Climbing Mount Rumsfeld

In humankind's pursuit of knowledge, we calculate the unknown unknowns

Illustration of climbers scaling a mountain.

Somewhere in my house, quietly turning to coal under a pile of paper, is a planetary calculator — astronomy statistics printed on two sliding pieces of cardboard — a free gift with the second issue of Starlord comic in May 1978.

Shifting the display to Pluto confidently declares that world to be moonless — as well established a fact as nearly 50 years of observations with the world’s best telescopes could make it. Since then, the Hubble Space Telescope and a flyby from the New Horizons probe have produced terabytes of data on Pluto and its five moons — their size, compositions, orbits, shapes, appearances, etc. — a torrent of brand-new information that nobody in May of 1978 had any reason to expect even existed. In Donald Rumsfeld’s immortal words, Pluto’s moons were an unknown unknown.

It’s those unknown unknowns that trip us up. We are in the position of a mountain climber who can only look down. There’s a clear view of the flags planted by previous generations of climbers, so we can see how far we’ve come, but we have no idea how high the mountain of unknown unknowns is. Have we tramped just the foothills of Mount Rumsfeld, or are we scaling the peak of knowledge?

We cannot see the future, but we can make estimates based on past performance. This is about as precise as guessing a stock’s value next year using a Wall Street Journal from last year. But the fact that we cannot get even a remotely accurate answer should not stop us from having a go. So join me in some wildly inaccurate back-of-the-envelope calculations based on unsupported assumptions and total guesswork as we try to estimate just how high Mount Rumsfeld goes.

Actually figuring out just how much the total of human knowledge increases is difficult. It depends a lot on what and how you measure — all that’s written? Spoken? Peer reviewed? Cited? Do you count from ancient Greece or the Industrial Revolution? Consider also the obsolescence of knowledge — things we no longer need to know. There are probably tricks to building a galleon known to 17th century shipwrights that are gone forever. And the correct use of a pen in rewinding cassette tapes will be lost with my generation.

Fortunately we don’t have to figure it out, as a quick internet search reveals estimates for annual increases in scientific knowledge ranging from 3 percent to 9 percent. Let’s pick an arbitrary 5 percent and start from an equally arbitrary 1663 when the Royal Society of London was granted its charter and see where that gets us. Feel free to divide or multiply the results below by… oh, pick a number.

Two people climbing a mountain, each with a dialog bubble overhead. The cliber in front asks 'How far,' the second climber replies, 'that's an unknown unkown.

Compound increases are tricky. They do not amount to much in the short term but build up considerably over time. Continue that 5 percent increase, and every century the sum of human knowledge expands roughly 130-fold. By 1763 the learned men of the Royal Society could look back on the ignorance of their 1663 peers with pride in their vastly greater learning. So too the folk of 1863 could laugh at the misplaced hubris of their 1763 ancestors... and so on. At a modest 5 percent increase in knowledge every year, scientific understanding from 1663 to today has been multiplied by 30 million. Hooke or Wren or Boyle or any of those Royal Society founders would likely admit to quite a bit of ignorance and list all the mysteries of their age, but they would probably never believe that human knowledge would increase 30 million-fold in 450 years.

And they’d be right. That’s because of another factor my Starlord planetary calculator embodies — the change in “fact” from zero to five for the number of Pluto’s moons. Sometimes our “facts” are simply wrong and much of each century’s hard-won knowledge will turn out to be worthless. This is what complex systems scientist and writer Samuel Arbesman calls the half-life of facts (and what New Scientist charmingly termed truth decay) — the time it takes for half the knowledge in a particular field to be overturned. In medicine for instance, “facts” seem to have a 45-year half-life; however, we’re looking for a figure to apply to all knowledge. For convenience sake, let’s say knowledge in general has a 50-year half-life. We still have a 5 percent annual increase in facts, but every 50 years we have to throw half of them out because they’re just plain wrong. That cuts into the 30-million-fold increase quite a bit. By the time we’ve allowed for truth decay, human knowledge has multiplied by roughly only 7 million times since 1663. Still pretty respectable, even if a lot, maybe most, of it is the sort of minutiae of interest only to specialists. Glyptology or limacology, anyone?

Now that we’ve established how much we’ve learned over the last few centuries (to no degree of rigor whatsoever), we can use the same figures to look ahead. If past rates of scientific advance are any guide (they’re not), we can expect the next 50 years to see knowledge increasing five- or sixfold. The next 50 years after that should see another 30-fold increase over current levels. We can’t say what that knowledge will be, of course. We might want all our advances to be in medicine, physics, and macroeconomics, for example, but for all we know those fields will stagnate while vexillology, sphagnology, and batology (the study of flags, moss, and brambles, respectively) leap ahead.

At the current rate of advancing knowledge, we will know everything about anything everywhere in another 1,700 years.

How long can these sorts of increases go on? Right now, we have some pretty big unknown unknowns. The dark energy and dark matter that make up 95 percent of the universe (if not themselves illusion) are good indictors that we have quite some way to go. And don’t forget the remaining 5 percent is everything we thought existed until just a couple of decades ago. All the trillions of suns with their trillions of planets are bound to have trillions of unknown unknowns of their own. It might be that in a few hundred years we work out the laws of physics completely and are able to make predictions about those trillions of worlds, but knowing all the rules doesn’t necessarily tell us how every game plays out. A century of experience with the laws of electromagnetism didn’t allow anyone to predict the electrostatic-caused spokes in Saturn’s rings before Voyager 1 and Voyager 2 flew past in 1980 and ’81.

Continue our 5 percent calculation for another thousand years, and we wind up with something like 140 trillion times the knowledge we currently possess. That’s enough to know every planet in a thousand galaxies as well as we currently know our Earth. Another 500 years should do for the remainder of the universe, and then we can start on the dark matter. How much there is to know about dark matter is itself an unknown unknown, but let’s say another 100 years should cover it. Then there’s dark energy. We’ll give that another century.

And there we are. At the current rate of advancing knowledge, we will know everything about anything everywhere in another 1,700 years. In practice we’ll probably take a bit longer by a few orders of magnitude, due to pesky banalities such as the speed of light and not having enough people to learn everything. However, I can see the end of the article approaching so I’ll leave that calculation as an exercise for the reader.

So how high does Mount Rumsfeld go? I think my original metaphor of a climber on a mountain was wrong. It turns out Mount Rumsfeld is more a continent-spanning range than a single mountain. And us? We’re ants on those Himalayas. The ceaseless striving of generations of scientists has propelled us to the very top… of the first blade of grass, in the lowest meadow of the smallest foothill. If we are brave and lucky, all yet lies before us. Allons-y!


Paul McKinley headshotPaul is a graphic designer, amateur photographer, part-time writer, and lifelong science geek who as a kid sat way too close to the TV to watch the moon landings. He writes the “Occasional Book”and “Crazy Idea” columns for the British Mensa magazine and can be contacted through his intermittent blog, The Occasional Book.
Irish Mensa | Joined 1984