Climbing Mount Rumsfeld

Somewhere in my house, quietly turning to coal under a pile of papers, is a ‘planetary calculator’ (astronomy stats on two sliding pieces of cardboard), a free gift with the second issue of Star Lord 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 biggest telescopes could make it. Since then, the Hubble telescope as well as the New Horizons probe fly-by has produced terabytes of data on the size, composition, orbits, shape, appearance etc of Pluto’s five moons. A torrent of brand new information that nobody in that May of 1978 had any reason to expect even existed. In Donald Rumsfeld’s immortal words, Pluto’s moons were an unknown unknown.

How much has yet to be discovered? What unknown unknowns lie before us? Just how high does Mount Rumsfeld go?

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 much farther 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 can’t see the future but we can make estimates based on past performance. This will be about as accurate as guessing next year’s share prices from last year’s Financial Times but the fact that we can’t get even a remotely accurate answer shouldn’t 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 knowledge increases is very difficult. It depends a lot on what and how you measure – publications, citations, on-line, journal only? Do you count from ancient Greece or the Industrial Revolution? There’s also the obsolesce 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 biro 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 increasing scientific knowledge ranging from 3% to 9% per year. Let’s pick an arbitrary 5% 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/multiply the results below by… oh, pick a number.

Compound increases are tricky. They don’t matter at all in the short term but build up quickly in the long term. Continue that 5% 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 quite 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% increase in knowledge every year, scientific understanding from 1663 to today has grown over thirty million times. Hooke or Wren or Boyle or any of those Royal Society founders would probably 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. They’d be right because of another factor that Star Lord ‘Planetary Calculator’ embodies – the change in ‘fact’ from zero to five as the number for moons of Pluto. Sometimes our ‘facts’ are simply wrong and much of each century’s hard won knowledge will turn out to be worthless. This is what mathematician Samuel Arbesman called the ‘half life of facts’ (and which New Scientist charmingly termed ‘truth decay’) – the time it takes half the knowledge in a particular field to be overturned. In medicine for instance, ‘facts’ seem to have a 45 year half life but we need an overall number. For convenience sake let’s say knowledge in general has a 50 year half life. We still have a yearly increase of 5% 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 we’ve only increased human knowledge roughly 7million 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 5 or 6 fold. 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 but for all we know those fields will stagnate while vexillology, sphagnology and batology will leap ahead (the study of flags, moss and brambles respectively).

How long can these sort of increases go on? Right now, we have some pretty big unknown unknowns. The Dark Energy and Dark Matter that make up 95% 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% is everything we thought existed up to a few years 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 we work out the laws of physics completely in a few hundred years and be 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 electromagnetics didn’t allow anyone to predict the spokes they cause in Saturn’s rings before Voyager flew past in 1981.

Continue our 5% calculation 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 Earth. Just to be sure, we’ll add an extra century for the rest of the Universe. 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. For convenience sake let’s 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 like the speed of light and not having enough people to learn it all. 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 the metaphor of a climber on a mountain was wrong. It turns out Mount Rumsfeld is more continent-spanning range than single mountain. And us? We’re an ant on those Himalayas. The ceaseless striving of generations of scientists have 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!

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