There is a widespread belief that, given enough time, chance, or randomness, can produce a very wide range of different possible outcomes, including those, such as the existence of Life on the planet Earth – and even the Universe itself, that are highly organized, varied, and able to evolve or develop in seemingly directed ways. A branch of mathematics, called probability theory, seeks to calculate precisely the probability of certain outcomes in a variety of different scenarios. With the decline in Christian societies in the belief in God, or divine agency, as an explanation for the existence of both Life and the Universe, as well as their particular features, many non-religious people have turned to the Idol of Chance in order to explain these things. However, contrary to this common belief, there are many things that chance, or undirected, random processes, simply cannot beget.
I do not know which human fool first made the declaration that, if you were to lock a bunch of monkeys in a room, each monkey provided with a typewriter, then eventually they would type the Complete Works of Shakespeare. It is astonishing how many times this preposterous declaration has been repeated by other imitating human fools. First of all, I do not believe that anyone has actually attempted this thought experiment; for if it were attempted, you would find that the monkeys would very quickly lose interest in punching the typewriter keys one after another, since this is, for them, a completely meaningless activity. These bored and, with the passage of time, increasingly frustrated monkeys would proceed to do all manner of things, such as tearing the paper out of the typewriter and crumpling, ripping, or trying to eat it, pushing or throwing the typewriter from the table, jumping up on top of it or on the table, and so on. In fact, if they were free to do as they pleased, it would soon be found that they would rather do anything except continue to press the typewriter keys in a random manner. Hence, the only way you could keep them at this monotonous and meaningless task is either by continually rewarding them or by forcibly constraining them, such as by strapping them to their chairs to keep them pecking at the keys. Unless one is prepared to inflict considerable frustration and suffering on these animals, one would be forced to abandon the experiment long before any one of these primates was able to type even two consecutive words without any spelling mistakes.
Of course, it is possible, without inflicting suffering on any living organisms, to create a computer program that could mimic the essential qualities of this thought experiment that is intended to demonstrate, given enough time, what astonishing things can be accomplished by pure chance. With the advanced state of computer technology, this program could be run day and night at very high speeds. But even in this case, there is a serious problem – the fact that, besides the twenty-six letter keys, every English-language keyboard is equipped with the ten number keys from “0” to “9”; moreover, there are also punctuation keys and other specialized keys, such as the “shift” and “return” keys, which must be pressed only in certain very precise situations, the first in conjunction with a letter key to make a capital letter, and the second in order to begin a new paragraph. The chance that a number key will be pressed is roughly ¼ or 25%. However, although numbers do occur in some of Shakespeare’s works, such as in the title, The Two Gentlemen of Verona, or the three weird sisters in Macbeth, they are generally written in letter, and not in numerical, form. Hence, there will be far too many numbers in the randomly-generated computer text. And the likelihood that a single play such as Hamlet, which contains more than 100,000 letters, including spaces, which must also be counted as “letters” since this is a randomly-generated text, could be produced by this random process is so low as to be equivalent to zero. Among these non-numerical, randomly-generated texts, very few of them will contain words in a meaningful sequence, let alone the exact sequence of words that comprise a play such as Hamlet. In other words, contrary to what some people believe, a literary work such as Hamlet cannot be generated by purely random processes. And the reason is that Hamlet, as well as all the other of Shakespeare’s many works, was not produced by a random process.
Of course, you could increase the likelihood that this program could achieve its objective by introducing rules such as, “There shall be no numerals in the text,” “A period, comma, hyphen, semicolon, or exclamation or question mark shall appear only at the end of a group of letters, and not at the beginning or between two or more letters,” “Each time there appears a period, exclamation mark, or question mark, it shall be followed by a space, and then the following letter shall be capitalized,” and so on. But with each new rule, one is clearly abandoning more and more the original premise of pure randomness, or chance, with which one began the experiment.
But even if one limits the possible number of different keys to thirty – the twenty-six letter keys along with a few punctuation and other keys – the number of different possible combinations of even a small number of consecutive characters is so large that the likelihood that a particular combination will appear randomly is vanishingly small. For example, in a sequence of twenty characters, there are 3020 different possible combinations, or roughly 3.5 x 1029. Even at the rate of one combination per second, it would still take more than 1022 years for every single possible combination to be listed, a time that is much, much longer than the estimated age of the Universe. And in a sequence of 112 characters, which is the length of the last sentence in this paragraph, the number of possible combinations is 30112 or 2.7 x 10165! Hence, in a randomly-generated sequence of more than 100,000 characters, which is the length of a work like Shakespeare’s Hamlet, although the probability that the exact sequence of letters contained in Hamlet could be generated randomly is not zero, in realistic terms, it is zero. This shows how absurd is the claim that this play, or any other long literary work, could be produced by chance.
In its original formulation, the monkeys typing at the typewriters, or the random character-generating process, is to be repeated an infinite number of times or for an infinitely long time, thus demonstrating mathematically that a highly unlikely event will achieve a probability of 100% of occurring if only it is repeated enough times. However, this is merely an abstract mathematical truth that has nothing to do with reality, since the world we live in is finite, meaning that it is not possible to do anything an infinite number of times or for an infinitely long period of time. Although there are individuals who use the word “infinity” glibly, whenever a person speaks of infinity, such as something being infinitely large, infinitely dense, infinitely massive, or occurring an infinitely large number of times, it is important to realize that one is not talking about reality. My concern is with reality and what is possible given the parameters of the world we live in, which parameters we cannot change as easily and as arbitrarily as we can in such hypothetical scenarios or thought experiments which some people are fond of considering. In other words, we should not make the mistake of supposing, as some people do, that such an abstract mathematical truth has any application to, validity in, or significance for the world we live in.
