My sister Corinne has a great love for horses. Part of it is the beauty of their motion. There are four natural and distinct gaits. The walk with its left hind, right hind, right front, left front four beat cadence transitions to a two beat gait called the trot as the horse speeds up. Now its legs are moving in unison in diagonal pairs. It is a very stable gait and the horse’s head is often very steady.
As the horse speeds up the cantor appears. Now you hear three beats and a pause and then three beats and a pause as one of the rear legs supports the horse as the other three move forward.
As the horse accelerates a four beat gait emerges. The horse is still pushing off with a rear foot - for brief moments it has entirely left the ground and is flying. The full gallop - as fast as a horse can move.
Galloping is not terribly efficient and the horse will tire quickly. The cantor is more efficient, but not by much. Walking and trotting, on the other hand, are great paces for a horse if it is to travel long distances. Horses have very narrow ranges of optimum speeds. People can tweak these ranges through breeding altering musculature and leg length, but the horse is a four speed creature with two economy speeds.
You might think leg length is an important determinant of the best running speeds in humans, but a look at elite runners - both distance and sprint - show they are mostly of average height. At six foot five Usain Bolt is a rare exception, but he is the exception in several other metrics.
An examination of the energy used to travel a fixed distance in running is fairly constant over a wide range of speeds - something that is unexpected and very different from horses and other four legged mammals. Adding to the puzzle is the most efficient walking speed.
I like to walk and have been on long walks with a variety of people. Most of us are of differing heights, but the average speed we walk at tends to be not that much different from the speed we use when we’re walking along. Most people walk somewhere between 3.0 and 3.4 miles per hour. The efficiency of walking is strongly peaked. If you walk at your own natural cadence you will burn fewer Calories per mile than you would if you were walking at a faster or slower pace.
This is very curious as people have very different leg lengths. At six foot one, but long waisted my 31 inch inseam gives me much shorter legs than six foot seven Colleen’s 40 inch inseam measurement, but her optimal walking speed is only a bit higher than mine and is a small amount lower than another friend who has shorter legs than me. We give up some efficiency, but it is generally easy for us to adapt our speeds to that of our friends and visa-versa.1
The physics and biology of mammalian location is non-trivial and still under active investigation. A recent paper that looked into the activity of some skeletal muscles involved in walking and running gives some fascinating insight that paints a picture deeper than the problem at hand.2
It turns out it is difficult to directly measure the efficiency of a specific muscle while it is working, but measuring its electrical activity with electromyography is a good proxy and you can estimate efficiency. Seventeen people were wired up and put on treadmills and asked to move at a variety of paces. Thirteen muscles were monitored and the muscle activity per distance travel was recorded.
The results are fascinating. The plot on the left shows the speed at which a particular muscle was most efficient with walking in black and running in grey. The plot on the right shows the speed of peak efficiency for each subject for walking and running.
Note that the muscle efficiencies don’t peak at the same walking speed - there is quite a bit of variation, particularly in running. Individually our leg skeletal muscles are not optimally efficient at a single speed.
You might think this is some sort of evolutionary failure, but it is probably the opposite. We don’t spend our time walking at the same speed even though we do have an optimal walking speed. We have the need for doing many other activities. We climb, dance, kick, sprint and have the need to match speeds of others. These different activities involve each of the muscles in different degrees. We don’t have the best possible efficiency at our optimal walking speed, but we have a huge amount of flexibility and we have a very wide range of running speeds at ok efficiencies. Often we are more efficient than the horse - my niece Magi participated in a man vs horse race and dropped all of the horses.
This illustrates something deep.
The best general purpose optimization often involves a mixture of non-optimized components. Making each component as good as it can be by itself and allowing it to operate where it runs best usually results in a larger system that is far from optimal. This is central to engineering which is the practice of finding and harmonizing a variety of pieces into a whole which is the best compromise.3
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1 How people communicate the proper walking speed is a fascinating look into the subtle non-verbal ways we communicate with others.
Note if you are walking for exercise and walk over a fixed distance slowing down or speeding up from your normal pace will burn more energy. Speeding up burns the most and if you are walking for a fixed amount of time - say and hour - the higher speed will usually burn the most energy.
The relationship between efficiency, performance and physical size is a rich subject area and sport is an excellent lens to illuminate interesting questions.
