The most instructive exercise conducted by Spetner involves setting up a calculation, running the calculation, considering the implications for the results, and making added adjustments to give some benefit for any doubts ... and then to look at the results overall.

To get an idea of how improbable something is, he describes the odds of getting all heads when simultaneously tossing 150 coins. ''This event will have a chance of one in 2¹⁵⁰, or one in about 10⁴⁵.'' [NOTE: One set of all 150 coins being heads in 10⁴⁵ = that is one chance in this many coin tosses 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000]

The kind of events that are supposed to run evolution take millions of years and large populations. There can't be many trials of this magnitude from which to find a winner. I'll compare the chances of some of the events of evolution with this event, which most people would call impossible. Spetner (NBC) Page 95

Now we see a comparison in the making. If it's virtually or absolutely impossible to get all heads for those 150 flipped coins, then how similar are the odds for getting all the steps and changes needed to get from one species to the next? If the odds look as improbable for creating the new species as it is to get all heads for the 150 coins ... then both events might be considered equally impossible. Spetner sets off to find out what is needed to make his calculation:

Summarized from Spetner (NBC) Page 96: For now, let's look at evolution through the eyes of a brady. What is the chance of the whole series of steps occurring? To calculate, we have to know: What the chance is of getting a mutation What fraction of the mutations have a selective advantage How many replications there are in each step of the chain of cumulative selection How many of those steps their have to be to achieve a new species If we get values for these parameters we can find in the chance of evolving a new species. Note that not any copying error can serve a typical step in cumulative selection. To be a part of a typical step a mutation must: 1. have a positive selective value, and 2. add a little information to the genome.

The basic point is Spetner's analysis identifies the necessary components to make a reasonable calculation. From his pages 96 & 97 and following we see:

 

''We already have the first of these parameters the mutation rate. The mean mutation rate for animals is 10-10.'' ''Note that we don't know if mutations can all be of the minimum size of one nucleotide and still satisfy the above two requirements.* But let me assume it is possible so I can proceed, even if it means giving away this point to the evolutionary side of the argument.'' [* None of the point mutations that have been observed satisfying these requirements.] ''G. Ledyard Stebbins, one of the architects of the NDT, has estimated that to get a new species would take about 500 steps [Stebbins 1966].'' ''Using the numbers cited by the experts, I find that one small evolutionary step would comprise about 50 million births.''

We see that 500 steps—i.e., unique mutations—will be required to get from one species to the next. We get that number from earlier in the discussion above.

 

What I mean when I say "to make the theory work" is that cumulative selection should lead to a new species by successfully completing 500 steps. But the completion of the steps is a random event—it's a matter of chance. We can only calculate the chance that it will occur. We shall have to adopt some level of chance of achieving a new species as our criterion that the theory works. Then we can a ask how many potentially adaptive mutations there must be to get to that level of chance. Spetner (NBC) Page 98

A few more factors need defining and then we are set to do a calculation.

First, based on an estimate by Richard Lewontin of Harvard University, for each species alive today there are 1,000 species that are extinct. So, to get a new species is a chance of 1 in 1,000. To this Spetner adds another factor of 1,000 because species are known to change little over time (this is called stasis). 1,000 times 1,000 = 1,000,000 ...

Let's then set the level of chance to one in a million. Thus we adopt the criterion that evolution can work if the chance of achieving a new species in 500 steps is at least one in a million. If the chance is less than that, we shall say that evolution does not work. Spetner (NBC) Page 99

The following might be a bit tricky to follow, but we'll give you a quote to illustrate how Spetner thinks through one of his steps leading to his final calculation.

Now let's find in the chance that a mutation in a particular nucleotide will occur and take over the population in one step. What's the chance that a mutation occurs in a specific nucleotide of the genome during one evolutionary steps? The chance of a mutation in a specific nucleotide in one birth is 10-10, and there are 50 million births in an evolutionary step. The chance of getting at least one of such mutation in the whole step is about 50,000,000 times 10-10, or one in two hundred. There is an equal chance that the base will change to any one of the other three. Then the chance of getting a specific change in a specific nucleotide is a third of that, or one in six hundred . Note that I have taken the mutation at each step to be a change in a single nucleotide. I don't know if there is always, at each stage, a single nucleotide that can change to give the organism positive selective value and to add information to it. No one really knows. But I have to assume it can if I am to get on with this study of cumulative selection. That's a pretty strong assumption to make, and there's no evidence for it. But if the assumption doesn't hold, the NDT surely won't work. Although we don't know if it holds, let's see if the NDT can work even with the assumption. Spetner (NBC) Page 100

There are a number of places in Spetner's discussion—and lengthy treatment in one chapter—to address issues stemming from the thinking and writings of Dr. Richard Dawkins. We can't give a complete accounting of the rebuttals Spetner develops to address points made by Dawkins. You can best appreciate this by reading Spetner's complete text (context is very important in accounting for his responses to Dawkins' many assumptions). But the issue of a species accumulating small changes over time is one of Dawkins' assumptions that Spetner refutes. Again, unless mutations survive long enough to spread throughout a population, then its more likely the mutation will vanish. Just because a mutation occurs is no guarantee it sticks over generations or time.

