The tortoise duct alluded to here is the Kurma Nadi. The Kurma Nadi is an energy channel that originates between the first and second Chakra at the base of the spine. It runs all the way to the hollow of the throat and regulates the stability of the body and mind.
By restraining our attention on the tortoise duct or Kurma Nadi, one develops steadiness of both body and mind.
We are not a dichotomy but a soma-psychic unit. Steadiness of body will assist and eventually translate into steadiness of the mind. This is one of the major implications of performing Asanas or Yogic Postures, developing steadiness of the body leading to the ability of remaining comfortably seated for a considerable amount of time (Be still) in order to still the mind and introspect into the depth of awareness itself (and know that I AM God).
The best way and sitting posture to develop stability of body implies stability of the spine and all that is centered around it and this depends largely on the firmness of Kurma Nadi. By keeping the head, neck and trunk straight and sitting in a meditative pose (it does not have to be Padma Asana or the Lotus Posture, Sukha Asana or the Ease Posture is adequate and most relevant for our modern bodies), one attains firmness in the energy that is controlled by the Kurma Nadi. The mind will follow the body’s steadiness and eventually settle in its own self.