Your Next Computer
Computers don´t always have to be digital. There are many models of classical computation that are not digital.
There are mechanical computers like the Abacus, the old rotary Curta-type calculators, and the one that is perhaps the most famous in history, the Babbage's difference engine.
We can also have optical computers that are made out of information carriers, which are photons, and not electrons, or biological computers, concept that is getting popular again due to the notion of deep learning and network of neurons that act as computation.
There are also a great number of conceptual models of computers, which do not realize computations today, like the Turing machine or the cellular automata.
We also have the conceptual model of DNA based computation, where you have strands of bases AGCT which has been shown to allow a kind of computation christened as DNA-computation.
In many ways, we are at the end of the road of silicon today. We cannot rely on Moore's Law much longer to provide an increasing scaling that is exponential of capability and size and power and weight to build our computers.
We need to look at different physical mechanisms to build computation. And that's why all of these different approaches where you represent information in different ways is so appealing to think about because maybe the next thing, beyond silicon, could be something different, that utilizes these ideas.
And maybe what we might discover is that it's already happening all around us, or within us, if we only know how to think about it in the right way.
Quantum computation is also a very promising way to overcome the end of the silicon era, but the broader view is to understand the physics of computation and think about how we can use physical and biological mechanisms, that exist today, to do computation. For example, how CRISPR/Cas9 may change the opportunities of what´s available for DNA computing.
Lots of things are changing in this avenue, and people don't normally think about it with their glasses of computation on as they should.
(*) based on Prof. Isaac Chuang, “Physical and conceptual models of classical computation” lecture at the “Quantum Information Science” edX MIT course