Read a history that spans times ancient and modern, as I’ve been doing lately, and you encounter a striking shift in the late Middle Ages. Until that point, documentary information is scarce, and narratives must be pieced together from smatterings of written matter and archaeological evidence. Afterward, historians face a growing surfeit of information, and their challenge becomes deciding what to pay attention to.

The rise of the printing press, which Johannes Gutenberg kicked off around 1440, is the most obvious reason for the shift. Also important is the spread of literacy and literary production (aided by the invention of spectacles) that began a few centuries before Gutenberg built his press.

Nowadays, we produce information by the exabyte-load. As Google’s Eric Schmidt said again and again in 2010:

There was 5 exabytes of information created between the dawn of civilization through 2003, but that much information is now created every 2 days.

The specifics of Schmidt’s pronouncement have been called into question, but he wasn’t wrong that the volume of information being produced has increased dramatically thanks to the Internet and the digitization of everything. I’m starting to worry, though, about the possibility of a new information Dark Age.

This is from a recent speech by Walter Isaacson , the biographer of Steve Jobs, Benjamin Franklin and Albert Einstein, whose next subject is Leonardo da Vinci:

Leonardo left more than 7,000 notebook pages of drawings, thoughts, and ideas. They’re all on paper, which makes them extraordinarily easy to access even after five centuries. Indeed, Leonardo’s notes are far easier to access than our emails, tweets, blog posts and Facebook pages will be five centuries from now. When I was meeting with Steve Jobs and we were trying to get the emails he had sent in the 1990s, they were impossible to retrieve, even by his tech people. When I asked a university librarian recently the best way to preserve some interesting emails I had, she said I should print them out on paper and put them in a box.

I have similar issues with my own published writing. I still possess copies of pretty much everything that’s come out on paper, but some work that appeared only in digital form is gone forever.

“The Web,” historian Jill Lepore wrote in the New Yorker last year, “dwells in a never-ending present.” She continued:

“It is — elementally — ethereal, ephemeral, unstable, and unreliable. Sometimes when you try to visit a Web page what you see is an error message: “Page Not Found.” This is known as “link rot,” and it’s a drag, but it’s better than the alternative. More often, you see an updated Web page; most likely the original has been overwritten.”

Lepore’s article tells the story of several people and organizations working to preserve the products of this ephemeral medium (the justly celebrated Brewster Kahle and his Internet Archive play a starring role). Such work is essential, but is it enough?

One of the strengths of paper as a data-storage technology is that it can preserve information that no one really intends to preserve. To someone with embarrassing photos on Facebook, it can seem as if the Internet does the same thing. But Facebook may be gone in a few decades, whereas paper has proved itself over centuries. Printing has the added benefit of mass redundancy — even if most copies of a book or old newspaper are destroyed, a few may live on in attics or libraries.

Historians will probably find a way to muddle through. So much information is being produced today that even if most of it is lost, they’ll still have a lot to work with — and easy online access to it. Also, however hard emails may prove to retrieve, they’re at least more durable than never-recorded phone calls.

Still, I worry about more apocalyptic scenarios. What if the electrical power goes out and nobody can figure out how to turn it back on? What if a super solar storm or a man-made electromagnetic pulse wipes out the electrical grid and much of our data?

In his classic work of 1790s techno-optimism, “Sketch for a Historical Picture of the Progress of the Human Mind” — an early English translation of which is available in full online via the Internet Archive — the Marquis de Condorcet speculated that if the printing press had been around when Rome fell, Europe never would have slipped into ignorance and disarray. He concluded that, thanks to Gutenberg, such backsliding was no longer a threat:

“How amidst that variety of productions, amidst that multitude of existing copies of the same book, amidst impressions continually renewed, will it be possible to shut so closely all the doors of truth, as to leave no opening, no crack or crevice by which it may enter?”

I think what this means is that if we want to ensure that our civilization lives on, we should probably be printing everything out and putting it in boxes.

Justin Fox is a Bloomberg View columnist who writes about business.