Think of the word “core” not in its sense of abs and lower back, but in its sense of a deep axis of the body, like an apple core. That axis will follow the line of your primary hip flexor muscle, the psoas, extending in both directions towards your feet and your head. You can trace the line of your core channel from your inner heels, through your inner thighs and your hip creases, coming together behind your navel and lengthening along the front of your spine towards your head. You can even include the line of your inner arms, from your inner armpits, through your biceps to your index fingers and thumbs. Initiate all your movements from the center of that core channel, specifically from a place somewhere between your navel and your spine.
As you organize your poses, think of two interlocking V-shapes to help you integrate your limbs into your core channel. Reach your tail and arms away from each other as one oppositional pairing, and your head and legs away from each other as the second. In some poses or transitions, one paring might make more immediate sense than the other. If you find this to be the case, perhaps repeat the pose or transition focusing on the less apparent pair in an attempt to integrate it into your movement or organizational patterning. Working in this way can help develop ease and efficiency as you clarify the pathways from your extremities–fingers/hands, feet/toes, tail and head–to your core channel and the front of your spine.
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