Probability of Evolution

The “Secret” is Safe

CRYTOGRAPHY REQUIRES A MIRACLE TO DEFEAT

Our nation’s security depends upon the ability to safeguard
classified information, preventing our adversaries from acquiring
knowledge about our intentions, methods, identities, capabilities,
and many other subjects. One of the methods employed to secure this
information is cryptography, which uses the principles of
mathematics in probability in the formation of coding systems that
encrypt sensitive communications. In fact, this is the domain of the
world’s largest security organization, the National Security Agency,
which is responsible for the development, implementation, and
oversight of all cryptographic systems used to protect United States
government sensitive and classified communications.

The actual method in which this security is achieved is in principle
quite simplistic—it is ultimately very simple mathematics—though the
numbers are quite staggering, even utilizing older cryptographic
systems. Using the old style computer “punched tape” as an example,
it can be seen just how the protection can be relied on with
absolute certainty (absent obviously, human failure). One particular
protocol that the old punched tape computers used had sections of 32
columns, with 8 positions in each column, residing on one inch wide
paper tape. Each “position” either had a hole punched through or did
not; to the computer, this meant either a “one” or a “zero” in
binary coding as the tape passed through the reading machine. Each
position then has 2 possibilities.

Since each position has 2 possibilities, each column of 8 positions
has 256 total possibilities for that column, shown in the math
function below:

Position: 1 2 3 4 5 6 7 8

2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256

Since there are 32 columns, the total possibilities for each section
is calculated by multiplying the 256 possibilities of each column
for the number of columns, or:

256 x 256 x 256 . . . etc., for 32 times, which equals approximately

1 x 1076.

This is a number much too large for the human mind to understand;
the total number of atoms in the entire universe is estimated to be
around 1080. There are multiplied billions of atoms in the ink in
the period at the end of this sentence.

The communications protected in this hypothetical encoding could be
analyzed by the comparison of the amount of time it would take to
randomly arrive at the correct combination for the “key” used in
encrypting the data. Here an arbitrary and incredibly high figure is
developed for the number of combination “tries” for a given time
period is used to determine the relative security of the information
encrypted. For example, if there were only 60 combinations possible,
and each “try” takes one minute, the relative value of one hour of
“crypto-security” would be assigned. Considering the advent of high
speed computers, capable of billions of calculations per second, the
arbitrary figure of 100 trillion calculations per second would
provide a wide margin of safety. Assuming that the minimum
crypto-security desired is ten years, the calculation would proceed
as:

100 trillion/sec. x 60sec./min. x 60min./hr. x 24hrs/day x
365days/year x 10 years.

The total number of “tries” accomplished in the foregoing attempt is
around 1.31 x 1022, a very large number, but is still far short of
the total of 1 x 1076. To determine just how close the attempt came
over the hypothetical ten-year attempt, the number of “tries”
performed is subtracted from the total possibilities:

1 x 1076

- 1.31 x 1022

1 x 1076

Notice that the result of subtracting the combination “tries” from
the total results in the same number as the total; with numbers this
large, mathematics does not work in the same concepts most
understand. Indeed, it is difficult to comprehend how a number such
as 10 to the 22nd power (1017 is the state of Texas filled to two
feet deep with half-dollars) removed from anything else has no
effect on the answer. It does indeed have an effect, though the
first number is actually so large that the difference between the
two in this case is so small that a scientific computer, using
exponential notation, cannot calculate it. In other words, given the
total of “tries” (at 100 trillion per second for 10 years) it is the
same as if no try at all had occurred; there is no chance at
solution.

Another way of expressing the impossibility of randomly arriving at
the correct combination can be seen by dividing the total (1 x 1076)
by the number of “tries” (1.31 x 1022) which provides the number of
cycles of the ten years would be required before all of the
combinations had been tried. This equals approximately 1054; which
means that performing 100 trillion combinations per second for ten
years would require 10 followed by 54 zero’s repetitions of the
ten-year attempt. Just 1012 repetitions would require 10 trillion
years!

It would seem obvious and perhaps gross understatement to say that a
miracle would be required to randomly or accidentally arrive at the
correct combination; in our hypothetical cryptographic system, the
security of our communications is quite safe. Yet this analogy is
actually quite closer to every human’s daily experience than most
would believe, and much more important than one can imagine.

