A few weeks ago I had a fascinating conversation with Ruby about models of the research process and how to improve it. This post outlines one particular model which I took away from that conversation: open problems as the primary factor which create a paradigm.
There’s a cluster of things like research agendas, open problems, project proposals, and/or challenges; we’ll refer to that whole cluster as “open problems”. The unifying theme here is the function(s) these things serve:
- Define a problem
- Provide context: why is the problem interesting/valuable? Why is it hard? What would a solution look like? What background work exists?
- Provide starting points/footholds/surface area - places for people to start working on the problem
- Create a status reward for solving the problem - mainly by making the importance and difficulty public knowledge
Let’s walk through each of those pieces.
First, an open problem defines a problem. That sounds obvious, but it’s more difficult than it sounds: defining a problem means setting it up in such a way that anyone who understands the problem-explanation can recognize a solution. For pre-paradigmatic fields, this is hard. What would a solution to e.g. an embedded agency problem look like? If someone proposed a “solution”, and we asked 50 different researchers whether this was actually a solution to the problem, would their answers all agree? Probably not, though the embedded agency sequence brought us a lot closer to that point.
Second, an open problem provides context. Why is the problem interesting/valuable? Why is it hard? This goes hand-in-hand with defining the problem: we define the problem in a particular way because we expect a solution to provide some value. If a solution to a differently-defined problem would not clearly provide the same value, then that’s an argument in support of our particular problem definition.
Third, an open problem provides starting points/footholds/surface area for people to tackle the problem. The problem definition and value-prop inevitably ties to background work and existing techniques, and explains why those techniques are not already sufficient. That provides a jumping-off point for newcomers.
Finally, establishment of an open problem creates a status reward for solving the problem. We define what a solution looks like, so others can easily recognize success. We explain why a solution would be valuable, and why it’s difficult. Once all those things become public knowledge, we have the recipe for a status reward associated with solving the problem.
Key thing to note: it’s not the problem difficulty and importance themselves which create a status reward. Rather, it’s the fact that difficulty and importance are common knowledge. In order to create the status reward, the importance and difficulty of the problem have to be broadcast to many people in an understandable way.
Put all these pieces together, and it looks like a recipe for creating a paradigm within a pre-paradigmatic field. We get common problems, standards for solving those problems, motivation for the problems, starting points for newcomers, and status points to incentivize participation, all in one fell swoop.
Potentially testable prediction: it seems like someone could create a field this way, de novo. The main requirements would be good writing skills and memetic reach - and having a good set of open problems, which we would hope is the hard part. The Sequences or some of MIRI’s work might even be examples. This seems like a testable, standalone model of the process of formation of new research fields.
To wrap it up, one note on the challenges which such a model suggests for research infrastructure. There’s potential for misalignment of incentives: the problems with highest return on investment (in terms of value of solving the problem) will not necessarily be the problems with highest status reward. Problems which are easier to understand will be easier to communicate to more people and therefore more easily achieve a high status reward; problems which are high-value but harder to explain will be harder to attach a large status reward to. This could potentially be addressed at the meta-level: create a framework for identifying important problems and recognizing their solutions, in such a way that people can easily understand the framework without necessarily understanding the individual problems/solutions.
Credit for this model is at least as much Ruby's as it is mine, if not more. He has additional interesting background info and different weights of emphasis, so take a look at his comments below.