Chapter 17

Andrew McIntosh, Mathematics

by Dr. Andy McIntosh on January 1, 2001

As a scientist, I look at the world around me, and observe engineering mechanisms of such remarkable complexity that I am drawn to the conclusion of intelligent design being behind such complex order.

Dr. McIntosh is Reader in Combustion Theory, Department of Fuel and Energy, University of Leeds in the United Kingdom. He holds a B.S. with first class honors in applied mathematics from the University of Wales, a Ph.D. in the theory of combustion from the Cranfield Institute of Technology, and a D.Sc. in mathematics from the University of Wales. He has contributed chapters to 10 textbooks dealing with combustion theory and published over 80 research papers. Dr. McIntosh is the author of Genesis for Today: Showing the Relevance of the Creation/Evolution Debate to Today’s Society.1


As a scientist, I look at the world around me, and observe engineering mechanisms of such remarkable complexity that I am drawn to the conclusion of intelligent design being behind such complex order.

No scientist is entirely objective. We are always governed by our assumptions. If a scientist does not believe in God, then his starting point of atheism will be bound to affect his judgment as he looks at the world around him. If his mind is closed to the possibility of a designer, his own assumption will force him to adopt what to many will seem an “unlikely” explanation for what he observes. (These matters of the philosophy behind the science of today are amplified in my book Genesis for Today. 2)

In my view we need to get back to the attitude of Einstein who, though he himself did not believe in an anthropomorphic deity, had a deep awe for the harmony of the universe. There was a humility in his brilliant scientific career which led to the discovery of the theory of special relativity and the consequent realization of the equivalence of energy and mass (through the famous equation E=mc2). This was followed by the momentous discovery of the theory of general relativity which showed for the first time the connection between gravity and time, and led to the demonstration of the curvature of the space-time continuum in the universe. He said in an interview in 1929:

We are in the position of a little child entering a huge library filled with books in many different languages. The child knows someone must have written those books. It does not know how. It does not understand the languages in which they are written. The child dimly suspects a mysterious order in the arrangement of the books but doesn’t know what it is. That it seems to me, is the attitude of even the most intelligent being toward God. We see a universe marvellously arranged and obeying certain laws, but only dimly understand those laws. Our limited minds cannot grasp the mysterious force that moves the constellations. 3

Such humility has been all but lost in our scientific world today. Many hold tenaciously to a strange view that theism is by definition excluded by science. Such a position is not logical, since theism or atheism is a product of one’s assumptions. I unashamedly start not only from a theist position (which rather than be contradicted by my scientific enquiries, is confirmed by them), but also recognize that God can reveal himself to us—this I believe He has done in Jesus Christ.

Order and the Second Law of Thermodynamics

There is a fundamental law in the universe to which there is no known exception. That is, that when there is any work done due to energy conversion, there is always some dissipation of useful energy. In purely thermodynamic terms, this means that, for a closed system, the measure of energy no longer available for useful work is increasing. This is called entropy. 4 Thus, in a closed system, the overall entropy is increasing.

No spontaneous reversal of this process has ever been observed for a closed system.
However, the law applies not only to the area of mechanics and engines. It applies to any system, since entropy is effectively a measure of the disorder in that system. In overall terms, disorder increases, cars rust and machines wear out. No spontaneous reversal of this process has ever been observed for a closed system.

For living systems, this law still applies. That which is dead (such as a stick or leaf from a tree) has no information or teleonomy within it to convert the sun’s energy to useful work. Indeed, it will simply heat up and entropy will increase.

Despite attempts by G. Nicolis Prigogine and coworkers to find auto-organization by random processes within living creatures, sustained order can never be achieved, because no new information is available. Indeed, after arguing that auto-organization by random processes may be possible in nonequilibrium systems, Prigogine states in the first reference:

Unfortunately, this (self-organization) principle cannot explain the formation of biological structures. The probability that at ordinary temperatures a macroscopic number of molecules is assembled to give rise to the highly ordered structures and to the co-ordinated functions characterizing living organisms is vanishingly small. 5

Entropy, information and the living world

The major obstacle to evolutionary theories as to origins is that information cannot be defined in terms of physics and chemistry. The ideas of a book are not the same as the paper and ink which constitute the book. Indeed, those same words and thoughts can be transmitted through an entirely different media (such as a computer CD-ROM, floppy disk or a tape recorder). The chemicals do not define the message they carry. Meaning cannot spontaneously arise, since meaning presupposes intelligence and understanding.

