Appendix 2:

The Probability Bound and the Resource Exhaustion Argument

(Crunching the Numbers)

__Whatever is a
Probability Bound?__

The probability bound, or probability boundary, is a threshold of improbability that mathematicians say rules out chance or accidental processes altogether, a boundary beyond which chance cannot go. Mathematicians vary in their opinion of what level of improbability should be used for this boundary. Professor William Dembski tells us that proponents of this concept through history, such as the famous French mathematician Emile Borel, or the secret code breakers of the National Security Agency, have suggested different magnitudes for this limit based upon their own perspectives and technical purposes.

While the language
of some writers on the subject seems to suggest that this boundary is a pure
mathematical and theoretical limit that absolutely precludes an event occurring
by chance, I think (because probability computations themselves tell us the
pure mathematical possibility of an event) we must consider the probability
bound a practical, not a theoretical limit. This is true only as long as the
mathematically computed probability remains the smallest fraction above zero.
In other words, what the mathematicians seem to be saying about the probability
bound is that for all *practical intents
and purposes* *in this universe* we
may consider an improbability that exceeds the probability bound limit to be a
physical impossibility for accident to produce in our universe, although some
minute theoretical chance remains in purely mathematical terms.

This is the only way I can make sense of the concept, as a practical not a theoretical limit. However, not being a mathematician, I am not sure that some of the mathematicians who have addressed the topic have not meant to say that, “Yes, the probability bound limit is a genuinely theoretical limit, not just a practical one.” William Dembski’s discussion seems to suggest this. To me this position produces a contradiction with probability theory numbers, which say the probability is still somewhat greater than zero. So I personally think that the purely theoretical version of the probability bound is a flawed concept. But, for our purposes here, the practical version at least is relevant to computing the plausibility of the concept of accidental evolution, even if the theoretical version has problems.

Regardless of
whether one calls it a practical boundary or a theoretical one, acknowledgement
that such a boundary exists seems to be implicit even in the work of famous
evolutionists. In his classic book, *This
View of Life*, George Gaylord Simpson cites Julian Huxley (page 202):
"to produce such adapted types by chance recombination...would require a
total assemblage of organisms that would more than fill the universe, and
overrun astronomical time."

One might call G. G.
Simpson’s way of formulating the problem as the “resource exhaustion argument.”
Modern mathematician William Dembski has his own version of the resource
exhaustion argument. It combines standard probability theory with the known
physical and time limits of our universe. Dembski argues that *any event with
a probability less than 10*^{-150}* cannot rationally be
expected to be the result of chance*. He calls this limit the “universal
probability bound.”

Dembski goes on to
say that 10^{-150 }is the most generous limit ever proposed in the
scientific literature. Emile Borel proposed 10^{-50 }as a universal
probability bound below which chance could definitely be precluded. Some
scientists use 10^{-94;} still others 10^{-120;} but no
professional involved in probability-based endeavors believes a probability
less than 10^{-150} can occur by chance.

Obviously, my
current estimate of the improbability of neo-Darwinian evolution here in *Evo-Smevo* goes thousands of orders of
magnitude beyond this threshold at less than 1 chance in 10^{-6,545,300}.
An event that exceeds the probability bound, even by such astounding margins,
clearly should not be expected to be the result of chance. Theories accruing
such a low probability cannot be considered scientifically credible.

Dembski’s argument
keys on the maximum number of physical events available in the history of the
known universe. To determine what that number is, he multiplies the estimated
number of physical particles in our universe, 10^{80}, times the number
of actions a single particle can perform per second, 10^{45}, times an
estimate of the number of seconds available in the history of the universe, 10^{25}.
Even if all the particles stay constantly “busy,” there is a maximum of roughly
10^{150} particle events available since the Big Bang with which to
accomplish the work of evolution (and absolutely everything else). In other
words, even if evolution were to exclusively use the smallest and shortest
event type available in the physical world (this is *very* generous as evolutionary events are obviously not that small),
there are at most 10^{150} separate events possible in the history of
the universe to date with which evolution could get the job done.

Standard probability theory requires the random trial and error search through half the available alternatives to make the occurrence of an event from random causes at least 50% probable. Probability theory is not something esoteric that I pulled in from left field here to make my case; it is a foundational tool of science, very much requisite to doing science at all. The entirety of science is a probabilistic endeavor.

Professional gamblers will quickly tell you that standard probability theory holds true in the long run over a large number of trials. Thus, to say with Doolittle, Dawkins, Strickberger and the neo-Darwinists that anything at all can happen in three or four billion years simply because it is a “large” amount of time, regardless of how steep the improbabilities become, is mathematically invalid, and therefore incorrect science. By definition, science must always go with the probabilities, not against them.