Another real-world example will serve to illustrate what I mean when I say that there are many things that chance cannot beget. At least in some countries, the hamburger has become a ubiquitous food object in recent decades. However, it is impossible for a hamburger to arise from purely random, meaning non-human-directed, processes. Even though a hamburger consists entirely of substances which all exist separately in the natural world – the wheat, yeast, and water in the bun, the ground meat in the patty, the cheese that was made from cow’s milk, and the sauces that were made, for example, in the case of ketchup, from tomatoes, vinegar, sugar, and various spices – it is simply not possible for these natural substances to be, as the case may be, ground, mixed, modified, leavened, solidified, fermented, shaped, strained, and/or cooked to come together in the familiar form known as a hamburger. In other words, no matter how long the Earth continues to exist, it will never happen that a hamburger will arise, somewhere on its surface, randomly. Stated in another way, the probability of this happening randomly is not a very low number – 0.0000… with a “1” at the end – but ZERO.
Even the cooked bread that forms the hamburger bun is unlikely to result from random processes, for this would require that a quantity of mature grains of wheat are first collected, somehow separated from their clingy, protective husks, accidentally pulverized into very fine particles, mixed evenly with water and a small quantity of yeast, kneaded, left to rise at a temperature that is neither too high nor too low while being protected from drying out, formed into buns, and cooked at a steady temperature until they are done but not overdone. In addition, the repeatedly transformed wheat kernels must be protected at all times from hungry animals during these randomly-occurring processes. The same is true of ketchup; for although it could happen that a fire roasts a ripe tomato that hangs on a tomato plant, or a tomato ripens until it becomes mushy, neither natural result remotely resembles the finished condiment known as ketchup. For one also needs to puree the tomatoes, strain out the solid parts like the skin and seeds, mix in small amounts of salt, vinegar, sugar, and spices, and cook the mixture at an even temperature for several hours to reduce it to the desired consistency. Moreover, the vessel in which the mixture is cooked, whether it is made from metal, glass, or fired glazed clay, is not something that occurs by chance in Nature.
Of course, in the case of simpler culinary dishes like roast chicken, it is possible that they could arise from random processes, since it could happen that a chicken, or any other bird or animal, is caught in a fire and burned to death. But the result would probably not much resemble roast chicken, since, although the fire may very well singe off all the bird’s feathers, it will cook the meat unevenly, with parts of the exterior charred or carbonized, while parts of the interior remain raw or undercooked. Moreover, the bird’s innards will still be in place, since these have not been removed prior to cooking, as is usually done when one prepares roast chicken. Furthermore, there is no equivalent in Nature to basting, or collecting the melted fat and juices from the bird while it cooks and pouring them over it to keep the meat from drying out and the skin from burning. In Nature, these liquids would simply fall to the ground and be absorbed by the earth. The greater the number of deliberate human processes that intervene between the unadulterated natural substance, animal, or plant and the finished dish, the less and less likely it is that the dish could result from random processes.
The question we should ask ourselves is, “Why do so many people mistakenly believe that a highly complex, ordered object like the works of Shakespeare could have been produced by a random process, such as monkeys randomly punching the keys of a typewriter?” The simple answer is, because they can conceive of the possibility that a room full of monkeys, each sitting at a typewriter and randomly pressing the keys, could produce the works of Shakespeare.
However, conception is not reality; and, as this example demonstrates, there are many instances where conception is not even possibility. Unlike children, whose experience of reality is limited, most adults know that there are many things that can be conceived but do not actually occur or exist in the world. And yet, even with their greater experience of reality, there are nevertheless many adults who make the mistake of assuming that, if it is possible to conceive something, then that means there exists the possibility of its being realized, however small this possibility may be. A common example of this is lotteries, where even though the probability of any one person winning the jackpot is exceedingly small, there are many people who continue to buy lottery tickets because they repeatedly conceive or imagine themselves winning the jackpot, so great is their desire for this highly improbable outcome to be realized.
But with some exceptions, such as sexual reproduction, the real world does not unfold like a lottery, the roll of a die, or even like the flipping of a coin. It is not the case that, in the Universe, there is a constant metaphorical reshuffling of the cards, flipping of a coin, or roll of a die with a large number of sides, each having the same probability of appearing on the uppermost side and thus being realized. Although these artificial human-created events – flipping a coin, rolling a six-sided die, picking a card out of a pack of fifty-two cards, or some other purely random process – are often used to model real-world events, there are many instances where they do not actually correspond to reality. And even in cases where they do model reality more or less approximately, there are many people who greatly overestimate what can be achieved by pure chance, because they are ignorant of the actual probability of a certain outcome occurring randomly.
Related to the previous question is the following question: “When we speak of the different possible outcomes of an event, such as rolling a die, choosing a card out of a pack of fifty-two different cards, or, following an act of sexual intercourse or fertilization, which of the many different spermatozoa will fertilize an egg, where do these alternative possible outcomes exist?” The answer is as follows: the outcome that is realized exists in reality; but the alternative outcomes that are not realized exist only in our brains. Before a die is rolled, a person can conceive that any one of the six possible outcomes can result, since one has experienced this occurring from having observed many previous rolls of a die. But afterwards, the number that is shown on the die’s uppermost side is realized, while the other five numbers remain as unrealized possibilities in that particular toss of the die. In some cases, our inability to predict the outcome is due to ignorance. In the card example, if one knew the position of each card in the deck, and if one were able to follow exactly the way this order is changed as a result of shuffling the deck, then one would still know exactly where each card was in the deck, and hence, there would be no doubt about, for instance, which card was on top of the deck once the shuffling was completed.
