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  • For most of us, two degrees Celsius is a tiny difference in temperature,

  • not even enough to make you crack a window.

  • But scientists have warned that as CO2 levels in the atmosphere rise,

  • an increase in the Earth's temperature by even this amount

  • can lead to catastrophic effects all over the world.

  • How can such a small measurable change in one factor

  • lead to massive and unpredictable changes in other factors?

  • The answer lies in the concept of a mathematical tipping point,

  • which we can understand through the familiar game of billiards.

  • The basic rule of billiard motion is

  • that a ball will go straight until it hits a wall,

  • then bounce off at an angle equal to its incoming angle.

  • For simplicity's sake, we'll assume that there is no friction,

  • so balls can keep moving indefinitely.

  • And to simplify the situation further,

  • let's look at what happens with only one ball on a perfectly circular table.

  • As the ball is struck and begins to move according to the rules,

  • it follows a neat star-shaped pattern.

  • If we start the ball at different locations,

  • or strike it at different angles, some details of the pattern change,

  • but its overall form remains the same.

  • With a few test runs, and some basic mathematical modeling,

  • we can even predict a ball's path before it starts moving,

  • simply based on its starting conditions.

  • But what would happen if we made a minor change

  • in the table's shape by pulling it apart a bit,

  • and inserting two small straight edges along the top and bottom?

  • We can see that as the ball bounces off the flat sides,

  • it begins to move all over the table.

  • The ball is still obeying the same rules of billiard motion,

  • but the resulting movement no longer follows any recognizable pattern.

  • With only a small change to the constraints

  • under which the system operates,

  • we have shifted the billiard motion

  • from behaving in a stable and predictable fashion,

  • to fluctuating wildly,

  • thus creating what mathematicians call chaotic motion.

  • Inserting the straight edges into the table acts as a tipping point,

  • switching the systems behavior from one type of behavior (regular),

  • to another type of behavior (chaotic).

  • So what implications does this simple example have for the much more complicated

  • reality of the Earth's climate?

  • We can think of the shape of the table as being analogous to the CO2 level

  • and Earth's average temperature:

  • Constraints that impact the system's performance

  • in the form of the ball's motion or the climate's behavior.

  • During the past 10,000 years,

  • the fairly constant CO2 atmospheric concentration of

  • 270 parts per million kept the climate within a self-stabilizing pattern,

  • fairly regular and hospitable to human life.

  • But with CO2 levels now at 400 parts per million,

  • and predicted to rise to between 500 and 800 parts per million

  • over the coming century, we may reach a tipping point where

  • even a small additional change in the global average temperature

  • would have the same effect as changing the shape of the table,

  • leading to a dangerous shift in the climate's behavior,

  • with more extreme and intense weather events,

  • less predictability, and most importantly, less hospitably to human life.

  • The hypothetical models that mathematicians study in detail

  • may not always look like actual situations,

  • but they can provide a framework and a way of thinking

  • that can be applied to help understand the more complex problems of the real world.

  • In this case, understanding how slight changes

  • in the constraints impacting a system can have massive impacts

  • gives us a greater appreciation for predicting the dangers

  • that we cannot immediately perceive with our own senses.

  • Because once the results do become visible, it may already be too late.

For most of us, two degrees Celsius is a tiny difference in temperature,

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B1 TED-Ed ball tipping point co2 tipping climate

【TED-Ed】Is our climate headed for a mathematical tipping point? - Victor J. Donnay

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    稲葉白兎 posted on 2015/07/09
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