LIFE REQUIRES AN EVEN BIGGER MIRACLE

Evolutionists contend that various chemicals (conveniently
collocated) bonded producing complex chains of enzymes, proteins,
fats and fatty acids, among many other compounds, that eventually
formed the first living cell. These chains are very much like the
previous analogy of cryptographic systems in that quite literally,
these compounds record information just as information is encoded in
a cipher. In fact, this is how scientists believe DNA actually
works, calling it the “Blueprint of Life,” minor changes in the
sequences having drastic results in the organism.

The evolutionary premise is that these compounds, gathered together
in a precise, ideal environment, and given some “spark” or infusion
of energy, formed the first living cell, the chains of enzymes,
proteins, and DNA “accidentally” or randomly arranged in the one
particular combination to achieve life. The mathematical analogy of
the hypothetical crypto-system previously detailed can be used to
illustrate the probability of this occurrence, thereby providing a
relative certainty (or uncertainty) that the evolutionary stance is
“safe.”

The minimum number of enzymes for the most simple, single celled
organism to live is around 250; these enzymes exist in a sort of
string, or perhaps better, a chain, each link being a particular
enzyme which must appear at that particular position. Just as in the
example of cryptography, margin of safety calculations are generally
performed on an exponential order of magnitude; that is, where there
could be failure, it must be on the side of security. With this in
mind, the question of the relative certainty of the mathematical
position of evolution can be analyzed.

In this case, the margin of safety will be excessive; instead of 250
enzymes, only 1/5th that number [50] will be used (this would be
roughly equal to using only 7 columns instead of 32 in the previous
model). Where 50 enzymes are present, there are 3 x 1064 possible
combinations (using a factorial, which in addition, assumes that
each unsuccessful “try” is not repeated; random chance actually
means that they can recur). Even though this number is well above
the “line of impossibility” (1055) set by scientists to rule out the
possibility of an occurrence, evolutionists usually respond with
essentially, “given enough time, anything is possible.”

To this then the previous method can be applied to determine if that
is indeed true, though the numbers will have to be “adjusted” to
allow for the evolutionary scale of time. Scientists (evolutionary
at least) believe that the earth is around 4.5 billion years old and
required about 2 billion years to cool sufficiently to support life.
Owing to the previous deference to the “margin of safety,” (and
evolutionary theory needing all the help it can get) the original
figure of 4.5 billion will be rounded up to 5 billion, and then
multiplied by six, for a total of 30 billion years. The original
arbitrary figure of 100 trillion tries per second will be retained,
only instead of ten years, the process will cover the 30 billion
year period. This yields a number around 2.82 x 1039; obviously
still short, though the subtraction will help understand how close
the ridiculously high number of 100 trillion tries per second
actually is. Therefore:

3 x 1064

- 2.82 x 1039

2.999999999 x 1064

In this case, the answer actually does change somewhat, though with
numbers this large it is difficult to discern exactly how much, and
in turn, how close the 100 trillion “tries” per second for 30
billion years actually came. The next step is to divide the total
possibilities by the total “tries” in that period to determine how
many times this 30 billion-year period would have to be repeated.

The number is actually quite staggering, and every bit as hard to
understand as the original: 3 x 1064 divided by 2.82 x 1039 equals
1.06 x 1024. What this means in actuality is that the 100 trillion
tries per second for 30 billion years would have to be repeated a
trillion, trillion times, or 1,000,000,000,000,000,000,000,000
times. In other words, the pace of 100 trillion tries per second
would have to continue for
31,000,000,000,000,000,000,000,000,000,000,000 years, which is 60
trillion, trillion times the estimated age of the earth.

It should be remembered that the base used was only 1/5th of the
total enzymes, calculated using a factorial, given 6 times the
estimated age, and the ridiculous figure of 100 trillion tries per
second. Further, not only are there 250 enzymes, there had to have
been more than 2,000 proteins; the factorial alone of this number is
around 3 x 105,735 (notice that the exponent itself requires a
comma). Indeed, Sir Fredrick Hoyle, an eminent British mathematician
and scientist, calculated the odds against the random formation of
the enzymes and proteins alone at 1040,000. Yet, this does not even
begin to address the more than 3 million “positions” of DNA, with
its 24 possibilities on each; this number is all but
incalculable—most scientists believe the number would have an
exponent that would have to be expressed in exponents!

It would seem quite “safe” to say that there is very little
“security” in evolution, though in this case it is not just national
security that may be in jeopardy, but rather one’s eternal security.
In other words, would you trust your life to such odds?

William B. Tripp, Ph.D., D.Th.

21 February, 2002