Creationism: another casualty of Innumeracy

December 20, 2006 | By | 11 Replies More

Some of us who sincerely treasure the scientific fact and scientific theory of evolution have brought on some of our own problems with our choice of nomenclature.  For instance, sometimes “random mutations” gets uncoupled from natural selection, leading some to believe that it is the randomness of the process that is the be-all and end-all of evolution. Consider also Francis Crick’s description of the associations of amino acids with their three base codons as a “frozen accident.”

Creationists, ignoring these (legitimate) scientific and scientific/poetic usages, have jumped all over the terms such as “random” and “accident” to characterize scientific evolutionary theory in the following warped way: “All life forms just suddenly spring into existence as accidents.”  Though I am aware that sophisticated creationists would embellish this attack, this characterization is certainly the straw man put forth by most of the people out there who tremble at the thought that human beings are (gad!) animals.

It recently occurred to me that, perhaps, creationists’ willingness to assume that evolutionists are claiming that complex life forms “just happen” might be another symptom of “innumeracy.”  It might be that they don’t understand how incredibly rare it is that biological “accidents” survive and reproduce.  In his bestseller, Innumeracy: Mathematical Illiteracy and Its Consequences (1988), John Paulos introduced the term “innumeracy” to refer to “an inability to deal comfortably with the fundamental notions of number and chance.”  Paulos bemoaned that innumeracy “plagues far too many otherwise knowledgeable citizens.”

How is Innumeracy related to Creationism?  It seems to me that creationists believe that evolutionary theory holds that after a relatively few accidents, complex life forms spring into existence.  This just couldn’t be, creationists argue.  That characterization doesn’t work for me either.  That is why I have termed it a straw man argument.

Perhaps skeptical creationists (they are selectively skeptical) would even refer to an illustration used by Daniel Dennett in his 1995 work, Darwin’s Dangerous Idea. Dennett stated that “the DNA in your body, unsnarled and linked would stretched to the sun and back several-10 or 100-times.”  A work of such immense complexity just couldn’t spring into existence by any simple accident, right?

But what if creationists better understood the enormous number of mutations that amounted to nothing compared to those that amounted to something?  What if they understood that we’re not talking about mere accidents.  We’re talking about unimaginably unlikely accidents that are equally rare and precious.  This idea reminded me of another illustration used by Daniel Dennett, also presented in Darwin’s Dangerous Idea.

Borrowing from a short story by Jorge Luis Borges, Dennett (on page 108) asks us to imagine a huge library full of all possible 500-page long books, each page with 2000 characters.  Each space on each page is either blank or has a character, each character being one of 100 standard upper and lowercase English/European characters.  Dennett does the finite math for us, calculating that such a library would contain 1001,000,000 books.  In comparison, there are only 10040 particles in the observable universe.  Therefore, Dennett’s “Library of Babel “is not remotely a physically possible object.”  He asked us to keep in mind that this is not a library of all possible books, since his library will not contain Greek, Russian, Chinese, Japanese or Arabic, characters, to name a few. Dennett uses this Library of Babel illustration as “an anchoring vision for helping to answer very difficult questions about the scope of biological possibility.” 

Consider, now, the “library of Mendel” which is composed of descriptions of genomes is “just a proper part of the Library of Babel.”  Each of the 500-page permutations of the four letters (the nucleotides that composed the letters of the DNA alphabet) are already in the Library of Babel.  Dennett warns that genomes are much longer than ordinary books, however.  Dennett writes that the information of the human genome would take up approximately 3000 of the 500-page volumes of Dennett’s library.

How big is Dennett’s Library of Babel?  Dennett warns that all of our metaphors for bigness (e.g., a drop in the ocean) fall comically short.  Not even an actual astronomical quantity (such as the number of elementary particles in the universe) “is even visible against the backdrop of these huge but finite numbers.” 

Somewhere in this vast library you can find a perfect copy of Moby Dick (and lots of imperfect copies—most of those so imperfect as to be unreadable).  As Dennett plainly points out, though, most of books in this Library would consist of complete “typographical gibberish.  “No rules of spelling or grammar, to say nothing of sense, prohibit the inclusion of a volume.”  When you compare the universe of meaningful books to the size of Dennett’s library you can see that almost everything out there is gibberish.  Almost everything in Dennett’s library is a non-useful accident.  The useful accidents are almost impossible to find.

