The autonomic nervous system is running our body without any thought from the "executive functions" of the brain. We breathe, our heart pumps and our digestive system all function even when asleep or if knocked unconscious. The ANS also includes bodily movements that follow without thought when music is played.
The antipode of Autonomic Dance is Cerebral Dance. Cerebral dancing is a series of choreographed moves that keep repeating themselves (if you are lucky) to the pulse. A remarkable amount of people in non-dancing cultures often complain they have two left feet. In reality they have a disconnected autonomic nervous system from music. It is not a person's fault. Cerebral dancing, I believe, comes from a culture and/or family which has devalued music and dance. My university, and example of cultural devaluation, had no dance department, and the music department had a large increase in funding only when the sports department needed musicians to play at their football half-time.
Try this: Focus on your dance in a similar way you might focus on your breathing in meditation. Alter both your breathing and dancing now by slowing them down, paying attention to phrasing and melody. If you allow the body to breathe or dance as it does naturally, you may find that if you are present within your own body. Once you begin being in yourself, observing and joining your ANS (the gods), you will find it easier to connect and be present with the person in front of you.
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Further reading: How music effects the ANS: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3011183/
Photo credit of ecstatic dance: https://wildlyfreewoman.net/tag/tonya-k-freeman/