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.