My phone can listen to what I say, translate it into French, and speak it back to me, albeit leveraging external compute power to do most of the heavy lifting. But it wouldn't be possible to provide that external compute power at scale 20 years ago.

I'm also sure that countless small innovations in bioinformatics add up collectively to significant changes over time, and those individual innovations are powered by the more broadly available increases in computing power.

We've also gotten the ability to do much better fluid dynamics modeling, astrophysics simulations (whether you believe them or not), climate models (likewise). I've made use of the processing power we have now to do a bunch of "experimentation" in representation theory, though that's not obvious from the resulting writeup, which is more or less algebraic proof.

In general, for a lot of research areas where we think we have a decent model of some of the things that are going on more computing power means more ability to use a computer to look for things to actually try in the lab (and thus refine the model) as well as more ability to collect and handle data.

And then there's the mundane bits, like being able to find existing work more easily, being able to typeset and disseminate your papers more easily and so forth.

Quantum computation as been explored but as yet we don't have a computer capable of executing the quantum algorithms.

That aside, all I'm saying is that exponential growth has a limit. That growth could be measured in MIPS or in algorithm performance, it doesn't really matter, but I don't think that growth will continue exponentially.

They're in their infancy, but we've already had a quantum computer factor 15. http://www.spectrum.ieee.org/computing/hardware/chip-does-pa...