This paper reviews several examples where humans have copied designs and innovations found in nature. The examples illustrate the fact that a fertile source of ideas for human innovations is the natural world. It also illustrates the fact that one of the major reasons for belief in God is the beauty, design, and ingenuity found everywhere in the natural world.
Humanity has some impressive accomplishments in science, technology, the arts, and music. The technological wonders of the last century have radically changed our world and benefit us all enormously. While basking in our accomplishments, though, it behooves us to acknowledge the fact that we have used the design found everywhere in the world God created as the source for many of our achievements (Forbes 2006).
The main pursuit of scientists and students of nature is to read the “book of nature” that God wrote.1 Most scientists spend their lifetime studying and learning from the wisdom displayed everywhere in creation (French 1988). These “lessons from nature” have inspired a new academic discipline called bioinspiration, meaning gaining inspiration from the natural world, or biomimetics, mimicking the natural world, often shortened to bionics (Allen 2010, p. 8; Bhushan 2007, p. 6). In short. bionics is the study of God’s design in order to solve scientific and engineering problems.
Most inventions, from airplane flight to Velcro®, were in some way inspired by the natural world (Forbes 2006). Swiss engineer, George de Miestral, obtained the idea for Velcro from observing the burrs that stuck to his dog’s fur. Upon examination with a microscope he discovered the little hooks on the burrs that attached to the dog’s fur (Challoner 2009, p. 733).
Humans are not the originators of the physical world, but often imperfectly copy it. In the fields of “engineering, chemistry, ballistics, aerodynamics—in fact in almost every area of human endeavor—nature has been there first” and the natural world God made is “infinitely more economical of resources and generally superior in performance” (Paturi 1976, p. 1). A few examples of this will eloquently illustrate the validity of this observation. The fact that “nature” invented many innovations first has long been recognized by scientists (Martin 1933, p. 14). This paper reviews only a few of the great numbers of examples to illustrate this fact.
The study of Morpho butterfly scales has allowed scientists to take heat detection to a new level of both sensitivity and speed (Jarvis 2012, p. 1). Existing infrared detectors require complex microfabrication and heat management technology (Pris, et al. 2012). Thermal imaging is used to detect heat variations in a wide variety of industrial, medical and military applications today, such as thermal vision goggles that allow soldiers to see at night with a high level of detail.
Study of the design of iridescent Morpho butterfly scales has given scientists insight into new and better thermal imaging systems. In these “resonators the optical cavity is modulated by thermal expansion and refractive index changes, causing wavelength conversion from invisible infrared to visible light” (Pris 2012, p. 1). Insight from the wing scale design has allowed significant advances in existing detectors.
Harvard researchers at the Wyss Institute for Biologically Inspired Engineering have created a tough, low-cost, biodegradable material inspired by insects’ hard outer shells. The material’s inventors say it has numerous applications and could provide a more environmentally friendly alternative to plastic. The new material is made from shrimp shells and proteins derived from silk called “shrilk.”
This clear, flexible, light material is as strong as aluminum twice its weight. Shrilk has enormous potential because chitin is one of the most abundant materials in nature found in everything from shrimp, snail, and clam shells to insect bodies. Thus, shrilk is not only low cost, but also can be used in applications demanding a lot of material.
Shrilk not only degrades in a landfill, but its basic components can be used as fertilizer. Instead of blindly combining the materials, the researchers looked to what they call “nature” to see not just what materials were used, but how. Fibroin, a protein derived from silk, and chitin, a a long-chain polymer of a N-acetylglucosamine, a glucose derivative, in an insect’s exoskeleton are layered, creating a stiff type of design, much like plywood. By mimicking nature’s design of layering the chitin and fibrous proteins, shrilk was created. The structural properties in nature are not chemistry only, but are also the result of the architectural design employed in their assembly.
The many modern fruits of bionics includes flight (Allen 2010; Piotrowski 1987). This science is not new: early humans built water dams after watching beavers. German scientists modeled their first jet plane after the shark’s efficient body design that allows it to rapidly travel through the water. Early jet planes were even painted to look like sharks. Siepen put it well, “man still has much to learn from birds about flying. Men shape their planes like birds and soar in imitation of them, but tailspins and other calamities unknown to birds are inseparable from man’s adventures in an element not his own, be he ever so skillful” (Siepen 1929, p. 767). Ever hear of a bird crashing to the earth due to wind shear or ice? Even though we have copied birds, we have a long way to go before our copy is perfected to a level to equal the abilities of birds and other flying creatures.
