Probability is that branch of mathematics which deals with "chance" — or, to be a bit more technical, uncertain phenomena. The probability of a given event is a number, between zero and one, which measures how likely it is that the event will occur. If an event is impossible, its probability is zero. If an event is an absolute certainty, its probability is one. A probability of 1/2 means that it is just as likely that the event will happen as it is that the event will not happen. Sometimes this situation is described by terms such as "50% chance," "50-50 chance," or "even money." The closer a probability is to one, the likelier the event is. For instance, an event whose probability is equal to 999/1000 is more probable than one whose probability is 9/10. On the other hand, the closer the probability is to zero, the less likely the event is. An event whose probability is 1/1000 is less probable than one whose probability is 1/10, Now to the question at hand. What does probability have to do with evolution? The theory of evolution claims that life, in all of its complexity, came into existence by chance. And since probability is the mathematics of chance, probability should have a great deal to do with evolution. In the following articles some of the relationships between evolution and probability are discussed.
Dr. William Stenger — Chairman, Department of Mathematics, Ambassador College, Pasadena, Calif.
If you flip a coin, there are two equally likely outcomes: The probability of "heads," is one out of two or l/2, and the probability of "tails" is one out of two or 1/2. If you flip two coins, a penny and a nickel, there are four (2 x 2) equally likely outcomes: The probability of two "heads" is one out of four or 1/4, the probability of two "tails" is 1/4, but the probability of one "head" and one "tail" is two out of four or 2/4= 1/2. If you flip three coins, a penny, a nickel, and a dime, there are eight (2x2x2) equally likely outcomes: The probability of three "heads" is l/8, the probability of three "tails" is 1/8, the probability of two "heads" and one "tail" is 3/8, and the probability of one "head" and two "tails" is 3/8.
Monkey Business
"GIVEN a monkey, a typewriter and a stack of paper, by chance alone, words, sentences, even whole books could be written." This is a doctrine deemed holy by a not-insignificant number of educated men in the biological and geological sciences today. "Given enough time, chance alone will produce simple life forms... given more time, complex form of life will come into being... given enough time, even man... highly intelligent man could arise." But is this true? And if true, what span of time would be needed? The Origin of Species — by chance alone? Could life forms — species — arise by chance "given enough time"? Could Darwin's book also have come by blind chance? Given a chimpanzee, a typewriter and a stack of paper, how long would it take the chimp to peck out just the title of Darwin's controversial book The Origin of Species? Eighteen letters and three spaces, a total of twenty-one strokes with the typewriter. And we will simplify the problem by allowing him to use all capital letters. It should take but a few hundred attempts? Or should it? Begin with a chimp — of course you must provide him with an intelligent human assistant to note his progress and to insert a fresh sheet of paper each time the chimp makes an error. How long will it take to type Darwin's title? Twenty-one strokes might take perhaps twenty-one seconds! That is IF he hit the right keys. There is a chance, you will admit, that he might by chance hit the right keys, even the first time. And that given enough time he would certainly get the title right. How long then to type out Darwin's entire volume? How long to type out the Encyclopaedia Britannica with its 24 volumes, each with over a thousand pages? And given enough time, how long for all the books and publications in the world? Do we acknowledge that given enough time this chimp could type out all the books in the world? By mere random pecking at the keys? And by analogy, do we then admit that life forms and man too could originate by chance?... that the millions of species and billions of billions of different individual creatures alive today are the result of blind chance?
Prepare to Multiply
Let us go back to our chimp and watch over his shoulder as he begins ARX BLMX... but wait, his human assistant removes the sheet of paper, turns in a fresh one and our chimp begins again. T — Success! He has hit a "T" by accident and we are on our way to words, then books... and even LIFE itself.... There are 44 keys on the typewriter (26 letters, 9 digits, a space bar and numerous symbols and punctuation marks). For simplicity, the other controls are being handled by our human assistant. He watches for errors (and success), changes sheets and times the proceedings. And feeds the chimp. The odds of getting that first letter right were 1 in 44 (that's how many keys there are on a typewriter), but he did it. Now only 20 more successful strokes to go: T, TH, THE! What were the odds on that first word? One chance in 44 on the T, one in 44 on the H, one in 44 on the E. Prepare to multiply 44 times 44 times 44. The answer is 85,184. By blind chance done, our chimp has only one chance in 85,184 of getting these first three letters correct. But let him proceed. One chance in 44 that he will hit the space bar next, then one chance in 44 of hitting the 0, then the R, then I, G, I and N. The odds now become astronomical, for 44 times itself 10 times turns out to be about 27,720 million million. Remember that each time an error was made, his assistant removed the sheet from the typewriter and inserted a fresh one. How high a stack of paper can we expect to result from our chimp typing out these first two words? On the "average," 27,720 million million sheets' would be wasted to achieve a two-word goal — THE ORIGIN — typed neatly on the twelfth line, where the human assistant started our chimp off. And the stack of 27,720 million million wasted sheets? How high? A thousand sheets of paper might be about six inches thick; two million sheets, a thousand feet high; ten million, roughly a mile high. But 27,720 million million sheets would reach into the heavens — out past the moon — all of the 93 million miles to the sun — and over a thousand million miles further for a total of 2,772 million miles. All this waste by using the "random pecking" method of a chimp to type out the first two words! THE ORIGIN... just that much by chance. How many tons of paper? Eight pounds for a thousand sheets. Four tons for a million sheets. Thus our chimp has wasted 110,880 million tons of writing paper — tens of thousands of times the production of the U. S. in a year.
