By: Walter L.Bradley

Walter L. Bradley received his B.S. in Engineering Science and his Ph.D. in Materials Science from the University of Texas in Austin. Married in 1965, he lives in College Station, Texas with his wife, Ann. He taught as an Assistant and Associate Professor of Metallurgical Engineering at the Colorado School of Mines before assuming a position as Professor of Mechanical Engineering at Texas A&M University (TAMU) in 1976. Dr. Bradley, also served as Head of the Department of Mechanical Engineering at Texas A&M University and as Director of the Polymer Technology Center at TAMU. He currently serves as Distinquished Professor of Engineering at Baylor University. Visit Dr. Bradley’s Online Faculty Office and read his personal story, etc.

 Introduction — What is implied by the concept of “an intelligently designed universe”?

What does it mean on a grand scale to assert that the universe is the product of an intelligent designer? In a scientific age that exalts rationalism and chance, what empirical evidence could possibly support such a claim? As humans contemplating the immense complexity of the cosmos, might certain features of the universe suggest that our “home” has in fact been carefully crafted for our benefit? Can our own human experiences of creativity and design illuminate the concept of a cosmic designer? These questions underlie the discussion of intelligent design theory, a resurgent area of inquiry by both Christian and secular scientists in search of a reasonable explanation for the marvelous complexity of the universe.

In his classic, Natural Theology (1802),{1} eighteenth-century English philosopher and theologian William Paley marshaled evidence for a designed universe from both the physical and biological sciences. However, his argument for design was called into question by Darwin’s theory of evolution. But new discoveries in the latter half of the twentieth century in the fields of astronomy, cosmology, and abiogenesis (the origin of life) have provided extremely compelling evidence for a designed universe. These findings have been publicized in the popular print media (Time, December 1992 and Newsweek, July 1998), featured in television specials on PBS and BBC, and disseminated through a wide variety of popular and scholarly books, including entries from prestigious academic publishing houses such as Oxford and Cambridge University Presses.

My personal experience as a lecturer supports the growing openness to intelligent design theory in the academic world. Having given over 135 talks on this subject to more than 65,000 students and professors at over 65 major university campuses from 1986 to 2002, I have observed a dramatic change in audience receptivity to the idea that an intelligent designer of the universe may exist. I have noted a widespread acceptance (albeit begrudging in some quarters) that this growing body of scientific evidence demands an intellectually honest reckoning, as no exclusively naturalistic explanation seems capable of rising to the occasion.

Before we examine the evidence from cosmology, physics, and chemistry that suggests the universe has been designed as an ideal habitat for life in general and for humans in particular, let me first clarify what is meant by the term “design.”

How Can We Identify Designed Objects in the Natural World?

Richard Dawkins, a British zoologist and one of the world’s foremost apologists for classical Darwinism, addressed the question of design in his 1996 essay collection, Climbing Mount Improbable,{2} by contrasting particular, designed artifacts with similar accidents in nature. Dawkins illustrates the concept of design with the example of Mount Rushmore, upon which are carved the clearly recognizable images of Presidents Washington, Jefferson, Lincoln and Theodore Roosevelt (Figure 1). By contrast, a naturally occurring rock in Hawaii casts a shadow that resembles President John F. Kennedy (Figure 2), illustrating an accidental occurrence in nature. It is self-evident that a sculptor (in this case, Gutzon Borglum) carved Mount Rushmore. The sheer number of details in which the Mount Rushmore faces resemble the faces of the four presidents testifies to the presence of an intelligent cause, a human sculptor. No one could seriously attribute these magnificent faces to the creative forces of wind, rain, sleet, and hail.

Figure 1. An intelligent design: Mount Rushmore with presidents Washington, Jefferson, Roosevelt, and Lincoln. Figure 2. An accident of nature: President John F. Kennedy’s profile formed by shadow cast by a large rock in Hawaii.

Dawkins defines designoids as artifacts of the natural world that appear to be designed but “have in fact been shaped by a magnificently non-random process which creates an almost perfect illusion of design.”{2} A designoid is an artifact in nature that looks like Mount Rushmore but can in fact be explained by natural processes (with, say, natural selection being the non-random process in the case of living systems).