One of the greatest discoveries was that of DNA by Francis H. Crick (UK) and James D. Watson (USA) in 1953. This molecule was found to be the universal storage medium of natural systems. A length of DNA is formed in such a way that two deoxyribose sugar-phosphate strands together form a double helix 2nm (10-9m) in diameter with a pitch of 3.4nm. Between these two strands are hydrogen bridges, across which four types of nucleotides are placed: Adenine (A), Thymine (T), Cytosine (C) and Guanine (G). Effectively these four nucleotides are the chemical alphabet for writing “words” on the chemical “paper,” which is the two sugar-phosphate strands. The helix enables a 3-dimensional storage of information formed by the patterns of the chemical letters used. The DNA string is like a sequence of dots and dashes in a coded message. The coded information using the letters (ACG, GUC, CAU, etc.) rides on the complicated chemical molecules, but is not defined by it. Information does not equal energy or matter.

In radio signals there is a carrier wave of much higher frequency than the information signal which rides on the back of the carrier wave. Once received, the carrier wave is not important and the message is converted to sound and speech. In exactly the same way, the information concerning one cell could have been written using entirely different coding, that is, a different ordering of the nucleotides. As long as the rules stay the same, it is unimportant. Alternatively, completely different chemistry could be involved, that is, a different “alphabet” leading to a completely new language structure. What is paramount in this discussion is that information (that is the setting of the rules, the language, code, etc.) has been there from the beginning. To argue that this came by chance is scientifically preposterous. As Professor Gitt has stated, “No information can exist without an initial mental source. No information can exist in purely statistical processes.” 6

Though Dawkins has argued for a seemingly endless series of small advantageous mutations singled out by natural selection operating at the micro level 7 there are formidable arguments against his position. Denton, in his book Evolution: A Theory in Crisis, 8 discusses the problem of pleiotropy, that is, one gene affecting a number of seemingly totally unrelated functions in living organisms. For example, changes in the coat color genes in mice also affect body size. The microbiologist Behe has also ably rebutted Dawkins in his book Darwin’s Black Box, 9 where he has shown that behind the many words of this arch-defender of Darwin, there is no mechanism in Darwinian evolution to add new information to a species at the macro level by a meaningful set of changes to the DNA letters, because “forward information” as to what the changes are aimed at is needed. Otherwise the intervening mutations have no advantage. Indeed, to form the code to begin with, it is vital that the sender and the receiver part of the cell both have prior agreement as to the meaning of the code, else there can be no communication. But Darwinian evolution only has chance mutations at its disposal. Because no “advance thinking” can possibly be allowed, there is no way that the nucleotides can arrange themselves in a “pre-defined code,” since this assumes prior knowledge. Thus, the very existence of the DNA-coded language stalls evolution at the first hurdle.

Flight in the natural world—complexity all can observe

Living creatures all have examples of irreducible complexity.
Examples of complexity in the natural world are not hard to come by. Living creatures all have examples of irreducible complexity as very ably demonstrated by Behe in his book Darwin’s Black Box. One of the best examples of complexity, which defies a series of “gradual” changes (as advocated by Dawkins in his book Climbing Mount Improbable), is flight. For controlled, heavier-than-air flight, there are four fundamental requirements: (1) a correct wing shape to give a lower air pressure on the upper surface, (2) a large enough wing area to support the weight, (3) some means of propulsion or gliding, and (4) extra surfaces, or a means of altering the main surfaces, in order to change direction and speed.

