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• I've been driving along Australia's famous Great Ocean Road.

• And I'm stopped here near the Twelve Apostles, which are these big sandstone bluffs.

• Actually, there's only eight of them left because the others have eroded over time.

• And erosion is really what's given us this coastline the way it looks now.

• So that brings to mind a question for me.

• Which is "How long is the Australian coast line?"

• Well, if you were to measure it out in lengths of 500 kilometers,

• You would find that it's about 12 and a half thousand kilometers long.

• But the CIA World Factbook puts the figure at more than double that. Over 25,700 kilometers.

• But how can it be that we have two different estimates for the length of the same coastline?

• Well this is called "The Coastline Paradox."

• The answer is, it depends on the length of measuring stick that you use.

• So, if you connect up the dots from cliff to cliff to cliff

• You get a shorter length of coastline than if you measure with a smaller measuring stick

• And measure into every inlet.

• So what length of measuring stick should we use?

• Well in theory, you can go all the way down to the size of a water molecule

• And if you do that, then the length of Australia's coast is virtually infinite.

• Do you believe me that you could have finite area object like Australia bounded by an infinite perimeter?

• It doesn't seem to make sense.

• But I can give you another example of this, it's called the Koch snowflake

• so what you do is you take a triangle with sides of length 1

• and then on each side

• add another triangle with sides of length a third

• Continute doing that again and again forever

• What you end up with is a shape which is a finite area but an infinite perimeter

• shapes like these are called fractals and many coastlines have the same

• fractal structure which means they have some sort of self-similarity on many

• different scales so you can zoom in and zoom in

• and the coastline looks roughly the same

• so if you want to know the length of a coastline you need to first specify the

• length of your measuring stick

• because that's what the answer depends on.

I've been driving along Australia's famous Great Ocean Road.

B2 中上級

# 海岸線のパラドックスとは？ (What Is The Coastline Paradox?)

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林宜悉 に公開 2021 年 01 月 14 日