1The probability of success is p=4410 and of failure is q=1-p. The probability of the chimp succeeding the first time is p, of failing the first time and succeeding the second is qp, of failing the first two times and succeeding the third is q2p, etc. Therefore, the expected number of wasted sheets of paper is 0p+qp+ 2q2p+3q3p+... =(1/p )-1, which is approximately equal to 4410.
How many trainloads of paper, and who would build the trains, and the railroads? How many square miles of timber would have to be cut to produce the pulpwood? How many lumberjacks? To inquire where we got the monkey (I mean chimpanzee) in the first place, and where the intelligent human assistant, and where the typewriter, would only cause further embarrassment at this point. And... whether any chimp would either submissively or mischievously peck keys at random? Finding the X, wouldn't he go XXXXXX, then XX, XXX, and then go off in search of something else to monkey with? But let us return to our chimpanzee. How long has this taken him? Not 21 seconds... not 21 years but...? Allow a second to insert the sheet, a few seconds to make an error and a bit more time to discover the error, stop the chimp and remove the paper. Five seconds per sheet would allow twelve sheets per minute, 720 sheets an hour and 5,760 for an 8-hour day. Our 27,720 million million sheets would then represent more than 4,800,000 million days. With 235 working days in a year (a month's vacation for other monkey business), our chimp is either 20,000 million years old... or we are four thousand million chimp generations later.
A Title for Darwin's Book
But we began a task; let us complete it. Twenty-one correct typewriter strokes will complete the title — THE ORIGIN OF SPECIES. And the chance of being correct in each stroke is only 1 in 44. (The chances of error are 43 in 44.) The odds to type out 21 correct consecutive strokes are 44 times itself 21 times, or in the mathematician's mode of expression 4421. A few minutes with logarithms changes 4421 to about 1034.5, then back to layman's mathematics as the number 325 followed by 32 zeros. (Six zeros would produce a million.) But adding 32 zeros produces an answer of 32,500 million million million million million. That many sheets would produce a stack 3,250 million million million million miles high! But that distance is ten thousand times the assumed extent of the universe. The number of sheets of paper is millions of millions of times greater than the estimated total number of stars (1,000 million million million) in the universe. "By faith Abraham..." firmly believed and obeyed a God he had seen, talked with and trusted, but by a superstitious faith the atheistic evolutionist is firmly convinced that a "monkey and a typewriter" "could" produce THE ORIGIN OF SPECIES. Or at least so goes the favorite analogy. Evolution "is now an integral part of all general education and culture. To suppose that it may some day be abandoned is to live in intellectual barbarism," writes evolutionist Henshaw Ward in his book Evolution for John Doe. Review the problem. Note the simplicity of the accomplishment — 21 correct typewriter strokes in a row. Done by intelligence by the chimp's human assistant, THE ORIGIN OF SPECIES would have required just about five seconds. Attempted by chance by a hypothetical chimp it would require 20,000 million years to produce the first two words, THE ORIGIN.
"If it really is true that {man} is merely the inevitable culmination of an improbable chemical reaction... then the fact that he has been able... to trace himself back to it is remarkable.... That chemicals which are 'merely material' should come to understand their own nature is a staggering supposition. It is also a preposterous one" (The Great Chain of Life by Krutch, quoted in LIFE, January 28, 1957, page 28).
The Origin of Life?
What is life? In the simplest physical description, life's blueprint is a delicately designed molecule three feet long and much, much thinner than a spider web. Each atom in this three-foot chain is precisely placed, as precisely as are the letters in a word and the words in a sentence. Each cell in our body contains an identically coded chain. Every living creature has its own ,unique pattern and seqclence of millions of atoms. To produce such a sequence of atoms by chance... is unthinkable. To have highly educated men today profess belief in such an untenable doctrine is, to put it mildly, incredible. And to have these educated men dogmatically teach that evolution is no longer a theory but a fact, and that to doubt it is to "live in intellectual barbarism," is a tribute to the capacity of the human mind for self-deception. But as a skilled secretary types out — THE ORIGIN OF SPECIES — in five seconds, so a skilled Creator arranged a few bucketfuls of red earth into a walking, thinking, living man in a very brief time one Friday about six millenia ago.
