Doesn't it depend on how much and the type of exercise one gets? Mr. M doesn't watch his calories, but maintains his weight by running 30-40 miles per week. He soon will begin training in earnest for the Boston Marathon and will drop a few pounds.
I hate to use a hackneyed expression, but a person who is training for marathons is the exception that proves the rule. The marathoner is getting a freakish amount of exercise--so much that it would literally kill a lot of overweight people.
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The AMA used to say "Burn the fats off at the gym in the flame of complex carbohydrates." This was still being taught in medical schools in the 1990s and maybe even later. But it is actually a preposterous oversimplification of the biochemistry of carbohydrates and of fats as well (as Dr. Barry Sears, a PhD physiologist, explained in his famous book
Enter the Zone).
I have known overweight patients who religiously followed the (old?) AMA advice and got even fatter. The problem is that the so-called "complex carbs" are starches that are converted into sugar in the GI tract almost as soon as they hit the small intestine. Moreover, this sugar is one of the most quickly
absorbed nutrients, and it rushes into the bloodstream and raises the blood sugar levels pretty drastically. Even a momentary elevation of the blood sugar concentration triggers the patient's pancreas to secrete insulin into the blood stream to quickly bring down the blood sugar concentration--and, unfortunately for the poor weight loss patient, one of the two main things the insulin does with the excess blood sugar is to make fat out of it. And once that sugar is turned into fat, it is exceedingly difficult to burn it off in the gym--because the calorie burn rate is not high enough to do much good. It takes a huge calorie deficit (exercise-plus-basal expenditure minus dietary calorie intake) of 4000 cals (if I recall the numbers correctly) to burn off a single pound of fat. That's way more than the total daily calorie intake of most folks--so, even if daily exercise could keep up with carbs, it is a pretty bad mistake to encourage the patient to gorge himself at the potato bar at lunch ("however much you like") and tell him to go to the gym four hours later. (Timing is also a big deal in weight loss, by the way.)
To make the whole mess even weirder, there are many situations in which exercise will trigger the burning of muscle protein instead of fat (not a good thing!). It turns out that we are designed to hang on to our fat for starvation times, even more so as we get older. (This reluctance of our bodies to mobilize our fat for energy is called the
girding reflex.)
In short, the most important feature of a good weight loss program is the almost complete elimination of sugar (certain fruits excepted, but very few--and certainly no fruit juice, no bananas, and no watermelon) along with the rather severe curtailment of starchy foods (potatoes, pasta, rice, bread, corn, etc.). Exercise, although important for several reasons, is definitely secondary in importance.
BTW, it's a good idea to be under the care of a knowledgeable physician to do a serious weight loss program, because there are other health issues beyond what I have mentioned. For example, kidney function can be compromised if the diet is too high in protein (a potential problem for some folks, especially diabetics, who try the Atkins Diet, by the way); also severe diets may also cause inadvertent deficits of vitamins, minerals, etc.; another problem is that a severe diet, one restricting the overall array of nutritious foods, tends to cause food intolerances ("allergies") in some patients by over-exposing the GI tract to the same foods over and over and over.
There are other issues of weight management that really good docs will know about, but most docs don't get a lot of training on nutrition (or food intolerances, either, for that matter) in medical school, in my opinion. I believe the schooling of doctors is getting better over time, but it takes a long time for the medical establishment to come around on some of these things. Back in the 1980s, Dr. Sears even said that if you want to figure out the best diet for a diabetic, look up the dietary recommendations of the American Diabetic Association--and do the opposite.