The Calculus Diaries - Jennifer Ouellette [76]
The calories we consume are only part of the equation. At the same time, we routinely overestimate how many calories we burn when we exercise. The caloric numbers reported by the displays on exercise equipment feed into this misconception, because they are not always accurate, partly because they are often incorrectly calibrated and partly because when it comes to human metabolism, one size does not fit all. New York Times reporter Gina Kolata, author of Rethinking Thin, reported that while a given activity might burn an average of 100 calories per hour, for example, the range for different people could be as low as 70 or as high as 130.
Bad habits can also affect the total of calories burned. Are you one of those people who hang on to the bars while on the treadmill? You burn 40 to 50 percent fewer calories for that same activity. Do you do the same exercise routine for months at a time? As your body grows accustomed to that effort, it will need fewer calories to perform that routine. And most of the calculations used to determine the number of calories burned for various activities fail to subtract the number of calories the exerciser would be using even if they were simply sitting at home reading or watching TV.
“For moderate exercise, the type most people do, subtracting the resting metabolic rate can eliminate as much as 30 percent of the calories you think you used,” Kolata writes. Even those supposedly adept at math can fall victim to self-delusion in this area. Kolata tells the story of meeting a mathematician at a conference who figured he could indulge in a slice of pie because he’d just run a quarter of a mile. “At 100 calories a mile, he might have burned 25 calories. . . . A piece of pie could easily contain 400 calories.”
Personally, I adhere to the Thermodynamics Diet. The primary objective is to optimize two variables, diet and exercise, to ensure either that your weight remains constant (for maintenance) or that you steadily burn more calories than you consume so as to lose weight gradually. You don’t need calculus for that, just basic arithmetic. But if it really were that simple, everyone would be slim.
First, there are economic factors at play with regard to diet: The harsh reality is that healthier foods actually cost more than junk food, so not everyone can afford a quality, well-balanced diet. Besides, some people really like pizza or French fries or a hot fudge sundae for dessert and would feel seriously deprived on a diet of lean protein, organic leafy greens, and whole grains. Surely quality of life must be factored into the equation as well. How do we find a balance?
Now calculus can be of service. In this case, we wish to maximize our “tastiness”: the pleasure we derive from our food intake, given a fixed number of calories we can consume per day and a fixed amount of money we can spend on groceries. To solve the conundrum, we can plot tastiness (designated by the variable y for “yummy”) as a function of diet, designated by f, for all the various foods we love that, taken together, comprise our diet. Given a diet restricted to 2,000 calories a day and a food budget of $40 per day, what small changes can we make among our current food items to maximize tastiness ( y) while staying within the boundaries imposed by those two constants?
For instance, we might love Snickers bars more than brown rice and carrot sticks, but if all we ate were Snickers bars, we would quickly exceed our caloric limit, and probably develop a vitamin deficiency in the bargain. Similarly, we might love the fresh organic mixed-greens salad with free-range chicken and a light vinaigrette available at our local health-food joint, but if that were all we ate, we would quickly exceed our food budget. So if we know what we’re eating each day now, what small change can we make in our diet to optimize how much we enjoy mealtimes?
This is a job for the derivative, with a twist. It is similar to the multivariable optimization problem we employed while house hunting, except