A Left-handed Twist... AMINO ACIDS IN METEORITES — EVIDENCE FOR EVOLUTION? by - R. A. Ginrkey
ACCORDING to modern evolutionary theory, primitive life first appeared on the earth several billion years ago when random combinations of simple molecules, such as methane, ammonia and water accidentally came together to form amino acids. These in turn eventually (supposedly) combined to yield exceedingly complex self-replicating proteins — "primitive" life. For years, many men, especially those religiously oriented, questioned whether such simple molecules could ever — by chance — produce amino acids, which are considerably more complex. Then, in 1953, Dr. Stanley Miller and other scientists demonstrated that if hydrogen, ammonia, methane, and water vapor were placed in a simulated "primitive planetary atmosphere," these simple molecules could indeed produce amino acids! More recently Fox and Windsor of the University of Miami succeeded in synthesizing some nine amino acids by heating ammonia and formaldehyde together at temperatures below 200 ° C. True, a source of energy in the form of ultraviolet light, an electric discharge or heat was needed, but this merely corresponded to radiation from the sun, or to the presence of lightning. CHALK ONE UP FOR EVOLUTION. Yet the question remained — could amino acids be produced by natural causes without the assistance of men? The answer turns out to be YES! Recently, scientists of the National Aeronautics and Space Administration reported the discovery of 17 different amino acids in a meteorite from outer space. Interestingly, the researchers found an almost equal number of "left-handed" and "right-handed" amino acids. What do we mean by "left-handed" and "right-handed" amino acids? Simply this: Every amino acid (with the exception of glycine) found in the proteins of living organisms, can exist in two forms, each one the mirror image of the other. Since they have the same spatial relationship as a pair of gloves, one type is arbitrarily called "right-handed" (D, dextro, right) and the other "left-handed" (L, levo, left). The two forms are identical. They have exactly the same chemical composition. They have exactly the same physical properties; exactly the same density, melting point, solubility, etc. In fact, were it not for the fact that they rotate a beam of polarized light in opposite directions, they would be indistinguishable. How did the scientists refute those who might claim that the meteoric amino acids were the result of contamination after reaching the earth? Here's the answer: The "left-handed" configuration of amino acids predominates on earth; yet the meteorite contained an almost equal number of "left-handed" and "right-handed" amino acids. Therefore, it was extremely unlikely that contamination of the meteorite had occurred. The NASA team concluded that the discovery of meteoric amino acids is "probably the first conclusive proof of extraterrestrial chemical evolution." That is, the discovery proved that amino acids could be produced away from the earth from simple molecules by natural causes. CHALK ANOTHER ONE UP FOR EVOLUTION? On the contrary. Chemical "evolution" is not biological evolution. Having a few chemicals randomly join together is incalculably distinct from the "simplest" living organism. In the following article, some of the incredibly improbable probabilities are discussed. And those calculations only tell us the likelihood that the molecules would "line up." For these molecules to actually chemically combine would be still further unfathomably unlikely. In
Illustrated amino acid molecules A and B have the same type of relationship as the pair of gloves shown above. like a pair of matching gloves, molecule A is very similar to molecule 6. They are, however, different molecules. Only the left-handed amino acid molecules are found in living things. According to probability, there ought to be as many right-handed as left — but there are none! Evolutionists cannot explain why. (See PDF for pictures)
addition, one would have to consider the chance that the resulting "chemical chain" would have the proper three-dimensional structure suitable for life. Furthermore, what the NASA men discovered actually highlighted the uniqueness of life by underscoring an embarrassing fact which every evolutionist must eventually face. Notice! Some "left-handed" and "right-handed" amino acids are energetically equivalent, it is ENTIRELY EXPECTED that random combinations of molecules will produce equal amounts of both right-handed (D) and left-handed (L) amino acids. This is exactly what was found in the "primitive atmosphere" experiments and the meteorite analyses. Now, IF life truly evolved following the random production of the D and L forms of the necessary amino acids, then we should find both forms of amino acids in the proteins of living organisms on earth! But such is NOT the case! ALL the amino acids which are constituents of proteins in ALL living things are the L-amino acids! The D-amino acids, while readily formed in the laboratory, are NEVER found in the proteins of any Known form of life! WHY? Is this incredible fact "just another accident," as most evolutionists are wont to claim, or is it a result of forethought and planning in every organism on earth? The answer should be obvious. The fact that the amino acids in living protein are all L-amino acids cannot be explained by evolutionary theory. However, it can be readily explained as the result of the purposeful design of a Supreme Designer! CHALK ONE UP, A BIG ONE, FOR THE CREATOR.