Many creatures are designed to run, fly, glide, and even parachute to the ground; all engineering marvels that humans have now effectively copied. Airplanes require ingenious feats of engineering, but, compared to birds, they are poorly maneuverable. The idea of flying first came from birds, and flying improvements were also inspired by various flying creatures.
Dragonflies can carry as much as fifteen times their own weight as they travel though the air, yet most high performance aircraft cannot lift much more than their own weight. Intrigued, scientists studied dragonfly wings and found that they function by generating lift as a result of producing an airflow “whirlwind.” Efforts are now being made to apply this principle to aircraft by designing wings that produce greater lift by “whirling the air” (Allen 2010, p. 116–117; Yulsman 1984, p. 87).
Owls use special curved feathers on the front row of their wings that change the direction of the air as it flows past, allowing them to fly at slower speeds than most other birds. Slower flight is also quieter—obviously of great value in hunting prey at night. Owls can sneak up on small game, such as rabbits and mice, with nary a whisper and frisk away what will shortly become a meal. For this reason, the study of owl flight has had a major influence on airplane and helicopter design, enabling them to not only fly faster in normal air travel, but also to fly at much slower speeds. The advantages are enormous: a few of the more obvious ones include less noise, shorter runways, and less costly airports.
We are very impressed with our modern, efficient jet engines, but octopi have effectively used jet-like propulsion millennia before us. Their system expand a muscular “sack” in their streamlined body to suck water in, then vigorously contract it to force a water jet spray out of a small, well-designed opening with enough force to propel them forward. Alternate expansion and contraction of their muscular sacks have effectively jet-propelled octopuses through their watery world for millennia (Cousteau 1973).
Human navigational experts have reached a level of technology that enables us to accurately sail across an ocean to reach a minuscule island, yet birds can migrate for many thousands of miles with such accuracy that they land on the same nesting sites each year (Baker 1980). The complex navigational equipment that comes “standard” in a bird’s head to achieve this feat weighs next to nothing. We have, so far, only imperfectly copied their system; our airplanes use navigation equipment that can weigh a ton and cost a fortune.
Humans have discovered numerous ways of detecting magnetic fields that we have put to use in thousands of ways. Yet, research has found many animals possess a sixth sense, namely magnetic field sensitivity, which they use for such purposes as a backup navigation system (Baker 1980; University of Illinois 2009). Bees expertly use the sun as a compass to make navigational calculations. At night, or on very cloudy days, they rely on extensive patterns of polarized sky light. And when those patterns are blocked or abbreviated by clouds, bees utilize a third, noncelestial reference system to guide them to their home—the earth’s magnetic field.
Humans have developed radar and sonar systems to guide their planes safely through fog and their ships through water. We have even bounced signals off the moon to learn about its surface. Bats have been effectively using the miracle of the modern science of radar echo location for millennia. Setting blindfolded bats loose in a dark room that was strung with many fine, silken threads revealed that they could effortlessly dart about without striking or breaking a single thread (Turner 1975).
Experiments on bats were first carried out in 1793 by the Italian monk, physiologist Lazzaro Spallanzani, who confirmed that bats were using sonar because they flew around in confused patterns if one ear was plugged (Munch 1974, p. 104). We now know that bats use ultrasonic vibrations that range from 12 to 120 kilohertz (humans hear from 20 to 20,000 hertz, a fraction of what bats use). Bats emit as many as sixty supersonic sound pulses each second that strike objects and bounce back to their ears. An accurate measure of the time required for the echo to return is used by the bats to calculate the location of objects. More amazingly, when bats send out their signals their ear muscles automatically shut off their hearing so that their radar picks up only the guiding echoes (Turner 1975).
Bats are not the only animals with this ability. The oil bird of South America is a cave dweller that effectively navigates around its dark world by emitting tones in the range of 6 to 12 kilohertz. So that the animal is not confused by the normal background cave echo, the waves they produce are much longer than those produced by most cave-dwelling insects.
