Nonsense. They aren't more complex at all. They certainly haven't taken over the world in any meaningful sense.

They have. Computers have made travel into space possible. Without them it's impossible.
Millions - more than a billion, probably 2 - of people work at computers daily. The rest of the world wants enough wealth to come to that point too. Computers(in a broader sense, but still) increased efficiency of every singe machine, any device existing. As soon as you're dealing with chips, you're dealing with computers. But even in a more narrow sense - the home pc, computers have taken over the world. With them came the internet, which is the second most important invention/development in the 20th/21st century. blah bla, you get the point.
All that happened in a couple of years.
And btw, of course there are other important things for humans as well, but our large scale development in research, daily life and the financial market is fully determined by computers, in the sense that it is software on computers and their functioning that actually keeps *society* going. The fact that we live how we live is because there are computers - whether you appreciate them or not. Not supermarkets, although they do play an important role in distributing food to large urban areas, nor teaspoons.
The difference is, they don't offer such possibilites. And: people don't need teaspoons to survive, they are a cultural phenomenon. You don't need the supermarkets, you need the food.
But you need the computer.
Writing a program to replicate a piano [or at least, given the typical way we have of processing audio, a recording of a piano] and writing software to play a score, is no more significant than someone sitting down at a piano, learning the piece and playing it.
The computer is just a tool and if they amaze you with something they do, it's a human that did it..
But it's the computer which transforms it.
The creator is meaningless if the doer doesn't transform what is given to him. Complex mathematical equations and patterns are not just there because they have to exist, but to have a purpose. And so, not only are we amazed by humans who create the algorithms, but by the computer which gives them a purpose and transforms a meaningless and unnessecary equation on a piece of paper into a whole universe of diverse and nonlinear interactions - determined by an underlying pattern. Creator and doer depend on each other and cannot be anything else than equally important, because you can't have one without the other.
So no surprise that there are similarities between humans and computers, such as that both are created (difficult statement, but hope you get the point

), both work within the parameters of their existence and both have a mathematically describable physical representation (i.e. 0 and 1 on points of physical memory and a number of electronic signals in the brain), but seem to be more than that in the sense that a computer works with zeros and ones, but look whats coming out of your monitor, and in the same way you are more than a bunch of electronic signals, aren't you?
And you see people's reactions, they see that despite a human being behind it what computers can do and it is foreseeable that there's a thin line between a robot and a human, and surely people will be extremely irritated when a generation of computers with such ai comes out, that it can interact with humans in such a way that a human starts to have emotions with a computer, in the same way people have emotional relations with a dog or a turtle oO Such thing as "absolute" doesn't exist, if just something pseudo-meaningful comes out of the computer it's sufficient for humans.
It's not so far off to expect that with a sufficiently complex algorithm, computers can approximate human (behaviour, speech, actions, etc), just like mathematics and science in general approximates universal reality. I'm not looking far into the future, or speculating, just keep the eyes open a little bit and look what they're doing today in AI and computer technology research and you see where it's going.
If you break a computer down to the smallest part, 0 and 1, this represents a decision - free will. Since that is undescribable for mathematics, patterns are created to approximate it. My belief is that the same applies to human reality, and therefore computers are a small scale model for the evolution of humans and ultimately the universe.
but not because they have more RAM in their PC.
As i said, algorithms lose their purpose if not tested (and transformed) by a computer, and without a computer quite a number of algorithms would not have come into existence (for whatever reasons - calculations needed to determine the aglorithm, testing, the mere fact that they are only for the computer).
I know not quite ontopic, but was necessary to make 2 points: Computers can approximate humans and can therefore play music. Will do one day, for reasons stated above.
Computers are not humans. But it definately is part of the subject to think about where to draw the line, when differences, through approximation, become so small that you cannot tell one from the other. Then what exactly is creativity, emotions - playing the piano?
Imo, merely a thought, an idea.