Opacity
Randomness is not an intrinsic property but a result of incomplete information. What appears random may be deterministic yet opaque to the observer, making the distinction between true randomness and deterministic chaos practically irrelevant.
THE IDEA
Once Again, Incomplete Information
Take a personal computer. You can use a spreadsheet program to generate a random sequence, a succession of points we can call a history. How? The computer program responds to a very complicated equation of a nonlinear nature that produces numbers that seem random. The equation is very simple: if you know it, you can predict the sequence. It is almost impossible, however, for a human being to reverse engineer the equation and predict further sequences. I am talking about a simple one-line computer program (called the “tent map”) generating a handful of data points, not about the billions of simultaneous events that constitute the real history of the world. In other words, even if history were a nonrandom series generated by some “equation of the world,” as long as reverse engineering such an equation does not seem within human possibility, it should be deemed random and not bear the name “deterministic chaos.” Historians should stay away from chaos theory and the difficulties of reverse engineering except to discuss general properties of the world and learn the limits of what they can’t know.
This brings me to a greater problem with the historian’s craft. I will state the fundamental problem of practice as follows: while in theory randomness is an intrinsic property, in practice, randomness is incomplete information, what I called opacity in Chapter 1.
Nonpractitioners of randomness do not understand the subtlety. Often, in conferences when they hear me talk about uncertainty and randomness, philosophers, and sometimes mathematicians, bug me about the least relevant point, namely whether the randomness I address is “true randomness” or “deterministic chaos” that masquerades as randomness. A true random system is in fact random and does not have predictable properties. A chaotic system has entirely predictable properties, but they are hard to know. So my answer to them is dual.
- a) There is no functional difference in practice between the two since we will never get to make the distinction—the difference is mathematical, not practical. If I see a pregnant woman, the sex of her child is a purely random matter to me (a 50 percent chance for either sex)—but not to her doctor, who might have done an ultrasound. In practice, randomness is fundamentally incomplete information.
- b) The mere fact that a person is talking about the difference implies that he has never made a meaningful decision under uncertainty—which is why he does not realize that they are indistinguishable in practice.
Randomness, in the end, is just unknowledge. The world is opaque and appearances fool us.
When to use it
In financial markets, stock price movements are often considered random. Applying opacity, a trader might recognize that the randomness could be due to incomplete information and seek better data or models.
In medicine, a patient's symptoms might seem random to a general practitioner but are predictable to a specialist with more information. This concept encourages thorough diagnostics.
In historical analysis, events that appear random may be the result of deterministic but opaque processes. Historians should avoid attributing randomness and instead acknowledge limits of knowledge.
In scientific experiments, randomness in results may stem from unmeasured variables. Recognizing opacity helps researchers design better controlled studies.
FROM THEORY TO EVERYDAY LIFE
In practice
Tent Map Computer Program
A simple one-line computer program (the tent map) generates a sequence of numbers that appear random but are entirely deterministic. Without knowing the equation, a human cannot predict the next number, so in practice the sequence is treated as random. Opacity can make deterministic systems appear random.
Pregnant Woman and Ultrasound
The sex of an unborn child is random to an observer who does not have an ultrasound (50/50 chance), but known to the doctor who performed the scan. This shows that randomness is simply a lack of information, not an intrinsic property of the event.
A MOMENT TO REFLECT
Put it to work.
Think of a recent event you attributed to randomness. Could it be that you simply lacked information? How would your understanding change if you had access to that information?
Consider a decision you made under uncertainty. How does the concept of opacity affect your confidence in that decision?
Identify a situation where two people disagree on whether an outcome is random. Is the disagreement due to different levels of information? How could you resolve it?
Often confused with
CONTINUE THE CONVERSATION
Source texts
- The Black Swan The Impact of the Highly Improbable With a new section On Robustness and Fragility (Nassim Nicholas Taleb)