Tachyon Pushing the Limits

I was just watching the PAX south tournament on youtube and I saw something that raised a question. It's probably been asked before but I couldn't find it in the forum anywhere.

So, with Pushing the Limits, can you keep taking 1 damage to keep taking turns? Allowing a full Health tachyon to have a total of 4 turns before another player can act? My gut says no, but the cards seem to say yes.