Sir Ronald Fisher did much of the original work in population genetics, and his work is still the standard in the field. He found from his studies that even good mutations are likely to disappear from the population. He said: "A mutation, even if favorable, will have only a very small chance of establishing itself in the species if it occurs once only. [Fisher 1958, p. 84] He noted that if evolution is to work, many adaptive mutants have to appear. Only in large numbers could mutants survive the vagaries of selection and takeover the population. But adaptive mutations are just too rare for that. How many mutants would have to appear to ensure their survival? It's a matter of chance; there's no way to ensure their survival. We can calculate the chance that a mutation will survive if we know the selective value. What is a typical selective value for the kind of evolution I am a discussing? In the opinion of the late George Gaylord Simpson, who was generally acknowledged as the dean of evolutionists, a "frequent value" is about a tenth of a percent. He felt that a hundredth of a percent "... may be less than the average" [Simpson 1953, p. 119]. I shall therefore choose 0.1% as a typical selective value. Spetner (NBC) Page 102

In fact we get a picture that mutations have to run wild to even test their prospects for persisting and thereafter for their ability to factor into an adaptive feature for any species. But here, just to be 'fair,' we see Spetner give some wiggle room for evolution.

Fisher's calculations show that for only one mutation with a tenth of a percent selective value the odds are 500 to one against its survival. There would have to be almost 350 such mutants to have a 50 % chance of survival. There would have to be more than 1100 of them to have a 90 % chance. For just a moment let's look at the chance of a species evolving into a new one if at each step there is only one potential copying error that can be adaptive. What we've found above is the chance of just one of the small steps occurring. To get a new species, 500 of them have to occur without any failures. As we shall soon see, for successful evolution the probability of each has to be very nearly one. The chance of 500 of these steps succeeding is 1/300,000 multiplied by itself 500 times. The odds against that happening are about 3.6 x 102,738 to one, or the chance of it happening is about 2.7 x 10-2,739. That's a very small chance! It's more than 2,000 orders of magnitude smaller than the chance of the event I call impossible. Spetner (NBC) Page 103

Even if we string 500 successful mutations together over time, we end up with odds that don't seem to favor evolution in the slightest!

... So we see that evolution will work only if there are at least a million potential adaptive mutations at each step. ... if a new species is to evolve from an old one, two conditions have to hold. They must apply to any stage in evolution. These considerations are: 1. An adaptation that adds information to the genome can always arise through a change in a single nucleotide. 2. At each stage of evolution there are about a million nucleotides in which a change will satisfy the first assumption. I could have put it these two conditions together and expressed them as one. But I'd rather look at them separately because they make to distinct points. Unless these conditions hold, the NDT will not work. To make the NDT work, I must assume these conditions hold. I'll call them the Darwinian Assumptions. Spetner (NBC) Page 104

There are more conditions to be met. Remember, each isolated mutation doesn't necessarily have to relate to any previous or subsequent mutation. Each event could be so independent as to not contribute to some correlated end point (e.g., the making of a new species by macroevolution). But to work additional conditions apply, mutations must ...

1. They must be able to be part of a long series in which the mutation in each step is adaptive. 2. The mutations must, on the average, add a little information to the genome. ... Curiously, no mutations that have selective value are known to satisfy this condition. They either reduce the information in the genome, or they seem to add too much. Some microevolution does not involve the mutation. It instead uses the variation already in the population. The evolution of industrial melanism in and the peppered moth is an example. Spetner (NBC) Page 106

Our account is brief. The points we are reviewing are sound. But further study will reveal to you the matrix of concerns comprehensively presented by Spetner. Addressing the proposition of evolution is itself a matrix of facts, assumptions, and views from the Darwinian and neo-Darwinian camps. Once we consider the traditional Darwinian view, as above, we next have to cover the neo-Darwinian (i.e., the recent genetic and molecular) perspective.