In the case of fertilization, the many different possibilities, represented by all the different genetic combinations that are contained in the individual spermatozoa, do in fact exist; but only one of them – the sperm cell that succeeds in fertilizing the egg – is realized, while all the other possibilities die, literally, thus remaining as unrealized possibilities. However, although there is indeed a degree of randomness in this process, in the sense of which of the many different spermatozoa, each containing a different genetic combination, will succeed in fertilizing the egg, it is a very peculiar kind of randomness, which I will call bounded randomness. This is illustrated by the fact that, for instance, a fertilized fish egg cannot give rise to a mammal, reptile, insect, or plant. Furthermore, a fertilized tuna egg cannot give rise to any other kind of fish, and neither can a fertilized bluefin-tuna egg give rise to a different species of tuna. In other words, with the exception of mutations, the genetic variation that exists within any given species is limited within narrow boundaries.
Another important point is that almost any one of the many other spermatozoa that did not succeed in fertilizing the egg could also have begotten a healthy, viable offspring. How do we know this? Although each fertilization of an egg by a sperm cell involves a particular genetic combination that is unlikely to be reproduced exactly in other eggs and spermatozoa – and, moreover, the particular genetic combinations contained in all the other spermatozoa that failed to fertilize the egg are also unlikely to be reproduced in future spermatozoa, the high success rate over a very great many births shows that this is a process with an extremely high rate of success, in the sense of producing viable, healthy, and fully functional offspring. In other words, sexual reproduction is a form of controlled randomness, or randomness within very tightly confined boundaries. For straying or venturing too far beyond these boundaries risks increasing the chances of reproductive failure, in the sense of begetting a non-viable, unhealthy, grotesque, atypical, or non-functional offspring.
The banality of this event masks the truly astonishing and miraculous nature of this singular event – the fact that the extraordinarily complex organisms that result from sexual reproduction is due to the union of two cells which were produced by two organisms that, prior to their mating, did not plot, plan, conspire, formulate, or in any other way organize to ensure that this union would produce viable, healthy offspring. This leads to the following question: Given its extraordinarily complex nature, with all the many different things that could, and occasionally do, go wrong, why is sexual reproduction such a highly successful process, in terms of its ability to produce healthy, viable, functioning offspring? The consideration of this question will lead one to realize that the likelihood that this process arose and was perfected by chance is about as high as the likelihood that a play by Shakespeare could also arise by chance.
To declare, as dogmatic Darwinians are wont to declare, that, like all other features of living organisms, sexual reproduction also arose from natural selection is to overlook the important fact that it is sexual reproduction that produces the widely varied materials on which natural selection can act. For without sexual reproduction, there is only identical reproduction, which produces far less variability and complexity than the other, and historically more recent, reproductive process. The difference between these two reproductive strategies is comparable to the difference between the simplistic military strategy that hurls wave after wave of identical unarmed soldiers against one’s adversary in the hope that these incessant numbers will succeed in overcoming it, and a much more nuanced, cunning, and reflective strategy that, with a smaller number of soldiers, uses an assortment of weapons, wiles, plans, formations, and stratagems to overcome one’s adversary or accomplish one’s goal.
Has the universe in 13.7 billion years of existence created all the possible fundamental particles and stable atoms? Yes. Now consider proteins. These are linear sequences of twenty kinds of amino acids that typically fold into some shape and catalyze a reaction or perform some structural or other function. A biological protein can range from perhaps fifty amino acids long to several thousands. A typical length is three hundred amino acids long. Then let us consider all possible proteins that are two hundred amino acids in length. How many are possible? Each position in the two hundred has twenty possible choices of amino acids, so there are 20 x 20 x 20 200 times, or 20 to the 200th power, which is roughly 10 to the 260th power possible proteins of 200 amino acids in length.
Now let us ask if the universe can have created all these proteins since its inception 13.7 billion years ago. There are roughly 10 to the 80th particles in the known universe. If these were doing nothing, ignoring space-like separation, but making proteins on the shortest time scale in the universe, the Planck time scale of 10 raised to the -43 seconds, it would take 10 raised to the 39th power times the lifetime of our universe to make all possible proteins length 200, just once. In short, in the lifetime of our universe, only a vastly tiny fraction of all possible proteins of length 200 can have been created. This means profound things. First, the universe is vastly non-ergodic in the physicists’ sense of the ergodic hypothesis at the foundation of statistical mechanics. It is not like a gas at equilibrium in statistical mechanics. With this vast non-ergodicity, when the possibilities are vastly larger than what can actually happen, history enters. Not only will we not make all possible proteins length 200 or 2000, we will not make all possible organs, organisms, social systems. There is an indefinite hierarchy of non-ergodicity as the complexity of the objects we consider increases.
In relation to the manifold possibilities raised in the excerpt, let us ask the following question: In an amino acid sequence that is, for example, two hundred units long, is it true that every single possible combination will give rise to a viable or useful protein, meaning a protein that could be incorporated or utilized in some manner in the body of a living organism?