Flight occurs in many branches of the living world: (a) birds; (b) insects: flies, bees, wasps, butterflies, moths; (c) mammals: bats; (d) reptiles: the extinct pterodactyls. Each class of creature is anatomically different, with no connection made even by the most ardent evolutionist. A tenuous connection has been attempted between reptiles (dinosaurs) and birds: it is seriously proposed that there was a “pro-avis” dinosaur that flapped scales on its arms to catch insects, and then changed its scales to feathers to gain airborne advantage on its prey. Even if one accepts the fossil record as a guide to change over millions of years, there is no evidence of any “pro-avis” creature ever existing in the fossil record. For the evolutionist, there is the scenario of flight evolving at least three times independently! The wings of the three main current groups of flying creatures today are substantially different: birds’ wings are made of feathers; insect wings are made of scales, membranes or hairs; and bat wings use skin spread out over a skeleton. So the evolutionist is faced with not just one impossible hurdle—that some reptiles grew feathers and began to fly—but two further hurdles. These are that flight evolved again when some rodents (mice? shrews?) developed a skin-like surface over their front legs to become bats, and then, quite separately, some insects grew very thin wings of scales, membranes or hairs to becomes flies, bees and butterflies!


A bird’s wings are made of feathers. A feather is a marvel of lightweight engineering. Though light, it is very wind-resistant. This is because there is a clever system of barbs and barbules. Each barb of a feather is visible to the naked eye and comes off the main stem. What is not generally realized is that on either side of the barb are further tiny barbules which can only be seen under a microscope. These are of different types, depending on whether they are coming from one side of the barb or the other. On one side of the barb, ridged barbules will emerge, while on the other side, the barbules will have hooks. Thus, the hooks coming out of one barb will connect with ridges reaching in the opposite direction from a neighboring barb. The hooks and ridges act like “velcro,” but go one stage further, since the ridges allow a sliding joint, and there is thus an ingenious mechanism for keeping the surface flexible and yet intact.

The next time you see a flight feather on the ground, remember it is a marvel of lightweight, flexible, aerodynamic engineering.

Reptile scales have no hint of such complicated machinery. Stahl has freely admitted, “No fossil structure transitional between scale and feather is known, and recent investigators are unwilling to found a theory on pure speculation.” 10

There is no genetic information within reptile scales to allow such a unique device as the sliding joint of a feather to be made. The tortuous route suggested by some of small “advantaged mutations” to scales leads to clumsy structures which are, in fact, a disadvantage to the creature. Not until all the hook and ridge structure is in place is there any advantage, even as a vane for catching insects! Unless one invokes some “thinking ahead” planning, there is no way that chance mutations could produce the “idea” of the cross-linking of the barbules to make a connecting lattice. Even if the chance mutation of a ridge/hook occurs in two of the barbules, there is no mechanism for translating this “advantage” to the rest of the structure. This is a classic case of irreducible complexity which is not consistent with slow evolutionary changes, but quite consistent with the notion of design.

But that is not all. Even if one had the feather, the delicate lattice structure would soon become frayed, unless there was also oil to lubricate the sliding joint made by the hooked and ridged barbules. Most of us realize that once the barbs of a feather have been separated, it is difficult to make them come back together. The feather becomes easily frayed in the absence of oil, which a bird provides from its preening gland at the base of its spine. Some of this oil is put on its beak and spread throughout the feathers, which for a water bird also gives waterproofing of its surface (thus, water slides off a duck’s back). Without the oil the feathers are useless, so even if a supposed land-dwelling dinosaur got as far as wafting a wing, it would be no use after a few hours!

As one might expect, however, the story does not end there either, for a bird can fly only because it also has an exceedingly light bone structure, which is achieved by the bones being hollow. Many birds maintain skeleton strength by cross members within the hollow bones. Such an arrangement began to be used in the middle of this century for aircraft wings and is termed the “Warren’s truss arrangement.” Large birds, such as an eagle or a vulture, would simply break into pieces in midair if there were some supposed halfway stage in their skeletal development where they had not yet “developed” such cross members in their bones.

Furthermore, birds breathe differently. The respiratory system of a bird enables oxygen to be fed straight into air sacs, which are connected directly to the heart, lungs and stomach, bypassing the normal mammalian requirement to breathe out carbon dioxide first before the next intake of oxygen. Human beings breathe about 12 times a minute, whereas small birds can breathe up to about 250 times a minute. This is thus a perfect system for the high metabolic rate of birds, which use up energy very quickly. In fast forward flight particularly, birds could not sustain exhaling against the oncoming airstream. Note also that birds are warm-blooded, which presents a vast biological hurdle for those who maintain a reptile ancestory for birds.

