Multi-level complex systems are inherently unpredictable

Nonetheless, in order to predict and manage the behavior of multi-level complex systems, we must be able to reason about how cause-and-effect crosses the levels -- because it almost always does.  However, tracking cause and effect through multiple levels is exceedingly difficult and often impossible.  The details of a hurricane or tornado are fundamentally not explainable by invoking the physics of individual air and water molecules[1].  Nor can a computer be understood by pondering the behavior of electrons, or logic gates.  Similarly, the behavior of even a single cell cannot yet be predicted by understanding its chemistry at a molecular level. We intuitively recognize these limits, and their consequences for predictability, in business, social, economic and ecological spheres as well as biology and computing.

Occasionally, multi-level phenomena become explicit and our inability to manage them has profound consequences.  For example, pharmaceutical drug discovery is a biological area in which we face many levels of complexity between the “cause” and the “effect.”  We seek to find a small-molecule, i.e., drug, that modulates some intracellular chemical pathway in a way that desirably affects the human body (or even the human mind) yet does not affect any other cellular process in a deleterious manner.  The major reason it is so difficult to find drugs and even more difficult to determine that they are safe and effective is that there are so many levels of complexity between cellular chemical reactions and whole-body effects and side-effects.  Similarly, in the computing realm, multi-level problems account for some of the most recalcitrant bugs we face.  Perhaps the most egregious example in computing is the prevalence of buffer-overrun exploits in Windows.  A buffer-overrun takes place, essentially, at the machine language level, i.e., the necessary code for array-bounds checking translates to perhaps a dozen extra machine instructions.  Yet the effects of buffer-overruns can be Internet-wide.  The “SQL Slammer” denial of service worm that slowed or blocked 80% of all Internet traffic for a few hours January 25^th, 2003, was due to a buffer-overrun in Microsoft SQL Server software.   And today, the third largest viral botnet in the world, known as Bobax, "...bores open a back door and downloads files onto the infected machine, and lowers its security settings.  It spreads via a buffer overflow vulnerability in Windows, and inserts the spam code into the IE browser so that each time the browser runs, the virus is activated." (see here)  So much of the spam that bedevils the entire Internet is due to a few incompetently-written machine instructions in Windows that allow a buffer overflow.

The “three-level rule”

There are cognitive, and even physical, limits to our ability to trace cause-and-effect through multiple levels. We can focus on the elements of one particular level and contemplate the “part/whole” relationships in two directions.  For example, we can think about how the elements, say molecules or machine instructions, are made up of atoms or orchestrated gates and how the properties of those atoms or gates affect the properties of the molecules or instructions.  With a switch of cognitive repertoire, we can also contemplate how the molecules interact with other molecules to form crystals or various chemical reactions or how machine instructions cooperate to carry out a function or subroutine.  A skilled practitioner – a chemist or programmer – may be able to think about interactions in both directions at once.  That is, a skilled practitioner may be able to reason simultaneously about three levels of abstraction.  But it is quite difficult and seldom even useful to do so.  Reasoning about four levels of abstraction at one time is, arguably, beyond the ability of the human mind.

Multiple levels place constraints on the freedom to evolve