The echolocation system used by dolphins allows them to be as skillful in water as bats are in air (Munch 1974, p. 108). Dolphins can avoid slim metal rods equally well whether day or night—and they can even distinguish between different fish of the same size by echo-location (Thomas, et al. 2002). Dolphins also use their system of navigation for communication. They can obtain a panoramic view of their environment by moving their head from side to side to scan a large area in front of them while producing as many as 100 sound bursts per second.
Creatures as small as spiders are master engineers that can spin webs stronger than steel using a material known for its strength that can easily hold many times their own weight (Ritchie 1979). Each spider type also has its own unique web style—a trade name of the builder—all of which display marvels of geometric design and workmanship. Some spiders can even dive under water in air-filled “diving bells,” a feat that they achieved millennia before humans invented their submarines and bathyspheres, a spherical deep-diving chamber in which persons are lowered by a cable to study deep-sea life.
Spiders lift heavy loads by dropping moist web strands from an overhead limb to the objects on the ground that they wish to hoist up to their nest such as nest building material and food. After fastening the object to the strand, they then wait for it to dry. As it dries, it shrinks and lifts the object slightly. More wetting and waiting causes more shrinking and more hoisting. Spiders patiently work with these web cables until the load is several inches above the ground, then they construct a nest in it. How this tiny arachnid learned to produce the right combination of material that shrinks when it dries so that this technique can be used to lift loads cannot be explained by gradual evolution. Nor can how they learned to properly apply the scientific principles involved to solve this problem. The big question, though, is, “If evolution were true, how did these spiders survive until they mastered these feats?”
Animals also display a high level of engineering skill. A bird nest shows skill in masonry, weaving, tunneling, statics (the science of construction such as bridges and buildings), and expert use of structural strength properties. Beavers build large dams out of trees and mud and construct spacious underground homes with underwater entrances that limit the entry of almost every would-be intruder. Silkworms manufacture a high quality strong thread called “silk” that has been used by humans for centuries to produce fine clothes and expensive scientific instruments (Ritchie 1979). Some creatures, such as certain water insects, manufacture tiny bricks that they use to build chimney-shaped towers (Martin 1933, p. 14).
Most wasps can construct a type of paper similar to human manufactured wood pulp paper (Martin 1933, p. 104). The familiar bees and wasps nests make paper that they form into a hexagonal shape, a strong design that wastes less space than a circle. Hexagons are now a common structural shape in buildings that are used in the framework of roofs and other structures. Bees also use a hook and eye system to help hold parts of the bee hive together similar to that used in clothing today instead of buttons.
Certain types of ants construct living bridges so that their comrades can traverse over water. Some ants practice animal husbandry—herding “aphids” that they “milk.” Other ants even grow plant fungus in an expertly prepared leaf garden. Yet other ants construct boats out of leaves to enable them to effectively float across water. Archerfish use a stream of water to accurately “shoot” resting insects above the water while the fish are still in the water, correcting for optical refraction caused by the water-air interface.
Every human-made building requires a ventilation system to circulate air. Bees effectively “air-condition” their hive with their wings that function as power-driven fans to maintain a constant airflow and clay termite mounds are designed so that their body heat produces ventilation through their tall, well designed, mound structures (Martin 1933, p. 104; Allen 2010, p. 118-119).
Although blind to red, bees are able to see ultraviolet (to which we are blind) as a separate color. Knowledge of this has helped humans to open the door to our discovery of infrared sensitive eyes in snakes, polarized light-sensitivity in bees, and even electrosensitive organs in fish (Forbes 2006).
Hypodermic needles used today to inject medicine into millions of patients, saving countless lives, are considered a wonder of modern medicine. Insects, though, were first—mosquitoes, wasps and bees all possess well-designed, effective, hypodermic needles. In the bee it is called a stinger because it is used to “sting” its enemies to protect itself.
Researchers are now studying insects to develop more energy efficient machines. Our earth-moving machines can carry tons of dirt, sand, and gravel for miles, and our modern energy-economy concerns have motivated engineers to double the gas mileage of many vehicles, but we have achieved nowhere near the efficiency level of many animals. A flea, for example, can pull 400 times its weight—yet not eat for as long as a year. Although less than an eighth of an inch long, it can jump from 13 to 36 inches, similar to a man using only his own power to jump over the 555-foot-tall Washington Monument.
