Even more fun, I learned from Bruce Schneier's blog post [1] that it takes a minimum 4.4E-16 ergs of energy for an ideal computer running at 4.4K to "flip a bit" in an ideal setting.

Wolfram says there are roughly 2E76 ergs of mass-energy in the universe. [2]

So even if all matter and energy in the universe were put together to power a computer that did nothing but count upwards from zero, there's only enough matter and energy in our universe for the computer to count to about 10^91, or roughly 2^304 [3]. That's not even counting trying to use each resulting set of bits for anything.

So I don't think we'd be able to design too many useful computers by flipping bits until a useful algorithm comes out (at least not in this universe.)

[1] https://www.schneier.com/blog/archives/2009/09/the_doghouse_...

[2] http://www.wolframalpha.com/input/?i=mass-energy+in+the+know...

[3] http://www.wolframalpha.com/input/?i=log2(mass-energy+of+the...)