Consider the wing-flapping motion of a bird. This motion requires a bird to have strong wing muscles, with a forward-facing elbow joint to enable the foreshortening of the wing used much in the upward stroke of most species, and in the dive of birds of prey. The versatility of the swivel joint at the base of the wing, coupled with the elbow joint on the wing itself and the smooth feather structure overlaying all, leads to great flexibility in the aerodynamics of the wing. Lift and drag can be balanced with instant movements, which in aircraft still require comparatively cumbersome changes of flap and ailerons.

Suppose we have an “almost” bird with all the above structures—namely feathers, preening gland, hollow bones, direct respiration, warm blood, swivel joint and forward-facing elbow joint—but no tail! Controlled flight would still be impossible. Longitudinal stability can only be achieved with a tail structure, which most small boys soon realize when making paper airplanes! But what possible advantage do all of the above have for any land-based “almost” bird? Such a creature would be easy prey to any hunting animal.

In the list of mechanisms (feathers, preening gland, etc.), all are essential. Attempt to drop one and the whole project fails! The tail is essential, and with the tail must come another muscle to operate the variable small, but all-important wing surface for instance, holding the plumage spread out and downwards when coming in to land. In other words, the tail is no use as a static “add-on.” It must have the means of altering its shape in flight. All these mechanisms are controlled by a nervous system connected to the on-board computer in the bird’s brain, all preprogrammed to operate within a wide envelope of complicated aerodynamic maneuvers.


One of the most delightful demonstrations of all of the above principles coming together involves the hummingbird. These small birds have the ability to beat their wings at up to 80 beats per second and, as is well known, can hover, fly backwards, forwards and sideways with ease (much of the information here is drawn from an excellent article by Denis Dreves 11). Speeds of 50 miles an hour are commonplace for these flying marvels. Fuel must be replenished very quickly because of the great turnover of energy. Consequently, the bird must feed on a food which can be broken down quickly into energy.

All this is achieved by feeding on the nectar of flowers, which requires the ability to hover and a thin long beak to get into the flower (e.g., a fuchsia for the rufous hummingbird). The bird also has a special tongue with two furrows, enabling the nectar to be stored on it. The long tongue goes in and out of the bill, at an unbelievable rate of 13 times per second and, when retracted, is curled up at the back of the head.

One can envisage the odd scenario of the supposedly half-evolved hummingbird either with the ability to hover and a sparrow beak, unable to feed, or the long beak but no ability to hover, which would mean flying into the flower with no ability to stop! All the requirements must be there to begin with.

The extreme maneuverability of hummingbirds is due to their having the ability to swivel the wing through a much greater angle than other birds. Consequently, the hummingbird can produce a power stroke on the upward motion of the wing as well as the downstroke, and the motion of the wing tip of a hummingbird in flight sweeps out a figure eight as the joint swivels round some 90 degrees first in one direction, and then about 90 degrees in the other direction. Further rotation is possible which means that the wing can thus beat a power stroke in any direction, with small asymmetries enabling sideways movements as well.

Flight cannot be explained by supposed evolutionary change. The attempts to find any transitional forms have all failed. Archaeopteryx has been shown to have fully developed flight feathers (thus, no half-bird), with other recognizable birds found fossilized at a lower level. Other supposed “pro-avis” creatures (half reptile/half bird) have never been found. The evidence is overwhelming that birds have always been birds, and is entirely consistent with their being created right at the beginning on Day 5, just as the Bible says.

It is not scientific to argue, on the one hand, for the obvious design of a Boeing 747, and then rule design “out of court” when considering the far more versatile flight of an eagle, falcon or the remarkable hummingbird. Modern minds within the secular media are presenting an unscientific duality of thought when praising engineering complexity in man-made machines, glorying in the great creative advances of mankind, but presenting the complexity in the world around us (of often far greater intricacy than man-made machines) as due to a gigantic unplanned cosmic experiment, with no Creator.

