The Clarke Horizon, Part 2

Okay, here’s an attempt at bringing the conversation about the “Clarke Horizon” down to Earth a bit. I’m going to attempt to recap everything I’ve said previously in less technical language and annotate a few concepts along the way. The discussion so far has led to some revisions of the original concept; I’m not going to stop to explain what’s changed — just take this post as the canonical “state of the idea” at this time.

Science fiction author Arthur C. Clarke famously proposed in 1973 that “any sufficiently advanced technology is indistinguishable from magic.” Let’s use this concept to define the “Clarke Horizon” — the point in the future where civilization operates in a manner that appears inexplicable — “magical” to an observer in the present. Most often this “magic” is technological (computers, for example, would be well beyond the Clarke Horizon of Roman civilization), but it may sometimes be social (for example, that modern cities can function as social entities at all would almost certainly be beyond the Clarke Horizon of our Neolithic forebears).

There’s a couple of important things to note here before we move on. The first is that the Clarke Horizon isn’t some fixed point in time — it’s measured relative to the “present,” whenever that happens to be. As previously noted, our own civilization lives beyond the Clarke Horizon of most of our ancestors.

Secondly, the Clarke Horizon doesn’t exist at a fixed “distance” from the present. During periods of rapid change the Clarke Horizon is much closer at hand than during periods of relative stagnation. Furthermore, the Clarke Horizon is more of a function of application than of general knowledge: Ubiquitous computing and augmented reality are rapidly moving us beyond the Clarke Horizon of those who lived in the late 19th Century, even though the principles that govern electricity and computation were well known by that time.

The concept of the Clarke Horizon is closely related to two other concepts — that of the “Singularity” and the “Seldon Crisis”.

The Singularity is a concept originally coined by mathematician Stanislaw Ulam in 1958 but popularized by science fiction author Vernor Vinge in the early 1990s. The Singularity represents the culmination of ever-accelerating technological progress, the point at which the rate of technological change becomes essentially infinite and all predictive efforts consequently break down. Since, at least at the present time, the distance between now and the current Clarke Horizon is primarily a function of technological change, we can redefine the Singularity in terms of this concept. To whit, the Singularity occurs when the time between the present and the Clarke Horizon shrinks to zero — in effect, civilization becomes magical right now for those of us actually living in it.

Now, for the Singularity to really be The Singularity, the distance between the present and the Clarke Horizon has to shrink to zero and then stay there. But suppose it doesn’t. Suppose that civilization only becomes magical for a short time. Things will eventually return to “normal” — but what constitutes “normal” is likely to be vastly different after our brush with the Clarke Horizon than before it. And the longer we remain within the Clarke Horizon, the wackier things are likely to become. Such a case has certain similarities to that of a Seldon Crisis.

The concept of a Seldon Crisis originated in Isaac Asimov’s Foundation trilogy, published during the early 1950s. Originally Asimov conceived of a Seldon crisis as (per Wikipedia) “a social and political situation that, to be successfully surmounted, would eventually leave only one possible, inevitable, course of action.” Over time, however, the popular conception of a Seldon Crisis has come to be that of a great (but predictable) confluence of social and political events that will serve to rapidly and profoundly rearrange the structure of civilization in ways that are difficult to understand to those living before the crisis.

It is this second definition that matches up with the situation where the present enters the Clarke Horizon for a short period of time, but then eventually exits. (This means, incidentally, that we can regard the Singularity as something akin to “the Seldon Crisis that never ends.”) Now, the whole point of the Foundation in Asimov’s novels is to use the fictitious concept of “psychohistory” to navigate the Seldon Crises that occur to minimize the galactic dark ages that are the novels’ setting. But if all bets are off once you’ve entered the Clarke Horizon, this would seem like a profoundly hopeless endeavor.

This is where calculus comes to the rescue. Human civilization doesn’t change that quickly most of the time, so it seems reasonable to assume that the function that describes the distance between the present and the Clarke Horizon is relatively “smooth” — and thus it makes sense to talk about the “velocity,” “acceleration,” etc. of the Clarke Horizon

relative to the present time. These are what mathematicians call derivatives, and they give us information about how the Clarke Horizon is “moving” relative to the present. Moreover, we’ve already noted that the Clarke Horizon is a function of several different variables — not just time, but also technology, social conventions, and probably a host of others.

Civilization becomes “magical” once you enter the Clarke Horizon, which implies a discontinuity — a sudden change in value — for at least some of these variables. Derivatives are meaningless at discontinuities, but so long as not every variable experiences a discontinuity, it is still possible to get a sense of what range of trajectories civilization might be on after traversing a Seldon Crisis. We could therefore imagine something like Asimov’s “Foundation,” whose job it is to identify approaching Seldon Crises and, once civilization has passed through, to quickly reestablish an acceptable trajectory by attempting to deduce the new values of the derivatives of the Clarke Horizon for those variables that suffered discontinuities during the Crisis.

Now, this may sound profoundly creepy to you. And it should. Having some organization whose purpose it is to “guide” civilization is immensely problematic (guide for whom and to what end?), but it’s worth considering one reason why we may want to invest in an institution like it: The Singularity. For the Singularity to really be The Singularity, not only do all of the variables that define the Clarke Horizon have to suffer discontinuities, but they can never actually have anything but discontinuities ever again. While some welcome such a “Rapture of the Nerds,” it seems highly doubtful that anything resembling civilization could survive such an event for very long. And that’s the best case scenario (depending on who you talk to, the existence of the Earth itself may be put in jeopardy by such an event).

We all want to live in the great big beautiful tomorrow, but it’s probably worth it to try getting there without traversing the Singularity. If we can come to understand the behavior of the Clarke Horizon well enough, it may be possible to choose trajectories for civilization that avoid Seldon Crises with lots of discontinuities, thereby minimizing the danger such events pose. A Foundation charged with this task might take as its Prime Directive (see, I can even work “Star Trek” into this!) that it should only seek to avoid the worst Crises, leaving as many trajectories of social and technological change as possible open at any one time. Perhaps it would be best to think of such an institution as something between an early warning system and a disaster preparedness agency whose purview is dislocations in civilization itself, rather than natural disasters.

There’s probably a whole new cross-disciplinary field of study here. Certainly we’re talking about something a lot heavier and with a broader scope than economics, political science, or social psychology currently has. Perhaps we should just call it “psychohistory”.


Nathan Acks
September 13, 2012