There is the magic trick version where the sword does not go down the esophagus, and the one where it’s actually swallowed. In the later, the performer aligns the mouth, throat and abdomen and literally swallows the sword (a blunt version). So…not quite magic, just a physical feat.
In the scenario where it’s a magic trick, they are creating some sort of illusion, but…I don’t think that is what you’re asking about!
Latest Answers