Infinite Monkeys Typing the Human Genome

Infinite monkeys aren’t needed to type out Shakespeare, nor the human genome. But both still seem impossible.

So just how did Shakespeare write Shakespeare? And just how did life build humanity?

Monkeys and other primates with a typewriter.

Infinite monkeys typing would churn out Shakespeare, and the human genome. But mostly they would churn out problems.

This post is part of a sequence of essays that will form the framework for my next book, Darwin, Dada, Dalí, Duke, & Devadevàya. I am pre-publishing my ideas in an effort to elicit comments and other feedback; please comment below. These essays will also be published on various academic and popular social media websites.

Infinite Monkeys, Infinite Shakespeare

It is a common bit of urban science that, if infinite monkeys were placed in front of infinite typewriters, one of them would bang out the complete works of Shakespeare.

It’s wrong, of course. One of them would not type out Shakespeare.

An infinite number of them would.

And not just Shakespeare. They would type out everything that has ever been written, and everything that ever will be written… and each of those an infinite number of times.  They would type my biography, in exquisite detail, an infinite number of times, and the biographies of you, and of everyone else. They would also type out our biographies with perfect predictions of what would have happened if we had made each tiny choice in our lives differently. And again, that’s for everyone who ever lived.

And even for everyone who never lived — all an infinite number of times. So infinities are not just large, they’re, well, infinitely large. Everything can happen.

Heck, everything will happen.

Insoluble Problems

All of this points up the absurdity of trying to wrap our heads around infinity. But the preceding brings up a second important insight about random chance and large numbers:  once our infinite monkeys have typed out the things that I just described, looking through all of it to find our biographies would require more time and energy — infinitely more time and energy? — than just getting on with our lives. There are problems that are just too large to solve.

Very small problems can also resist solution. Remember, physicists still can’t resolve a 3-body gravitational situation, and mathematicians have no general solution for the Traveling Salesman Problem.

To our purposes here on considering the role of biology in the larger scope of human progress, one of the very large problems science can’t solve is predicting the future. That’s because the future is infinite, as well.

Science & Prediction

Predicting the future is the whole point of science, however.  Modern science begins with the war machines of the Renaissance: What trajectory will drop a cannonball in precisely the right place? It proved to be an important question. A century or two later, Newton would describe an ever-lengthening cannonball trajectory to explain celestial orbits.

In ‘pure’ scientific research we sometimes lose site of the importance of prediction.  But an activity isn’t science until it generates a testable theory, which means a theory that predicts what will happen.  Which means that science is always an attempt to predict the future.

Or rather, science and experiment attempt to tell the future when many things are controlled for. If we don’t eliminate the many confounding aspects outside of the experiment, if we can’t neutralize the messiness of reality, there is no strong predictability.  The system becomes too large to resolve, and accurate prediction becomes impossible.

This is true even for some of the most complex of our undertakings, such as sending a person to the moon.  Launching a rocket, as complex as the rocket is, is still a relatively straight-forward physics & engineering problem.

Unless there’s wind. If there’s much wind, the flight trajectory becomes iffy, and NASA postpones the mission.  One of the reasons we launch rockets from Cape Canaveral is the mild, i.e., predictable weather.

So outside of our blinkered experiments, predicting the future with certainty isn’t possible. Which means that for many of the big problems of life, for systems where there are many independent factors and actors, there is not much predictability.

So how should we go about making intelligent choices?

Hard Science vs Soft Science

This is why biology, as a hybrid between ‘hard’ and ‘soft’ science, is so important. Hard science says that A plus B always yields C.  Soft science says that A plus B often yields C, but it may also give us D, E, Ω, 我,  or even something we’ve never seen before.  So while hard science gives us accurate formulas and tight predictability, soft science can only offer us general patterns with fuzzy outcomes. For complex systems, that’s the best we get; the general models and trends of soft science become our only option in the real world, where hard science and strong predictability fail.

So for the very large problems of life, the only sensible way forward is to look at the understood possibilities, try not to worry too much about other possibilities, then pick some reasonable path and and continue on our journey.

That, by the way, was a plot-spoiler.

Finite Shakespeare

Let’s return to our problem of our copying quadrumanids.1)One of the old names for primates was Quadrumana, or ‘four-handed’.  As noted, even problems much smaller than infinity can pose insurmountable obstacles to human understanding.

