Gyromancy is a method of divination

Divination

Divination is the attempt to gain insight into a question or situation by way of an occultic standardized process or ritual...

 in which a person spins around inside or walks the circumference of a circle drawn on the ground, the perimeter of which is marked with the letters of an alphabet. The divination is inferred from the letter at the position where the person either stumbles or falls across the circle’s edge. The person would repeat the practice "...till he evolved an intelligible sentence, or till death or madness intervened." The dizziness

Dizziness

Dizziness refers to an impairment in spatial perception and stability. The term is somewhat imprecise. It can be used to mean vertigo, presyncope, disequilibrium, or a non-specific feeling such as giddiness or foolishness....

 brought on by spinning or circling is intended to introduce randomness or to facilitate an altered state of consciousness

Altered state of consciousness

An altered state of consciousness , also named altered state of mind, is any condition which is significantly different from a normal waking beta wave state. The expression was used as early as 1966 by Arnold M. Ludwig and brought into common usage from 1969 by Charles Tart: it describes induced...

.

The word is derived from Medieval Latin

Medieval Latin

Medieval Latin was the form of Latin used in the Middle Ages, primarily as a medium of scholarly exchange and as the liturgical language of the medieval Roman Catholic Church, but also as a language of science, literature, law, and administration. Despite the clerical origin of many of its authors,...

, gyromantia, which is derived from Greek gyros (circle) and manteia (oracle).