Clearly not, for this would be like saying that every single combination of purely random letters constitutes a meaningful text, or that a random sequence of musical notes will give rise to a harmonious melody. In fact, just as the vast majority of random combinations of letters or musical notes will be meaningless or sound like noise, the vast majority of amino acid sequences will probably be useless or non-viable – that is, they cannot give rise to, or be helpful in sustaining, life.
The key question then, is, How did Nature, which according to Darwinians is a completely blind and non-directed process, differentiate between those relatively few proteins that would be useful in supporting or perpetuating life forms, and the very many others that are not useful for this purpose? Of course, the obvious answer is that those proteins that were not useful would not have survived in the body of a living organism, while those that were useful survived and were reproduced many, many times. However, this standard answer merely postpones, without resolving, the fundamental difficulty that we are considering. For the point of this question is made clear if we ask it at the very beginning of life: If organic molecules such as proteins arose randomly, and if the vast majority of amino acid sequences are neither viable nor useful for life, meaning that the probability of a useful sequence arising by chance is very, very low, then how did life get started in the first place? The likelihood of this happening by chance is further reduced by the fact that, prior to the existence of life, the physical world was most certainly not trying, at a furious rate – like a human-designed computer program that tries out very large numbers of random combinations of certain variables to see whether it can produce a certain result or not, random combinations of different organic molecules to see which ones would be viable and give rise to life. For to assume this would mean that the non-living physical environment that was the early Earth was attempting to produce life, which is contrary to what Darwinians believe and hold as scientific gospel.
The same problem exists when we consider sexual reproduction, since this process consists only of the random permutations of successful outcomes, genes, or proteins, since the great majority of fertilizations result in healthy, viable, living organisms. Since sexual reproduction, and evolution in general, is assumed to be a non-directed process, how was it able to generate these successful outcomes in the first place, when these outcomes are vastly outnumbered by the much larger number of unsuccessful outcomes? For, in my opinion, to assume that these successful outcomes arose by chance is no different from believing that one of Shakespeare’s works could also arise by chance.
In the essay, “The Cloud Cuckoo Land of False Ideas,” we considered the highly unreliable nature of our human ability to conceive things that differ from reality, since many of these conceptions are either improbable, meaning have a low probability of occurring, or impossible, meaning have no possibility of occurring, given the parameters and restrictions of the world we live in. An example is the common belief in the past that the Earth was flat. Although most people can easily conceive of such a large, flat object orbiting a star like our Sun, the reality is quite different. Given our knowledge of the way the Universe operates, in particular Newton’s Law of Gravitation, we now know that it is impossible for a large planet like the Earth to have a flat, rectangular shape, for such large objects tend to assume a spherical shape, since this is the only possible stable shape. Similarly, although it can easily be conceived, the widespread past belief that the Sun revolves around the Earth is also impossible, for given the vast difference in their masses – the Sun is about 330,000 times more massive than the Earth – it cannot happen that the more massive object revolves around the less massive object.
These considerations lead to the following important principle: Although conceivability implies neither probability nor possibility, many people make this mistaken inference, by assuming that if they are able to conceive something, then that means that it is either probable or, at the very least, possible. Another way of stating this principle is that, given the laws and conditions of the world we live in, we humans are able to conceive of many things that are impossible, while we fail to recognize their impossibility. I will call this fairly common error the Conception Fallacy. There are two basic forms of this fallacy: believing that an impossible event is possible, and believing that an improbable event is probable – that is, overestimating its probability. Although many things that are possible, such as building flying machines, cloning living organisms that normally reproduce sexually, sending a man to the moon, making moving pictures, and creating new chemical substances that didn’t exist before, were unexpected or inconceivable to most people before they were realized by some individual, this does not mean, as some people take it to mean, that anything that can be conceived is therefore possible.
In addition, the more often a person conceives or imagines something happening, such as winning a lottery, Nobel Prize, or Olympic gold medal, dying in a car or plane crash, marrying the person of one’s dreams, being infected by a deadly disease, becoming rich or famous, human beings colonizing other planets in the Universe, and so on, then the more probable one will believe this event or outcome to be. And yet, considered objectively, there is no correlation between these two things – the number of times one conceives something happening and the actual, or objective, probability estimate that it will happen. It is important to recognize that there exists no correlation or necessary relationship between subjective probability and actual probability estimates, for these two things are determined differently. If there were no difference between them – that is, if subjective probability never deviated from objective probability – then human behaviour would be much more rational, and common activities like gambling and buying lottery tickets would be much less popular than they are.
In the two cases that we have considered in detail – monkeys producing Shakespeare’s works and chance producing a hamburger – despite their impossible nature, a filmmaker could create the illusion of possibility by showing a monkey pressing the keys of a typewriter, and then, cutting to the page, a line from one of Shakespeare’s plays, such as “O, pardon me, thou bleeding piece of earth,” appearing on the page, thus making it look like the monkey is actually typing these words. Similarly, a filmmaker could show a rocky or deserted landscape, and then, by stopping the film and placing a hamburger in the frame before restarting the film, make it appear that a hamburger has miraculously appeared in the world through pure chance. But these cinematographic illusions, which are often employed by filmmakers in order to present a certain sequence of events to the viewer, mask the essentially impossible nature of these two events.