The larger the
sampling base, the more nearly will results tend to match the predictions of
probability theory. Therefore, the large expanse of time in evolution tells us
that we can very confidently expect standard probability assumptions to hold
true, not that we can disregard them. The total physical event process of
evolution of all life forms on earth, being *very* large, tells us the
same thing. We can safely make the assumption of a probability outcome near the
standard expectation predicted by probability theory.

Given our estimate in
Table 1 of the probability of accidental evolution, half of the available
alternatives equals 5 X 10^{6,545,300}. There
are only 10^{150} physical events available in the history of our
universe (and those are extremely small events), so obviously evolution won’t
be able to try anything near half the alternatives. In fact, the time and
physical resources of our universe would be exhausted before trying even a
trillionth of a trillionth of a trillionth…(continued to 500,000 occurrences of
“trillionth”) of the alternatives!

The number of alternatives involved in random chance-based evolution
are so large that one needn’t proceed further to see that the universe
doesn’t have sufficient resources to get the job done via the accidental neo-Darwinian
process. Our universe cannot afford to deal out half the cards in the game of
random chance-based evolution. It can’t even get close. **Therefore, science
is not entitled to affirm accidental evolution as more likely than a
non-accidental process. **

While this
mathematical proof of resource exhaustion fully defeats the credibility of the
theory of accidental evolution, it is easy to get lost in the abstractions of
enormous numbers. In an attempt to make the point somewhat more concrete, I
will now attempt to propose my own *common
sense* application of the resource exhaustion-probability concept.

My form of the resource exhaustion argument hinges on the fact that accidental processes tend to be very wasteful, making a big mess while exploring so many failed alternatives. It is based upon the same mathematical principles, but focuses on the trillions and trillions of tons of biotic waste materials an accidental evolutionary process would necessarily produce.

__One Big Mess—the Cost of Doing Business with an Accident__

Empiric observations
confirm what probability theory tells us because when we look at random
processes in biology we see that they just don’t seem to be contributing
anything useful to what evolution needs to get the job done. Thousands of
mutagenesis experiments have been performed and no viable mutations significant
enough to evidence progressive macroevolution have been observed (generally no
viable mutations at all). Under such prolonged heavy bombardment by mutagens,
some laboratory specimens, the fruit fly, for example (which is the most common
laboratory subject) should have evinced *some* macroevolutionary
potential.

The force of the evidence is so compelling as to suggest that some natural law or other requires this result: a law that forbids random processes from frequently producing nontrivially ordered results and forbids the random production of functional order of the magnitude we see in living systems. Maybe there is actually a natural law that says “Don’t hire accident as your architect for life,” just as there is a common sense rule derived from standard probability theory that says “Don’t hire monkeys to type your literary masterpiece (or your prenuptial agreements).”

Seeing no such law established in our current theoretical base other than the definition of entropy in thermodynamic law (which is a close relative) and in standard probability theory itself (which is not a law of physics, but of math), I will now propose one. The underlying concepts for this proposal do not originate with me, although the specific formulation is mine. Professor William Dembski has previously made a similar proposal under the moniker “Law of Conservation of Information (LCI).” Dembski credits Peter Medawar as having previously originated the LCI concept in a somewhat weaker form.

I have attempted this reformulation because I assume that most readers prefer a common sense discussion to technical math. I occasionally use a little basic math, but not much. Whether it has really turned out to be less technical than Dembski I will have to leave to the reader to judge. I simply followed where the logic of the formula led me.

Don’t let my use of a strange acronym scare you off; the underlying concepts are simple. I call my version of Dembski’s LCI, “ORLEF-B” (Ordered Result Limitations for Entropic Forces—Biology). ORLEF-B says there are one or more natural laws that constrain the increase in order that can arise as the result of the application of an accidental, random, or disordered force to a biological system.

To be clear, what I
am doing here is **not** merely a restatement of the 2^{nd} Law of
Thermodynamics. The 2^{nd} Law says something different. It says that
entropy (disorder) tends to increase in a closed system and never decreases.
The 2^{nd} Law of Thermodynamics applies only to the larger universe as
a complete system. It also assumes our universe is a closed system that
receives no energy transactions from outside. The 2^{nd} Law does allow
for local increases in order, but only when they are offset by decreases in
order occurring elsewhere in the universe. The 2^{nd} Law stipulates
that no increase in the total order of the universe is possible.

ORLEF-B is different. ORLEF-B is not concerned with the overall tendency to disorder in the closed system of the entire universe. It is concerned with the destructive effects that we see disordered event processes (random mutations) to have on highly ordered biological machines (the rule is assumed to hold for other kinds of machines as well). ORLEF-B proposes three things in general terms: 1) it is both a logically and mathematically justifiable assumption that that which consistently tends to destroy biological machines (random mutations) will not build any biological machine of substantial complexity without first wasting an enormous amount of resources; 2) random mutations will not be able to advance the functional complexity of existent biological machines without seriously damaging them and also wasting an enormous amount of resources; and (3) the physical laws that govern our world entail that the costs in matter, energy, and time required for random forces to create and evolve our known tree of life would far exceed the resources that have been available in our universe through its history.