The first step in evaluating the possibility of intelligent design is to examine closely the characteristics (or artifacts) of the natural world in order to assess whether all external “appearances” of design are merely “designoids,” or whether they are, in fact, true examples of design by an intelligent Creator. Let us begin by considering the essential elements of intelligent design by human beings.

How Does An Engineer Design Consumer Products?

Design engineers using their understanding of natural laws, as described by mathematics, and their capacity to prescribe the conditions under which these natural laws function locally to produce a purposeful outcome. Let me illustrate. Suppose I wanted to throw a water balloon from the leaning Tower of Pisa in Italy to hit a friend walking on the plaza below. Solving the differential equation that Newton discovered for motion in a gravitational field, I would obtain a solution in the form of a simple, algebraic equation that describes the descent of the water balloon to its target below.

H(t) = h0 – (Gm /r2) t2 /2 – v0t (1)

Here “H(t)” represents the height of the balloon as a function of time (“t”); “G” is a universal constant signifying the strength of the gravitational force of attraction; “m” and “r” are the mass of the Earth and the radius of the Earth, respectively; and “h0” and “v0” are the height of the tower from which I shall throw the balloon, and the vertical velocity with which I shall throw the balloon, respectively. By entering the numerical values for “G,” “m,” and “r,” I obtain Gm/r2 = 32.2 ft/s2 , usually designated “g.” Now Equation 1 can be simplified to:

H(t) = ho – g t2 / 2 – vo t = ho – 32.2 t2 / 2 – vo t (2)

I can now solve Equation 2 for the time “t” it will take for the water balloon to reach the ground [H(t) = 0] if I specify the height of the tower [ho] and the initial velocity [vo] with which the water balloon is thrown. This equation may be used to guarantee that my balloon arrives at the plaza at just the right time to hit my strolling friend. Simply dropping the balloon will also accomplish my goal. I specify v0 = 0 and H(t) = 0 and solve for the correct time to drop the balloon.

Human Design Consists in Setting the Boundary Conditions

These three essential factors to predict the motion of my water balloon are the same ones generally necessary to achieve design outcomes in engineering. They are:

  • the mathematical form that nature takes (see Equations 1 and 2);
  • the values of the universal constants (G in Equation 1) and local constants (the radius of Earth, r, and the mass of the Earth, m, in Equation 1); and
  • the boundary conditions (the height [h0] and initial velocity [v0] in this example.

Note that the engineer has no control over the laws of nature and the mathematical forms they assume. Neither does the engineer have any control over the values of the universal constants, such as the gravity force constant. The engineer can only set the boundary conditions; for example, when drawing up blueprints to specify exactly how a device will look and operate when it has been manufactured.

If we revisit the design process, this time using the more realistic–though complex–example of automobile design, the engineer must carefully prescribe the boundary conditions such that the chemical energy released by the internal combustion of gasoline is converted into mechanical energy in the form of torque to the car wheels. Furthermore, the dimensions for each engine part are of critical importance. The absolute size and shape of each part is determined by the car’s desired weight, speed, passenger and luggage capacity, and other performance specifications. These factors determine the size of the engine cylinders and pistons and the rate of gasoline injected into the engine cylinders, the scale of the brake and suspension systems, the size and type of tires, and so forth. And whatever their absolute characteristics, the parts chosen must also be scaled in relationship to one another so that they can work together harmoniously.

Notice that many of the specifications are related to each other and therefore cannot be independently specified or assigned. The greater this interdependence of specified boundary conditions, the more complex and demanding is the design process. Small errors in the specification of any such requirement will produce either a car with very poor performance or, worse, a car that does not function at all.

In summary, we can see that human design consists in specification of conditions under which the laws of nature operate to produce a purposeful outcome. In the next section, we will see that cosmic design involves specification of not only the conditions under which the laws of nature operate, but the laws themselves and the universe constants that scale the “building blocks” (e.g., rest masses of elemental particles), “energy blocks” (e.g., quanta of energy), and the fundamental forces in nature to provide the purposeful outcome of a habitable universe for life, and life itself!

