What should I make my computer do while I'm away from keyboard? [duplicate]

Yes, there is. There are quite a few projects that use idle computers for scientific research, the most famous (at least the ones I know) are:

• SETI@home:

  SETI@home is a scientific experiment that uses Internet-connected computers in the Search for Extraterrestrial Intelligence (SETI). You can participate by running a free program that downloads and analyzes radio telescope data.

• Folding@home:

  Help Stanford University scientists studying Alzheimer's, Huntington's, Parkinson's, and many cancers by simply running a piece of software on your computer.

  The problems we are trying to solve require so many calculations, we ask people to donate their unused computer power to crunch some of the numbers.

If you're only interested in administrative tasks, you could lso consider running things like updatedb to refresh locate's database.

Wikipedia has a list of distributed computing projects that you could contribute to.

You could also "mine" bitcoin, although I'm not sure how much money you'd net after paying for electricity.

I personally think this is a beautiful question.

I myself run Folding@home some nights on my machine, although I have a very old PC. If you have a good set of hardware equipments, you might want to try it too. It is basically a distributed computing project, trying to find cures for some kinds of cancers.

I found them one night, when I was thinking about: "Would we be able to build the strongest supercomputer in the world, by uniting all the seemingly small PCs and smartphones, and then let the users use this power on a shared basis. Like when you want to do some processing and need a powerful CPU, well, you can use this huge network of CPUs." Then I googled for "Shared computing", and I was directed to this Wikipedia article. In there you can find a huge list of such projects that you could and might possibly want to devote your computing power to.