There is an important application of the concepts that we have been considering: just as it is impossible that a complex, human-generated work such as Hamlet, or even the more prosaic hamburger, could have arisen by chance, in a Universe that was not designed to support Life, it is equally impossible that Life could have arisen by chance. For the present orthodox scientific belief is that Life – which is a highly ordered, complex, and astonishingly varied kind of existence that, even if it exists elsewhere in the Universe, is extremely rare – arose on the Earth by chance, and not as a result of divine intervention, or some other kind of purposive, meaning non-random, process. The separation that exists between organic molecules, some of which can be produced by random processes, and Life is far greater than the separation between all the individual ingredients of a hamburger and a hamburger, since in the latter case, these differences are merely transformative mechanical processes – such as hulling, grinding, pureeing, straining, mixing, forming, and cooking – and finally assembling the ingredients together. But the transition from non-life to Life involves a mysterious process that, despite the many remarkable discoveries made by scientists, is still unknown. Since the Theory of Evolution has probably been the single greatest reason for the prevalence of this widespread belief, one way of considering this debate is by asking, “What exactly did Darwin’s Theory of Evolution by Natural Selection demonstrate?”
The immediate result of Darwin’s theory was to show that the creation story contained in the Book of Genesis is wrong – that, contrary to what Christians believed at the time, and to what some of them continue to believe, each species that exists, as well as those that existed in the past, was not created by divine fiat, as is claimed in the Bible. However, later generations of Darwinians extended this result by declaring that Darwin’s theory also demonstrates that life itself arose by chance. This latter belief, although it may seem like a simple logical extension of the Theory of Evolution by natural selection to the origin of Life, does not in fact follow from it. In other words, the belief that Life arose by chance, which, in many people’s view, now forms an integral part of the Theory of Evolution, is in fact the result of a sophistical extension of this theory into areas where it has no validity. For those who are determined to account for all aspects of Life by purely mechanical laws and processes, the question of how Life first arose poses one of the most serious and, in my opinion, insoluble difficulties.
For natural selection to produce its amazing, ordered, and diversifying effects, it must first have materials on which to operate. How are these materials produced? Very simply, they are produced by one of two different processes: identical reproduction and sexual reproduction. This means that the Theory of Evolution by natural selection, which is a theory that attempts to account for certain features of living organisms, has no validity outside of biology, or the study of living organisms. In particular, this means that natural selection cannot be used to explain or account for the origin of life, since it was only with the beginning of life that natural selection first had living materials on which to act.
This latter point is shown by the fact that every attempt to account for the origin of life by purely random processes is either laughably incomplete or pseudoscientific in nature. To conclude, as many scientifically-credulous persons have done, from the mere fact that certain organic molecules can be produced by applying electricity to a liquid or gaseous compound that contains simpler molecules or chemical elements or compounds, which are believed to have been common on the Earth around the time that Life first appeared, is to make a wholly unwarranted leap of faith. For organic molecules, even if they are able to replicate themselves, are not alive; if they were, then it should be possible to create a new life form from these replicating organic molecules. What this means is that the divide that separates Life from the many different forms of non-life is a fundamental one, which we clever humans, despite all our efforts to understand and overcome it, have not been able to accomplish.
The fundamental nature of this divide is shown by the fact that, despite our comprehensive and detailed understanding of many of Nature’s processes, both living and non-living, and despite both our extraordinary creative abilities and our ability to manipulate, modify, clone, and breed living organisms so that they develop certain characteristics, no human being has yet succeeded, beginning solely with non-living substances, in creating a living organism that is able to replicate itself indefinitely, whether by identical or sexual reproduction. For if Life did indeed arise by chance, then we extremely clever and capable human beings – living, as we do, on a planet that is equipped with all the many different things and conditions that Life requires to exist and thrive – should have been able to realize this goal; for our detailed and comprehensive understanding of the processes of Life greatly reduces the boundaries of chance by, for example, eliminating many substances that are unlikely to give rise to life, while guiding our efforts to produce a living organism from non-living substances.
By now, the conclusion to which I am advancing should be obvious: Life cannot have resulted from chance or purely random processes – no more than could a hamburger or Shakespeare’s works, given the parameters that are postulated in each case – because, given the parameters, laws, mechanisms, properties, and regularities of the non-living Universe, it is not the kind of thing that can be begotten by chance. And this conclusion is true no matter how long the Universe continues to exist, for the probability that Life arose on the Earth by chance is not a vanishingly small number, represented by a decimal point followed by a series of zeros with a “1” at the end, but ZERO.
The inability of many people to understand this important point is due to several things: first, they are familiar with all sorts of different life forms which exist on the Earth, which experience blinds them to the essentially miraculous nature of Life; second, they can conceive in their brains of a very simple, primitive life form that developed billions of years ago from inanimate matter – the primordial life form that begot an incredible succession of varied life forms with the passage of time; and third, they have no personal experience of how vast, barren, and extremely inhospitable the rest of the Universe is to life. In spite of the recent advances and discoveries made in astronomy and cosmology, these limitations on people’s understandings, along with many people’s earnest yearnings for life to exist elsewhere in the Universe apart from our planet, very clearly distort their beliefs about the Universe we live in. In other words, all these people are committing the Conception Fallacy, since their fanciful conceptions of the Universe, in terms of its ability both to generate life randomly and support it indefinitely, do not correspond to reality.
There is another point which I would like to discuss, without, however, defending it with the same insistence or degree of conviction as my belief in the preceding point: the belief that sexual reproduction evolved from identical reproduction, which is probably the consensus among those who accept the Theory of Evolution. Because we are so familiar with both the existence and the mechanisms of sexual reproduction, along with the many different kinds of organisms which it produces, it is extremely difficult for most people to imagine what Life was like before it existed. Furthermore, it is also difficult for most people to understand just how radical an advance this new kind of reproduction was from identical reproduction. If sexual reproduction did in fact evolve from identical reproduction, then this is a process that should continue to occur, at least occasionally, and therefore should be observable. But if it is such a rare and singular event that it only occurred once in the course of the evolution of life on Earth, then this extraordinary rareness should lead us to question this belief.