None of the above examples show the kind of mutations that the NDT needs. In fact, there are no known cases of evolution that meet the conditions of cumulative selection. There are some known cases of evolution with copying errors, but they show only a kind of microevolution that one cannot extend to macroevolution. None of them adds information. All that I know of, actually lose information. There are no known as examples of copying errors that have been observed and that have been studied on the molecular level that qualify to be a step in cumulative selection. We shall therefore find we have to reject Darwinian Assumption 1, and consequently we shall have to reject the NDT. Spetner (NBC) Page 107

You'll find details on rejecting Darwinian Assumption 1, and others, in Spetner's text. But for the moment, let's be clear. Macroevolution is assumed such that we are told ancestor species (simple cells on primitive earth) gave rise to all the life forms we see today. The calculations say this is not happening. But microevolution occurs ... so we are saying evolution of a fashion does occur. This gives us a path from one species to the next, but more like from bird to bird, or fish to fish, or horse to horse, but not bacteria to man. The shorter range evolution known as microevolution has been extrapolated to define macroevolution. We have documented microevolution, but as noted here and on other pages in this Science Area, there are problems in producing certainty for macroevolution. In fact, the evidence says macroevolution does not occur. This is the point Spetner is making with the math.

Dr. Spetner reminds us that not only is there a first of 500 steps to his example, a step that is one of a million possible steps, but there are all the remaining steps counting down to the last of the 500 steps leading to a new species.

The process has a huge amount of freedom. If an evolutionary path were to begin a second time from the same point, the first outcome would not repeat. The odds against it repeating is a million multiplied by itself 500 times, or 103,000, to one. By comparison, the odds against the event called impossible are only 1045 to one. The species resulting from the second path would almost certainly be different from the first. Spetner (NBC) Page 108

Spetner furthermore has us think of the evolutionary process as working through a maze. At every level a new mutation ... and by the time we escape the maze all the mutations have to be acquired without being fatal or disappearing. The following might be a bit technical, but think of the phenotype as features we see (e.g., height, hair color) and genotype as the genetic information stored in the DNA. When the information of the genotype is expressed, we see it in the phenotype. In terms of the maze ...

Let the maze be built on the basis of the phenotype—it will still have an enormous number of paths. The maze for the phenotype may have fewer branches at each node than the maze for the genotype. There may be less than a million—maybe only ten thousand. In that case there would be 10 2,000 branches. The odds against coming out the same place twice would still be enormously larger than the odds against what we called the impossible event. Since we would still have to call it impossible, we have to rule out phenotypic, as well as genotypic, convergence. Spetner (NBC) Page 114

In general terms, a phenotypic change is something we can see as a difference in appearance. The outward change should also relate to a change in the genetic information (genome) inside the organism's cells.

Spetner continues in a discussion with examples that the neo-Darwinians cannot explain. And his probability analysis continues to show as impossible and not merely improbable. Intriguing, these examples further tip the scales against the standard storyline for evolution. Spetner's point is this is not obvious when evolutionists don't want to do the math. But making the calculations makes an incredible point. One we dare not miss.

To have a chance of at least one in a million of getting one adaptive recombination in 10 trillion replications, there would have to be 10 2017/ 1019 adaptive ones. That means that 10 1998 potential recombinations would have to be adaptive. With this number of adaptive possibilities, there would be a one-in-a-million chance that one of them will appear in the population during the million generations. Actually, to get this chance of an adaptive recombination that will survive in the population, we need somewhat more than 101998. But never mind. That number is already too big to allow convergence. I hope I have shown you here why the NDT doesn't work. I have shown it through an example. Fred Hoyle, astronomer, mathematician, Fellow of the Royal Society, and retired professor at Cambridge University, together with Chandra Wickramasinghe, chairman of the Department of Astronomy and Applied Mathematics of the University of Cardiff, have arrived at the same result in a more general mathematical way. They have presented a mathematical disproof of the NDT in a small book of only 34 pages, entitled Why Neo-Darwinism Does Not Work. They call what they have done a "simple and decisive disproof of the 'Darwinian' theory." [Hoyle and Wickramasinghe 1982]. Spetner (NBC) Page 119

Like it or not, this computational assessment leaves us with a conclusion.

The NDT's claim is the same as Darwin's. It claims to explain how all life evolved from some simple beginning. It claims to explain how all the complexity of life evolved in a natural way as a process that occurs through a combination of chance and the known laws of nature. It, too, claims to have substituted chance for design. I have shown so far that on a theoretical grounds random mutations cannot form the basis of evolution. The information of life could not have been built up the way the NDT says it was. Evolutionists have not succeeded in finding a random source of the variation that will make the NDT work. Spetner (NBC) Page 120

The following quotes are offered to indicate Spetner is not alone. We readily agree that these are taken from their greater context. So, we also encourage you to look up the sources as cited and read further.