This can (in theory) be computed with confidence and empirically confirmed. ORLEF-B is a hypothesis that can be tested extensively to gain greater and greater corroboration for the rule and more precision in the math. Tests involve observing what random forces are seen to do in the universe on different event scales and noting how many (if any) biological machines are spontaneously produced or enhanced by random forces; noting the change in magnitude of functional complexity produced by random mutations; and by calculating the resource cost to the universe for the entire process.

One goal of ORLEF-B research would be to quantify the effects of a typical random mutation transaction and to develop a reliable average value for a constant reflecting the ratio of cost in expended resources to units of functional biological complexity achieved. Should such research ever be undertaken, conclusive evidence for ORLEF-B should not be long in coming.

It is possible that there is no scientist who will dispute ORLEF-B even now, minus the further philosophical conclusions I have drawn from it. The current evidence suggests that accidental mutations fail to produce viable evolutionary form change in living creatures no matter which route they are proposed through. Incremental accumulations of single nucleotide changes initially do less harm than larger transfers, but this process alone is too slow to meet the evolutionary timetable, and when the small accumulations add up to the equivalent of a larger genetic transfer the living system suffering the mutation is seriously harmed.

ORLEF-B implies
that, if *beneficial* large mutations did occasionally occur, more
complete information concerning the circumstances would reveal them not to be
fully accidental. ORLEF-B codifies into natural law the age-old wisdom of
common sense: “Accidents don’t make machines, they break machines.”

Due to the subtlety, complexity, and variety of biological subsystems, it will take a lot of future research to hone the ORLEF-B constant to precision (and the value of the constant will vary for different kinds of systems). Nonetheless, it is easy to demonstrate that the ORLEF-B constant must fall within a certain range. That range guarantees that the cost of generating Earth’s tree of life with a random process would be so exorbitant as to far exceed the time and physical resources available in the history of our universe.

On a common sense level ORLEF-B merely confirms what we already know intuitively: random forces do more harm than good. They especially harm the fragile complex designs of sophisticated living machines. ORLEF-B says that, when the complexity of a machine goes beyond a critical threshold (and all of life is past that threshold), random forces will not be able to progress the system design, but rather will only degrade it. Only the rarest of exceptions is allowed, and the resource cost for those exceptions would be exorbitant.

In simplest form, ORLEF-B can be stated as follows: “ORLEF-B requires that the aggregate total mass of disordered results produced by random mutations to biological systems will always vastly outweigh any ordered results produced by those same mutations (with statistically insignificant numbers of exceptions).”

Being a close relative of Dembski’s LCI, it is possible that ORLEF-B can be derived from it. I leave that question to professional mathematicians. I think ORLEF-B is also at least partially implicit in the definition of entropy itself and will turn out to be derivable from thermodynamic law combined with the molecular/elemental transactional formulae of chemistry and physics.

Translated to terms
directly relevant to evolutionary science, ORLEF-B says that **each and every** random mutational
transaction can be expected to fail to produce viable biological form change
modules that will eventually combine to produce macroevolution. In a sense,
then, ORLEF-B is the exact converse of neo-Darwinian theory. ORLEF-B says that
accidental evolution can’t happen in this universe.

Neo-Darwinian
evolution says that in a purely random system mutations will produce any level
of complex design given sufficient time, and that our world is sufficiently
random that random mutations aided by natural selection could have produced the
tree of life in approximately 4 billion years. ORLEF-B says no, that will never
happen because our world is not sufficiently random to allow most mutations to
be called “random;” the modules of evolutionary change are too complex for a
random mutation to produce them in real evolutionary time at all; and, (now we
get to the key testable element of ORLEF-B) if sufficient random mutations were
in fact employed to produce the tree of life, *it would entail the production of a quantity of bio-refuse and disabled
species designs vastly exceeding the total mass of our universe*.

In LCI Dembski says something very similar: you can’t get more complex specified information (CSI) out of a physical process than goes into it. Dumping more and more random mutations into a system doesn’t produce increased order; it only tends to break the ordered systems already present. What this suggests for making our evolutionary language more honest is that when mixed forces (partially ordered and partially disordered) are introduced into a system, we should attribute any net increase in order produced to the effects of the ordered components, not to the effects of the disordered components.

In addition to correcting misleading language, what I wish to do with this ORLEF-B argument is to add to evolutionary discussions a mathematical constant with a definite value (or range of values) that can be used in answering concrete questions concerning resource exhaustion. In other words, I want to put this endless and futile politicized debate in evolutionary biology to bed once and for all by installing into the accepted theoretical base a recognized scientific axiom that authoritatively answers the question, “Could an accident have done this or not?”