Needs Statement for a Habitable Place in a Suitable Universe

We teach mechanical engineering students to begin the design process by specifying as clearly as possible the “needs statement” for their project. Then, the assignment for the semester is to develop a design solution that accomplishes the “need(s)” specified for the project. In similar fashion, the minimal needs to be satisfied for a universe to be capable of supporting life of any imaginable type, not just life as we know it, must be identified. Like our automobile illustration, many of the specifications will necessarily be interrelated to make a functional universe. From this essential “needs statement” we can then see how these needs (or design requirements) are met in our universe. We are essentially doing reverse engineering, constructing the blueprint backwards from the product (like an illicit manufacturing company copying a competitor’s product). Only then will we be ready to entertain Dawkins’ question, “Are there many ways in which these requirements could be satisfied within nature?”{2} Or are the conditions so unique and interrelated that their collective satisfaction by accident would be a “miracle” in its own right? Let us then begin by drafting a “needs statement” for a habitable universe. Then we shall see how these requirements are satisfied in our universe.

Needs Statement for a Suitable Universe

An abbreviated list of requirements for a universe suitable to support life of any imaginable type must include the following items:

  • Order to provide the stable environment that is conducive to the development of life, but with just enough chaotic behavior to provide a driving force for change.
  • Sufficient chemical stability and elemental diversity to build the complex molecules necessary for essential life functions: processing energy, storing information, and replicating. A universe of just hydrogen and helium will not “work.”
  • Predictability in chemical reactions, allowing compounds to form from the various elements.
  • A “universal connector,” an element that is essential for the molecules of life. It must have the chemical property that permits it to react readily with almost all other elements, forming bonds that are stable, but not too stable, so disassembly is also possible. Carbon is the only element in our periodic chart that satisfies this requirement.
  • A “universal solvent” in which the chemistry of life can unfold. Since chemical reactions are too slow in the solid state, and complex life would not likely be sustained as a gas, there is a need for a liquid element or compound that readily dissolves both the reactants and the reaction products essential to living systems: namely, a liquid with the properties of water.
  • A stable source of energy to sustain living systems in which there must be photons from the sun with sufficient energy to drive organic, chemical reactions, but not so energetic as to destroy organic molecules (as in the case of highly energetic ultraviolet radiation).
  • A means of transporting the energy from the source (like our sun) to the place where chemical reactions occur in the solvent (like water on Earth) must be available. In the process, there must be minimal losses in transmission if the energy is to be utilized efficiently.

Unless ALL of these conditions and many more not included in this list are met, we would have a universe that would preclude the possibility of conscious, complex life forms. However, it is possible to meet all of these conditions for the universe and still not necessarily find a suitable habitat in the universe for complex, conscious life. Therefore, we might say that the above requirements for our universe are necessary, but not by themselves sufficient, conditions for a habitat suitable for complex human life. Next we try to identify the additional conditions within such a suitable universe that would provide a place of habitation for conscious, complex life.

Needs Statement for a Habitat Place in the Suitable Universe for Complex, Conscious Life

An abbreviated, but illustrative, list of additional requirements must be specified for a place of habitation in this universe. First, we need a star that is located in a relatively “quiet” region of the universe (e.g., not too many neighbors that are producing high intensity, sterilizing radiation). This star needs to have its highest intensity of radiation in the range that is suitable to drive the chemical reactions essential to life without destroying the products of these reactions. Furthermore, this star needs to have a very special satellite within its solar system. A partial list of the requirements this satellite must meet include:

  • a planet or moon that is terrestrial–or, solid rather than gaseous;
  • a temperature range suitable to maintain the universal solvent as a liquid rather than a solid or gas;
  • just the right concentration of heavy (radioactive) elements to heat the core of the planet and provide the necessary energy to drive plate tectonics, to build up land mass in what would otherwise be a smooth, round planet completely covered with solvent;
  • just the right amount of solvent (carefully coupled to the plate tectonics activity) to provide a planet with similar proportions of its surfaces as oceans and land mass;
  • just the right protection from the destructive forces in nature such as radiation and asteroids over a reasonable amount of time; and
  • just the right stabilized axis tilt and angular velocity to give moderate, regular, and predictable seasons and moderate temperature fluctuations from day to night.

While one is temped to think that these requirements are easily met, given the large number of stars, it should be noted that there are few places in the universe sufficiently free of sterilizing radiation to provide a suitable solar system. The number of candidate “neighborhoods” is further reduced by the requirements of a sun with the right amount of mass to give the right electromagnetic radiation spectrum. Furthermore, the occurrence of a suitable satellite in conjunction with such a star is even more problematic. Only the earth in our solar system of sixty-two satellites meets the above requirements for a “home” (earth) in safe “neighborhood” like our sun and solar system, which are well placed in a quiet place in a suitable universe as described above.

