Complexity. It sounds very sciency, doesn’t it. Everyone loves to talk about complex

problems and complex systems, but no one has any idea what it means. I think that

understanding complexity is THE biggest gap in science today. What do we even mean

by complexity? What do we know about it? And what’s the problem with trying to explain it?

That’s what we’ll talk about today. Before we talk about complexity,

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How complex do you think these objects are: a rock, a clockwork, a baby. I am guessing most

of you would rate the baby the most complex, the clockwork somewhere in the middle, and the

rock the least complex. Unless possibly you’re a geologist working on a grant proposal, in which

case you probably shouldn’t be watching YouTube. But why? I mean, babies aren’t all that difficult,

are they? Stuff goes in one end and comes out the other, and for the first couple of months that’s

pretty much it. Ok, you might say, but they grow, they learn to speak, they go on and win Nobel

prizes, sometimes. Clockworks don’t do that. The baby’s more complex not because of what it does,

but what it could go on to do. How can we possibly scientifically capture a property like that?

Maybe let’s start with a simpler example. Coffee. Or, if you’re British, imagine it’s tea. And we

pour milk into it. Initially you have the coffee and milk separated. That’s very orderly, very

non-complex. Then you mix them together and well some complex things happen. Then it’s completely

mixed and that’s maximum entropy and non-orderly again. So complexity is somewhere in the middle

between the two, between strict order and maximum disorder, between very low and very high entropy.

This isn’t just the case for latte, it’s also the case for the entire universe. The universe started

out in a very orderly state, with energy and matter smoothly distributed in space. Smoothly,

but not perfectly smoothly, with some tiny quantum fluctuations in it. Then universe began to expand,

and gravity did its thing. The places where matter and energy were a little more dense,

collapsed, and heated up. They went on to form stars and then galaxies and galaxy clusters.

And some of those stars got planets and on at least one of those planets, life evolved.

Yet as time goes on, entropy continues to increase. The stars will burn out,

the universe will cool, and life will no longer be possible. Complexity,

life, society, technology, is only possible in this intermediate phase,

between order and disorder, between low and high entropy. The difficulty is making

this intuition scientifically precise. And so far, no one’s come up with a convincing idea.