Uh huh. Where, please?
Example locations where this has been defined include Mass Driver's post here where he defined it slightly differently as "to quickly, recursively self-improve so as to influence our world with arbitrarily large strength and subtlety". I think he meant indefinitely large there, but the essential idea is the same. I note that you posted comments in that thread, so presumably you've seen that before, and you explicitly discussed fooming. Did you only recently decide that it wasn't sufficiently well-defined? If so, what caused that decision?
Possibly a few hours or weeks?!?
Well, I've seen different timelines used by people in different contexts. Note that this isn't just a function of definitions, but also when one exactly has an AI start doing this. An AI that shows up later, when we have faster machines and more nanotech, can possibly go foom faster than an AI that shows up earlier when we have fewer technologies to work with. But for what it is worth, I doubt anyone would call it going foom if the process took more than a few months. If you absolutely insist on an outside estimate for purposes of discussion, 6 weeks should probably be a decent estimate.
Vague definitions are not worth critics bothering attacking.
It isn't clear to me what you are finding too vague about the definition. Is it just the timeline or is it another aspect?
This might be a movie threat notion-- if so, I'm sure I'll be told.
I assume the operational definition of FOOM is that the AI is moving faster than human ability to stop it.
As theoretically human-controlled systems become more automated, it becomes easier for an AI to affect them. This would mean that any humans who could threaten an AI would find themselves distracted or worse by legal, financial, social network reputational, and possibly medical problems. Nanotech isn't required.
Michael Anissimov posted the following on the SIAI blog:
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Kaj's commentary: if you haven't done so recently, do check out the SIAI publications page. There are several new papers and presentations, out of which I thought that Carl Shulman's Whole Brain Emulations and the Evolution of Superorganisms made for particularly fascinating (and scary) reading. SIAI's finally starting to get its paper-writing machinery into gear, so let's give them money to make that possible. There's also a static page about this challenge; if you're on Facebook, please take the time to "like" it there.
(Full disclosure: I was an SIAI Visiting Fellow in April-July 2010.)