Understanding why designs get stuck in a basic form can help engineers pursue fruitful avenues of design.
The Promise of Design Evolution
Oct 28, 2020
by Adrian Bejan
But that raises a question: If evolution is so ongoing and everywhere, why do so many things look as if they are stuck in time? The cat and the dog both feature milk and four limbs, the same as they ever were. Or, so it seems. Even in technology evolution, which happens over a much shorter time scale, we see the ossification of form. The pencil is a long cylinder, not a cube; the fork has three or four tines, not seven; the ox cart and the automobile have settled on two axles and four wheels.
Freedom is physics, not opinion. Like everything physical (that is, part of nature), freedom is measurable—in this case, the measurement of how many physical features are free to be changed in the configuration of a system. Also, the physical effect that the ability to change has on other measures of physical performance, such as efficiency, power, and performance, can itself be measured. In human-made designs, freedom is also measured as the number of “degrees of freedom,” those palpable features that can be changed freely and independently of other features.
The effect that freedom has on design has its limits, however. The reason is the phenomenon of diminishing returns, which is as much a part of physics as freedom, economies of scale, hierarchy, and evolution. Diminishing returns are observed in freely evolving flow architectures that have become "mature."
At the mature stage in the evolutionary design, the new changes that continue to occur have a marginal or imperceptible effect on the broad outlook and performance of the whole flow architecture. Understanding the interaction between diminishing returns and freedom can help engineers pursue fruitful avenues of design and ignore those that can offer no meaningful improvements.
Evolution Does Not End
Diminishing returns is a universal phenomenon that accompanies evolution. Consider animals in the fossil record. When a kind of animal has been present for a long time, the pace of changes in its form begins to slow. When the evolving "animal" is old enough, the improvements are imperceptible, to the point that the observer believes that evolution has ended. Some animals, such as sharks or horseshoe crabs, have had the same basic form for long enough that they are called “living fossils.”
This observation is mistaken. Evolution does not end; it just waits to be kick-started by its unruly environment in a new direction.
Consider the possibilities for designing a solid, rigid body that transmits a load. A cantilever beam is not usually thought of as a flow system because it is a piece of solid material, yet, a flow system it is. It facilitates a “flow of stresses.” When a load is placed at the free end, it is transmitted along the beam to the armpit, where the beam is implanted in the vertical wall. The load is transmitted by means of stresses, which fill the body of the beam.
The cantilever beam is an artifact, one of the earliest contrivances dating back from before antiquity. The following description uses the language of mechanics, although the subject applies equally to the evolutionary design of the limbs of trees and the bones of animals.
First, the beam exists because it has a purpose. The beam improves the life, movement, and survivability of the greater system that adopts it. The greater system is the living human and the life of the whole society, in motion. The purpose of the beam is to support the end load without breaking and without bending too much. Resistance to breaking means that the internal stresses must not exceed a maximum allowable stress level. Next, to satisfy the requirement of not bending too much means that the beam must have a certain stiffness, which is accounted for by a specified downward deflection of its tip. The cantilever beam is essentially an elastic spring, a blade with a specified spring constant.
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One of the simplest beam designs is the solid rod with a round cross-section. The analysis of such a beam is relatively simple and known as slender-beam pure bending theory. We can skip the details and retain the measure of the overall performance of design, which is the size of the beam, that is, the amount of material that one must purchase and use to construct the beam.
Evolution begins as engineers search for designs that serve the same need while requiring less material. Such designs are accessible through a series of changes in beam morphology, each change having the effect of removing from the beam some material that is not stressed as highly as the highest stressed regions inside the beam.
In the simplest version of a cantilever, the highest stresses occur in the two armpits at the wall, the dorsal (the back, in tension), and the ventral (the belly, in compression). The lowest stresses (zero, in fact) occur at the free end and along the centerline of the solid rod. Those observations reveal the two directions to freedom so that the beam design can evolve in order to perform its function with less material:
- Shaping the beam by removing material from near the tip. This way, the beam becomes tapered, thick at the base, and thin at the free end, like all tree branches. A cantilever in this form could perform as well as a solid cylinder but with a volume only one-third as large—dramatic savings.
- Hollowing the beam, so that the solid rod is replaced by a tube, like the bone of a bird. A hollow tube can be designed to perform as well as a solid cylinder but with only one-half the material, which is also a dramatic savings.
