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CHAPTER 7: How Large Numbers Can Help You 
How Large Numbers Can Help You Although we must keep all our confidence in our science,
SERIOUS REASONING MAY require effort. It is the delightful sort
of effort that may reward the thinker with valuable insights
about the nature of things. Why Understanding Large Numbers Is Important
If one wishes to arrive at a high degree of certainty regarding the question of evolution, either for himself or in order to
help others, it is vital to grasp the real meaning of the kind of
numbers we are encountering.
Take the number of seconds in any considerable period. There
are just 60 in a minute, but in an hour that increases to 3,600
seconds. In a year, there are 31,558,000, averaged to allow for
leap year. Imagine what a tremendous number of seconds there
must have been from the beginning of the universe until now
(using 15 billion years, which is one of the standard estimates
by evolutionists). It may be helpful to pause a moment and
consider how great that number must be.
It is 4,000 times larger than the number of atoms in that super universe
we just imagined.^{5} A Number Too Big to Imagine
Try as we may, that slender probability for the chance formation
of a protein is a number too large to grasp. Let’s ponder
it awhile. That big figure, 10^{161}, represents the odds against one
protein in five billion years. We can now calculate how long
a period would be required in which we could expect one success
on the average.
The Case of the Traveling Ameba
Imagine an ameba. This microscopic onecelled animal is
something like a thin toy balloon about onefourth full of water.
To travel, it flows or oozes along very slowly.
would require the time for one round trip multiplied by the
number of atoms in the universe, 5 x 10^{78}. Multiplying, we get
10^{107} years, rounded. That is the length of time for the ameba
to carry the entire universe across, one atom at a time.
Why Some Probabilities Are So Small
CharlesEugène Guye was one of the most brilliant thinkers
of this century. This noted physics professor at Geneva called
attention to the rapidity at which the number of outcomes
can increase: “It is sufficient to recall that a hostess can arrange
20 diners round a table in more than two million million million
ways. What would it be if it were necessary to place one
thousand?”^{8}
occupied. The total possible arrangements in such a situation
comes to 20 x 19 x 18 x 17 x . . . x 1, called 20 factorial, and
written in this interesting notation: 20! That is why, incidentally, we have not put exclamation points after some of the
amazing figures we have computed. The exclamation point would
change the meaning to factorial.
The Laws of Chance Are Dependable Pierre Lecomte du Noüy, noted French scientist who escaped Nazi occupation in 1942 and came to the United States, wrote, The socalled “laws of chance” borrow their accuracy (which is considerable on our scale of observation) from the fact that no privileged atoms exist (from the particular point of view considered) and that, on an average, they all behave in the same unpredictable, disorderly manner.^{9}In other words, we can expect things to average out according to those laws, and we are not to think anything is likely to behave contrary to the law of large numbers, if it depends on chance alone. Throughout science, engineering, and business, you find almost absolute dependence upon these laws. It is logical that the same principles which are used in planning skyscrapers can be trusted when we apply them to the probability of proteins forming by chance. Calculations Can Be Scientific – a Repeatable Study Remember that the essence of the scientific method is the repeatable experiment with the same outcome if the experiment is carried out in the same way, no matter who does it. Anyone can check on the reality of the multiplication rule and the
mathematical formulas we have used. If doubts recur, one can
go back and recheck until he is assured they are correct. The
principles of probability are known and unhesitatingly trusted
by engineers, astronauts, and all who use mathematics.
Modern Atheism’s Substitute for God In April, 1967, the international magazine, Réalités, printed an interview with French philosopherscientisttheologian Claude Tresmontant, whom we have quoted earlier. The magazine, in its introduction to the interview, referred to Tresmontant’s book, The Problem of the Existence of God Today, using these phrases: “closely argued reasoning,” and “the almost overwhelming mass of learning with which it is weighted.”^{10} In the interview, Tresmontant, after stating that Plato, Aristotle, and others “thought that the world was a great living being, a Divine Animal,” said, “Modern atheism still maintains that the world is the only Being.” He then elaborated on what that would mean as to the nature of matter: Since it is assumed that this matter is increate and eternal . . . it must have produced, from its own resources, everything that has appeared in the universe, both life and thought.With incisive reasoning, Dr. Tresmontant points out the implications of this substitution of the material universe for God. I maintain that it must be gifted with great wisdom and incomparable genius. I would even say that matter must be credited with all the attributes that theologians specify as belonging to God: autonomous being, ontological seIfsufficiency and creative genius.^{12}By this he shows that atheists cannot expect to escape the need for God – the same kind of God as described in the Bible – as the only rational explanation of the universe. The general rule on the way things are is becoming clearer as we go on. Chance cannot create complex, orderly, operational systems. Neither can it account for beauty. To attribute to blind chance the perfume of a rose or the playfulness of a lamb is to ignore all logic.
Speaking of large numbers, Lecomte du Noüy commented,
“It is evident that exponents of over 100 lose all human significance. The nearest star is 40 x 10^{21} microns from us.”^{13} (A
micron is one thousandth of a millimeter, which itself is about
one twentyfifth of an inch.)
If the probability of an event is infinitely slight, it is equivalent to the practical impossibility of its happening within certain time limits. The theoretical possibility . . . can be so small that it is equivalent to a quasicertitude of the contrary.^{14}We have seen that an ameba could transport six hundred thousand trillion trillion trillion trillion universes, an atom at a time, across the diameter of the entire universe, travelling at the rate of an inch in fifteen billion years, during the time in which chance could be expected to arrange one average protein molecule.^{15} Perhaps the reader would agree that a probability so
slight as this surely qualifies, in Lecomte du Noüy’s
phrase, as a quasicertitude of its practical impossibility.
^{1} Pierre Lecomte du Noüy, Human Destiny (New York: Longmans, Green & Co., 1947), p. 38. ^{2} A moment’s thought shows that in the case of the sweepstakes, it is certain that someone will win. This is an entirely different type of situation from the kind we are studying. ^{3} Encyclopaedia Britannica, (1967), s.v. “galaxy.” ^{4} According to Jesse L. Greenstein, who was then head of the Astronomy Department at California Institute of Technology (personal conversation, Novemher, 1971), 10^{78} was the figure based on a 10billionlightyear radius. Since 15 billion light years is now the accepted view, we calculate that the number of atoms is around 5 x 10^{78}. (The earlier 10^{78} was “approximate.”) Current estimates of radius range from 10 to 20 billion light years, although there is still uncertainty of measurements beyond a few hundred light years. ^{5} 10^{161} = (2.5 x 10^{157}) x (4 x 10^{3}) ^{6} 10^{64} divided by 15 billion (1.5 x 10^{10}) = 6.6 x 10^{53} ^{7} Wernher von Braun, Space Frontier, New Edition (New York: Holt, Rinehart and Winston, 1971), pp. 108, 109. ^{8} CharlesEugène Guye, PhysicoChemical Evolution (New York: E. P. Dutton & Co., 1925), p. 164. ^{9} du Noüy, Human Destiny, p. 41. ^{10} Réalités, Paris, April, 1967, p. 45. ^{11} Ibid., p. 46. ^{12} Réalités, Paris, April, 1967, p. 46. ^{13} du Noüy, Human Destiny, p. 32. ^{14} Ibid., p. 30. ^{15} Note that all through this chapter, the figures we used were those obtained under those tremendous concessions to make it easier for chance to succeed. Under realistic figures, the odds would have been even greater against its success.

Chapter 6 