From Denton:

The inability of unguided trial and error to reach anything but the most trivial of ends in almost every field of interest obviously raises doubts as to its validity in the biological realm. Such doubts were recently raised by a number of mathematicians and engineers at an international symposium entitled "Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution", a meeting which also included many of leading evolutionary biologists. The major argument presented was that Darwinian evolution by natural selection is merely a special case of the general procedure of problem solving by trial and error. Unfortunately, as the mathematicians present at the symposium such as Schutzenberger and Professor Eden from MIT pointed out, trial and error is totally inadequate as a problem solving technique without the guidance of specific algorithms, which has led to the consequent failure to simulate and Darwinian evolution by computer analogues. Denton (ETC) Page 314

Think of Spetner's calculations in terms of getting a new protein to be correct and functional. Look at what it takes to make this happen!

There are, in fact, both theoretical and empirical grounds for believing that the a priori rules which govern function in amino acid sequence are relatively stringent. If this is the case, all the evidence points in this direction, it would mean that functional proteins could well be exceedingly rare. The space of all possible amino acid sequences (as with letter sequences) is unimaginably large and consequently sequences which must obey particular restrictions which can be defined, like the rules of grammar, are bound to be fantastically rare. Even a short unique sequences just ten amino acids long only occur once by chance in about 1013 average-sized proteins; unique sequences twenty amino acids long once and about 1026 proteins; and unique sequences thirty amino acids long once in about 1039 proteins! Denton (ETC) Page 323

From Bradley and Thaxton:

Neglecting the problem of reactions with non-amino acid chemical species, the probability of getting everything right in placing one amino acid would be 0.5 * 0.5 * 0.5 = 0.0125. The probability of properly assembling N such amino acids would be .0125 * .0125 * ... continued for N terms of .0125. If a functional protein had one hundred active sites, the probability of getting a proper assembly would be .0125 multiplied times itself one hundred times, or 4.9 * 10-191. Such improbabilities have led essentially all scientists who work in the field to reject random, accidental assembly or fortuitous good luck as an explanation for how life began. Bradley and Thaxton (CH) Page 190

Oller and Omdahl state (and in agreement with the quoted point made above by Denton ...) with regard to a symposium entitled " Mathematical challenges to the Neo-Darwinian interpretation of evolution" held on April 25th it and 26, 1962:

 

In "Algorithms and the Neo-Darwinian Theory of Evolution" Marcel P Schutzenberger of the University of Paris calculated the probability of evolution based on mutation and natural selection. Although with many other noted scientists, he concluded that it was "not conceivable" because the probability of the chance process accomplishing this is zero: "there is no chance (< 10,000-1000) to see this mechanism appear spontaneously and, if it did, even less for it to remain. ... Thus, to conclude, we believe that there is a considerable gap in the Neo-Darwinian theory of evolution, and we believe this gap to be of such a nature that it cannot be bridged within the current conception of biology." Oller and Omdahl (CH) Page 274

From the perspective of making functional DNA ...

 

... In a the October 1969 issue of Nature, Frank Salisbury of Utah State University, then on leave at the Division of Biomedical and Environmental Research at the U.S. Atomic Energy Commission, examined the chances of occurrence of one of the most basic chemical reactions for the continuation of life. This reaction involves the formation of a specific DNA molecule. (It is important to realize that Salisbury was assuming that life already existed. His calculations do not refer to the chance of the origin of life from dead matter—something infinitely more improbable—but to the continuance of already-existing life.) Oller and Omdahl (CH) Page 276

Dr. Salisbury calculated the chance of this molecular evolution on a possible 10²⁰ planets —all with hospitable biologic conditions. Remember, this number of planets is infinately more than the number estimated that could exist in the universe. He allowed 4 billion years for the chance existence of this molecule on all of these planets. This is not a calculation for life, but only calculating the chance of one appropriate DNA molecule.

Salisbury concluded that the chances of this one tiny DNA molecule's coming into existence over 4 billion years, with conditions just right, on just one of these almost countless number of hospitable planets, including the earth, as one chance in 10415. This figure far exceeds the standard of Borel's law, which says that beyond a certain point improbable events never happen, regardless of the time span involved. Indeed, 10+50 planets would pack the known universe, yet the chance that life could evolve from dead matter on any one of them is still beyond possibility. Oller and Omdahl (CH) Page 276