What is the algorithmic lens?

If you are a regular reader then you are probably familiar with my constant mention of the algorithmic lens. I insist that we must apply it to everything: biology, cognitive science, ecology, economics, evolution, finance, philosophy, probability, and social science. If you’re still reading this then you have incredible powers to resist clicking links. Also, you are probably mathematically inclined and appreciate the art of good definitions. As such, you must be incredibly irked by my lack of attempt at explicitly defining the algorithmic lens. You are not the only one, dear reader, there have been many times where I have been put on the spot and asked to define this ‘algorithmic lens’. My typical response has been the blank stare; not the “oh my, why don’t you already know this?” stare, but the “oh my, I don’t actually know how to define this” stare. Like the artist, continental philosopher, or literary critic, I know how ‘algorithmic lens’ makes me feel and what it means to me, but I just can’t provide a binding definition. Sometimes I even think it is best left underspecified, but I won’t let that thought stop me from attempting a definition.

If you are not a regular reader then — chances are — you are one of the 33 thousand views that have come here from Reddit. If you don’t know what Reddit is then you must watch CGPGrey’s explanation before you can continue:

My interaction with Reddit started out of vanity, the simple ego stroking of driving large amounts of traffic to this blog or other projects (like StackExchange; I originally joined Reddit to help advertise that I am involved in CogSci.SE). The gamification of seeing the visitors counter creep up helped me find the motivation to write posts more often, and the dismal performance of many of my early shares guided me in what to do and not to do. Like many users, however, I quickly discovered that links are just the tip of the reddit iceberg. The greatest part is the community that builds around various subreddits and the discussions in the comments. One of these discussions, is a great starting point for defining the algorithmic lens. The following is the definition by user @quattro from an r/bioninformatics discussion of my recent post on what theoretical computer science can offer biology:

While we would all love better algorithms to calculate estimations for our models and handle larger amounts of data, this post is discussing how can we view biology through the algorithmic lens. That is to say, how can evolution itself accomplish certain computational challenges?

The bread and butter of theoretical computer science is the ability to take an abstract problem and show that it requires some resources [be it time, or memory, or communication] by reducing a known/characterized problem to it.
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THIS is what is meant by “What can theoretical cs offer biology”. Not necessarily “better algorithms”, but “what is required resource-wise for nature to accomplish these things”?

This really highlight what sets computational complexity apart from most other disciplines of thought. Science and engineering can usually tell us what can happen or how things can happen, but it rarely ever gives us negative statements. With the exception of some examples in physics (like conservation of energy and laws of thermodynamics ruling out perpetual motion machines), science almost never says “this can’t happen”, especially in cases where the mechanisms that could potentially achieve the impossible goal are not well characterized. Computational complexity on the other hand, takes a macrodynamic goal (to solve some problem) and a broad macrodynamic resource like time, space, or energy and then tries to characterize what any microdynamic process (algorithm) can achieve with those resources. Since any scientific theory is going to have to be mechanistic (else, we would not view it as an explanation), and algorithms capture all mechanistic procedures this places no restrictions on the conceivable processes. Algorithmic generality is especially useful in settings like biology and ecology where historicity and experimentally inaccessible time-scales limit the detail to which we can know microdynamic processes, or in economics, and social sciences where theorizing a process affects the system being studied, sometimes in an adversarial way. This ability and desire to deal rigorously with questions at such a general level is what sets the algorithmic lens apart from typical science.

The second strength of @quattro’s definition is the implicit demarcation between the algorithmic and computational lens. The computational lens is boring, at its shallowest it is just the use of computing machines to automate tasks in science (sometimes at the cost of understanding), and at its deepest it just continues the historic trend of drawing analogies between our current highest technology and the unknown. Saying that the brain, evolution, or the universe is like a computer is seldom explanatory and often misleading. Realizing that any scientific theory is a language and corresponding model of computation, and thus tools from the analysis of algorithms and computational complexity can be used to turn its heuristic models into abstractions, is much more exciting. The former is the computational view and the latter is the algorithmic lens.

Of course, I can’t claim title over the algorithm lens. The concept has been advocated before me, and I view Christos Papadimitriou’s talk and Julia Kempe’s course as inspirations for my views. I also realize that my current attempt is not inclusive of all the tools and thoughts of theoretical computer science, and I need to extend the definition from just Theory A to including both Theory A and B. How does the algorithmic lens make you feel? Is my definition off? How would you define it?