Evolving Darwin: Evolution is Not Random Larry Yaeger Complex Networks and Systems Center, Cognitive Science Program http://informatics.indiana.edu/larryy firstname.lastname@example.org Introduction Discussion & Conclusions Though evolution benefits from random variation (and subsequent selection), the process of evolution is almost The last sentence of Darwin’s Origin of Species: First, the obvious: Five seconds for evolution; many times the age of the universe for the randomly typing entirely unlike a truly random process. Yet through ignorance or deliberate misrepresentation proponents of monkeys. Clearly, evolution is not random. The enormous difference in these times makes it clear just how “There is grandeur in this view of life, with its several powers, having been originally breathed into Intelligent Design and other forms of creationism routinely draw upon misleading metaphors of randomness—a startlingly different evolution is from a random process. tornado assembling a 747, or a blind person solving a Rubik’s cube—to cast aspersions on the validity of a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law Evolution does benefit from randomness. Evolution would get stuck in dead ends were it not for a fresh, Darwinian evolution. of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, ongoing supply of variety from which to select. But the variation and selection process by which evolution Here I will draw upon the common metaphor of monkeys typing randomly on typewriters to produce a work of and are being, evolved.” progresses is very much different from a random assembly of parts. literature—in this case the final sentence of Darwin’s Origin of Species—to highlight the extreme difference Yet one way Intelligent Design (ID) believers and other creationists routinely lie with statistics is to equate the between randomness and evolution. First I will calculate the length of time we would expect one million kinds of random processes represented by our monkeys with the process of evolution. Members of the lay monkeys to require in order to generate Darwin’s text at random. Then I will document the amount of time it public may be genuinely unaware of the distinction between random and evolving processes, but the more actually takes to evolve this text. Finally I will discuss the rather extreme difference between these two scientifically knowledgeable ID proponents are most certainly aware of the difference, yet they continue to processes—more than the lifetime of the universe vs. a few seconds—and thus demonstrate the extreme fallacy Evolutionary Time misrepresent the facts, presumably in order to further their religious agenda. being perpetrated by those who treat them as synonymous. What happens if instead of attempting to randomly assemble Darwin’s sentence we choose to evolve it? If Another, related way that ID proponents at least err, and most likely lie, is to claim that there is no possible way Monkey Time evolution is random, then based on what we just calculated we should expect to fail miserably. If, on the other for a given structure to have evolved gradually, hence it must have been assembled all at once, placing it back in hand, evolution is not random, but instead draws on its previous successes to incrementally improve from one the realm of the typing monkeys. Their term for this is “irreduceable complexity”. Though they make bolder The task we will set our one million monkeys is the accurate reproduction of the final sentence of Darwin’s generation to the next, maybe there's hope for such an approach. claims, all they really should be able to say is that they, specifically, do not know how the gradual evolution Origin of Species by a purely random flailing at the keys of a hypothetical typewriter. To simplify their task To see what evolution is capable of, I implemented a fairly standard Genetic Algorithm (GA) in the C took place. Instead they say that gradual evolution is impossible. This is like saying something is unknowable, (and our math) we will imagine a specially prepared typewriter that has exactly and only the 27 keys needed to programming language. (The source code is available here: http://informatics.indiana.edu/larryy/evotext.c) The simply because it is unknown, yet the gulf between unknowable and unknown is greater even than the gulf produce the desired sentence. artificial world implemented in this GA consists of a modest population of 250 individuals. Each individual is a between the monkeys and the Genetic Algorithm. All modern technology, all biological understanding, all We can start by determining the probability that any one letter typed by a single monkey is the correct letter, string of 324 characters—the length of the desired sentence. The individual strings are initialized randomly astronomical knowledge, including the simple fact that the Earth is not at the center of the universe, was once which is just one out of the 27 possible characters, so: from an alphabet of 68 characters (many more than our monkeys had to contend with, and covering all of the unknown, yet enquiring minds studied the world around us and gradually brought more and more of the nature p(letter) = 1/27 characters I used to evolve Shakespeare’s Hamlet, in a different set of experiments documented here: of our world into the realm of the known. The evolution of any particular biological system or structure is not Then the probability that all 324 characters (counting letters, spaces, and punctuation) will be typed correctly by http://informatics.indiana.edu/larryy/Yaeger2009_EvolvingHamlet.pdf). unknowable, even if it is currently unknown. The ID proselytizers’ “irreduceable complexity” is a fiction and a a single monkey is just the product of all those independent letter probabilities, or: Each generation, the