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