For instance, if we only want a single copy of Shakespeare, we don’t need an infinite number of primates. I downloaded the complete works of Shakespeare from and pasted it into LibreOffice WriteWrite says the document contains 958,340 words and 5,382,946 letters and spaces. If we round the latter number up to 5.4M characters, and accept a character set of 37 letters, numbers, and a space, then we only need about 37×105,400,00, or 2×108,500,000 primates. Which is a relief, because that is much smaller than infinity.

Cover of the nonfiction book, 'Kings, Conquerors, Psychopaths'.

Biology, psychiatry, and civilization.
Kings, Conquerors, Psychopaths:
From Alexander to Hitler to the Corporation.

Click the image for a larger view, click here for more information.

But then, everything is much smaller than infinity.

Then, if we extend the time frame and let our printing primates try repeatedly, we can shrink that number yet again. But it is not really helpful either way, because to produce enough primates and typewriters, even through the 14 billion years that the universe has existed, there is not be enough matter and energy within said universe. In fact, there wouldn’t be enough matter and energy in a billion trillion quadrillion universes.

So for our discussion, 2×108,500,000 primates might as well be an infinity, because it still represents an impossibility.  Numbers that big are much larger than our brains, our mathematics, or our computers can deal with in any useful way.

Shakespeare vs the Human Genome

And yet, as large as that estimated number is, it is nevertheless exquisitely small compared to number of generators, primate or otherwise, that we would need to randomly generate the human genome.

The DNA in each human cell2)Or almost every cell; human red blood cells and platelets contain no DNA, nor do the dead cells of our skin, hair, and nails. contains the entire human genome, about 3B ‘base pairs’, which we can think of as molecular letters. There are only four such letters, or base pairs, and they serve as identifiers to ‘type out’ the links in a strand of protein. The resulting proteins are either used directly in things like muscle fiber and the support structure of our bodies; or they fold themselves into enzymes, which then direct and enable chemical pathways, so that they build everything else the body needs.

Fortunately, 3B base pairs is more than we really need to build a human. In truth, only about 8% of the human genome appears to be active. Now, the other 92% is not insignificant, as the total DNA in a typical 70kg (155lb) adult amounts to about 100 grams, or around a quarter of a pound. However, if the DNA of the human genome were laid end-to-end, it would reach the sun and back 600 times.

But by reducing our number to 8% of the total DNA, we ‘only’ need 240M base pairs in the blueprint for building a human. Nevertheless, 4240,000,000 (or 10140,000,000) is much larger than the number of primates (2×108,500,000) we would need to randomly type us up even one copy of Shakespeare.

Shrews and Butterflies

All of these numbers represent more than simple diversion, however. They raise a couple of important questions:

Just how did Shakespeare write Shakespeare?

And just how did life create a human being?

Those questions may seem fatuous, but by the end of this book they may not still seem so ridiculous. As brilliant as The Taming of the Shrew might be, it dims in marvelousness and complexity when compared to the everyday, humdrum, garden variety of shrew. Likewise, Puccini’s Madama Butterfly contains some of the most exquisite music ever written, but its brilliance pales when compared to a real butterfly.

Order from Randomness

The point is, neither Shakespeare nor biology produced their respective genius in a completely random fashion, as typing monkeys would have done. Yes, Shakespeare’s effort is intellectual, whereas the rest of nature is a spontaneous event, a remote result of the Big Bang. (Some would argue that Shakespeare and life are a result of the Big Deity. Many people scoff at that, but uncritically accept the Big Bang, even though both of them require a generous dollop of magic and mysticism. But I digress. For this argument, we’re sticking with the Big Bang.)

Nevertheless, Shakespeare and life provide an essential insight going forward. We have some rudimentary ideas about the extraordinary circumstances that produced the shrew and the butterfly. Both of those are much more complicated and less likely than human creativity.  Making a Shakespeare is a lot more complicated than writing Shakespeare.

Exploring Genius

In effect, the genius of natural selection is greater than the genius of humanity. So it would not be surprising that, by studying the much larger problems that evolution solves, we might gain insight into fostering human creativity, progress, and yes, even genius.  I suggest that progress in life can shed light on how we might generate more progress in our lives; even including more great literature and music.

Biological innovation can provide insight into human innovation, and how we might promote and accelerate human progress.  But first, we must accept that the best tools we have for proceeding are the general patterns and inconsistent outcomes of ‘soft’ science.

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Footnotes   [ + ]

1. One of the old names for primates was Quadrumana, or ‘four-handed’.
2. Or almost every cell; human red blood cells and platelets contain no DNA, nor do the dead cells of our skin, hair, and nails.

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