“In general, we imagine rivers to be subject to a kind of dynamic equilibrium, largely stable geologic features, with processes like regional incision or subtle shifts in mountain building causing short- and medium-term variation around some slowly changing mean condition, but in fact it is far more common to see dramatic change over short periods, with long periods of stability between in what geologists refer to as 'dynamic metastable equilibrium.'It is the same with families, memory, the history of a person's life, what we believe to be true.”
“This is the cycle of a dynamic society. Equality is never a final state, democracy never a stable equilibrium: they are processes, they are struggles. Our task is now to recognize that that struggle is ours.”
“If we increase r [in a logistic map] even more, we will eventually force the system into a period-8 limit cycle, then a period-16 cycle, and so on. The amount that we have to increase r to get another period doubling gets smaller and smaller for each new bifurcation. This cascade of period doublings is reminiscent of the race between Achilles and the tortoise, in that an infinite number of bifurcations (or time steps in the race) can be confined to a local region of finite size. At a very special critical value, the dynamical system will fall into what is essentially an infinite-period limit cycle. This is chaos.”
“There are no coincidences in life. What person that wandered in and out of your life was there for some purpose, even if they caused you harm. Sometimes, it doesn’t make sense the short periods of time we get with people, or the outcomes from their choices. However, if you turn it over to God he promises that you will see the big picture in the hereafter. Nothing is too small to be a mistake.”
“As Paul Saffo, a forecaster of large-scale change at Discern Analytics, observes wisely, 'Change is never linear. Our expectations are linear, but new technologies come in S curves, so we routinely overestimate short-term change and underestimate long-term change.' Never mistake a clear view for a short distance, he adds.”
“Another thing is, people lose perspective. It is a cultural trait in America to think in terms of very short time periods. My advice is: learn history. Take responsibility for history. Recognise that sometimes things take a long time to change. If you look at your history in this country, you find that for most rights, people had to struggle. People in this era forget that and quite often think they are entitled, and are weary of struggling over any period of time”