Our dream of cryogenic (very low-temperature) preservation of life, has so far failed—but the flea does it quite well. If frozen, the creatures are fine when thawed out. They have survived in the frigid Antarctic under thick layers of snow and ice, and have been known to live for as long as seventeen months without food, but probably could survive for much longer. This is how they live in extremely cold places that have long, very cold winters.
We were not even first to master radio communication: female moths send out a radio frequency signal over a large area to enable distant male moths to pick up their messages. Before their radio system was discovered, scientists believed that the female moth used only odors to attract males. This view was revised after efforts to interfere with the odor call failed. Researchers eventually learned that the female moth possesses a “broadcasting station” and the male a “receiving set” nearby his antennae (Burton 1985).
Although humans can copy some things from insects, others are far more difficult to duplicate. An excellent example is bioluminescence—the production of light by fireflies, glowworms, shrimp, jellyfish, bacteria, worms, mollusks, fish, and even some single-celled organisms (Rehder 1988).
Complex chemical light-producing systems, chemiluminescence, are called cold light systems because the chemical reaction produces much light and very little heat. To increase the light intensity the eyes of some living organisms use a pigment cell layer that functions as a reflector and transparent tissue shaped to form an effective lens. Modern spotlights, automobile headlights, and flashlights are all patterned after this reflector-lens design. Although the chemistry of cold light has been studied for some time, scientists still do not understand the process, and have not been able to produce a practical way to do what animals do naturally. Light emitting diodes (LED’s), which use electric current to produce cold light, thus are called electroluminescence, are the closest we have come to the efficiency achieved by natural bioluminescence systems.
It is now known that animal bioluminescence is caused by a highly efficient system using a protein called luciferin and an enzyme known as luciferase (Munch 1974, p. 118). Luciferase is a catalyst that produces cold light from luciferin in the presence of oxygen. Humans have, so far, unsuccessfully tried to copy the luciferin-luciferase system to achieve a high efficiency light generating system for practical use—normal incandescent light bulbs produce as much as 95% heat and only 5% light—an enormously inefficient and wasteful system of lighting. Fluorescent lighting is at best only 10% to 15% efficient and bioluminescence systems have a amazing 96 percent efficiency (Shelton 2008)!
If the process of cold light could be mastered and inexpensively produced, it would revolutionize our nation as much as Edison’s original light bulb did. The reaction that produces cold light in these animals “is the most efficient energy-changing system known . . . far superior to anything human engineers have invented for changing chemical or electrical energy to light energy” (Munch 1974, p. 119).
Although we have produced electroluminescent materials similar to the chemiluminescence achieved by animals, we have not yet learned to economically and effectively produce light as animals do. Chemiluminescence in animals is highly efficient compared to human lighting systems. Florescent lighting is only about 22 percent efficient compared to around 90 percent for some animal chemiluminescence systems (Roda 2010). Our best scientists are also trying to copy the ability of plants to exploit renewable solar energy (Balzani 1994, p. 31). Scientists are making progress and are now elated to have mimicked the first vital step in photosynthesis (Bullis 2008). And although humans harnessed electrical energy only recently, electric eels have been generating up to 700 volts to stun larger animals to defend themselves for millennia.
Researchers discovered that rats’ teeth are always sharp because their teeth design consists of a hard surface on one side and a soft surface on the other. As they are used, the soft part wears down much faster, keeping the teeth continuously sharp. This finding was applied in developing a saw blade that sharpens itself. This blade is constructed from tungsten carbide powder that is mixed, pressed, and heated. When cutting metal, it lasts up to six times longer than the next best blade in common use today.
Human-designed clocks come in a variety of sizes, shapes, and accuracies. Yet many plants and animals have built-in clocks that use a mechanism which still baffles scientists (Ward 1971, Mathur 2005, pp. 122-134). Some crabs can tell time, a fact known because they respond to tide cycles—but if moved in a location with a different time for the tide cycle hey still react with the same accurate timing. We now know that a crab’s physical reaction is not due to perceiving time from the environment, but its own internal built-in clock. Even plants such as algae operate on cycles, and if put in a different environment, the same cycle persists (Binkley 1990).
Fiddler crabs change color to camouflage themselves as the tide goes out, an ability not linked to the tide, but to the animal’s internal clock. The cycle occurs even if they are removed far from the ocean. The cycle is also not linked to a twenty-four hour day, but occurs fifty minutes later every twenty-four hours. Only the start of the cycle is connected to the particular locality in which the crab lives. The cycle is set when the crab is born and, once set, accurately corresponds with the tide until it dies (Winfree 1987).