Flying insects

Flying insects have no connection whatsoever with birds, and yet flight is fully developed in all the fossils of flies, moths and butterflies. There is not any contender at all for any transitional forms. The wings of such creatures are exceedingly fragile, made of scales, membranes, or sometimes hairs or bristles. They start as larvae or grubs, with some feeding on totally different substances than the adult (e.g., caterpillars and butterflies). The best example is the dragonfly, which starts as a nymph underwater, obtaining oxygen from the water; yet no adult dragonfly could possibly exist in the same surroundings. It is quite common for dragonflies to reach speeds of 30 miles per hour, but no transitional fossils exist. The evidence is, in fact, of much larger, fully developed dragonflies with a wingspan of two to three feet in the past, 12 indicating decline today, rather than advance. The related damselfly has the remarkable ability to hover as well, such that the sophisticated aerodynamics of the four wings operating independently inspired the design of early forerunners of the modern helicopter.

The complexity of the life cycle of creatures such as the butterfly (caterpillar to chrysalis to butterfly) and the dragonfly (water nymph to dragonfly), and their perfect wing structure as adults, points to intricate design which cannot be explained by small changes. The survival of each species is dependent on all the mechanisms being present to begin with.

Migrating butterflies

The monarch butterfly of North America migrates 2,000 miles from California in the northwest (or Ontario in the northeast) to the over-wintering site of central Mexico. More amazing is the following fact: some adults who make the journey back are fully mature, so that some females lay eggs and die en route northward.

These offspring, after going through the caterpillar/chrysalis stage, continue the migration northward. More remarkable still is the fact that not all these make it back to the northeast of America, so another generation, the third, then finally completes the journey, fulfilling the aspiration of grandma! This, of course, means that a remarkable system of information is bound up in the genetic coding of each butterfly, such that it “knows” at what stage of the migrating cycle the group of butterflies is in. This information is passed on to each generation. Such a delicate mechanism shouts intelligent design!

Furthermore, it has been established that magnetite has been found in the bodies of monarch butterflies (and also honeybees), indicating that they are able to orientate themselves by sensing the earth’s magnetic field. Their eyes are also sensitive to polarized light from the sun, again giving them a direction cue. The two eyes, far from being simple, are actually each made of 6,000 separate lenses! There are no half-formed butterflies in the fossil record. They are similar to modern ones—fully formed and ready to go!

Flying mammals—bats

Bats are entirely different from birds and insects, with wings made of skin and a radar system of echo-sounding with pinpoint accuracy, enabling the bat to find insect food on the wing, with unbelievable precision. No half-bat has ever been found in the fossil record, and it would be hard to imagine how such a halfway creature could survive. Flight alone is only possible with fully developed wings. This combined with the sophisticated radar is yet another example of irreducible complexity.

Combustion and the bombardier beetle

Lastly, an example from combustion—the bombardier beetle. This creature requires an explosive mixture (hydrogen peroxide and hydroquinone), a combustion chamber to contain the chemicals, exhaust nozzles to eject the mixture into which two catalysts are also injected (the enzymes catalase and peroxidase)—all this at the right moment to make the violent reaction take place as the mixture leaves the back end. The bombardier beetle manages it all with ease, along with the capacity to send four or five bombs in succession into the face of a predator, controlled by muscles and directed by a reflex nervous system. This is combustion theory and practice par excellence! Even the combustion chamber of the latest Rolls Royce Trent Gas Turbine would not reach the complexity of this little creature.

All the above requirements would have to be in place at the same “evolutionary moment”! There is no way any “intermediate” could survive because of the risk of either (1) blowing him/herself to smithereens (because he has the combustible mixture and the catalyst, but no exhaust system), or (2) slowly eroding his/her insides by having a combustible mixture, all the necessary exhaust tubes, but no catalyst, or (3) being eaten by predators despite trying to blow them away with catalysts through a fine exhaust system, but no combustible mixture! For the creature to function, everything must all be in place together—as a good Rolls Royce engineer knows—for aircraft gas turbines to work!

Consistency with a biblical worldview

As a scientist, I see nothing to discount straightforward belief in Scripture, when considering the mechanisms in nature. Those which have been considered in this chapter could be added to by many more intricately balanced mechanisms which overwhelmingly testify to a creative hand.

As a scientist, I see nothing to discount straightforward belief in Scripture.
Many, of course, refuse to acknowledge the evidence for design in nature because they make the untestable assumption of atheism. If someone seriously did doubt the design of a modern airliner, that person could be convinced by taking him into an aircraft factory and introducing him to the teams of design engineers. In the same way, man’s prejudice against design in creation can only really be answered by a radical change of heart and by personally meeting the Author of all. In the end the difference between these two worldviews is due to religious differences. I believe that it is because humans do not want to be accountable to a Creator God that they persist with a theory which has little evidence to support it.

