the new updated version delivers back to the grid about 70 percent of the total watts produced.

  Boesel is a personal trainer by profession, and his outlook is distinctly scientific. He admits he was overly optimistic at first about how efficient his gym would be, figuring he could go off the grid completely and generate 100 percent of his energy needs. But after doing the actual experiment for nearly a year, the data told him differently, so like any good scientist, he revised his hypothesis and is seeking to refine it further. The sticking point lies in the inevitable losses that occur whenever energy changes from one form to another. Stupid entropy ruins everything.

  Take a standard rowing machine. If I row furiously for ten minutes, I would burn about 100 calories. This is sufficient to run a 100-watt bulb for one hour—at least on paper. Remember that some energy is always lost in the conversion; in the case of gym rats, we lose energy by sweating off excess body heat, not to mention the enormous amount of energy required for basic bodily functions. We breathe more heavily when we exercise, and our blood circulates at a higher rate, on top of the energy required just to keep our muscles moving. So not all of the energy we generate is converted directly into useful mechanical movement. In reality, we would be fortunate to harness 50 percent of that estimated output.

  The upshot is that one person on one machine simply won’t make much of a difference. Taggett estimates that one person produces about a penny’s worth of electricity in an hour. But if a gym has forty retrofitted machines, all in use during the two-hour evening peak period, those exercisers would generate approximately 25 kilowatt hours of electrical energy during those two hours—equivalent to running several households for a day. This is another optimistic assessment, assuming all the exercisers are actually exerting themselves, rather than strolling on the treadmill in designer gym togs, chatting on their cell phones and not breaking a sweat. Those people bring down the overall energy output.

  To maximize his savings, Boesel has combined his retrofitted machines with other energy-saving strategies. The gym has SportsArt EcoPower treadmills that run on one third less energy than traditional motors, and when machines are not in use, Boesel switches them off. The average treadmill takes between 1,500 and 2,000 watts to operate, the equivalent of nine Lance Armstrongs chugging at full power. Boesel also added solar panels to the building’s exterior, and is careful not to run the A/C continuously. He has managed to keep his electricity costs to a bare minimum—about 9 kilowatt hours per month—and believes that in time, he can break even on those costs, generating 100 percent of the gym’s electricity needs. At present, he figures he saves between $75 and $150 per month in electricity costs.

  While Boesel estimates he can produce 75 to 80 watts consistently during his usual hour-long cardio workout, I have significantly less mass, and therefore my output is closer to 45 to 50 watts (produced continuously during the same time period),
although I am not consistent: sometimes the gauge dips into the 30-watt range when I slack off the pace a bit. Seeing just how little usable energy I produce on Boesel’s retrofitted elliptical is a sobering eye-opener.

  Math and calculus also play a significant role in maintaining a healthy weight. The combination of how much food we eat and how much we exercise largely determines our weight, and in times of plenty, it is all too easy to consume more food than we need. Not surprisingly, human beings throughout history have devised all manner of bizarre strategies for combating their expanding girths.

  BATTLE OF THE BULGE

  It might be said that William the Conqueror had an overdeveloped sense of entitlement. He was the only son of Robert, Duke of Normandy, but his parents never married. His illegitimacy didn’t keep him from inheriting the duchy of Normandy when his father died in 1035, on the way back from the Crusades. But he aspired to be king of England as well, having been promised the throne by King Edward the Confessor, who had no direct heirs. On his deathbed, however, Edward had a change of heart: He named Harold, son of the Duke of Essex, as his successor. Incensed, William invaded England in September 1066 and defeated the newly crowned King Harold at the Battle of Hastings. William became king of England.

