Animated Lego video presents classic poison bottles puzzle

The Riddler has poisoned Catwoman. He tells Batman he can save her by giving her an antidote, which is in one of 1000 barrels in a room. The other 999 barrels have more poison. The Riddler will let Batman use his antidote detecting machine. What is the smallest number of tests he needs to conduct to guarantee he finds the antidote?

This is a cool stop-motion Lego video version of the poisoned wine problem I posted earlier this year:

You are a king and have invited 1,000 guests to a party. Each guest has brought one bottle of wine. But before any of the wine has been opened, your chief spy takes you aside and tells you that he is certain that one, and only one, bottle of wine contains a poison that will kill anyone who drinks even a drop. The poison takes one hour to kick in. The king has 10 prisoners he doesn't mind killing. How does he use them to identify the poison wine and get rid of the bottle (and the person who brought it) so he can get on with the party?