These two design evolutions—tapering and hollowing—are the "pioneering" designs, the first announcements of the invention that material can be saved by morphing the beam. Later, as the design matures, the design evolution starts from either of those steps: If the shaped design is already available, then it is ripe to be subjected to hollowing. The next result then is a tapered beam that is also hollow, like the top of the original Bic pen, or like the root of the goose feather. Likewise, if the design of a hollow tube is available, then further evolution would subject it to tapering.
Through either path, the ultimate destination would be the same, with a cantilever with just one-sixth of its original mass. But in each case, the material savings from the second step would be much less dramatic. For the step of hollowing out a tapered cantilever, the material saving is one-half of one-third or one-sixth of the original mass. For the tapering of a hollow beam, it would be two-thirds of one-half or one-third.
In either case, notice the diminishing returns that come when the design tends to maturity. Diminishing returns become the norm as a design evolves by acquiring more and more changes that have proved to be beneficial in the past, when they were invented and implemented in isolation. Those changes brought the greatest returns when they were new and not contaminated with similar ideas.
The Compounding of Innovations
Diminishing returns are everywhere, most visibly in the human sphere, in the evolution of performance, in the shapes of boats, cars, and airplanes, and the evolution of records in sports.
For example, someone could ask why speed records are broken more frequently in swimming than in running. The reason is that running is the “mature” design of human locomotion. We are born to walk and run—we are terrestrial beings. For modem humans, swimming is a young form of locomotion, something to be relearned after the prehistoric aquatic phase of human evolution. (There is ample evidence that at some point in the evolutionary past, human ancestors spent time in the water and developed adaptations—lack of hair, flipper-shaped feet—suitable for aquatic environments.) Each swimmer must learn how to swim to increase his or her access to movement on the globe, to avoid being stuck on one side of the river, and to gain access to the other side, which is greener. Running on soft sand and snow also requires learning.
Experts on one thing or another will surely jump in with other explanations for the difference between the frequency of records in swimming and the frequency of records being broken in running. They might mention the changes in equipment (suits, shaved body, pool depth, water quality). This argument is correct, and it reinforces the explanation given in the preceding paragraph. The equipment technology for swimming is young, and the equipment technology for running is mature. The equipment and the rules of the sport are more likely to change in swimming than in running. The swimming pool is more likely to be improved than the track.
The reality of diminishing returns is the compounding of innovations, and it is rooted in physics. Old inventions are mature, full of sequential improvements that have become superimposed. These have very small returns from new design changes that are added on. Nowhere is this phenomenon more evident than in the evolution of steam turbine power plants, which dates back to the late 1800s. Two of the most essential design changes were reheating the steam and heating the water (the feed) before entering the boiler.
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The secret to inventing a more efficient power plant is to morph the circuit executed by its working fluid (that is, steam) such that it is at a higher temperature when being heated and at a lower temperature when being cooled. The more efficient design is the one that occupies a wider temperature gap between the heat source and the heat sink.
One approach for widening the gap is to increase the temperature of the steam as if flows in the turbine. The stream of high temperature and high-pressure steam arrives from the boiler and a subsequent heat exchanger in the same fire house, called a superheater, and flows through turbines that generate power. The steam expands, its pressure decreases, and so does its temperature. The design change consists of intercepting the stream halfway through the turbine, and heating it in a special heat exchanger called a reheater, which is also exposed to the fire. This way, the turbine becomes segmented into two turbines, one for high-pressure steam and the other for low-pressure steam, and the temperature of the steam (averaged over the two turbines) is higher than what it was before the reheater was invented.
Downstream of the low-pressure turbine, the steam is condensed into liquid water in a heat exchanger (called the condenser) exposed to the cold ambient. Next, the liquid flows through a pump, which increases the water pressure to the high level required for boiling water at a high temperature when exposed to the fire.
Another design improvement was implemented just after the pump, preheating the pressurized water stream before it flows into the boiler. The smart way to heat the water fed to the boiler (called feedwater) is by placing the water in contact with steam bled from the turbines. This heating invention is valuable because it avoids the mistake of placing the cold water from the pump in direct contact with the fire. Heat transfer across huge temperature differences is a killer of efficiency. The thermodynamics term for this mistake is irreversibility or entropy generation.
Important is that there are two very good inventions, one is reheating, and the other is feedwater heating. If implemented, each invention causes an increase in the efficiency of the whole power plant. The efficiency [η] is the ratio of the shaft power delivered by the turbines divided by the rate of heating (or the rate of fuel consumption) administered to the steam before expansion through the turbines.
