Ontology of player & evolutionary game in reductive vs effective theory

In my views of game theory, I largely follow Ariel Rubinstein: game theory is a set of fables. A collection of heuristic models that helps us structure how we make sense of and communicate about the world. Evolutionary game theory was born of classic game theory theory through a series of analogies. These analogies are either generalizations or restrictions of the theory depending on if you’re thinking about the stories or the mathematics. Given this heuristic genealogy of the field — and my enjoyment of heuristic models — I usually do not worry too much about what exactly certain ontic terms like strategy, player, or game really mean or refer to. I am usually happy to leave these terms ambiguous so that they can motivate different readers to have different interpretations and subsequently push for different models of different experiments. I think it is essential for heuristic theories to foster this diverse creativity. Anything goes.

However, not everyone agrees with Ariel Rubinstein and me; some people think that EGT isn’t “just” heuristics. In fact, more recently, I have also shifted some of my uses of EGT from heuristics to abductions. When this happens, it is no longer acceptable for researchers to be willy-nilly with fundamental objects of the theory: strategies, players, and games.

The biggest culprit is the player. In particular, a lot of confusion stems from saying that “cells are players”. In this post, I’d like to explore two of the possible positions on what constitutes players and evolutionary games.

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Poor reasons for preprints & post-publication peer-review

Last week, I revived the blog with some reflections on open science. In particular, I went into the case for pre-prints and the problem with the academic publishing system. This week, I want to continue this thread by examining three common arguments for preprints: speed, feedback, and public access. I think that these arguments are often motivated in the wrong way. In their standard presentation, they are bad arguments for a good idea. By pointing out these perceived shortcoming, I hope that we can develop more convincing arguments for preprints. Or maybe methods of publication that are even better than the current approach to preprints.

These thoughts are not completely formed, and I am eager to refine them in follow up posts. As it stand, this is more of a hastily written rant.

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Preprints and a problem with academic publishing

This is the 250th post on the Theory, Evolutionary, and Games Group Blog. And although my posting pace has slowed in recent months, I see this as a milestone along the continuing road of open science. And I want to take this post as an opportunity to make some comments on open science.

To get this far, I’ve relied on a lot of help and encouragement. Both directly from all the wonderful guest posts and comments, and indirectly from general recognition. Most recently, this has taken the form of the Canadian blogging and science outreach network Science Borealis recognized us as one of the top 12 science blogs in Canada.

Given this connection, it is natural to also view me as an ally of other movements associated with open science; like, (1) preprints and (2) post-publication peer-review (PPPR). To some extent, I do support both of these activities. First, I regularly post my papers to ArXiv & BioRxiv. Just in the two preceeding months, I’ve put out a paper on the complexity of evolutionary equilibria and joint work on how fibroblasts and alectinib switch the games that cancers play. Another will follow later this month based on our project during the 2016 IMO Workshop. And I’ve been doing this for a while: the first draft of my evolutionary equilibria paper, for example, is older than BioRxiv — which only launched in November 2013. More than 20 years after physicists, mathematicians, and computer scientists started using ArXiv.

Second, some might think of my blog posts as PPPRs. For example. occasionally I try to write detailed comments on preprints and published papers. For example, my post on fusion and sex in proto-cells commenting on a preprint by Sam Sinai, Jason Olejarz and their colleagues. Finally, I am impressed and made happy by the now iconic graphic on the growth of preprints in biology.

But that doesn’t mean I find these ideas to be beyond criticism, and — more importantly — it doesn’t mean that there aren’t poor reasons for supporting preprints and PPPR.

Recently, I’ve seen a number of articles and tweets written on this topic both for and against (or neutral toward) pre-prints and for PPPR. Even Nature is telling us to embrace preprints. In the coming series of posts, I want to share some of my reflections on the case for preprints, and also argue that there isn’t anything all that revolutionary or transformative in them. If we want progress then we should instead think in terms of working papers. And as for post-publications peer review — instead, we should promote a culture of commentaries, glosses, and literature review/synthesis.

Currently, we do not publish papers to share ideas. We have ideas just to publish papers. And we need to change this aspect academic culture.

In this post, I will sketch some of the problems with academic publishing. Problems that I think any model of sharing results will have to address.

