Exponential growth is typically limited in some way, so that it becomes "S"-shaped, i.e., it approaches an asymptote. Such trends follow the differential equation: dN/dt = k•N•(1-L/N), so as N approaches the limit, L, the factor (1-L/N) approaches zero, thereby stopping the exponential component's influence in the simpler equation dN/dt = k•N, whose solution was exponential. The "S"-shaped curve is pervasive in technological change, and to use simple exponentials is to argue that there are no limits to growth.

What does this mean? Anything rational? Risk vs. Gamble? Gamble here means taking a very large risk past a certain threshhold? Since this guy is a grad student in journalism, I think he should be held to a high standard in terms of lanugage use.

"In his closing arguments last week, the prosecutor, Charles Testagrossa, said, “We ask the police to risk their lives to protect ours.” I agree. But they shouldn’t have to gamble with them.

Kyle K. Murphy, a former lieutenant in the New York Police Department, is a graduate student in journalism at Columbia."

Exponential growth is typically limited in some way, so that it becomes "S"-shaped, i.e., it approaches an asymptote. Such trends follow the differential equation: dN/dt = k•N•(1-L/N), so as N approaches the limit, L, the factor (1-L/N) approaches zero, thereby stopping the exponential component's influence in the simpler equation dN/dt = k•N, whose solution was exponential. The "S"-shaped curve is pervasive in technological change, and to use simple exponentials is to argue that there are no limits to growth.

A good rule of thumb is: All trends have limits.

What does this mean? Anything rational? Risk vs. Gamble? Gamble here means taking a very large risk past a certain threshhold? Since this guy is a grad student in journalism, I think he should be held to a high standard in terms of lanugage use.

http://www.nytimes.com/2008...

"In his closing arguments last week, the prosecutor, Charles Testagrossa, said, “We ask the police to risk their lives to protect ours.” I agree. But they shouldn’t have to gamble with them.

Kyle K. Murphy, a former lieutenant in the New York Police Department, is a graduate student in journalism at Columbia."