CHAPTER 6:  EMERGING PROPERTIES: MORE IS DIFFERENT

”MORE IS DIFFERENT”，再多一點點就會造成不同，再堅持一下下就會扭轉整個局面！這句話可是有數學根據的。


Crowd behavior is much more predictable than the behavior of any individual.   

群眾的行為是有模式的，比較好估計。各人的和單一的行為卻是不可估的！

This fact applies equally to inanimate objects.  

作者居然用inanimate這個字眼來形容：死的物體（無氣息的、不會動的）

Toss a coin, and you cannot predict whether it will come up heads or tails; no matter how many times you toss it, the probability of it coming up heads or tails remains fifty-fifty.  However, if you toss a coin a million times, you can be certain it will come up tails roughly 500,000 times.  While no gambling establishment can predict which number will come up on a single roll of dice, they can predict with some confidence the outcome of a great many rolls—that’s how they make their profit.

連我都快去開賭場了，不是當睹客喔，是當「場長」，歡迎光臨。 

In a sense, all the patterns of nature, from flowering trees to ocean swells, from mountains to koala bears, are the emergent properties of simple interactions between subatomic particles that over time add up to far more than the sum of their parts.

Time may well be the ultimate emergent property.  A single particle can go backward or forward in space or time—it makes no difference—and there’s no clear way to tell which is which.  The only time that exists is the atom’s own internal clock—the frequency at which it vibrates.  But put a bunch of atoms together, and no one has any problem telling which way time flows: It’s always in the direction of disorder. Left to their own devices, food rots, skin wrinkles, paint peels, mountains erode, stockings run.   And yet, there is not hint of this large-scale headlong rush toward disorder within any single atom alone. 

In one sense, “more is different” is the mathematical version of the old saying about the straw that breaks the camel’s back.  At some point, more changes everything(64).

{This change can be negative or positive following the “tipping point.”]

What this means for public policy, Gladwell says, is that we shouldn’t jump to conclusions about the effectiveness or failure of social policies without taking the tipping point into account.  We shouldn’t conclude, say, that the welfare system doesn’t help people get out of poverty because it hasn’t accomplished that goal yet.  We shouldn’t conclude that money spent on inner city schools is wasted because it hasn’t shown results compared to money put in.  It could be that we simply haven’t yet reached the tipping point.

THE MATHEMATICS OF PREDICTION:  CHAPTER 7

The Galileo spacecraft cruised the solar system for six long years before arriving at the giant planet Jupiter in December 1995—the final destination of a 2.3-billion – mile journey that looped twice around the earth and once around Venus.

It was a very tricky maneuver.  The probe’s entry had to be as precise as a hypodermic needle slipping in beneath the skin.  If the entry angle was too shallow, the probe would bounce off the planet’s atmosphere like a stone skipping from the surface of a pond; too deep, and it would be destroyed before it could phone home any information.

As the world now knows, on December 7, at exactly 5:06 P.M. Pacific time, precisely as planned, the tiny probe dove through Jupiter’s pastel-colored clouds cleanly enough to earn it an Olympic gold. Despite the duration [6 years] and distance [2.3 billion miles], its aim on arrival was picture-perfect.

This is the kind of spectacular success that leads people to believe science is good at predicting just about anything: the next earthquake, the next cancer victim, the next stock market crash, the global climate twenty or two hundred years from now.

連二十年都無法估計，更何況兩百年。

But prediction is neither the goal nor the forte of science.  If truth be told, the physicists can’t even perfectly predict where a Ping-Pong ball will bounce on the other side of the table (69).

The kind of prediction science does so well might better be described as pattern perception.  Galileo got to its target not by predicting the future, but by following well-known patterns to their logical conclusions.  Objects in motion follow well-understood paths as they coast and fall and loop around bodies in space.  If you know the patterns, it becomes a matter of mere calculation to get Galileo to Jupiter on target (72).

Prediction, said physicist Frank Oppenheimer, “is dependent only on the assumption that observed patterns will be repeated.  The merchant, the politician, the parent, the artist, and the doctor all depend for their success on the subtleties of pattern recognition. . . . The predictions of the physicists, the psychologist, or the economist in no way set them apart from the rest of humanity” (74).

In these cases, researchers trying to predict the future trends often rely on a technique called curve fitting I which a mathematical function is found that describes an existing pattern. 

The problem is, the same curve can be described by very different equations.  Author and physiologist Robert Root-Berstein has described the dangers of over reliance on this technique of curve fitting as a way to extrapolate into the future, and he points to some notable failures—for example, in predictions about the spread of AIDS or the threat of global warming.  Just twenty years ago, he points out, articles in science journals warned of a coming ice age and the potential for galloping glaciers (75).  

He argues instead that we first need a deeper understanding of the basic phenomena involved; that we need to learn much more abut climate and disease and population before we can sensibly begin to predict the future.  Predictions based on extrapolation can’t be any more accurate than the models we begin with.  The Galileo spacecraft fount its way to Jupiter right on target because celestial dynamics are well understood. The same cannot be said of many other sciences .

Encoded into physics is the Heisenberg uncertainty principle, this weird fuzziness of the subatomic realm seems to put a natural limit on what we can know.  . . . A simple prediction such as where a particular drop of water will fall as it crashes over Niagara Falls is beyond our capabilities.  It simply requires too much information (76).

Consider the information required to predict the trajectory of a ball batted into right field by a baseball player.  For openers, you would need precise information about the velocity and spin of the ball, the elasticity of the materials, the interaction of surfaces, the weight and structure of the batter’s hands, not to mention winds, temperature, humidity, and so forth.  Newton’s laws are simple enough, but the ingredients added by reality make the problem overwhelmingly complex.  Plus, someone could throw a popcorn box at the ball, or a bird could fly into its path (76).

The same tangle obscures the exact origin of many health problems, for example, why one person gets cancer and another doesn’t.  Genetics, environment, and behavior all interact in ways too complicated—at least for now—to sort out (78).

According to Ivar Ekeland in the Broken Dice, “If we want to know what the weather will be like one year from today, we have to take everything into account, from the butterflies flying in the Amazon jungles to the candles burning in churches”.

一年以後的天氣是不可預測的！