Known unknown unknowns

I  listened today to the podcast of science fiction writer Bruce Sterling’s Long Now Foundation talk from 2004 on “The Singularity: Your Future as a Black Hole”.  The talk is available here.  Sterling describes some of the ideas of  mathematician and science fiction writer Vernor Vinge’s conception of the singularity as a scary moment in time where super human intelligence ends the human era and we have no way to predict what will happen.  I won’t address the issue of whether or not such a moment in time will or not happen in the near future or ever.  I’ve posted about it in the past (e.g. see here, here and here).  What I do want to discuss is whether or not there can exist events or phenomena that are so incomprehensible that it will reduce us to a quivering pile of mush.  I think an excellent starting point is former US Secretary of Defense, Donald Rumsfeld’s infamous speech from 2002 regarding the link between Iraq and weapons of mass destruction prior to the Iraq war, where he said:

[T]here are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns – there are things we do not know we don’t know.

While Rumsfeld was mocked by the popular media for this seemingly inane statement, I actually think (geopolitical consequences aside) that it was the deepest thing I ever heard him say. Rumsfeld is a Bayesian! There is a very important distinction between known unknowns and unknown unknowns.  In the first case, we can assign a probability to the event.  In the second we cannot.  Stock prices are known unknowns, while black swans are unknown unknowns.  (Rumsfeld’s statement predates Nassim Taleb’s book.)  My question is not whether we can predict black swans (by definition we cannot) but whether something can ever occur that we wouldn’t even be able to describe it much less understand it.

In Bayesian language, a known unknown would be any event for which a prior probability exists.    Unknown unknowns are events for which there is no prior.  It’s not just that the prior is zero, but also that it is not included in our collection (i.e. sigma algebra) of possibilities. Now, the space of all possible things is uncountably infinite so it seems likely that there will be things that you cannot imagine. However, I claim that by simply acknowledging that there exist things that I cannot possible ever imagine, is sufficient to remove the surprise. We’ve witnessed enough in the post-modern world, to assign a nonzero prior to the possibility that anything can and will happen. That is not to say that we won’t be very upset or disturbed by some event. We may read about some horrific act of cruelty tomorrow that will greatly perturb us but it won’t be inconceivably shocking.  The entire world could vanish tomorrow and be replaced by an oversized immersion blender and while I wouldn’t be very happy about it and would be extremely puzzled by how it happened, I would not say that it was impossible. Perhaps I won’t be able to predict what will happen after the singularity arrives but I won’t be surprised by it.