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