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The random number generator generator (or monkeys at typewriters) analogy is deeply flawed. The entire point of natural selection is that it is non-random.

Think instead of a stochastic optimization process that provides feedback at each iteration, and introduces psuedo-random noise that is seeded from the previous iteration.

To extend our metaphor to ridiculous lengths, consider instead of a room full of monkeys typing away randomly, you have a machine that punishes monkeys that type in the "wrong direction," and rewards monkeys type something that is approximately closer to War and Peace. After each reward/punishment round, the monkeys would start their editing on strings that were rewarded in the previous round. This process would be expected to converge much more quickly.

> An analogy I've heard is that if it's possible for (in your example) yeast to evolve into a cat given enough time, then it should also be possible for a room full of monkeys randomly mashing on keys to collectively type a perfect replica of War and Peace (or insert other long book here).

Replace the monkeys with a fair random number generator, and not only is it possible, but once you have defined the keys available and the output sought and other parameters, you can mathematically calculate the average number of steps before the RNG generates the work in question. (The answer is not never, though it may be very long.)

But evolution isn't like that anyway. You aren't randomly generating a sequence until you generate the genetic code for a cat, for instance.

> And compared to an organism, 'war and peace' wouldn't even account to a single cell's worth of DNA which is insanely complex with so many parts that must exist simultaneously with others to coexist.

This is the classic creationist argument from irreducible complexity, which is basically an argument from a failure of imagination -- one of the things we keep learning as we understand more about the paths on which things evolved is that features which seem irreducibly complex in living things actually do have incremental evolutionary paths where there is function at steps along the route.

> Put another way, imagine there's a computer with a random number generator spitting out letters (1-52 (a-z,A-Z, ignoring punct) in perfect randomness. How long would it take the computer to create 'War and Peace'?

As others have already stated, this isn't how natural selection or evolution works.

The mutations are, as far as we know, random. The organism they work on isn't recreated each time. That is, it's incremental.

> And compared to an organism, 'war and peace' wouldn't even account to a single cell's worth of DNA which is insanely complex with so many parts that must exist simultaneously with others for the cell to survive.

This is an argument from ignorance. At what level is something 'too complex' to have evolved? Depends on who you ask. Behe, Dembski, et al, attempted to answer this with "irreducible complexity", but it is flawed, and not accepted by any credible scientific community. It ignores exaptation by definition, and then is promoted as proof of intelligent design.

But even still, the bacterial flagellum, eye, and other previous examples of "irreducible complexity" have been shown to have evolutionary paths--from existing organisms. So now, all of a sudden they aren't irreducibly complex.

So it seems irreducible complexity depends on our knowledge ("This part seems like it can't function alone, since I can't find any examples to the contrary"), not any objective property of the organism itself. That's not how science is done.