## Computational kindness and the revelation principle

In EWD1300, Edsger W. Dijkstra wrote:

even if you have only 60 readers, it pays to spend an hour if by doing so you can save your average reader a minute.

He wrote this as the justification for the mathematical notations that he introduced and as an ode to the art of definition. But any writer should heed this aphorism.[1] Recently, I finished reading Algorithms to Live By by Brian Christian and Tom Griffiths.[2] In the conclusion of their book, they gave a unifying name to the sentiment that Dijkstra expresses above: computational kindness.

As computer scientists, we recognise that computation is costly. Processing time is a limited resource. Whenever we interact with others, we are sharing in a joint computational process, and we need to be mindful of when we are not carrying our part of the processing burden. Or worse yet, when we are needlessly increasing that burden and imposing it on our interlocutor. If you are computationally kind then you will be respectful of the cognitive problems that you force others to solve.

I think this is a great observation by Christian and Griffiths. In this post, I want to share with you some examples of how certain systems — at the level of the individual, small group, and society — are computationally kind. And how some are cruel. I will draw on examples from their book, and some of my own. They will include, language, bus stops, and the revelation principle in algorithmic game theory.

## Hamiltonian systems and closed orbits in replicator dynamics of cancer

Last month, I classified the possible dynamic regimes of our model of acidity and vasculature as linear goods in cancer. In one of those dynamic regimes, there is an internal fixed point and I claimed closed orbits around that point. However, I did not justify or illustrate this claim. In this post, I will sketch how to prove that those orbits are indeed closed, and show some examples. In the process, we’ll see how to transform our replicator dynamics into a Hamiltonian system and use standard tricks from classical mechanics to our advantage. As before, my tricks will draw heavily from Hauert et al. (2002) analysis of the optional public good game. Studying this classic paper closely is useful for us because of an analogy that Robert Vander Velde found between the linear version of our double goods model for the Warburg effect and the optional public good game.

The post will mostly be about the mathematics. However, at the end, I will consider an example of how these sort of cyclic dynamics can matter for treatment. In particular, I will consider what happens if we target aerobic glycolysis with a drug like lonidamine but stop the treatment too early.

## Multiple realizability of replicator dynamics

Abstraction is my favorite part of mathematics. I find a certain beauty in seeing structures without their implementations, or structures that are preserved across various implementations. And although it seems possible to reason through analogy without (explicit) abstraction, I would not enjoy being restricted in such a way. In biology and medicine, however, I often find that one can get caught up in the concrete and particular. This makes it harder to remember that certain macro-dynamical properties can be abstracted and made independent of particular micro-dynamical implementations. In this post, I want to focus on a particular pet-peeve of mine: accounts of the replicator equation.

I will start with a brief philosophical detour through multiple realizability, and discuss the popular analogy of temperature. Then I will move on to the phenomenological definition of the replicator equation, and a few realizations. A particular target will be the statement I’ve been hearing too often recently: replicator dynamics are only true for a very large but fixed-size well-mixed population.

## Systemic change, effective altruism and philanthropy

The topics of effective altruism and social (in)justice have weighed heavy on my mind for several years. I’ve even touched on the latter occasionally on TheEGG, but usually in specific domains closer to my expertise, such as in my post on the ethics of big data. Recently, I started reading more thoroughly about effective altruism. I had known about the movement[1] for some time, but had conflicting feelings towards it. My mind is still in disarray on the topic, but I thought I would share an analytic linkdex of some texts that have caught my attention. This is motivated by a hope to get some guidance from you, dear reader. Below are three videos, two articles, two book reviews and one paper alongside my summaries and comments. The methods range from philosophy to comedy and from critical theory to social psychology. I reach no conclusions.