# Where Does Complexity Come From? (Big Picture Ep. 3/5)

The universe as a whole evolves towards increasing entropy, or disorder -- a tendency physicists
call the Second Law of Thermodynamics.
This movement toward disorganization might lead you to think that organized structures
– like, say, living beings – would never spontaneously come into existence.
Of course entropy can go down in part of the universe -- you can trade a decrease in entropy
in one place (like cooling water so it crystallizes into ice) for an equal or larger increase
in entropy somewhere else (like heating the back of your fridge).
Order increases here, but only at the cost of decreasing order there.
But we can still ask: why do intricate, complex structures come into being in the universe,
if the overall tendency is toward increasing disorder?
The secret is that order and complexity are very different ideas.
Entropy measures how many different ways you can make an arrangement of small-scale particles
that have the same large-scale properties: like, 37 degrees celsius, brown hair, good
at soccer, and so on.
[There are lots of different ways!].
Complexity, on the other hand, is a measure of how hard it is to describe a set of large-scale
properties.
Simple systems are easy to describe; complex systems require a lot more information.
For example, take a cup filled with half coffee and half milk.
It starts off in a state with relatively low entropy – you could swap coffee molecules
with each other, or milk molecules with each other, without changing things substantially.
But if you swapped coffee molecules with milk molecules that would be a noticeable change.
It’s also a simple setup -- milk on top, coffee on the bottom.
Now, as the milk and coffee begin to mix, entropy goes up – where they are mixed together,
swapping some coffee molecules for milk molecules no longer makes much of a difference.
But the system also becomes more complex - to describe what you see, you would have to specify
exactly how all of those tendrils of milk and coffee intricately swirl into each other.
Continuing on, entropy keeps going up, until the milk and coffee are completely mixed together
and swapping any molecules of coffee and milk with any others doesn’t really make any
difference at all.
That’s equilibrium, where there are a huge number of arrangements of the molecules that
look essentially the same.
But this highly-mixed equilibrium is once again simple: it’s just a homogenous mixture
of coffee and milk; no more complicated fractal swirly stuff.
This general principle is borne out time and time again: while entropy increases, complexity
initially grows, then decays.
Complexity can be a natural step along the path to increasing entropy.
The best example is the universe itself.
The early universe was very smooth and very dense: that’s low-entropy, and also extremely simple.
The far future will be smooth again, but very dilute: that’s high-entropy, and again extremely simple.
It’s now, in the medium-entropy middle, that things look complex.
Stars and galaxies and veins of minerals in rock and swirling clouds and amino acids and
proteins and human beings and cats – we’re at the exciting, beautiful stage of the coffee
mixing!
But just as with the coffee and milk, in the far distant future complexity will decrease
again, and complicated stuff like us will at last be simplified out of existence.
Hey, Henry here, thanks for watching.
This is the third video in a series about time and entropy made in collaboration with
physicist Sean Carroll.
The series is supported with funding from Google’s Making and Science initiative,
which seeks to encourage more young people (and people of all ages) to learn about and
fall in love with science and the world around them, and the videos are based off of Sean’s
book “The Big Picture: On the Origins of Life, Meaning, and the Universe Itself,”
which you can find online or in bookstores around the world.