  William may have conquered England, but he lost the battle of the bulge. In fact, he became so fat in the years after his victory at the Battle of Hastings that King Philip of France (no doubt disgustingly svelte) cruelly described him as “looking pregnant.” William was purportedly hurt, but there was truth to the statement: By that time, he could barely stay on his trusty steed. He took to staying in his rooms, subsisting on nothing but alcohol for days at a time,44 but his self-designed weight loss technique failed him in the end. When William died of abdominal injuries in 1087, after falling off his horse at the Siege of Mantes, he was so fat that he barely fit into his fancy stone sarcophagus. In fact, all the pushing and shoving to get the warrior’s body—horribly bloated from the heat of the day—into the coffin caused it to burst, filling the church with the stench of decay.

  William the Conqueror is in good company. Excess flab (not to mention bloating) is hardly a new problem for the human race. Some modern archaeologists believe the ancient Egyptian queen Hatshepsut was quite heavy and may have been diabetic. Baseball legend Babe Ruth was notorious for his twelve-hot-dog lunches and missed much of the 1925 baseball season with what sportswriters dubbed “the bellyache heard round the world.”45 And U.S. President William Howard Taft infamously gained so much weight while in office that he got stuck in the White House bathtub.

  In the latter days of the Roman Empire, people attending sumptuous feasts would gorge themselves on delicacies, and then repair to the vomitorium to purge their bodies of all that excessive indulgence—back when bulimia was cool. Bingeing and purging lost its cachet as the centuries passed, and people turned to complicated fad diets to control their girth. The English Romantic poet Lord Byron struggled mightily with his weight, despite his reputation as a ladies’ man (clubfoot and all). He routinely went on extreme “slimming” regimens like vinegar diets to keep his weight under control.

  Around the same time, a Presbyterian minister named Sylvester Graham—one of America’s earliest vegetarians—introduced the “cracker” diet, eschewing meat, rich spices, coffee, tea, tobacco, and alcohol in favor of whole-grain breads and crackers. In the early twentieth century, a San Francisco art dealer named Horace Fletcher—“the chew-chew man” or “the great masticator”—advocated controlling food consumption by chewing one’s food at least thirty-two times (once for each tooth) until it was liquid, then spitting out any nonliquid residue. He lost over fifty pounds with this method, and felt one could absorb the nutrients without consuming all the calories from food.

  Fad diets inevitably spawned a plethora of bestselling diet books. As early as 1727, a man named Thomas Short published The Causes and Effects of Corpulence, in which he advised the obese to move to arid climates, having observed (somewhat unscientifically) that heavier people tended to live near swamps. In 1864, a portly English casket maker named William Banting published his Letter on Corpulence, detailing how he lost fifty pounds by subsisting on lean meats, dry toast, fruit, and vegetables. It sold 58,000 copies, and the practice of dieting was known as banting for decades afterward. In 1919, Dr. Lulu Hunt Peters published another bestselling diet book, Diet and Health, which introduced mass audiences to the concept of counting calories to control weight. The book sold more than 2 million copies, advocating a strict 1,200-calorie regimen.

  Do you think the Aktins and South Beach diets were innovative? Think again. Back in the 1920s, William H. Hay, for example, believed proteins, starches, and fruits should be eaten separately to avoid “acidosis,” claiming it “drained vitality and led to fat.” He also recommended a daily enema to “flush out the poisons”—an approach that can still be seen today in the practice of colonics. Vilhjalmur Stefansson’s The Fat of the Land praised the traditional Inuit diet of caribou, raw fish, and whale blubber, with almost no fruit, vegetables, or carbohydrates. In Look Younger, Live Longer, Gayelord Hauser drew the admiration of Hollywood actresses Greta Garbo and Paulette Goddard with his emphasis on vitamin B-rich foods like brewer’s yeast, yogurt, wheat germ, and blackstrap molasses. He was also one of the first to develop his own line of special foods and supplements in accordance with that diet plan. Then there was the “magic pairs” diet, extolling the supposedly increased fat-burning properties of certain food combinations—lamb chops and pineapple, for example.