Similarly, most possible DNA sequences, the vast majority actually, “are surely gibberish, recipes for nothing living at all.  That is what Dawkins means, of course, when he says that there are “many more ways of being dead (or not alive) than ways of being alive.”

Therefore, it is really (really) unlikely that nature will put together new biological accidents that live and reproduce.  I suspect that creationists assume that evolutionists claim that biological accidents resulting in new life forms are about as likely as automobile accidents; that they happen regularly.  This makes no sense to them.  If I understood evolution in this way, it wouldn’t make any sense to me either.  Dennett’s Library of Babel helps to dispel this statistical misconception.  

Not all accidents are the same.  Some are extremely unlikely.  So unlikely that you should write them off as “simply not going to happen.”  Unless you have 4.5 billion years to work with and quadrillions of little accident generators (microorganisms and, eventually, organisms) working overtime.  But guess what?  We do have 4.5 billion years and a planet full of accidents waiting to happen. 

Then again, I suppose that creationists, if they understood the numbers better, would argue that it proves that the creation of new life forms is so utterly improbable that “God” must’ve done it.  This is but another version of the design argument.  Innumeracy is part of this common misunderstanding too.  This problem is also caused, I suspect, by the fact that most creationists don’t recognize the incremental non-totally random nature of the very rare successful mutation “accidents” that do occur.  You don’t start from ground zero and then shoot up a sheer cliff into a fully formed complex life form. A good place for exploring that incremental changes drive evolution is Richard Dawkins’ Climbing Mount Improbable. 


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Category: American Culture, Evolution, Religion, Science, Statistics

About the Author ()

Erich Vieth is an attorney focusing on consumer law litigation and appellate practice. He is also a working musician and a writer, having founded Dangerous Intersection in 2006. Erich lives in the Shaw Neighborhood of St. Louis, Missouri, where he lives half-time with his two extraordinary daughters.

Comments (11)

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  1. grumpypilgrim says:

    First, let's distinguish between creation (not creationism) and evolution: creation refers to whatever caused (reproductive) life to come into existence on our planet; evolution refers to what happens to that life from one generation to the next.

    With this distinction in mind, let's focus on creation. Did life arise on our planet because it was created by a supernatural being, or did it arise without such intervention? Creationists argue that life is exceedingly unlikely to have arisen without supernatural intervention; therefore, they claim supernatural intervention must have been involved.

    This argument is rooted in the belief that life is exceedingly unlikely to have arisen without supernatural intervention. This is not necessarily a bad argument: even evolutionists acknowledge that life has apparently only been created once in the 4-billion-year history of our planet.

    However, the argument misses some key points. First, we don't know the minimum criteria for creating reproductive life. For all we know, reproductive life might be very easy to create — indeed, it might be sprouting up all over our universe — and our planet might just be a relatively poor environment for life to arise in. For all we know, our planet might not be unique in having life; it might be unique in having life that took such a long time to appear. For all we know, life might appear on other planets in a matter of thousands or millions of years and, thus, not be as unlikely as the creationists claim. Maybe life is very likely to occur "by accident" (without supernatural intervention) and only on our planet *appears* to be unlikely.

    Second, we also don't know how frequently life is created on our planet. Maybe life arises relatively often on our planet and we just don't realize it, because the new life forms are quickly destroyed by the life forms that are already here. This isn't far-fetched: existing life forms, having lived here for 4 billion years, would presumably be good at killing off invaders, especially some new life form that has never had to fight for its survival. Maybe life has appeared on earth only once in 4 billion years simply because subsequent creations were quickly killed by the "natives." For all we know, a new life form might have been created just this afternoon, without supernatural intervention, in my laundry hamper, but maybe it won't survive my next laundry day. Maybe this is why the creation of life appears to be a rare event on our planet.

    Third, with many billions of galaxies in our universe, and many billions of stars in each galaxy, and many billions of years of elapsed time, there are many opportunities for life to arise "by accident." Maybe our planet was simply one of the lucky ones where life arose. It is the same with, for example, state lotteries: just because only one person in a hundred million wins, it doesn't mean supernatural intervention caused that person, against all odds, to win. He was simply lucky. It's like when someone survives an airplane crash: regardless of the odds against their survival, it doesn't demonstrate supernatural intervention, it simply demonstrates that very small odds of survival, when combined with a relatively large number of airplane crashes, will occasionally produce a survivor.

    Issues like these need to be kept in mind when the "improbability" of life arising on our planet is used to support the creationist argument for supernatural intervention. We know so little about the actual odds, and about the other factors that impact the odds (e.g., the size of the universe of possible trials), that such arguments have little merit.

