Conscious after decapitation?

When I was a kid and we studied the French Revolution, and, of course, the guillotine, the class buzzed with rumors that the executed could briefly maintain consciousness after decapitation. Damn Interesting just reposted a short piece on that notion of "Lucid Decapitation." From Damn Interesting:
 Content Guillotine In the heyday of the guillotine during the French Revolution, it is said that many of the condemned were asked to blink for as long as possible after decapitation. While many reportedly did not blink at all, some complied for as long as thirty seconds. Still other observations describe much more specific reactions to stimuli following beheading. Consider the case of Languille, a convicted murderer who was guillotined in France. He was observed by Dr. Beaurieux during his execution at 5:30am on June 28th, 1905. As written in Archives d'Anthropologie Criminelle, here are the doctor's observations:

Here, then, is what I was able to note immediately after the decapitation: the eyelids and lips of the guillotined man worked in irregularly rhythmic contractions for about five or six seconds … I waited for several seconds. The spasmodic movements ceased.

The face relaxed, the lids half closed on the eyeballs, leaving only the white of the conjunctiva visible, exactly as in the dying whom we have occasion to see every day in the exercise of our profession, or as in those just dead.

It was then that I called in a strong, sharp voice: 'Languille!' I saw the eyelids slowly lift up, without any spasmodic contractions … Next Languille's eyes very definitely fixed themselves on mine and the pupils focused themselves … After several seconds, the eyelids closed again, slowly and evenly, and the head took on the same appearance as it had had before I called out.
Lucid Decapitation