How do we communicate location on the human body, and why is it not feasible to simply use the terms up/down and above/below?

Simply saying "up" or "down" might be confusing anytime you're describing people in different positions, e.g. when describing movements made by gymnasts.
I.e. If you're standing normally, your head is above your heart. When doing a handstand, your head is below your heart, but whether standing on your feet or on your hands, your head is always superior to your heart because anatomical terms are always used with reference to the anatomical position: standing upright, arms to the side, palms facing forward, etc.

Some terms are used to facilitate comparison between species, such as cranial/caudal. In a human, cranial is upwards, but in a fish, it's forwards. Since the comparable structures are oriented differently, it might be tricky to simply refer to some structure as facing "upwards", since "upwards" means different things in different species.

A special lexicon is used when talking about parts of the body. This vocabulary is called Anatomical terminology. This is used as universally by medical practitioners to avoid ambiguity and error. The words used are not common and therefore have less probability of being confused for other meanings.

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