This natural clock may provide an intriguing solution to the human problem of jet lag or “time motion sickness.” Animals such as clams have built-in clocks and can tell when a high tide is going to occur even if they are far removed from their home waters. They retain their sense of time in relation to their home high tide no matter where they are and regardless of the surrounding conditions. If we could understand how they maintain their time relationship, the jet lag problem would be better understood, and maybe even solved.
Only recently have humans been able to accurately measure temperature. Many plants, and even some reptiles and insects, are keenly aware of the heat level, and if we learn to read their signs, we can likewise read the temperature (Levenson 1989). The number of chirps the snowy tree cricket produces per minute corresponds to the air temperature, and can be translated into the temperature with an accuracy level of within a degree or two (Walker 1962, p. 427).
The ability of machines to travel on all types of terrain was possible only in the last century with the invention of snowmobiles, four-wheel-drive Jeeps, and pneumatic tire vehicles. Smooth travel on really rough terrain, though, has eluded our best engineers until researchers studied “daddy-long-legs.” Their ability to coordinate their jointed legs to smoothly transverse across extremely uneven surfaces has aided in the development of “walking machines” designed to carry humans across terrains presently accessible primarily by helicopters. Insects such as daddy-long-legs have been designed to effortlessly solve some of the most frustratingly complex problems that engineers and roboticists are now struggling with (Kleiner 1994; Brand 1987).
Transversing a flat terrain is a relatively easy feat, but a device capable of making the constant adjustments required to “walk” across an uneven surface is a much more difficult task. Spring-loaded tires absorb some bumps, as do vehicles that can toss and turn easily, but researchers are hoping to develop non-wheeled devices that can walk across ocean floors or distant planets. The Ohio State University’s Robert McGee noted that we know the insect design works exceptionally well in nature (McGhee 1979, pp. 176–182). To duplicate the daddy-long-leg’s technical achievements, McGee and other researchers are analyzing the animal’s movement.
To do this, researchers built a rough terrain using wooden blocks and filmed arachnids strolling across their obstacle course. They then determined the “logic” the animals used to transverse the obstacle course and from this data inferred the nervous system’s organization. Next, they attempted to reproduce the mechanical aspects of the feat. The researchers have found the animals’ eyes are not essential for navigation, but instead they use their longest pair of legs as “feelers” to sweep the ground ahead, then program each leg to stop at a different point so as to maintain a level body (Corn 1987). After years of research, compared with the average arachnid, walking robots are pitiful shufflers, but advances are being made as computer technology develops (Kleiner 1987, p. 27; Berardelli 2009). As of 2012 we still have not been able to achieve the effectiveness of these animals.
When humans turn their powerful light and radio telescopes toward the heavens, they view supernovas, white dwarfs, red giants, spiral nebulae, globular star clusters, billions of galaxies, and trillions of stars. They observe our eight planets and scores of comets move about the sun, all in well-defined orbits, running on an amazingly precise schedule. Even our most powerful telescopes are still too nearsighted to see the boundaries of our seemingly endless universe.
Some speculate that it is even possible for stars to produce gamma-ray lasers called grasers. Humans did not develop a successful maser until the mid 1950s—and this was hailed as a dramatic scientific breakthrough that now has had an enormous impact on society. Yet, the heavens have generated these high-energy excited atom systems since their creation—for what reason, we do not yet know, but speculation abounds (Hecht and Teresi 1982). Lasers and masers are a system used to amplify light (electromagnetic radiation) enormously so the light can be powerful enough to burn holes through steel.
Laser light is aligned so that it does not spread out much as it travels on its path, thus becomes less intense as it travels away from the laser source. Scientists have sent a laser to the moon with so little spread as it travels towards its destination, thus very little light loss from the light beam, that it is visible on the moon. The term laser originated as an acronym for “Light Amplification by Stimulated Emission of Radiation.” A maser is a similar system except it uses microwave radiation instead of visible light. MASER, stands for “Microwave Amplification by Stimulated Emission of Radiation.”
Humans have built complex masers and lasers for use in medicine, electronics, communications and other fields. Yet radio astronomers have found that modern science has been scooped by natural systems that do not need a jungle of coaxial cables, power supplies, and strip-chart recorders to build a maser (Nourse 1989).
