Not that strenuously:
"Correct, I think," said Professor McGonagall. "Although wizards are advised to avoid being seen by their past selves. If you're attending two classes at the same time and you need to cross paths with yourself, for example, the first version of you should step aside and close his eyes at a known time - you have a watch already, good - so that the future you can pass. It's all there in the pamphlet."
"Ahahahaa. And what happens when someone ignores that advice?"
Professor McGonagall pursed her lips. "I understand that it can be quite disconcerting."
You're right, I misremembered. Still, I think there is a lot to suggest that interacting directly with one's time-clones (as opposed to waiting with one's eyes closed while a clone drops off a message, for example), particularly in battle, is a bad idea. You would never observe a future-you doing something ineffective in combat---failing to dodge or block, or casting an ineffective spell, for example---since, after observing that mistake, you would be prepared for it in the future. So the only consistent possibilities involve losing or running away before ...
EDIT: New discussion thread here.
This is a new thread to discuss Eliezer Yudkowsky's Harry Potter and the Methods of Rationality and anything related to it. With two chapters recently the previous thread has very quickly reached 500 comments. The latest chapter as of 17th March 2012 is Ch. 79.
There is now a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author's Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: one, two, three, four, five, six, seven, eight, nine, ten.
As a reminder, it's often useful to start your comment by indicating which chapter you are commenting on.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: