Sometimes it happens when it takes a bit longer to answer a question (got interrupted or something), that we get a captcha. Why is this?
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Since the page shown is a hip reference to a FOTC video about robots, I've always imagined that there was (or still is) a robot in the wild that deliberately takes a long time between a form fetch and a posted answer.
It must be thinking that returning a form with 1K characters in a field only 100 ms after fetching the page would obviously not happen with a human, so it should wait for a while before answering.
So it waits. And since we get the "I'm a human" page after several (ten?) minutes, it must wait quite a while.
Unfortunately, the threshold time that causes the CAPTCHA page seems to be just about as long as it takes to actually verify the facts of an answer as well as get distracted by at least one unrelated Wikipedia link and possibly one phone call from a customer wondering if you've finished his project (that he hasn't authorized to start) yet.
Edit: I've expanded and tried to clarify the point I wasn't making as well as I could have.
To trigger CAPTCHA:
basically we are flagging anything that looks suspicious, and forcing users to prove they're not bots.
edit: due to popular demand, I removed the maximum time check -- so only minimum times are checked when posting now.
Could it be possible that the session cookie has expired, so it looks to the server that you're jumping in and answering as the first action in a new session. I'd class posts without a session cookie as suspicious (on the premise "that you've come straight to posting without reading the form")