The body sites where the position sense signals initiate, has been mapped at the surface of the brain sensory cortex in a configuration resembling an upside down human body, the homunculus, the legs up top, followed down by the arm and a huge hand, and lower down by an even larger face with a prominent mouth (FIG. 2 top). The more the incoming signals the larger the represented image of that body part in the brain.
The original signals that enter this system come from mechanical stretch receptors located inside muscles and tendons in our legs and arms. Without the information from our musculotendinous receptors, we cannot even maintain “the upright posture” with our eyes closed, (known in neurology as the Romberg’s sign).
On the other hand (or leg), adding another limb,the "third leg", for sensing body position (Fig 1) is an invaluable assistant for any walking imbalance whether from leg numbness, weakness or imbalances such as Parkinson disease.
And finally to geometry, remember that two points (or feet) define a line, but three points (adding the third leg) becomes a plane (or support base), just like the "tripod" for your camera.
The most common causes of deficient ascending pathways are: diabetic neuropathy, multiple sclerosis, vitamine B12 deficiency, neuropathies in general and aging. Fortunately, we were graciously provided with a redundant system when our arm is used as a direct conduit to the ground with a staff (the third leg in fig.1); since the position sense signals from the arm will be carried in the same ascending pathway as those from the legs, they will provide the same brain center with supplemental informacion to help in executing a correction in posture and a return to balance.
Impaired balance may also occur in brain conditions like Parkinson, MS or brain tumors with no apparent or primary deficiency in the ascending pathways. Yet the supplemental information arriving the brain via the third leg significantly improves walking balance and stride length in parkinson patients as shown in videos taken by me and presented to Parkinson Support Groups.