2 The musculoskeletal system of humans is not tuned to maximize the economy of locomotion
David R. Carrier, Christoph Anders, and Nadja Shilling
Abstract
Humans are known to have energetically optimal walking and running speeds at which the cost to travel a given distance is minimized. We hypothesized that “optimal” walking and running speeds would also exist at the level of individual locomotor muscles. Additionally, because humans are 60–70% more economical when they walk than when they run, we predicted that the different muscles would exhibit a greater degree of tuning to the energetically optimal speed during walking than during running. To test these hypotheses, we used electromyography to measure the activity of 13 muscles of the back and legs over a range of walking and running speeds in human subjects and calculated the cumulative activity required from each muscle to traverse a kilometer. We found that activity of each of these muscles was minimized at specific walking and running speeds but the different muscles were not tuned to a particular speed in either gait. Although humans are clearly highly specialized for terrestrial locomotion compared with other great apes, the results of this study indicate that our locomotor muscles are not tuned to specific walking or running speeds and, therefore, do not maximize the economy of locomotion. This pattern may have evolved in response to selection to broaden the range of sustainable running speeds, to improve performance in motor behaviors not related to endurance locomotion, or in response to selection for both.
3 A week or so ago I was in an email conversion where someone noted a Steve Job’s quote and I reacted. I think Apple is an excellent example of a company that understands not only how to make these engineering compromises, but also that the final product involves more compromises than are possible if you “just” use the discipline of engineering. Consumer electronics has evolved beyond engineering.
[friend quoting Jobs} “When you first start off trying to solve a problem, the first solutions you come up with are very complex, and most people stop there. But if you keep going, and live with the problem and peel more layers of the onion off, you can often times arrive at some very elegant and simple solutions. Most people just don’t put in the time or energy to get there. We believe that customers are smart, and want objects which are well thought through.” - Steve Jobs
[me] Absolutely - and this is *so* different from ordinary engineering and product development.
[friend] How so?
[me] This is a *very* long subject so I'll try to just hit a few points. Engineering is all about finding a compromise among various components to create something that makes specifications. Great engineers are really good at this and I have enormous respect. The key point is there is an end point - after all, something has to ship on a certain schedule. When you are doing this you can only work within a fixed domain. It can happen that you bump into something new as you work on something, but that is rare and certainly not your job description. In recent years the goals of a product are specifications and hitting price targets.
Apple certainly does engineering, but it is a different scale. Other non-engineering disciplines are involved. During the design phase there is this tendency to keep going deeper. Occam's razor is a fundamental driving principal. You need to simplify wherever possible *even* if you didn't think it was possible at first. There is also a sense of artistic elegance and pride that comes into the optimization.
All of these competing subcomponents and pieces of software have qualities of their own - along with time dependent evolution curves. You need to be suboptimal on several to make the global result better. Much of conventional engineering ignores the fact that real consumers also like to see elegance and a simple UX mixed in too … in fact those may be the defining characteristics of a product. And the product needs to dance properly with other products in addition to the person who uses it. Getting these details right is an entirely different skill set and Apple has built an organization that understands this deeply. Artists get it deeply.
Jobs once described himself not as a technologist, but rather as an artist who paints with technologies.
My heritage and way of looking at the world is through the perspective of science. Here you are trying to figure out how nature works. There is an absolute you are working towards, but she tends to reveal herself only when questioned properly and then only a bit at a time as you need to find better questions to progress. I was not attracted to biology or chemistry as they are so complex. (they are still very beautiful - but it is a preference of mine) I found physics to be my sport as it is so simple - you only look at the most simple systems, but you want to go in as deeply as possible. The idea is to find the really fundamental questions. I find the people who have sensibilities most similar to mine are artists and composers.
Apple is the company with these sensibilities as they are trying to peel the onion back as they progress. The analogy isn't great - they are probably closer to biology as they are working in a complex environment -- Jobs, in a different time and if he would have had academic leanings - may have made a great biologist.
As these products that combine art, electronics and computation progress conventional engineering is going to be an increasing failure as a global solution. It is a piece of what needs to be done, but the integration with other disciplines is central and, I think, a requirement for success in at least the consumer product environment. There are so many things that need this approach. It is terrifically exciting.