Proteins By Chance? by W. Stenger
JUST HOW likely is it that amino acids could randomly produce a "simple" protein? Let's suppose we had a "soup" full of amino acids. We want these acids to link up at random to form a relatively simple protein consisting of 100 amino acids. How many different combinations are there? Suppose there are 20 different types of amino acids available. If we wanted a chain of two acids, there would be 20 possibilities for the first acid and 20 for the second — or a total of 20x20=400 possibilities. Similarly, if we wanted a chain of three acids there would be 20x20x20=8,000 possibilities. Therefore, for a protein consisting of a chain of 100 acids, we have
20x20x...x20
=20100
100 times
possibilities. But 20100 is approximately equal to 10130, that is, 1 followed by 130 zeros. Is it reasonable to believe that such a protein could have been formed by chance during the history of the universe? Scientists have stated that there may be as many as 1022 stars in the observable universe. Let's be generous and say 1,000 times as many, or 1025, stars just to be on the safe side. Instead of allowing just one planet like earth for each star, we'll give each star ten such planets for a total of 1025 "earths" in the universe. Let's also give each "earth" oceans the same size as our earth's Oceans — about 1046 molecules. Again, we'll be generous and fill the oceans with a "soup" of amino acids rather than sea water. So we have 1026x1046=1072 amino acids floating around. In order to give the evolutionists a sporting chance we'll let all of these acids link up into chains 100 acids long every second. Since 100 = 102, this would give us 1072+102= 1070 chains per second. A year has less than 108 seconds, but we'll round it off and say we have 1070 chains per second times 108 seconds per year for a total of 1078 chains per year. Now all we need is an upper bound on the age of the universe. Various estimates have been given, but a safe upper bound is about 10 billion (=1010) years. Therefore, we would have 1078x1010=1088 chains formed in all our "oceans of amino acid soup," on all our "earths," around all the stars, for all the years the universe has existed! But we have already seen that there are about 10130 possibilities. It can be shown1 that the probability of forming by chance the given protein consisting of 100 amino acids in 1088 tries is less than 1088/10130=1/1042. How probable is this? Less probable than a chimp typing The Origin of Species by chance! Thus the odds against such an event are beyond astronomical! Even though we have been exceedingly generous, the odds that one small protein could have evolved are infinitesimally small. The odds against an average-size protein of 500 amino acids evolving are, of course, far greater. Of course, an evolutionist (or maybe even a sincere skeptic) can always claim (preposterous as it seems) that it could have happened. Reasoning based on probability alone cannot lead to a conclusion that a protein could not form at random. But it does show the FANTASTIC ODDS AGAINST IT HAPPENING! We realize that we are not the first ones to analyze evolution from the point of view of probability. Others before us have also shown the FANTASTIC ODDS involved. Then why do evolutionists still cling to their beliefs? Here are some of the evolutionists'
1Let p = 10130 be the probability of success in one try. The probability of failure is q=1-p. The probability of at least one success in n=1088 tries is p+qp+q2p+...+qn-1p np=1088/10130.
counter-arguments — and the answers: 1) You can't prove anything by probability. Some people say you can't prove the world exists, you can't prove cyanide is poison unless you try it, etc. What kind of proof do you want? Do you want proof that the sun is "coming up" tomorrow or that things fall down, not up? The proofs-of the laws of probability are stronger than the proofs of these acknowledged physical laws. Probability has stood the test of time. From "back-alley" dice games to highly sophisticated research laboratories the laws of probability have proven themselves to be just as dependable as the law of gravity. In fact, the laws of probability are intrinsic to the gathering of virtually all quantitative scientific information. A true scientist does not jump to conclusions based on a few bits and pieces of evidence. In science, no conclusions should be drawn — no facts established as facts — without a rigorous test of the hypotheses BY MEANS OF THE LAWS OF PROBABILITY! 2) Not all chains of amino acids are equally likely to be formed. The ones needed for life are more likely than the others. This is pure speculation.
The mathematics of probability shows the fantastic odds against one small protein being formed by chance even under the most ideal conditions.
There is no evidence that such is the case. The idea is based on an analogy with other rare and completely unrelated chemical reactions (selective autocatalysis). Even if some chains could be proved to be more probable, this would not prove evolution. Quite the contrary, it would prove the existence of a law, which in turn demands a LAWGIVER. 3) Even though the probability is immeasurably small, it still is not zero. Therefore, it could have happened. Do you want to believe in such an improbable event? Is such a belief rational? Would you be willing to bet your life on it? Would you send your child to school on a school bus which had one chance in 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000 (=1042) of arriving safely? Even if the evolutionists' arguments were right — which they are not — and a protein could be formed by chance, would that be life? Is that all there is to life — a blob of protein? Is a dead dog alive because he has protein? No — protein is just one small piece of an intricately complex puzzle which only the INFINITE MIND of a DIVINE CREATOR is capable of solving.
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