If one considers the mechanics of identical and sexual reproduction, one will see that they are similar but completely different mechanisms: whereas identical reproduction results in the production of two genetically identical “offspring” from a single “parent,” sexual reproduction results in a single genetically different offspring from the union of two sexually compatible and genetically different organisms. In other words, whereas identical reproduction results in the production of two organisms from one organism, sexual reproduction results in the production of one organism from two organisms.
There is another way that we can tackle this question. Assuming that sexual reproduction evolved from identical reproduction, we can ask, how often did this pivotal event occur? Of course, it is impossible to answer this question conclusively; for although the fossil record suggests that it occurred only once, it is also possible that it occurred many times, but after the first occurrences, the organisms that resulted failed to survive and perpetuate this novel form of reproduction, and therefore it is unlikely that their remains will be found in the fossil record. But it is important to recognize that, although the latter scenario is possible, there is not the slightest evidence for it. There are, however, several facts that are pertinent to the present discussion.
First, the fossil record of the evolution of Life on Earth shows that, for approximately the first two billion years – or more than half – of its existence, there were no sexually-reproducing organisms. In other words, during that very, very long period of time, at least as far as we can tell, the only kind of reproduction was identical reproduction. Second, during the much shorter time that human beings have been studying other life forms, I believe we can confidently say that no one has ever observed an identically-reproducing organism making the transition to reproducing itself sexually. In terms of our earlier discussion of probability, if this transition did indeed result from random evolutionary processes, since each instance of identical reproduction represents the opportunity to observe this transition, or at least the beginning of this transition, considering how often identical reproduction takes place on the Earth on a daily or yearly basis – a very large number that no one can estimate with much degree of accuracy, this shows that it is an extremely unlikely event. Third, these two methods of reproduction are discrete and discontinuous, in the sense that there exists no intermediate form of reproduction that combines elements of both, or that lies somewhere in between them. The discreteness that was assumed to exist, prior to the Theory of Evolution, between different species does in fact exist between identical and sexual reproduction, since there are no intermediate modes of reproduction between them, as there exist in the fossil record intermediate species, or common ancestors, between two seemingly separate species. Hence, it is wrong simply to assume that sexual reproduction evolved from identical reproduction through the processes of mutation and natural selection, as most evolutionists do.
Together, these three observations show that the development of sexual reproduction was a different kind of event than the evolution of organisms. For even today, we observe many examples of the numerous changes that organisms undergo due to natural or human selection. In other words, unlike the transition from identical to sexual reproduction, evolution by natural selection is an observable event. What these three observations suggest is that the development of sexual reproduction – or its appearance, as I prefer to call it, since I do not believe that it evolved from identical reproduction – was an event that was perhaps as rare, singular, and mysterious as the first appearance of Life on our planet. Although I do not believe it is possible to demonstrate conclusively – which is why one should not be dogmatic about such matters – that sexual reproduction arose as the result of divine selection or invention, what the preceding discussion should make clear is that the naive belief that it arose from identical reproduction via the general processes of mutation and natural selection is highly problematic and therefore extremely unlikely.
It may have occurred to some readers that there is a suspicious similarity between what I have called the Hamburger Argument and William Paley’s Watchmaker Analogy. Indeed, some sceptical atheists may object that there is no difference between them, and therefore my prosaic argument is susceptible to all the criticisms that have been made of Paley’s better-known, and perhaps more dignified, analogy. However, I am using this argument for a similar but slightly different purpose than the one to which Paley put his analogy, since I am most certainly not arguing that the existence of hamburgers means there must be a God, only that a hamburger cannot arise from purely random processes, because it is not the kind of thing that can be produced by chance. Another important difference is that Paley wrote Natural Theology, in which work he presented the Watchmaker Analogy, before Darwin published his seminal work, On the Origin of Species, in which the Theory of Evolution was first presented to the world. Hence, Paley was not able to modify his arguments or views by taking into consideration the implications of Darwin’s theory on them.
As I have declared repeatedly, I am not denying the reality of evolution through natural selection. What I am denying is the widespread belief that this principle can explain everything about terrestrial life – meaning every single one of its features – including the first appearance of Life on the Earth, the sudden appearance of sexual reproduction after a very long period during which there existed only identical reproduction, the fact that we humans, alone of all the many different organisms that have existed on our planet, are able to understand – in precise, comprehensive, and mathematically complex detail – the operations of the Universe, and the fact that, in a Universe that was not designed to support life, the Earth has numerous protective features and finely-tuned homeostatic systems and processes that enable Life to continue to flourish on our planet, and without which it would very quickly cease to exist. Although the inanimate and non-directed process of evolution by natural selection can indeed produce complex and highly ordered results, there are many things that it cannot produce. Contrary to what neo-Darwinians and many others believe, the Law of Natural Selection is not a globally valid law without exceptions, and the Theory of Evolution, about which so much noise has been made and controversy engendered, is not a globally valid theory that is true without numerous exceptions to it.