One type of maser was discovered in the variable giant red stars, and later other types were found, including stellar water and silicon monoxide masers. Learning how they produce masers could do much to improve scientists’ electronic masers used for industry. Although only molecular masers have been observed coming from space, some scientists believe that optical lasers, free electron lasers, and chemical lasers all exist in outer space.
Switching our examination from the incomprehensibly vast to the unimaginably minute, we can use the electron microscope to probe normally invisible wonders. With a scanning-tunneling electron microscope, humans can now visualize immensely tiny structures of marvelous order and intricacy. And each electron, neutron, proton, and hundreds of other subatomic particles are likewise a world that is just now being explored. A vast world exists at this level waiting to be discovered: a world humans did not create, but one that takes a studious, intelligent person years to properly begin to understand. Even a lifetime of study can barely uncover nature’s wonders. A comparison of our achievements with those of our Creator’s, such as those discussed above, should humble us before God.
In nature, all cells function at the micro- to the nanoscale level, and understanding “these functions can guide us to imitate and produce nanodevices and nanomaterials. Abstractions of good design from nature are referred to as biomimetcs” (Bhushan 2007, p. 6).
An example is the amazing ability of a family of lizards called Geckos that run up a vertical wall and then walk upside down across the horizontal ceiling.2 To achieve this feat they rely on their approximately
… half a million submicrometer keratin hairs, called spatulae, which are what make their feet … so sticky. Each hair is 30—130 µm long and is only one tenth the diameter of a human hair and contains hundreds of projections terminating in 0.2—0.5 µm spatula-shaped structures. The foot typically has about 5000 hair/mm2. Each hair produces a tiny force (˜ 100 nN), primarily due to van der Waals attraction, and possibly capillary interactions (meniscus contribution), and millions of hairs acting together create a large adhesive force on the order of 10 N with a pad area of approximately 100 mm2, sufficient to keep geckos firmly on their feet, even when upside down on a glass ceiling (Bhushan 2007, p. 6).
The next question scientists had to answer is how to break the bonds that hold them to the ceiling. Scientists determined that the bonds between the keratin hairs and the surface are broken by “peeling,” in a similar way that occurs when one removes adhesive tape. Scientists
… are attempting to create a new type of adhesive tape by mimicking the structure of gecko or spider feet. Geim et al. reported the fabrication of a “gecko” tape made by microfabrication of dense arrays of flexible plastic pillars that are little more than 2 µm tall with a pitch on a similar scale (Bhushan 2007, p. 6).
Humans are in awe when standing before creation, from the tremendous expanse of the universe to the infinitesimally tiny. Contemplating the lessons found in the infinite variety of plant life that tastefully clothes every type of terrain, and fashionably changes its cover to fit the area and season, inspires respect. A close look at the millions of animal life types with which the earth teems staggers the imagination. Knowledge of this should humble us before our awesome God and Creator, and force us to realize how ignorant we are before Him.
It would be unreasonable to conclude from these marvels that the workings of natural law, time, and chance alone produced it all. When we see the enormous intelligence implanted in so-called unreasoning creatures, we appreciate that they are the result of the wisdom and power that designed them. Scanning the heavens and marveling at the myriad of stars it contains—about 6,000 are visible on a clear night—reminds us that “The heavens declare the glory of God; and the sky shows his handiwork” (Psalm 19:1).
Since scientists study more of these wonders of creation than others and of all persons they should vividly see the great wisdom and power of the Creator who made all things, although, sadly, many are blind to this fact (Romans 1:18–23; 2 Peter 3:5). Many human inventions only poorly copy God’s creations—and our imitations took the best human minds and centuries to develop. The meek person realizes that much of the universe will probably forever be beyond the power of the human brain to comprehend and understand.
What does a study of the natural world—of which we have only given a few simple examples—tell us about its origin? In the words of Paturi, “Since Darwin, biologists have been firmly convinced that nature works without plan or meaning, pursuing no aim by the direct role of design. But, today we see that this conviction is a fatal error” (Paturi 1976, p. 11). After all has been said, the conclusion is “You are worthy, O Lord, To receive glory and honor and power; For You created all things, And by Your will they exist and were created.” (Revelation 4:11)
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