In the next sections, we will see how these universal and local “needs” (or design requirements) are met by: the specific mathematical form encoded in nature, the exact values of the universal constants in our universe, and the remarkable “coincidence” that initial (or boundary) conditions are exactly what they must be. We will also see that the “evolutional” or developmental path that our universe navigated is consistently remarkable, making the origin of our “Garden of Eden” all the more wondrous and enigmatic.

Blueprint for a Habitable Universe – Mathematics and the Deep Structure of the Universe

Mathematics–in contrast to mere calculation–is an abstract intellectual activity that began in Greece in the sixth century BC. Pythagoras was a key figure, as were his successors, Euclid and Archimedes. Their studies focused especially on geometric objects such as straight lines, circles, ellipses, and conic sections (i.e., the curves made by cutting a cone with a plane).

In the third century BC, Appolonius of Perga wrote eight monumental volumes devoted to these curves, describing their properties as “miraculous.” Yet the geometric and mathematical formulations to which they devoted themselves were actually descriptions encoded into the very fabric of nature. Imagine the delight of Johannes Kepler (1571-1630) some eighteen centuries later, when he discovered that the orbits of planets around the sun conformed to these same beautiful but abstract mathematical forms. Kepler declared: “The chief aim of all investigations of the external world should be to discover the rational order and harmony which has been imposed on it by God and which He revealed to us in the language of mathematics.”{3}

Galileo Galilei (1564-1642) asserted that “the laws of nature are written by the hand of God in the language of mathematics.”{4} In his Mathematics: The Loss of Certainty,{5} historian Morris Kline demonstrates that the religious mathematicians of the sixteenth and seventeenth centuries–including Newton, Galileo, Kepler, and Copernicus–viewed the universe as orderly and capable of mathematical description precisely because a rational God had fashioned it thus. These scientist-mathematicians believed that, since God had designed the universe, then “all phenomena of nature would follow one master plan. One mind designing a universe would almost surely have employed one set of basic principles to govern all related phenomena.”{5}

Only in the 20th century have we come to fully understand that the incredibly diverse phenomena that we observe in nature are the outworking of a very small number of physical laws, each of which may be described by a simple mathematical relationship. Indeed, so simple in mathematical form and small in number are these physical laws that they can all be written on one side of one sheet of paper, as seen in Table 1.

Physicists and Nobel laureate Eugene Wigner in his widely quoted paper, The Unreasonable Effectiveness of Mathematics in the Physical Sciences notes that scientists often take for granted the remarkable–even miraculous–effectiveness of mathematics in describing the real world. Wigner muses:

The enormous usefulness of mathematics is something bordering on the mysterious . . . . There is no rational explanation for it . . . . The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.{6}

Albert Einstein was struck by the wondrous orderliness of the world.

You find it strange that I consider the comprehensibility of the world (to the extent that we are authorized to speak of such a comprehensibility) as a miracle or as an eternal mystery. Well, a priori one should expect a chaotic world, which cannot be grasped by the mind in any way . . . . [T]he kind of order created by Newton’s theory of gravitation, for example, is wholly different. Even if man proposes the axioms of the theory, the success of such a project presupposes a high degree of ordering of the objective world, and this could not be expected a priori. That is the “miracle” which is being constantly reinforced as our knowledge expands.{7}

Table 1. The Fundamental Laws of Nature.

  • Mechanics (Hamilton’s Equations)
  • Electrodynamics (Maxwell’s Equations)
  • Statistical Mechanics (Boltzmann’s Equations)
  • Quantum Mechanics (Schrödinger’s Equations)
  • General Relativity (Einstein’s Equation)

Yet even the splendid orderliness of the cosmos, expressible in the mathematical forms seen in Table 1, is only a small first step in creating a universe with a suitable place for habitation by complex, conscious life. The particulars of the mathematical forms themselves are also critical. Consider the problem of stability at the atomic and cosmic levels. Both Hamilton’s equations for non-relativistic, Newtonian mechanics and Einstein’s theory of general relativity (see Table 1) are unstable for a sun with planets unless the gravitational potential energy is proportional to r-1, a requirement that is only met for a universe with three spatial dimensions. For Schrödinger’s equations for quantum mechanics to give stable, bound energy levels for atomic hydrogen (and by implication, for all atoms), the universe must have no more than three spatial dimensions. Maxwell’s equations for electromagnetic energy transmission also require that the universe be no more than three-dimensional.

