Energy Expense

Energy Expense in Gait Produces a Time Scale

The final chapter of this story has to do with causation.  What is there about people or the environment that creates limits on what can be linked together in the mind?  Why can’t we hear music when the notes arrive at intervals longer than 2 seconds?  Why can’t we dance to 30 bpm?  Why do concepts become inactive after a few seconds? Somehow we ended up with this limitation and there has to be a reason.

Coming up with an account of why we have this or that ability is a fairly subtle undertaking in psychology.  Consider for example our ability to see.  We see because we have visual cortex and eyes.  We see because we have learned to see over our life span: appropriate developmental experience is required for seeing to occur in any given individual.  We see because our ancestors evolved from primitive slimy things with skins that sensed heat.  Heat sensitivity evolved into eye cups and then into eyes.  And finally we see because we live in a world that is illuminated by light and filled with solid reflective objects.  All of these levels of explanation are relevant to the question of how it is that we can see.  However, the final level, the recognition that we live in light has the most motive power.  The light drives all other forms of explanation.  Animals see because their interactions with environment are aided by the ability to extract reflectance information.  And each animal sees in its own way in congruence with the environment that it lives in, its ecology.  Frogs for example, do not see objects.  They cannot see a fly unless it is moving.  What they see is movement of dark specs, moving shadows, reflectance edges, and overall dimming.  That is it, but it suffices for a small amphibian that lives at the water’s edge.  Human seeing is similarly constrained by our ecology and by the goals we have at any given moment of time.  Seeing is about the acquisition of information  not about the acquisition of images.  The same ideas are relevant to hearing.

The same kind of level splitting certainly applies to the question of why our thoughts remain active for only a few seconds, why we cannot experience rhythms that are slower than 30 bpm and we cannot construct melodies from music that is played slower than our metronomes.  Although they are not presently available, neuroscience will eventually derive chains of neuronal interactions that mediate auditory and motor responses on the time scale of a few seconds.  Presumably the locus of these neurons will  be in the thalamus where perceptual and motor pathways intersect, but this is merely a guess.  There must, however, be something about our interactions with the environment that create this time scale in the first place.  Our sensory systems have the properties they do precisely because they are tuned into our ecology.  And the two most fundamental facts about our ecology is that we live in a gravitational field and that there is a solid surface of support beneath us.  Interaction begins with movement which in humans has evolved into primarily waking and running.  Walking and running are rhythmic motions and everything we sense occurs on board a body that is generating these rhythms.  The auditory system evolved along with a body that was generating rhythm.  Perhaps these rhythms became part of the way our cognitive processes incorporated time.

Anybody who has run for exercise probably knows that calorie consumption is determined by how far you run, not by how fast you run.  If you run a given distance at a high speed you burn more calories per minute but you end up running fewer minutes than if you had run more slowly.  It all balances out because energy consumption is proportional to speed for running.  The same is not true for walking and this is where things become interesting.  The adjacent figure shows the amount of energy consumed per meter (per kilogram of body mass) for various walking and running rates.

This quantity is referred to as the efficiency.  The filled circles are running data that can be found in any textbook on exercise physiology.  The solid line, called the Rose-Gamble law, describes the energy expense for walking a fixed distance.  What this figure shows is the walking, unlike running, has different efficiencies at different speeds.  There is a well defined minimum at about 1.2 meters per second at which point human locomotion achieves its best energy efficiency.  Prior to the invention of the wheel, there was no more energy conservative way to move across ground than to walk at about 1.2 m/s.

The key difference between the energetics of walking and running is that in running the legs are used as springs while in walking they are used as pendulums; masses suspended at a pivot point – in this case, the hips.  There is very little difference between the kind of pendulum that keeps time in grandfather clocks and the free swinging motion of a leg.  The only difference is that mass is distributed throughout the leg and in timekeeping device the mass is located in a bob attached to a virtually massless string.  The physics is the same and it is the physics that is going to tell us everything we need to know.  The most important feature of the pendulum is that it has a natural period.  The time it takes for a pendulum to swing through one cycle is independent (to a very good approximation) of the height from which the pendulum is released.  For a simple pendulum made from a bob supported by a string, the natural period is 2p times the square root of (string length divided by the gravitational acceleration at the earth’s surface).  The natural periods of real legs have been determined by suspending the legs of cadavers and they differ only marginally from the simple pendulum.  The natural period of the legs of early humans, determined from fossilized remains, was about 1.5 seconds.

When we walk with our legs swinging at their natural period we expend minimal energy.  At this period the legs are most responsive to the muscle contractions that drive their motion.  All pendulums absorb energy most efficiently when they are driven at their natural period.  Because our legs are pendulums we don’t have to know how fast to swing them, they swing at with a period close to 1.5 seconds by themselves.  In this way we achieve efficient walking without us having to actually know anything.  Our legs know.  No selection pressure is needed to develop humans that walk efficiently.  The Rose-Gamble law has applied to every person that has ever walked.  It also applies to four legged animals and so to all of our primary predators.