The Evolution Game: A Computer Simulation *
By Paul D. Ackerman
* The present paper was presented at the 15th Anniversary Bible-Science Convention in Anaheim, California, August 1979. It is also contained in the published proceedings of that convention obtainable from The Bible-Science Association, 2911 East 42nd Street Minneapolis, Minn. 55406.
One of the most troublesome arguments put forward by our evolutionist friends has been the argument that with increasing amounts of time the evolution of matter and motion, stellar bodies, and ultimately life itself becomes more and more likely. Harvard professor George Wald has stated the argument as follows:
"The important point is that since the origin of life belongs in the category of at-least-once phenomena, time is on its side. However improbable we regard this event, . . . given enough time it will almost certainly happen at least once. . . Time is in fact the hero of the plot. Given so much time, the `impossible' becomes possible, the possible probable, and the probable virtually certain, One has only to wait: time itself performs miracles." (Wald, 1956, p.12)
Physicist Vvilliam R. Bennett Jr. has recently written in regards to one of the most famous forms of the argument Bennett states: "Nearly everyone knows that if enough monkeys were allowed to pound away at typewriters for enough time, all the great works of literature would result," (Bennett 1977, p.694)
There is something about this argument that the human mind finds intuitively persuasive. Obviously if the monkeys were to type long enough one of them would inevitably type the word "to." And with just a little more time surely no one would be surprised to find the word "two," And if such circumstances produced "to" and "two" then why not eventually "four," "eight," and finally a complete sentence, paragraph and so on.
But the counter-argument is also intuitively powerful. In the same article devoted to the random monkey argument Bennett has also reproduced a marvelous passage from a book by John Tillotson published in 1719. The book was titled Maxims and Discourses Moral and Divine and contains the following quote:
"How often might a man, after he had jumbled a set of letters in a bag, fling them out upon the ground before they would fall into an exact poem, yea or so much as make a good discourse in prose? And may not a little book be as easily made by chance, as this great volume of the world? How long might a man be in sprinkling colours upon a canvas with a careless hand, before they could happen to make the exact picture of a man? And is a man easier made by chance than his picture? How tong might twenty thousand blind men, which should be sent out from the several remote parts of England, wander up and down before they would all meet upon Salisbury Plains, and fall into rank and file in the exact order of an army? And yet this is much more easy to be imagined than how the innumerable blind pans of matter should rendezvous themselves into a world." (Bennett 1977, p.695)
In answer to the latter question of blind matter coming together into a world, the modern physicist would say that the matter got compacted enough to be gravitationally bound and collapse into a solid body. But that just pushes the question back a step making it more difficult to grasp clearly. How did the matter get close enough to be gravitationally bound? The evolutionist answers that the smaller cloud was part of a larger cloud that was disturbed by shock waves from a nearby galaxy. Still the same exact question remains completely unanswered although it has been pushed back one more step and is now quite difficult to think about in a clear way. How did the matter rendezvous into the original cloud and galaxy complex? The evolutionist answers that it was an accidental result of the big bang. How did the blind matter in the original ball rendezvous before the big bang? The problem remains exactly the same although it is now much more difficult to think about clearly.
The problem of "clear thinking" in regards to probabilities has recently received attention in the social science literature (Einhorn a Hogaith, 1978; and Shweder, 1977). The basic conclusion of these articles is that we as humans find it very difficult to think clearly and accurately about probabilities.
Our strong suit appears to be in the area of discovering "symbolic and meaningful connections" rather than correlational ones (Shweder. 1977, p. 637). When all the various factors are compiled it becomes apparent that the time plus chance model is not one that readily lends itself to logical and rational analysis by either the expert or non-expent. The goal of the present simulation research is to promote clear thinking in this area. The question is whether or not time is in fact on the side of evolution as Wald and Bennett maintain, It is the author's contention that it definitely is not. To put it simply, if a monkey is going to type a great literary work he needs to get it done in a hurry. Time will work against him - and against any real process in the real world - and not for him.
