Map:Territory::Uncertainty::Randomness – but that doesn’t matter, value of information does.

by Davidmanheim 4y22nd Jan 20162 min read21 comments

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In risk modeling, there is a well-known distinction between aleatory and epistemic uncertainty, which is sometimes referred to, or thought of, as irreducible versus reducible uncertainty. Epistemic uncertainty exists in our map; as Eliezer put it, “The Bayesian says, ‘Uncertainty exists in the map, not in the territory.’” Aleatory uncertainty, however, exists in the territory. (Well, at least according to our map that uses quantum mechanics, according to Bells Theorem – like, say, the time at which a radioactive atom decays.) This is what people call quantum uncertainty, indeterminism, true randomness, or recently (and somewhat confusingly to myself) ontological randomness – referring to the fact that our ontology allows randomness, not that the ontology itself is in any way random. It may be better, in Lesswrong terms, to think of uncertainty versus randomness – while being aware that the wider world refers to both as uncertainty. But does the distinction matter?

To clarify a key point, many facts are treated as random, such as dice rolls, are actually mostly uncertain – in that with enough physics modeling and inputs, we could predict them. On the other hand, in chaotic systems, there is the possibility that the “true” quantum randomness can propagate upwards into macro-level uncertainty. For example, a sphere of highly refined and shaped uranium that is *exactly* at the critical mass will set off a nuclear chain reaction, or not, based on the quantum physics of whether the neutrons from one of the first set of decays sets off a chain reaction – after enough of them decay, it will be reduced beyond the critical mass, and become increasingly unlikely to set off a nuclear chain reaction. Of course, the question of whether the nuclear sphere is above or below the critical mass (given its geometry, etc.) can be a difficult to measure uncertainty, but it’s not aleatory – though some part of the question of whether it kills the guy trying to measure whether it’s just above or just below the critical mass will be random – so maybe it’s not worth finding out. And that brings me to the key point.

In a large class of risk problems, there are factors treated as aleatory – but they may be epistemic, just at a level where finding the “true” factors and outcomes is prohibitively expensive. Potentially, the timing of an earthquake that would happen at some point in the future could be determined exactly via a simulation of the relevant data. Why is it considered aleatory by most risk analysts? Well, doing it might require a destructive, currently technologically impossible deconstruction of the entire earth – making the earthquake irrelevant. We would start with measurement of the position, density, and stress of each relatively macroscopic structure, and the perform a very large physics simulation of the earth as it had existed beforehand. (We have lots of silicon from deconstructing the earth, so I’ll just assume we can now build a big enough computer to simulate this.) Of course, this is not worthwhile – but doing so would potentially show that the actual aleatory uncertainty involved is negligible. Or it could show that we need to model the macroscopically chaotic system to such a high fidelity that microscopic, fundamentally indeterminate factors actually matter – and it was truly aleatory uncertainty. (So we have epistemic uncertainty about whether it’s aleatory; if our map was of high enough fidelity, and was computable, we would know.)

It turns out that most of the time, for the types of problems being discussed, this distinction is irrelevant. If we know that the value of information to determine whether something is aleatory or epistemic is negative, we can treat the uncertainty as randomness. (And usually, we can figure this out via a quick order of magnitude calculation; Value of Perfect information is estimated to be worth $100 to figure out which side the dice lands on in this game, and building and testing / validating any model for predicting it would take me at least 10 hours, my time is worth at least $25/hour, it’s negative.) But sometimes, slightly improved models, and slightly better data, are feasible – and then worth checking whether there is some epistemic uncertainty that we can pay to reduce. In fact, for earthquakes, we’re doing that – we have monitoring systems that can give several minutes of warning, and geological models that can predict to some degree of accuracy the relative likelihood of different sized quakes.

So, in conclusion; most uncertainty is lack of resolution in our map, which we can call epistemic uncertainty. This is true even if lots of people call it “truly random” or irreducibly uncertain – or if they are fancy, aleatory uncertainty. Some of what we assume is uncertainty is really randomness. But lots of the epistemic uncertainty can be safely treated as aleatory randomness, and value of information is what actually makes a difference. And knowing the terminology used elsewhere can be helpful.

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