  The twentieth century also brought the advent of diet pills and all manner of strange gadgets that were claimed to help dieters melt off the poundage while still eating whatever they liked. It all started when workers at a munitions factory in World War I inexplicably lost weight, and doctors concluded that a chemical known as dinitrophenol—used in the making of dyes, pesticides, insecticides, and explosives—was responsible for raising their metabolisms, so they burned more calories. By 1935, over a hundred thousand Americans had used diet pills made with dinitrophenol. Unfortunately, the side effects were nasty: There were several cases of blindness and a handful of deaths, and dinitrophenol was taken off the market.

  My personal favorite weight-loss mechanical device is the belt-driven fat massager that wrapped around one’s torso and supposedly helped jiggle fat away. It was one of many Nautilus-like machines introduced beginning in 1857 by a Swedish physician named Gustav Zander. Zander Rooms were all the rage at elite spas in the second half of the nineteenth century. Today there are Vision-Dieter Glasses, designed to make food look less appealing, and Mini-Forks to encourage diners to take smaller bites, not to mention the Diet Dam—basically a muzzle to discourage you (and those around you) from eating by making you look like Hannibal Lecter. The invention of liposuction offered a shortcut to trimming unwanted stores of fat from hips, stomach, and thighs, and in the 1950s, rumors abounded that wealthy dieters were ingesting pills containing tapeworms to help them lose weight. After dropping sixty-five pounds, opera singer Maria Callas was among those rumored to have tried the tapeworm diet, perhaps because she had a known fondness for raw steak and raw liver.

  The latest technology offering new hope for expanding waistlines and flabby thighs is the free-electron laser (FEL) at Thomas Jefferson National Accelerator Facility in Virginia, affectionately known as J-Lab. FELs are useful for any number of practical applications, but back in 2006, a team of J-Lab scientists demonstrated that the laser could burn away fat in the body without scorching the top layer of protective skin. This is a very exciting development, possibly leading to revolutionary new laser therapies to treat such chronic bugbears as severe acne, artery plaque, and of course, cellulite. It offers the tantalizing possibility of a whole new way to get thinner thighs in thirty days, with no need for even a lick of exercise.

  The researchers tested the concept first on actual human fat (obtained from “surgically discarded normal tissue”) and then on skin-and-fat tis
sue samples taken from a pig. Just where did they get the pig fat for the experiment? I’m so glad you asked. Ordinarily, laboratories order their supplies from specialty outlets that cater to the tightly controlled specifications of the lab in question. In this case, for some reason, the shipping company refused to transport the pig fat the J-Lab scientists had originally ordered.

  Nobody wanted to cancel the experiment, so they paid a visit to a local pig farmer. They purchased a single pig, and asked the farmer not to wash it down with vinegar—the usual custom—because vinegar would react badly with the laser. The farmer shrugged, did as he was told, and the pig met its fate. The scientists picked out a few prime pieces of pig fat and gave the rest of the pig back to the farmer. Not only did the farmer get a lot of free pork that day, he no doubt still regales his friends with the tale of those crazy scientists who paid full pig price for a few pieces of lard.

  That pig died so that we might one day zap away our deposits of unsightly cellulite. But before you throw caution to the winds and order a second helping of panang curry, or an extra-large blueberry muffin with that grande mochaccino, let me emphasize that the J-Lab experiment was merely proof of concept. We are nowhere near the point where we can indulge our food cravings and burn the resulting fat away whenever we like. Operating an FEL is expensive, as is the capital expenditure required to build one. Nor is scheduling beam time at the facility as easy as scheduling an appointment with your local liposuctionist. Commercial development of any new technology takes a great deal of time and money before it can be successfully brought to market.

  We are still looking for that magic bullet for effortless weight loss. It would be wonderful to lose weight with no muss or fuss; no need to obsessively write down in a food diary the caloric content of every morsel of food that passes one’s lips; no need for specially prepared meals or supplements, elaborately orchestrated food combinations, or those telltale minute surgical scars from conventional liposuction. But there is simply no substitute for the old-fashioned method of combining a sensible diet with regular exercise to burn more calories than you consume. I guess you could call this the Thermodynamics Diet, and it has a distinct advantage over competing fad diets: It has withstood the test of time.