This fact is reflected in what scientists call the Second Law of Thermodynamics which states that all real processes in the physical universe go irreversibly downhill toward increasing disorder and randomness. In terms of the typewriting monkey example it means that along with the accumulating chance of producing something meaningful as time increases, there must also be a consideration of the accumulating chance that the monkey, typewriter or both will break down as time increases, Any real world system posited by Wald, Bennett or anyone else to produce potentially ordered and meaningful outcomes will inevitably be subject to the process of decay and disordering known as the law of entropy or Second Law of Thermodynamics. Further, any such posited system will upon examination be found to contain greater organizational complexity than its postulated product
A perfect example of "hidden" complexity accounting for an ordered product rather than mere time plus chance is clearly evident in the interesting research of W.R. Bennett, Jr. (1977) in relation to the typing monkey problem. Bennett set out to simulate the typing monkeys by use of a computer. Bennetts computer monkeys were able to produce poignant literary phrases such as the following:
.....WE PLAY MEANS HOLY FOOL..." .....HAVE MANY JUDGEMENT WAS IT..." .....AS MAKES SO BUT OUR HEART OURSELF..."
The question is, how did they do it? Bennett realized that if his computer monkeys were not given some help they would never "within our lifetimes and computer budgets" produce anything approaching the above literary gems. (Sarcasm is intended as playful rather than nasty.) ln fact when Bennett gave his computer monkeys no help they produced nothing more impressive than the following:
AOOAAOQHYOLMLCHFKCWSEG LGJNLPFSU NUPCAZYORPIFZ
How then did Bennett help his computer monkeys? What he did in effect was to give them magic typewriters. Instead of the ordinary typewriter which has one key for each letter and one space bar, imagine one which has 6,934 "space" keys, 3.277" E" keys. 21 "X keys and so forth. The number of keys for each character reflects the relative frequency of occurrence forthat character in Act Ill of Shakespeare's Hamlet which Bennett used as a model.
The computer monkey types a letter with his magic typewriter, but before he can type a second character the typewriter magically changes its keyboard. This change reflects the relative frequency of letters in Hamlet preceded by the letter which the monkey just typed. For instance, if the monkey had typed the letter "0" then the keyboard would change so that all the keys were the letter U." Bennett worked these transformations out to four characters which reaches to the limit of our present feasible computer storage capabilities. If the computer monkey had just typed "LORD" then the keyboard would mostly consist of space keys with a number of "S" keys but no "X" keys and so forth. After the fifth character is typed then the keyboard returns to the original magic keyboard with 6,934 "space" keys, 3,277" E" keys, etc.
When we realize how the phrases were produced they no longer are surprising or remarkable. In the real world the remarkable thing would not be the literary output of the monkeys but the magic typewriter. Thus we see that however interesting Bennett's work might be for his intended purpose of increased understanding of "intelligence," it bears no relationship whatever to evolution and the argument that time is on the side of evolutionary development.
THE EVOLUTION GAME: A SIMULATION
As stated earlier a computer simulation of the time plus chance evolutionary model which is really to the point must contain provisions for decay and deterioration as well as meaningful output In terms of the typing monkey we must include an estimate of the likelihood that the typewriter or monkey will break down in some way. Imagine the following simple game involving flips of a coin. Let us assume that in a certain period of time - say one million years- our typing monkey would have a 25% chance of producing a certain Shakespearean sonnet Therefore in order to see if our monkey has typed the poem in the first million years we flip a coin twice. If both flips come up heads then we would have our masterpiece. However, before we do this we need to take into account the possibility that something will happen to the monkey or that the typewriter will break down before the sonnet is produced. Let us assume that the probability of something happening to the monkey before he types the sonnet is 50%. Let us also assume that the probability of the typewriter breaking down is 50%. Therefore we must flip our coin twice to see how the monkey and typewriter fare. If we get "heads" on both flips everything is fine and we can proceed to the two flips described above to see if the poem is produced. If we do not succeed in getting the poem during the first million years then we repeat the procedure again to simulate the second million years, and so forth.
There is, of course, a good chance that something will go wrong with either the monkey or typewriter before very long. This is determined by obtaining a "tail" on one or both of the two preliminary coin flips that accompany each simulated time period. If this happens then we have a broken element in the monkey and/or typewriter and, of course, no poem is possible until the broken element or elements are fixed. Now what is the probability that some occasion of energy input into the broken element as produced by a passing storm, earthquake, etc. will result in the repair of that element? Let us assume that there is a 25% chance that such an occasion will repair the damage in question.