In attempting to decide which events are due to the operations of the natural laws that scientists have discovered and formulated, and which events are due to divine intervention, selection, invention, or modification, I will formulate the following guidelines or criteria: the more singular, inexplicable, or non-reproducible an event is, then the more likely that it is due to the latter, and not to the former, cause. Clearly the appearance of Life on Earth qualifies as an instance of divine intervention, since it satisfies all three of the aforementioned criteria: it is singular; it is inexplicable – despite many people’s unjustified belief that we humans understand exactly how life first started; and, in spite of some individuals’ repeated attempts to create life from non-living elements, so far no one has been able to reproduce this singular event. In my opinion, the appearance and subsequent perfection of sexual reproduction is another clear instance of divine intervention. The extraordinary abilities that we humans possess, in terms of creativity and our ability to understand the Universe’s operations, which greatly outstrip the abilities of all other living creatures in these regards, is also due to divine intervention, for they are both singular and inexplicable according to the Law of Natural Selection. Whether these abilities are reproducible depends, of course, on God, for only God is able, if It so chooses, to endow another species besides our own with the ability to understand these things.
I believe that God has intervened in countless other instances besides the ones that I have mentioned. I have only presented these few instances because the evidence for them is strongest. For the lesson to be learned from the past, when numerous natural phenomena that were attributed to God’s agency were later explained by science, shows that one should be circumspect in calling something miraculous, or due to God’s intervention.
Beginning in the sixteenth century, as science began to make inroads on the domains of human knowledge that were claimed by religion and theology, many religious people strenuously denied the claims made by scientists, dogmatically declaring that they were wrong because they contradicted the orthodox religious teachings and beliefs of the time. Today, we are seeing the reverse phenomenon exemplified by the many scientific atheists who dogmatically declare that any talk of God is wrong and therefore inadmissible because such a scientifically heretical belief contradicts the orthodox scientific teachings and beliefs of our time. The lesson to be learned from our species’ dogmatic, intolerant, and error-prone past is that it is best not to be dogmatic, for such dogmatism will render one blind to, while making one deny, the evidence which points the way to the truth about the world we live in.
The belief that science has been able to explain ALL the phenomena that our ancestors, due to their vast ignorance, formerly called miraculous is plain and simply wrong. Despite its many undeniable successes, there yet remains a residue of phenomena that science has not been able to explain, and, in my opinion, will never succeed in explaining. Moreover, in the case of the things that science cannot explain, such as the appearance of Life on Earth, many people mistakenly believe that, given the very long age of the Universe, such a singular and inexplicable event could have occurred by chance. But “chance” in this sense is merely another word for our ignorance, which we use to conceal this ignorance from ourselves, since it offends our belief that there is nothing that we supremely intelligent and godlike human beings aren’t able to understand about the world. If we examine the matter a little more deeply, we will see that the many things that the legion of scientifically-credulous people at the present time mistakenly attribute to the powerful Idol of Chance are little different from our credulous ancestors’ ignorant beliefs about the causes and origins of the events which they observed in the world around them.
 Although the two following character sequences are not entirely random, they were generated by my pressing the keys of my computer keyboard with my eyes closed and the index finger of one hand moving in a random manner over the keys. However, in a truly random sequence with, for example, 30 different possibilities, there is a 1/30 chance that any given character will be reproduced in the next character, something that I avoided doing by moving my finger away from a key once it had been pressed. They do, however, give a good sample of the sort of thing that a room full of monkeys typing randomly at typewriters would produce.
6ki/ cdsyouyfk;pyersxhk, y807tfvgjn,km gtuoljgtr79lkn htrer690okl
 Although this statement may appear tautological, it is not. Why it is not tautological will be explained in the course of this essay. Of course, this statement also applies to every other written text in the history of the world, and not just to the works of Shakespeare.
Even though there are a great many meaningful texts, in the sense that they are grammatically correct and make sense, which could be generated by this process, the set of all meaningful texts of a given length is still much, much smaller than the set of all possible combinations of randomly-selected characters of that length.
 Human beings in particular may be haunted or tormented by unrealized possibilities, such as the mate that one was not able to wed, the baby or child that was not conceived or, if it was conceived and born, did not survive to adulthood, the victory that slipped through one’s fingers, the job that one was not able to obtain, the brilliant business idea that was not implemented, or the key decision or action that was not taken at the appropriate moment.
 Like many another analogy, this one oversimplifies reality and overlooks important details in the author’s attempt to make his point as convincingly as possible. For, contrary to the picture that it presents, identically-reproducing organisms are not so simple and without guile, cunning, and stratagems as it suggests. For example, bacteria can and do exchange DNA in order to better adapt themselves to a changing environment.
 In another book where the author discusses this same example, he declares, “At modest levels of complexity and above, the universe is hugely non-ergodic; that is, it does not repeat itself.”* Hence, by “non-ergodic,” he means “non-repetitive” or, stretching the meaning of the term a little, “unique.”
* What We Believe but Cannot Prove, p. 86. Edited by John Brockman. Harper Perennial, New York, 2006. (In the original text, “universe” is spelt “university”. I have corrected this obvious error.)
 Beyond Mechanism: Putting Life Back Into Biology, Foreword: Evolution beyond Newton, Darwin, and Entailing Law by Stuart A. Kauffman. Edited by Brian G Henning and Adam C. Scarfe. Lexington Books, Plymouth, UK, 2013.
 In the case of the past, where we have little or no evidence, in many ways our conception of the past is or constitutes the past, at least until it is modified by new discoveries or is displaced by a new picture. For example, prior to the age of scientific discovery, the creation story contained in the Book of Genesis constituted, for Christians, the picture of how the Universe and Life first began.
 The astonishment that greeted the cloning of large animals such as sheep and dogs was due to the usage of the other kind of reproduction, namely identical, to reproduce an organism that, in normal situations, is only able to reproduce sexually.
