Kind: captions
Language: en
[Applause]
[Music]
I've been driving along Australia's
famous Great Ocean Road
and I'm stopped here near the 12
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 coastline? Well, if you were
to measure it out in lengths of 500 km,
you would find that it's about 12,000 km
long. But the CIA World Fact Book puts
the figure at more than double that,
over 25,700
km. 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'll 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 a 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 cotch
snowflake. So what you do is you take a
triangle with sides of length one and
then on each side add another triangle
with sides of length a third. Continue
doing that again and again forever. And
what you end up with is a shape which
has a finite area but an infinite
perimeter.
Shapes like these are called fractals.
And many coastlines have this 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.