Richard Courant illustrates this felicitous meeting of natural laws with the example of sound and light: “[O]ur actual physical world, in which acoustic or electromagnetic signals are the basis of communication, seems to be singled out among the mathematically conceivable models by intrinsic simplicity and harmony.”{8}

To summarize, for life to exist, we need an orderly (and by implication, intelligible) universe. Order at many different levels is required. For instance, to have planets that circle their stars, we need Newtonian mechanics operating in a three-dimensional universe. For there to be multiple stable elements of the periodic table to provide a sufficient variety of atomic “building blocks” for life, we need atomic structure to be constrained by the laws of quantum mechanics. We further need the orderliness in chemical reactions that is the consequence of Boltzmann’s equation for the second law of thermodynamics. And for an energy source like the sun to transfer its life-giving energy to a habitat like Earth, we require the laws of electromagnetic radiation that Maxwell described.

Our universe is indeed orderly, and in precisely the way necessary for it to serve as a suitable habitat for life. The wonderful internal ordering of the cosmos is matched only by its extraordinary economy. Each one of the fundamental laws of nature is essential to life itself. A universe lacking any of the laws shown in Table 1 would almost certainly be a universe without life. Many modern scientists, like the mathematicians centuries before them, have been awestruck by the evidence for intelligent design implicit in nature’s mathematical harmony and the internal consistency of the laws of nature. Australian astrophysicist Paul Davies declares:

All the evidence so far indicates that many complex structures depend most delicately on the existing form of these laws. It is tempting to believe, therefore, that a complex universe will emerge only if the laws of physics are very close to what they are….The laws, which enable the universe to come into being spontaneously, seem themselves to be the product of exceedingly ingenious design. If physics is the product of design, the universe must have a purpose, and the evidence of modern physics suggests strongly to me that the purpose includes us.{9}

British astronomer Sir Fred Hoyle likewise comments,

I do not believe that any scientist who examines the evidence would fail to draw the inference that the laws of nuclear physics have been deliberately designed with regard to the consequences they produce inside stars. If this is so, then my apparently random quirks have become part of a deep-laid scheme. If not then we are back again at a monstrous sequence of accidents.{10}

Nobel laureates Eugene Wigner and Albert Einstein have respectfully evoked “mystery” or “eternal mystery” in their meditations upon the brilliant mathematical encoding of nature’s deep structures. But as Kepler, Newton, Galileo, Copernicus, Davies, and Hoyle and many others have noted, the mysterious coherency of the mathematical forms underlying the cosmos is solved if we recognize these forms to be the creative intentionality of an intelligent creator who has purposefully designed our cosmos as an ideal habitat for us.

Blueprint for a Habitable Universe: Universal Constants – Cosmic Coincidences?

Next, let us turn to the deepest level of cosmic harmony and coherence – that of the elemental forces and universal constants which govern all of nature. Much of the essential design of our universe is embodied in the scaling of the various forces, such as gravity and electromagnetism, and the sizing of the rest mass of the various elemental particles such as electrons, protons, and neutrons.

There are certain universal constants that are indispensable for our mathematical description of the universe (see Table 2). These include Planck’s constant, h; the speed of light, c; the gravity-force constant, G; the rest masses of the proton, electron, and neutron; the unit charge for the electron or proton; the weak force, strong nuclear force, electromagnetic coupling constants; and Boltzmann’s constant, k.

Table 2. Universal Constants.

  • Speed of light
c = 3.0 x 108 m/s
  • Planck’s constant
h = 6.63 x 10-34 J-s
  • Boltzmann’s constant
k = 1.38 x 10-23 J / oK
  • Unit charge
q = 1.6 x 10-19 Coulombs
  • Rest mass proton
mp = 1.67 x 10-27 kg
  • Rest mass of neutron
mn = 1.69 x 10-27 kg
  • Rest mass of electron
me = 9.11 x 10-31 kg
  • gravity force constant
G = 6.67 x 10-11 N-m2/ kg2

When cosmological models were first developed in the mid-twentieth century, cosmologists naively assumed that the selection of a given set of constants was not critical to the formation of a suitable habitat for life. Through subsequent parametric studies that varied those constants, scientists now know that relatively small changes in any of the constants produce a dramatically different universe and one that is not hospitable to life of any imaginable type.

