Gait and Memory
There is a coincidence of time scales between walking and thinking. Memory activation decays on a time interval of about 1.5 seconds (the metronome limit) and gait rhythm has a period of about 1.5 seconds. Either this is an extraordinary coincidence or is a reflection that our memory systems have been tuned to stay active for a gait cycle. Coincidences do occur but they are not likely to arise through adaptation. If the time scales are the same it is because there is linkage between moving and hearing.
In the first place our bodies have a feel to them, we experience our motion not as a series of disconnect efforts, but as a fluid stream. This stream has a lot of structure that depends on what we are doing. When we are walking there is periodicity at all three levels of kinematics; position, velocity, and acceleration. The three levels of periodicity gives walking its feel. Without a clear sense of the walking feeling gait would be an uncoordinated and dangerous endeavor. Anyone who has worked on a motor skill understands the importance of feel. Without feel action is uncoordinated and tentative.
Feel requires memory activation. Without activation there is no way that our movement would be perceived to be connected. In order for gait to be experienced as connected, motor memory must last over the gait cycle. This is not an issue that has been investigated formally but it seems unlikely that motor activation lasts longer in that successive footfalls seem to create new motor images that overwrite what is currently in memory. In so far as natural terrains (not sidewalks) change subtly with each footfall, it would not be adaptive for walking to generate vivid impressions that extended several steps backwards into the past. One cycle seems like the right amount of activation and gait cycles last for about 1.5 seconds. This is the natural time scale for motor activation to generate the feeling of movement.
At the same time the cadence of walking generates the feeling of walking, it also creates a soundscape that is pulsing exactly at the gait period. This soundscape is literally a melody made of crunching, snapping, thumping, and scuffling sounds. The same activity generates both a kinesthetic pattern as well as an auditory pattern. They are separately experienced because touch and hearing are distinct modalities, but the information they extract from self-motion is essentially the same. Both modalities are solving a common problem in contour formation and unless there is some specific reason to the contrary, it makes sense that they have the same logic when it comes to putting together discrete moments into patterns. This is essentially the argument for why hearing ended up with activation time scales that are based on gait.
At a deeper level, the energetics of gait and the experience of temporal patterns both form high-pass filters. A high-pass filter is a device that passes the high frequencies but not the low. Frequency is generally “something per second”. In music the relevant frequency is the cycles per second of a sound source or the cycles per second of modulator. The same idea is relevant here but now frequency is not cycles per second but the rate at which successive events (notes for example) are provided; literally events per second. In this sense Mr. PC is a high frequency song and Blue Monk is a low frequency song. They are both songs and equally songlike. Mr. PC is just fast sounding and that is a critical part of its aesthetic. From the point of view of contour formation, cognitive limitations are felt principally at the low frequency end, starting at about 30 bpm or ½ Hz. This is the effective boundary beyond which successive events lose their coupling. Since there is just one effective boundary we end up with pattern recognition being high-pass instead of band-pass.
Our bodies also behave as high-pass filters and this can be seen quite clearly in the Rose-Gamble law for energy consumption in walking a unit distance. Energy costs are not the same for fast walking and slow walking. Slow walking is prohibitively expensive as can be seen by the almost vertical ascent of the costs below about 1/2 meters/second. There is a hard limit on the low end for the sounds and kinesthetic feel we produce by our own motion. On the fast-walking side of the Rose-Gamble law the energy costs increase at a much slower rate. Efficiency is reduced only by 20% or so when we walk rapidly up to around 3 miles/hr. What this means practically is that the sweet spot where walking is most effortless is more of a low frequency cut-off than a well-defined and stable minimum. What this means mathematically is that the Rose-Gamble law expresses a filter that passes high frequency motion but not motion much slower than the natural pendulum period of our legs. It is an empirical fact that the mind’s ability to represent temporal structure and the energy required to move the body have the same filtering characteristics.
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