 In the preceding list, I have included outcomes that are largely independent of our actions and those, such as winning a gold medal or becoming rich or famous, that are, at least to some extent, dependent on our actions. But the principle I have advanced holds in both cases, for the more often one imagines the desired or feared outcome happening, then generally the more likely one believes it is.
 In “The Science Myth: The Humanity Experiment,” I have explained why I prefer to use this term instead of the more common term, “asexual reproduction.” Although, contrary to its name, variations can result from identical reproduction, either by mutation or by mistakes in the copying process, clearly the aim of this mode of reproduction is to produce an exact replica of itself, which means that the degree of variation from generation to generation is much lower than in sexual reproduction. The historically inaccurate term “asexual reproduction,” since this reproductive process preceded on our planet, by several billions of years, the appearance of sexual reproduction, masks the important fact – a fact which I wish to emphasize – that it is a fundamentally different process from sexual reproduction.
 Although one may say things like, “The Universe evolves according to certain laws,” or “In the evolution of stars or galaxies, one can see…” one does not mean that these things evolve in accordance with the evolutionary law of natural selection, or the “survival of the fittest,” for the Universe evolves according to very different laws, namely, the laws of physics. Although there may be certain physical phenomena that are analogous to reproduction, predation, disease, speciation, natural selection, and so forth, one must not be misled by these similarities into believing that the Theory of Evolution can explain the phenomena that are studied by physicists, chemists, geologists, or astronomers. At present, the word “evolution” is being used to denote any kind of seemingly purposive or directed change on the Earth or in the Universe.
As we can see, not all forms of change that occur in the Universe are instances of evolution arising from natural selection. The particular outcomes that result from natural selection are due to the delicateness of life, to the fact that every living organism can die, and does die eventually. If living organisms were immortal, then there would be no Law of Natural Selection, since there would be nothing for Nature to select, in the sense of one organism surviving for a longer period of time, or begetting more offspring, than another. It is for these reasons that this biological law has no applicability outside the realm of living things.
There is a school of philosophy of science called reductionism, according to which the laws of, for instance, chemistry can be derived from, or reduced to, the laws of physics, the laws of biology can be derived from, or reduced to, the laws of chemistry and physics, and so forth. But this naive belief is very often wrong, for the laws or regularities that are observable at different levels of material organization or existence – at, for instance, the subatomic, atomic, molecular, organismic, ecosystemic, planetary, solar-systemic, galactic, intergalactic, or cosmic level – are usually different from each other. From a comprehensive knowledge of physics in its present state, it is impossible to derive a priori – meaning without any real-world observation – all the laws of chemistry, biology, or astronomy. This is another illustration, if such an illustration is necessary, that the Universe does not accord with, or unfold, proceed, or operate in conformity to, our human rules of logic and deduction.
In the realm of human behaviour, Richard Dawkins’ popular term “meme” is based on his reductionist belief that the laws and phenomena of human behaviour can be reduced to, or derived from, biological, and specifically genetic, laws like the Law of Natural Selection. As he has explained, he invented this word to emphasize the many similarities between the evolution of living organisms and the evolution of human cultures: just as the gene is the basic unit of biological transmission, so, according to Dawkins, the meme is the basic unit of cultural transmission. But despite Dawkins’ assurance, the laws and theory of human behaviour are completely different from biological laws. There is no equivalent in the biological realm to the important phenomena of admiration, embarrassment, contempt, and laughter, for these are, with perhaps the exception of admiration, since there are other animals besides humans that imitate, uniquely human phenomena. It is for this reason that the concept of the meme has not been very fruitful, and why Dawkins was not able to formulate the Theory of Imitation, for he was prevented from making this important discovery by his fixation on the evolutionary principle of natural selection. In other words, in theoretical terms, the concept of the meme is a dead end, leading nowhere.
 In attempting to answer the question, “How did sexual reproduction evolve from identical reproduction?”, we must be careful not to commit the Conception Fallacy. For although it is quite easy to imagine that a sexually-reproducing organism could have evolved from an identically-reproducing one, this ease of conception masks the numerous difficulties of this event occurring as the result of purely random processes, as is assumed by most evolutionary theorists.
 This latter observation is true even in the case of organisms, such as fish, molluscs, insects, frogs, turtles, and other creatures, that produce more than one offspring following a single act of sexual intercourse or fertilization, since each individual offspring is the result of the fertilization of one egg by a single sperm cell.
 This observation is not invalidated by the fact that there exist some species that are able to reproduce both identically and sexually, depending on the circumstances; for once sexual reproduction arose, it was possible that some organisms would use both methods at different times or in different situations.
 The first and third of these criteria – singularity and non-reproducibility – are clearly related to each other, since if something is singular, then that means it is also non-reproducible; conversely, if something is reproducible, then that means it is not singular. However, in spite of this relatedness, I believe it is useful to list these terms separately, as they denote slightly different aspects of the same concept.
 In the past, because people were not able to observe, for example, the tiny eggs laid in food and feces by flies, which later became fly larvae, many people believed in the doctrine of spontaneous generation, the belief that life could arise spontaneously from non-living things. Although there are few people who would maintain this belief in the case of terrestrial life, far from being extinguished, this belief has recently been transferred to other planets and moons located elsewhere in our solar system and the Universe. This example clearly shows that, contrary to what many people believe, these kinds of naive, superstitious beliefs are still alive and flourishing in our supposedly rationalist, scientific age.