The “just so” nature of the universe has fascinated both scientists and laypersons, giving rise to a flood of titles such as The Anthropic Cosmological Principle,{11} Universes,{12} The Accidental Universe,{13} Superforce,{14} The Cosmic Blueprint,{15} Cosmic Coincidences,{16} The Anthropic Principle,{17} Universal Constants in Physics,{18} The Creation Hypothesis,{19} and Mere Creation: Science, Faith and Intelligent Design.{20} Let us examine several examples from a longer list of approximately one hundred requirements that constrain the selection of the universal constants to a remarkable degree.

Twentieth-century physicists have identified four fundamental forces in nature. These may each be expressed as dimensionless numbers to allow a comparison of their relative strengths. These values vary by a factor of 1041 (10 with forty additional zeros after it), or by 41 orders of magnitude. Yet modest changes in the relative strengths of any of these forces and their associated constants would produce dramatic changes in the universe, rendering it unsuitable for life of any imaginable type. Several examples to illustrate this fine-tuning of our universe are presented next.

Balancing Gravity and Electromagnetism Forces – Fine Tuning Our Star and Its Radiation

The electromagnetic force is 1038 times stronger than the gravity force. Gravity draws hydrogen into stars, creating a high temperature plasma. The protons in the plasma must overcome their electromagnetic repulsion to fuse. Thus the relative strength of the gravity force to the electromagnetic force determines the rate at which stars “burn” by fusion. If this ratio of strengths were altered to1032 instead of 1038 (i.e., if gravity were much stronger), stars would be a billion times less massive and would burn a million times faster.{21}

Electromagnetic radiation and the light spectrum also depend on the relative strengths of the gravity and electromagnetic forces and their associated constants. Furthermore, the frequency distribution of electromagnetic radiation produced by the sun must be precisely tuned to the energies of the various chemical bonds on Earth. Excessively energetic photons of radiation (i.e., the ultraviolet radiation emitted from a blue giant star) destroy chemical bonds and destabilize organic molecules. Insufficiently energetic photons (e.g., infrared and longer wavelength radiation from a red dwarf star) would result in chemical reactions that are either too sluggish or would not occur at all. All life on Earth depends upon fine-tuned solar radiation, which requires, in turn, a very precise balancing of the electromagnetic and gravitational forces.

As previously noted, the chemical bonding energy relies upon quantum mechanical calculations that include the electromagnetic force, the mass of the electron, the speed of light (c), and Planck’s constant (h). Matching the radiation from the sun to the chemical bonding energy requires that the magnitude of six constants be selected to satisfy the following inequality, with the caveat that the two sides of the inequality are of the same order of magnitude, guaranteeing that the photons are sufficiently energetic, but not too energetic.{22}

mp2 G/[_ c]>~[e2/{_c}]12[me/mp]4 (3)

Substituting the values in Table 2 for h, c, G, me, mp, and e (with units adjusted as required) allows Equation 3 to be evaluated to give:

5.9 x 10-39 > 2.0 x 10-39 (4)

In what is either an amazing coincidence or careful design by an intelligent Creator, these constants have the very precise values relative to each other that are necessary to give a universe in which radiation from the sun is tuned to the necessary chemical reactions that are essential for life. This result is illustrated in Figure 3, where the intensity of radiation from the sun and the biological utility of radiation are shown as a function of the wavelength of radiation. The greatest intensity of radiation from the sun occurs at the place of greatest biological utility.

Figure 3.

(Figure 3.1.)

(Figure 3.2.)

(Figure 3.3.)

(Figure 3.4.)

Figure 3. The visible portion of the electromagnetic spectrum (~1 micron) is the most intense radiation from the sun (Figure 3.1); has the greatest biological utility (Figure 3.2); and passes through atmosphere of Earth (Figure 3.3) and water (Figure 3.4) with almost no absorption. It is uniquely this same wavelength of radiation that is idea to foster the chemistry of life. This is either a truly amazing series of coincidences or else the result of careful design.

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