If no small portion of it is a good idea by itself, then I don't think it really is a good idea.

Not a good idea, or not a feasible idea? I can think of dozens of good ideas that cannot be reduced to some kind of minimal, doable project.

Well it all gets down to definitions and its more of a rule of thumb. However, I'm very suspicious of ideas that seem to be good only because the complexity gives them a certain gravitas. Its sort of a version or expansion (or misappropriation) of Gall's law:

“A complex system that works is invariably found to have evolved from a simple system that worked. The inverse proposition also appears to be true: A complex system designed from scratch never works and cannot be made to work. You have to start over, beginning with a working simple system.”

Please list a dozen. I like the challenge of attempting to break problems down into small parts. THx.

What less than a search engine can you build if you've got pagerank? in fact you can't even know if pagerank works unless you have a search engine.

Sure, but you don't need to index the entire internet to build PageRank; only a subset of pages that form a graph. And, it's pretty easy to break the notion of building a search engine into smaller, discrete steps-- hell, I'd imagine that it could be done by two Stanford grad students.

Or "not a feasible idea.. yet", I have some ideas which I definitely do not have the resources to pull off and don't know how to split into small chunks which I can, but I may well have the resources in a year or two, so it might be worth keeping them until then.

Yes, release early and iterate