Although both reheating and feed heating lead to improvements in the efficiency of the steam turbine cycle, the efficiency increase caused by one method is greater when the method is implemented for the first time, alone. Note the distinction between efficiency [η] and the efficiency increment [Δη] resulting from one or more design changes. The efficiency is the highest when reheating, and feed heating are used at the same time.
The impact of a single method depends on whether the other method was implemented already. Big returns are registered when the invention is applied first, by itself. Later, as the flow architecture is mature, decorated with beautiful features like a Christmas tree, diminishing returns come from a subsequent increase in global performance.
There is a lot more to what I selected here for illustration. For example, the number of feed heaters is free to vary. Each feed heater is a flow system with its own flow architecture that can be morphed freely toward better performance, i.e., greater efficiency at the whole system level. It turns out that the design with only one feed heater causes an efficiency increase of 9 percent, whereas the design with an infinite number of feed-heating stages causes an increase of 20.7 percent. In other words, the fresh invention (a single feed heater) delivers half of the benefits offered by the most mature and perfected version of the invention, continuous feed heating.
It’s never like the first time. Returns are like squeezing a lemon. The biggest squirt comes when you first squeeze it.
Between the Possible and the Impossible
“Gilding the lily” is an apt metaphor for the evolutionary phenomenon that has become mature. Where there is freedom, evolution happens, and along with diminishing returns in global performance, it gives birth to diversity and complexity. Gilding the lily is most of what goes on in a mature science. It is a good thing, but only up to the point that announces its presence naturally, and when it does, it changes the movie plot.
One way to envision the diversity and complexity of evolutionary design is to image a graph of performance over time. On that graph, the totality of designs would make up a volume, like a mountain, with the crest being marked by the pioneering designs that at the time were the most efficient or best performing. In other words, the body of the mountain accounts for the multitude of designs that are less efficient or lower performing than the designs that define the crest.
For steam power plants, for instance, the body of designs would have been rising over the past 300 years, following the crest of second law of thermodynamics efficiency, which is the ratio of the power output of the design divided by the corresponding power output of an ideal design (known as reversible engine, or Carnot engine). That number cannot be greater than 1; therefore, the crest of the mountain cannot push through the ceiling represented by [ηII] = 1. Consequently, the crest must be concave, and the concavity in this graph is an illustration of the phenomenon of diminishing returns in the evolution of mature flow architectures.
The subtle aspect that this science illuminates is what is impossible. This knowledge is very valuable. If we know it, we do not waste our time touching and feeling our way over the cliff. This way we avoid the big mistakes. All science is about finding the limit between the possible and the impossible, and how to push the limit, if possible.
This conclusion applies broadly and reaches back to the physics of social organization. The unending evolutionary design of society is better known as politics—the proposals, commands, and implementations of changes in the regulations to human flow on the earth's surface, such as the polis (the city, in Greek). Changes happen all the time: some changes are big, while many are small, and some are sudden, cataclysmic, while most are tiny, slow, and imperceptible. Changes happen because every one of us has the urge to change something. Humans cover the range from the complacent to the revolted, with the many dissatisfied in between.
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Otto von Bismarck famously said, “Politics is the art of the possible.” This wisdom is old, shared broadly, and known by other names, such as realism, compromise, tradeoff, flexibility, perfection is the enemy of performance, can’t win them all, and the benefit of changing one’s mind. More powerful and useful is to have this wisdom put on a scientific basis, because “the possible” is essentially an infinity of possibilities. With freedom, the social flow architecture can be changed in all sorts of ways, minor and major, related to each other or not related.
When it comes to the possible, the sky is the limit. If there is freedom, anything goes... until the morphing design hits the wall between the possible and the impossible. Without freedom, the design is stuck far from the better ideas that would be accessible if freedom to question were encouraged.
The way forward is to become better educated about the impossible and to implement what is possible and free, economical, safe, robust, resilient, and long-lasting.
With science, every new generation is brought up with a greater ability to construct and predict its own future.
It is also true that every new generation arrives soaked in unpredictability. Individuals and ideas cannot be predicted. They are like the eddies that rotate “the wrong way” on the surface of the flowing Danube. To focus on the individual is to be blind to the whole. The evolving flow design that serves all the eddies is the river basin, the whole. This is why the future of the whole is the important picture to paint—the better the science, the more clairvoyant and far-seeing the painter.
Adrian Bejan is the J.A. Jones Distinguished Professor at Duke University in Durham, N.C. He has authored more than 30 books and received numerous honors, most recently the Benjamin Franklin Medal and Humboldt Research Award. This essay is adapted from his latest book, Freedom and Evolution: Hierarchy in Nature, Society and Science, published by Springer Nature.