fitness of all members of the population is evaluated by counting up the number of fallacy. p(sentence) = (1/27)324 characters that match the text of our sentence—the number of correct characters in correct positions in the text. It is worth noting one difference between natural selection in the real world and the kind of evolutionary process So with a million (106) monkeys all trying their best, we can calculate the probability that any of them gets it So just like the monkeys, the evolutionary software only “gets it right” if it puts all the right letters in all the used here in the evolution of Darwin’s sentence: In evolving our text, the GA has been given a target, while, of right by multiplying the probability for an individual monkey by the number of monkeys: right places. course, biological evolution has no specific target. Undoubtedly some ID zealots will leap on this fact and cry p(SENTENCE) = (1/27)324 x 106 Using a standard GA technique known as Tournament Selection (with a tournament size of 5) each existing foul. But specifying a target was only required because we wanted a specific outcome. Imagine a designer If we let the monkeys give it an arbitrarily large number of attempts—call it N tries—then the probability that generation gives “birth” to the succeeding generation, with individuals of greater fitness giving birth to more being asked to design… something… without being told what it is we wanted designed. Or imagine our any monkey got it right on any of those N attempts is determined from one more multiplication: offspring. This is true “survival of the fittest”, in a probabilistic fashion. Again using a standard GA technique, monkeys flailing away at their typewriters, but the person tasked with checking to see if they got it right not offspring are the product of the genes of both parents, using 100-point crossover, with auto-annealed mutation knowing what “right” is. These tasks would make our monkey’s universe-dwarfing time to produce Darwin’s p(SENTENCES) = (1/27)324 x 106 x N rates varying from 1 to 100 characters per individual (1/324 to 100/324). sentence seem brief. Similarly, the GA has to know what “right” is in order for it to achieve that specific goal, Now we can’t actually say when a monkey will type the sentence with 100% certainty, but let’s say we’re happy I successfully evolved Origin’s final sentence in approximately five seconds on my MacBook Pro laptop and having a pre-specified text is a perfect match to the random assembly task of the hypothetical monkeys, who to accept a confidence level of 99%; i.e., we will satisfy ourselves with a probability of 0.99 that the monkeys computer. In fact, I evolved it a number of times and can reliably do so on demand. It usually takes between were likewise only deemed to have succeeded when they produced that specific text. will accomplish the task. In that case: about 700 and 1,100 generations, and between four and six seconds. Curiously, having a specific goal is actually a more difficult task, in some ways, than evolution’s open-ended 0.99 = (1/27)324 x 106 x N Below is a sample run of my “evotext” program evolving Darwin’s sentence. The printout includes the first 70 amplification of useful traits. Think of water flowing down a hill. Evolution, like gravity, just gets the water And solving for N: characters of the best sentence from every 50th generation as the text evolves. Notice how it starts off down the hill, no matter how many courses the water takes, along how many faces of the landscape, and no N = 0.99 x 27324 x 10-6 matter how many different pools at different elevations the water ends up in. By contrast, evolving Darwin’s completely random, but rapidly begins to approximate the desired sentence and only has to fine tune a handful To figure out how long it takes to make these N attempts, we need to know how long each attempt takes. If we of characters outside these first 70 characters after the 450th generation. After evolution has completed its task, I sentence is like requiring all the water to flow into a single, specific pond. In this pair of situations—evolving a assume (generously) that the monkeys are as fast as an advanced human typist—120 words/minute—and the run a “diff” utility that compares the input file, “text.txt”, and the output file, “output.txt”, to see if there are any specific outcome vs. promoting anything that works—natural evolution actually has the easier task. average word length is 6 characters (5 is a common estimate of average word length, but we’ll throw in the differences. As the utility says, the files are identical. Another distinction between biological selection and the kind employed here is that in the evolving-text case, adjacent space for free), then we can imagine our monkeys typing at the prodigious rate of 720 [Luggage:evotext2] 09:27:47 $ date ; evotext ; date there actually is a designer—me. I can imagine someone seizing on this fact to say, Hah, you see, there must be characters/minute. If we continue to be kind to our monkeys and let them start over immediately anytime they Sun Dec 13 21:27:54 EST 2009 a designer after all! But, first of all, one should realize, again, that this task was an artificial one, designed to make a mistake, then the average number of characters typed in a given trial will be ½ of the total number of Using tournament selection with a tournament size of 5 accomplish a specific goal, whereas evolution doesn’t have or need a specific goal. Rather, biological evolution characters (since some mistakes will happen on the first letter, some on the last, sadly, and some on every letter Mutation rate = 0.0308642 (10/324) proceeds by a process of random exploration and selectional winnowing, and will favor anything that works— in between), or 162 characters. Thus, on average, each attempt will take 162/720 = 0.225 minutes, or 13.5 textAlphabetSize = 27, alphabetSize = 68, numLetters = 324 nothing is specified a priori. seconds. And the total time to achieve a 99% confidence level that one of the monkeys will have produced the textAlphabet = ,.;Tabcdefghilmnoprstuvwxy desired sentence will be: alphabet = ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz .,;:!?