So, you may want to ask, concerning ORLEF-B, “Minus extensive additional research to refine it, how can ORLEF-B be of present use in answering the question of whether accidental evolution is possible.” While ORLEF-B can’t presently quantify the biological effects of random forces in specific contexts with precision, it can answer the big question of the plausibility of accidental evolution by means of computing an undisputable underestimate of the total resource costs. If an undisputable underestimate is too much for our universe to afford, then accidental evolution must be dismissed as scientifically untenable.

ORLEF-B provides an indirect test for the theory of accidental evolution in terms of the presence or absence of dysfunctional designs in the fossil record. While evidence of many of an accidental evolutionary process’s attempts at dysfunctional designs might plausibly be expected to have disappeared due to conditions not conducive to making fossils, ORLEF-B predicts that the total biomass of such dysfunctional designs would have been so enormous as to exceed the Earth’s total biomass by an astronomical volume. Thus, accidental evolution did not occur if ORLEF-B is true.

The *known sensitivity of developmental systems*,
in addition to biological complexity generally, makes the scenario of aborted
design failures (and absence of fossil records for failed designs) fully
plausible. But what value shall we initially set for the ORLEF-B constant just
to get a feel for how such a study would work and to generate an initial
ballpark estimate? What ratio of entropic __un__usable waste byproducts to
ordered structures and systems does an accidental process typically produce?

I propose what I
consider a safe and conservative starting value of a ratio of 10^{116}
disordered units to every ordered biologically viable unit produced by
accident. This is a composite of Meyer’s/Axe’s probability determination for *randomly*
synthesizing a **single** new protein from nonliving chemicals (10^{-125})
and the corresponding probability value for randomly synthesizing a **single**
new protein inside a living organism (10^{-77}). Both of these
obstacles (and many others) have to be overcome by a random process to generate
the tree of life.

Keying on protein synthesis is proper because all living things are composed of proteins and proteins are key components of most life-critical processes. The degree of efficiency of random processes generating life forms, as opposed to, say, generating much simpler inert substances like coal or water, should be similar to that for random protein synthesis. However, this is still only a rationally guided guess. The proper ratio for the ORLEF-B constant could turn out to be somewhat smaller than what I have proposed, or perhaps somewhat larger. But let’s run the math using my proposed initial value to get a concrete feel for how the process of evaluating accidental evolution using the ORLEF-B constant actually works.

The current biomass
of Earth is estimated at 1,850,000,000,000 tons. Arbitrarily assuming living
systems are at least 90% ordered yields a *well-ordered* biomass of more than 1,665,000,000,000 tons, or approximately
1.6 **X** 10^{12} tons. At
2,000 pounds per ton that is 3.2 X 10^{15} pounds of well-ordered
biomass. Using 10^{116} as the value for the ORLEF-B constant,
producing that well-ordered biomass of 3.2 X 10^{15} pounds requires a
large mess of disordered byproducts equal to 3.2 X 10^{131} pounds. **This exceeds the total mass of the universe
by trillions and trillions of times.**

Reasonable estimates of the mass of the universe have been
made in the range of 3 X 10^{55 }grams on the low end to as much as
1.6 X 10^{60}
kilograms. A kilogram equals 2.2046 pounds. Converted, the high end estimate of
the mass of the universe is somewhat less than 3.53 X 10^{60 }pounds.
So, initial estimates for the ORLEF-B constant show accidental evolution on
earth to have been impossible in this universe.

Is ORLEF-B really a serious candidate for a natural law (or at least a biological axiom derivable from biological complexity and mathematics)? There are three good reasons to assume ORLEF-B holds true:

(1) Meyer
cites peer-reviewed random protein synthesis studies to ground his estimate
that random processes will produce biological junk (or poison) 10^{77}
times for every time they create a useful protein even within a living system
with strict controls in place to protect the host creature. That number grows
to 10^{125} for random mutations outside a living system.

(2) Thousands of mutagenesis studies show that no biologically viable ordered results have come from billions of random mutations.

(3) Thermodynamic science’s definition of entropy says that truly random energy can never be reclaimed to do any useful work, in biology or anywhere else. Genuinely random mutations would be close relatives of entropic forces, seldom having a positive effect on an ordered biological system.

How many more studies
must reveal exactly the same results before standard scientific (inductive)
logic justifies the assumption that future accidental mutations will not be
beneficial, and that infrequent neutral or mildly beneficial mutations will
never link to form the large and highly complex combinations of multiple gene
sets, gene expression markers, and the corresponding microtubule alterations
needed to cause **macro**evolution? Good science does not permit the
maintenance of a purely theoretical assumption in the face of universally
contradictory empirical data.