[evan_au (OP)]

On a recent Naked Genetics podcast, an interviewee repeated the common assertion that "The most complex object in the universe is the human brain.".

Perhaps this originated with the comment from Michio Kaku that  "The human brain has 100 billion neurons, each neuron connected to 10 thousand other neurons. Sitting on your shoulders is the most complicated object in the known universe."

But, surely:

• A whale brain would have a similar density of neurones as a human brain, and is physically larger, so wouldn't that make a whale brain more complex than a human brain?
  
• A human contains a human brain, so wouldn't that make a human more complex than a human brain?
  
• The Earth carries many humans and whales, so wouldn't that make the Earth's ecosystem more complex than the human brain?
  
• The universe holds many planets, stars and other objects (including the Earth), so wouldn't "The most complex object in the known Universe" be "The Universe"?

[jccc]

The universe is in your head. Otherwise, where is it?

[alancalverd]

The universe is in your head. Otherwise, where is it?

Everywhere, by definition.

The problem is that we have no definition of complexity. If anything, the fact that we can map some of the connections in the human brain and they seem to be fairly consistent over time, makes it a lot less complex than a jar of gas where we understand the interactions between any two molecules but cannot predict the position of any one for more than a picosecond.   

[Bored chemist]

We have no suitable definition of complexity and also no real definition of object.
Is "the internet and all the human brains working with it" an object?.
If so, it's more complicated that any brain by a handful of orders of magnitude.
On the other hand, is "the human brain" an object, given that it is known to be made of interconnected module?

[CliffordK]

There are some computer programs that take hundreds, or perhaps thousands of man-years to write, and we all know how much trouble some computer software companies have getting them right the first time.  No doubt something like the Space Shuttle is a quite a feat of engineering.

A lot of this is Earth-Centric.  At this point, we don't know if there are any living organisms as complex as an amoeba living elsewhere.  However, if ameoba-like organisms are quite common as some people believe, then it is quite possible that Earth-life is quite mundane compared to what is found elsewhere in the universe.