On the other hand let us assume that there is a 75% chance that the typewriter or monkey will deteriorate further as a result of the energy input. Thus, if we have a broken element we flip a coin twice. If we get two heads the element is repaired. If we get one or two tails, then the broken element in the typewriter or monkey has not been fixed and we now have an additional broken element. In each simulated time period there would be two coin flips for every broken element that has accumulated. Two "heads" means the element is fixed and subtracted from the total of accumulated broken elements. One or two "tails" means that a new broken element is added to the accumulated total to be dealt with on the next simulated time period. There is a chance to get the poem during each simulated time period. For instance if at a given time there are ten broken elements, 20 consecutive "heads" would be needed in order for there to be an opportunity for the monkey to begin typing again. The probability of getting 20 consecutive heads would be .5020 = .0000009. Of course, the probability that there would be even further deterioration would be 1 - .0000009 = .9999991.
Playing this evolution game by hand can be a very useful teaching tool in public presentations. However it is not feasible to carry the game out beyond a few steps because of the time and number of coin flips involved. For this reason, this author prepared a computer program to extend the game out. Basically the computer simulated the coin flips required for each simulated time period. Based upon the outcome of these flips the computer would assess whether the sonnet had been produced as well as calculate the number of coin tosses needed to simulate the next time period. This process was carried out until 130 time periods had been simulated or until the number of consecutive heads required to obtain the sonnet exceeded 1400.
The results confirm the Contention that if something meaningful is to be produced it must occur quickly before the optimal conditions (which have simply been granted for the sake of argument) deteriorate beyond any hope of restoration. Given the assumed probabilities (which the author believes in fact to be fartoo generous) the chance of obtaining a sonnet after the first four or five simulated time units becomes essentially zero. Table I contains the obtained values for a number of typical runs of the evolution game program.
Table I. Number of ~heads~ required to produce sonnet at successive time periods for eight runs of the ~evolution game.~
Evolution Game Runs
1 2 3 4 5 6 7
1 -- 4 4 4 4 4 4 4 4
2 -- 6 6 6 4 8 6 8 6
3 -- 10 10 10 8 16 10 16 10
4 -- 20 14 8 14 24 10 30 8
5 -- 34 20 16 16 30 6 40 10
6 -- 54 26 24 30 48 4 60 8
7 -- 90 36 36 50 64 6 104 14
8 -- 150 64 52 80 98 10 158 18
9 -- 236 106 90 140 118 14 248 36
10 -- 340 148 144 244 162 20 364 50
11 -- 514 226 218 382 250 30 516 56
12 -- 752 328 342 606 384 50 790 92
13 -- 1134 514 518 876 598 80 1232 124
14 -- 1400+ 762 816 1272 866 136 1400+ 194
15 -- 1126 1204 1400+ 1262 212 282
16 -- 1400+ 1400+ 1400+ 354 434
17 -- 562 602
18 -- 786 916
19 -- 1176 1398
20 -- 1400+ 1400+
A basic element of the creation model for all natural science, social science and humanities disciplines is that things do not just happen. All things in the created universe including the molecules and galaxies studied by the natural sciences; the learned behavior, perceptual phenomena, political and economic cultural achievements studied by the social sciences; and the artistic and historical achievements examined by the humanities - must be understood as products of pre-existing, more highly organized structures and systems. This tracing-back process, of course, arrives in an obviously finite number of steps logically, necessarily and finally at the God of the Bible - the great and living I AM THAT I AM (Exodus 3:14). It is hoped that the simulation game and other considerations expressed in this article might make a useful contribution in making this basic principle more obvious and apparent to those who struggle thoughtfully with the creation/evolution question.
Bennett, W.R., Jr., "How Artificial is lntelligence?", American Scientist, Vol. 65, Nov-Dec., 1977, pp. 694-702.
Einhorn, H.J. a Hogarth, R.M.," Confidence in Judgement: Persistence of the Illusion of Validity," Psychological Review, 1978, Vol. 85, No. 5, pp. 395-416.
Shweder, Richard A., "Likeness and Likelihood in Everyday Thought Magical Thinking in Judgments about Personality," Current Anthropology, Vol.18, No.4, Dec.1977, pp. 637-657.
Wald, George, "The Origin of Life," The Physics and Chemistry of Life, by the Editors of Scientific American, New York: Simon and Schuster, 1955, pp. 3-26.