## CARBON CALCULATION

In “The Last Resort,” Richard Conniff states that “our cars each typically emit 4.6 [metric tons, or about five U.S. short tons] of carbon dioxide a year.” I would appreciate an explanation as to how this figure was derived. Assuming an average vehicle is 4,000 pounds, I find it hard to believe that in a given year, an automobile produces more than twice its weight in carbon dioxide.

For example, if a car drives an average of 10,000 miles a year and gets 20 miles per gallon, it will consume 500 gallons of gasoline in a year. Gasoline weighs around six pounds per gallon, so if the assertion from the article is correct, that means burning 3,000 pounds of gasoline would produce more than three times its weight in CO2.

JOHN CARDWELL Supply, N.C.

CONNIFF REPLIES: Cardwell’s question brings up one of the facts about greenhouse gas emissions that I found hardest to fathom when I first encountered it: although a gallon of gasoline is indeed six pounds, we put more than 19 pounds of CO2 into the atmosphere for every gallon that our cars burn (not counting additional emissions released by manufacturing and transporting the fuel to market). How could that be?

Gasoline is nearly 90 percent carbon. And through combustion, nearly every carbon atom in the gas combines with two oxygen atoms. Oxygen is 1.33 times heavier than carbon. Thus, for six pounds of gas, more than five pounds of carbon combines with around 14 pounds of oxygen. The Environmental Protection Agency arrived at the figure for a vehicle’s annual emissions by assuming the average car has a fuel economy of about 22 miles per gallon and drives about 11,500 miles each year. That adds up to about 523 gallons and produces a dismaying annual total of more than 10,000 pounds, or about 4.6 metric tons, of CO2.

## FIT INHERITANCE

“Evolved to Exercise,” by Herman Pontzer, discusses research showing that over two million years human physiology adapted for a high level of physical activity.

I wondered if there is a relation between our past of body exertion and our hairlessness relative to great apes. Humans can sweat copiously to maintain coolness, which must be done during bouts of prolonged exercise. I would think that sweating would not be nearly as effective soaking through a thick coat of fur. My take is that as we evolved to undergo increasing exertion under a hot sun, we concomitantly lost more and more body hair.

BARRY SILER Loveland, Colo.

Pontzer states that “our taking fewer than 10,000 daily steps is associated with increased risk of cardiovascular and metabolic disease.” That so-called benchmark value of 10,000 steps a day gained popularity in the media mostly because it simplifies matters, and it can be traced back to a marketing slogan for a Japanese pedometer decades ago. Three recent studies, in which I was not involved, reviewed existing evidence for benchmarks in human physical activity, finding large differences between needs for daily activity among children, adolescents, adults and older people, and those with chronic diseases.

I understand the need to be concise in a magazine article. But reproducing a one-size-fits-all benchmark number for all groups in the population, which is not based on scientific research, could possibly be damaging to public health.

ARNO MAETENS Doctoral researcher in social health sciences, Vrije University Brussels

PONTZER REPLIES: Regarding Siler’s suggestion: Skin doesn’t fossilize, but most paleontologists would agree that hairlessness and sweating likely evolved along with increased physical activity early in the genus Homo. Humans are the sweatiest animals on the planet, and our ability to stay cool allows us to keep going in conditions that make other mammals melt.

The 10,000 steps per day benchmark widely used in public health is a nice, round number that’s easily remembered, but Maetens is quite right that it’s not necessarily the best fit for all populations. Children should be getting more than that (11,000 to 15,000 is a good goal), while older people and those with limited mobility can aim for less. The good news for anyone anxious about the perfect number of steps for them is that more is almost always better. Barring any health conditions that are aggravated by exercise, there’s no evidence that too much walking is ever bad for you, regardless of what my kids say when we’re out hiking.

## UNOBSTRUCTED PAIN

“What Ails a Woman’s Heart,” by Claudia Wallis [The Science of Health], discusses research by cardiologist C. Noel Bairey Merz and others on INOCA (ischemia and no obstructive coronary artery disease), a condition in which patients without blocked arteries nonetheless experience poor blood flow through the heart.

If ischemic chest pain can be caused by peripheral vascular dysfunction, as the article describes, can’t that also happen in people in whom testing shows them to have some coronary artery stenosis (blockage or narrowing of the arteries)? In those cases, perhaps the stenosis is a red herring, and coronary artery bypass grafting is the wrong treatment. That could explain some of the patients who don’t fare well after bypass surgery.

STEVE WISE Charlotte, N.C.

BAIREY MERZ REPLIES: Wise makes a good point. Recent evidence from the ORBITA trial demonstrates that angina is not improved by stenting, suggesting that ischemia symptoms may, in fact, more often be caused by coronary microvascular dysfunction.

## TRICK OR FEAT

In “The Particle Code,” Matthew von Hippel consistently refers to mathematician Alexander B. Goncharov’s observation that mathematical period theory can be used to simplify loop computations in particle physics as a “trick.” But that observation shows such computations can be decomposed into an alphabet of simpler functions, which can be assembled only according to a simple grammar. That seems quite profound to me. Could the alphabet and the grammar correspond to some underlying structure in particle theory?

DOUG HOOVER Sunnyvale, Calif.

VON HIPPEL REPLIES: There may well be a deeper meaning to the kinds of “alphabets” that appear in particle physics calculations. Physicists suspect they are related to a result of Nobel laureate Lev Landau, called the Landau equations. But this is still not fully understood.

## ERRATUM

In “The Particle Code,” by Matthew von Hippel, the lower graph in the box showing “Euler’s formula visualized as a circle, then projected through time” inaccurately represented the curve for cosine (x). The corrected illustration can be seen at www.scientificamerican.com/eulers-formula-projected