  2. Marc Holt says:

    Please go to and post this topic for discussion. I think it will generate a lot of interest there.


    Marc Holt

  3. Dan Klarmann says:

    Let's remember the Young Earth hypothesis that underlies most of the Creationist arguments I've seen. Given that there were only 6 days for all evolutionary change, it is pretty unlikely.

    If we choose to believe in the measurements of geology, tectonics, microbiology, astronomy, radiology, and all the other disciplines that clock the Earth as several thousand-million years old, chances do improve.

  4. Erich Vieth says:

    Thanks, Marc. I took your advice and posted this on Richard Dawkins' site. We'll see if how many people notice and react to the post. After all, there is a LOT going on over there.

  5. Erich Vieth says:

    Paulos himself wrote on probability and Creationists. It's an article that overlaps a bit with this post. See:

  6. grumpypilgrim says:

    Going back to Dennett's "Library of Babel," and its perfect, and many imperfect, copies of "Moby Dick," there is another point we could make: the sequence of symbols (letters, spaces, punctuation marks, etc.) that we English-speakers define as making the "perfect" copy only has that status because of the particular set of syntax rules that we use today in the English language. It is "perfect" because it follows the syntax rules for modern English, enabling us to translate the symbols into meaningful thoughts. Apply a different set of syntax rules (e.g., the syntax rules for some other language or even for "Old English") and some other version of the book would become the perfect copy and our copy would become another of the many imperfect ones.

    Now, apply this same thought process to evolution. We look at our planet, apply the syntax rules for life as we know it today, and, behold, we find "perfect" strings of DNA that correspond to today's life forms. However, what we don't know is how many other strings of DNA might be "perfect" if we were to merely apply different syntax rules for life — syntax rules that might exist on other planets or that might have existed on our own planet in the past (including in places we have not yet looked, or in places that no longer exist because of geologic changes). By "syntax rules for life," I mean things such as the climate, the atmospheric composition, the availability of food, the existence of predators, etc. Clearly, the fact that our planet, millions of years ago, supported many life forms that it does not support today indicates that the "syntax rules for life" on our planet have changed over time, so this idea has validity.

    Why do I mention it? Because when creationists talk about the "improbability" of life as we see it today on our planet, they are applying a very narrow set of syntax rules (i.e., the ones that work for the species we see today), yet we know for a fact that these rules are too narrow to account for the full history of life on our planet. This is part of the reason why we must call their argument a straw man.

    Why is it important for us to do so? Because at the moment when "life" first began on our planet — i.e., the moment when some molecule could perform metabolism, reproduction and adaptation — our planet's climate and atmosphere were different (perhaps more conducive to the creation of life), there was no competition for "food," and there were no predators around to destroy it, so its odds of survival would probably have been a lot higher than they might be today. In other words, perhaps just about any "syntax rule" would have enabled that first life form to be a "perfect copy" of something, simply because many syntax rules would have been possible. Going back to the "Library of Babel," consider a book that has only one letter in it: for example, the letter "I." Such a book would be relatively easy to generate "at random" from even a large collection of letters and it would be meaningful in many languages, because it would satisfy many different "syntax rules." Likewise, perhaps the appearance of life on our planet was both relatively easy to generate "at random" from even a large collection of molecules and also had available to it a relatively wide range of viable "syntax rules for life" (i.e., more than exist today). In other words, perhaps life on our planet was not as improbable as the creationists would want us to believe. Give a million chimps a million typewriters, and a million years to write a book, and likely one of them would eventually type the letter that means something in some language.

  7. Erich Vieth says:

    Here's a video of John Paulos discussing the role of probability in religious belief systems.

  8. Erich Vieth says:

    The power and elegance of evolution is lost on those who are not comfortable with numbers, as suggested in Richard Dawkins' article titled "The Illusion of Design," found in the November 2005 issue of Natural History Magazine:

    "The achievement of nonrandom natural selection is to tame chance. By smearing out the luck, breaking down the improbability into a large number of small steps–each one somewhat improbable but not ridiculously so–natural selection ratchets up the improbability. As the generations unfold, ratcheting take the cumulative improbability up to levels that–in the absence of the ratcheting –would exceed all sensible credence. Many people don't understand such nonrandom cumulative ratcheting. They think natural selection is a theory of chance, so no wonder they don't believe it!"

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