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There's some science on training those muscles, even without upside down drinking. "Dry swallowing" while on an incline seems to do the trick just fine.

https://pmc.ncbi.nlm.nih.gov/articles/PMC9550520/

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In Japan, I learned to drink water upside down to stop hiccups. Works for me, whereas drinking normally doesn't.
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How do you get your body to be upside down?
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You bend over and curl your head towards your body.
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Did it work?
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