-&()"'| At least as significant, once I set my evolutionary system in motion, I never intervened again. It ran to used = ^ ^^^^^^^^^ ^^^^^ ^^^^^^^^ ^^^^ completion, evolving Darwin’s sentence in fairly short order, with no further input of any kind from me, the T = 0.99 x 27324 x 10-6 x 13.5 seconds All letters in text are present in the alphabet designer. This has some interesting resonances with the way that many reputable scientists and persons of faith In principle we can just punch these numbers into our calculator and out will pop the answer. However, most 0: zMDAl::xY(gv)wcRoizF(gU.pGEGp;|ZACam?OTOK ]GhXXF!HK oflNmqUMeTleW)AMKT (10/324) [m=10.00, u=0] reconcile evolution and creation. If one imagines the universe to have been created by a deity of whatever sort, calculators will overflow trying to determine the value of 27324 and just tell us that it will take infinitely long. 50: TUereLi( -icnEeNr C,Xth:sVviMwFg!:PGCviHwRIV khsIsfjeraB KCfVJs, SZqin (128/324) [m= 9.09, u=250] 100: TMere is opan eUrD'& this vixwN;f!lifef]wRty its sFvera- pafeys, SaXin (191/324) [m= 6.21, u=250] then left to operate in accordance with those divinely specified physical laws for the rest of time, there need be Desiring a bit more precision and finiteness than that, we can turn to the arbitrary-precision arithmetic language, 150: TYere is gran[eur z& this vikw Lf life]jwEth its s&veral poweLs, ha;in (239/324) [m= 2.90, u=250] no conflict between faith and science. Each may have its own domain, and one’s faith needn’t be threatened by bc, available on Macs and other unix-based computers. (See 200: TPere is gran[eur 'n this view Lf lifef wCth its several poweLs, haXin (265/324) [m= 1.98, u=250] science, nor should it compel anyone to rail against humankind’s increasing understanding of the universe. http://www.opengroup.org/onlinepubs/9699919799/utilities/bc.html.) There we determine that 27324 is: 250: TPere is granceur 'n this view Lf life, with its several poweLs, ha[in (280/324) [m= 1.00, u=250] Indeed, scientists of faith frequently feel themselves to be studying the universe in order to better know the 57790917239978102632256205681208657797695143289975626010601468196134056967662170791963 300: There is granyeur kn this view Lf life, with its several poweLs, hamin (294/324) [m= 1.10, u=250] 350: There is granyeur kn this view Lf life, with its several powers, haXin (301/324) [m= 1.00, u=249] mind of their god. I do not happen to share this faith, but have no conflict with those who do. Their faith is 725865409773298249768068523762078717664412328148991110219893626746295971458702064848002 their own, and I needn’t approve of it anymore than they need approve of my beliefs. Science and religion at 400: There is grandeur ,n this view pf life, with its several powers, havin (309/324) [m= 1.00, u=248] 01674705652294724096533249518940204877395324639788131832520832027576032013991732297960 450: There is grandeur in this view of life, with its several powers, havin (315/324) [m= 1.00, u=248] least can be orthogonal to and independent from each other. Science doesn’t, nor need it try to, disprove 309733205603223410225339446291939752788083738046123832011731080701072835430334397824287 500: There is grandeur in this view of life, with its several powers, havin (318/324) [m= 1.00, u=250] religious beliefs. Conversely, religious beliefs needn’t and shouldn’t impinge on science, including one of its 936519798143322588859488202477619317521946004614282570982305116569081265722243735082297 550: There is grandeur in this view of life, with its several powers, havin (320/324) [m= 1.00, u=247] most fundamental, clear, empirically demonstrated observations: evolution. 9427333705214063427609809190641 600: There is grandeur in this view of life, with its several powers, havin (321/324) [m= 1.00, u=246] 650: There is grandeur in this view of life, with its several powers, havin (322/324) [m= 1.00, u=239] The stark, nigh infinite difference between our randomly typing monkeys and an evolutionary process for and we may therefore calculate the time it takes our monkeys to randomly type Darwin’s beautiful sentence to 700: There is grandeur in this view of life, with its several powers, havin (322/324) [m= 1.00, u=237] obtaining the text of Darwin’s sentence hopefully makes clear just how very different evolution is from be approximately: Result: (324/324) randomness. And, by implication, how very wrong it is to apply arguments based on random processes to T = 0.99 x 5.779 x 10463 x 10-6 x 13.5 seconds In 714 generations, evolution produced a match that is 100.0% accurate biological evolution. When done from ignorance, it is sad but perhaps excusable; when promulgated by Output saved to output.txt = 7.724 x 10458 seconds someone scientifically learned enough to know better, it is, quite simply, a lie. Sun Dec 13 21:27:58 EST 2009 Since the entire history of the universe is estimated to be 1018 seconds, this is a very long time indeed! Maybe [Luggage:evotext2] 09:27:58 $ diff -s text.txt output.txt the calculator that wanted to call it infinity was close enough. And it would appear to be entirely reasonable to Files text.txt and output.txt are identical state that such an event occurring by random chance is, for all intents and purposes, impossible. Submitted to the New Scientist “Sampling Darwin” competition, December 2009.
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