Furthermore, in the view of this author, there is much in the fossil record which is entirely consistent with catastrophic destruction in a worldwide Flood. We have for too long underestimated the forces of nature, and only perhaps in recent decades have geologists (some reluctantly) returned to a catastrophic view of many rock layers.

In June 1991 the volcano Pinatubo in the Philippines erupted with a cloud of ash 130,000 feet (over 24 miles) high and 10 miles wide. Pyroclastic flows devastated the landscape, with later further volcanic ash and mud flowing for thousands of square miles. The volcanic blast in 1883 at Krakatau (in between the Sumatra and Java islands of Indonesia) was even greater; this was heard 2,900 miles away, with rocks thrown 34 miles high into the atmosphere and dust falling 3,313 miles away ten days after the explosion. A tsunami (tidal wave) 100 feet high was created, which travelled right across the Indian Ocean at 450 mph, and volcanic mist circled the earth and turned the sun blue and green.

On May 18, 1980, probably the most well-documented recent volcanic eruption took place at Mount St. Helens in Washington state. The top of the mountain was completely removed and a hot blast ripped away 150 square miles of forest. The movement of the mountain caused a wave nearly 900 feet high to move across Spirit Lake, with the effect that approximately one million tree trunks found their way into the lake. Many others were pushed further down into lower regions by mudflows and were actually observed upright, roots down, moving at great speed in the mudflows.

Not until this eruption had it been quite appreciated what the immediate aftermath of volcanic eruptions can sometimes cause. Sediments 600 feet thick were exposed by subsequent mudflows carving their way through the initial sediments before they had hardened. The Toutle River canyon, formed in 1980, is effectively a miniature 1/40th version of the Grand Canyon. The implication is that the Colorado River is not the way the world’s greatest canyon was formed, that is, by slow erosion. All the evidence is consistent with massive volcanic and sedimentary upheaval on a continental scale, followed by the bursting of great dams of water, and clay breaking and causing subsequent massive mudflows, entirely consistent with the description in the book of Genesis of the Great Flood.

When the Bible speaks historically (and literary experts agree Genesis is written as history), I believe we can trust what it says.

In Six Days

Can any scientist with a Ph.D. believe in the idea of a literal six-day creation? In Six Days answers this provocative question with 50 informative essays by scientists who say “Yes!” Taking a factual and scientific look at the evidence for evolution, physicists, biologists, and chemists conclude that evolution may offer no more evidence than traditional religion, and factually, it may lag behind.

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  1. Andrew McIntosh, Genesis for Today: Showing the Relevance of the Creation/Evolution Debate for Today’s Society, Day One Publications, Epsom, United Kingdom, 1997.
  2. Ibid, chapter 2, “Genesis and Science.”
  3. Denis Brian, Einstein: A Life, J. Wiley, New York, p. 186, 1996.
  4. McIntosh, Genesis for Today, Appendix A.
  5. I. Prigogine, G. Nicolis, and S. Babloyant, Thermodynamics of Evolution, Physics Today 25(11):23–8, 1972; G. Nicolis and I. Prigogine, Self Organization in Non-equilibrium Systems, Wiley, New York, 1977.
  6. Siemens Review, vol. 56, part 6, p. 36–41, 1989.
  7. See Richard Dawkins, The Selfish Gene, Oxford University Press, New York, 1989; The Blind Watchmaker, Penguin, New York, 1991; and Climbing Mount Improbable, Norton, New York, 1996.
  8. Michael Denton, Evolution: A Theory in Crisis, Adler and Adler, Bethesda, MD, p. 142–156, 1986.
  9. Michael Behe, Darwin’s Black Box, Free Press, New York, p. 220–221, 1996.
  10. Barbara J. Stahl, Vertebrate History: Problems in Evolution, McGraw-Hill, New York, p. 349, 1974.
  11. Creation 14(1):10–12, 1992.
  12. See David Attenborough, Discovering Life on Earth, Little, Brown, Boston, MA, p. 60–61, 1981.

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