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Antoni Gaudi and learning algorithms from Nature

Happy holidays.

A few days ago, I was exploring Barcelona. This means that I saw a lot of architecture by Antoni Gaudi. His works have a very distinct style; their fluid lines, bright colours, myriad materials, and interface of design and function make for very naturesque buildings. They are unique and stand in sharp contrast to the other — often Gothic revival and Catalan Modernisme — architecture around them. The contrast is conscious; when starting out, Gaudi learned the patterns of the neo-Gothic architecture then in vogue and later commented on it:

Gothic art is imperfect, only half resolved; it is a style created by the compasses, a formulaic industrial repetition. Its stability depends on constant propping up by the buttresses: it is a defective body held up on crutches. … The proof that Gothic works are of deficient plasticity is that they produce their greatest emotional effect when they are mutilated, covered in ivy and lit by the moon.

His buildings, however, do not need to be overgrown by ivy, for Gaudi already incorporates nature in their design. I felt this connection most viscerally when touring the attic of Casa Mila. The building was commissioned as an apartment for local bourgeois to live comfortably on the ground floor off the rents they collected from the upper floors. And although some of the building is still inhabited by businesses and private residence, large parts of it have been converted into a museum. The most famous part among tourists is probably the uneven organic roof with its intricate smoke stacks, ventilation shafts, and archways for framing other prominent parts of Barcelona.

This uneven roof is supported by an attic that houses an exhibit on Gaudi’s method. Here, I could see Gaudi’s inspiration. On display was a snake’s skeleton and around me were the uneven arches of the attic — the similarity was palpable (see below). The questions for me were: was Gaudi inspired by nature or did he learn from it? Is there even much of a difference between ‘inspired’ and ‘learned’? And can this inform thought on the correspondence between nature and algorithms more generally?

naturalarches

I spend a lot of time writing about how we can use algorithmic thinking to understand aspects of biology. It is much less common for me to write about how we can use biology or nature to understand and inspire algorithms. In fact, I feel surprisingly strong skepticism towards the whole field of natural algorithms, even when I do write about it. I suspect that this stems from my belief that we cannot learn algorithms from nature. A belief that was shaken, but not overturned, when I saw the snake’s skeleton in Gaudi’s attic. In this post, I will try to substantiate the statement that we cannot learn algorithms from nature. My hope is that someone, or maybe just the act of writing, will convince me otherwise. I’ll sketch my own position on algorithms & nature, and strip the opposing we-learn-algorithms-from-nature position of some of its authority by pulling on a historic thread that traces this belief from Plato through Galileo to now. I’ll close with a discussion of some practical consequences of this metaphysical disagreement and try to make sense of Gaudi’s work from my perspective.

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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.

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A year in books: Neanderthals to the National Cancer Act to now

A tradition I started a couple of years ago is to read at least one non-fiction book per month and then to share my thoughts on the reading at the start of the following year. Last year, my dozen books were mostly on philosophy, psychology, and political economy. My brief comments on them ended up running a long 3.2 thousand words. This time the list had expanded to around 19 books. So I will divide the summaries into thematic sets. For the first theme, I will start with a subject that is new for my idle reading: cancer.

As a new researcher in mathematical oncology — and even though I am located in a cancer hospital — my experience with cancer has been mostly confined to the remote distance of replicator dynamics. So above all else these three books — Nelson’s (2013) Anarchy in the Organism, Mukherjee’s (2010) The Emperor of All Maladies, and Leaf’s (2014) The Truth in Small Doses — have provided me with insights into the personal experiences of the patient and doctor.

I hope that based on these reviews and the ones to follow, you can suggest more books for me to read in 2016. Better yet, maybe my comments will help you choose your next book. Much of what I read in 2015 came from suggestions made by my friends and readers, as well as articles, blogs, and reviews I’ve stumbled across.[1] In fact, each of these cancer books was picked for me by someone else.

If you’ve been to a restaurant with me then you know that I hate choosing between close-to-equivalent options. To avoid such discomfort, I outsourced the choosing of my February book to G+ and Nelson’s Anarchy in the Organism beat out Problems of the Self by a narrow margin to claim a spot on the reading list. As I was finishing up Nelson’s book — which I will review last in this post — David Basanta dropped off The Emperor of All Maladies on my desk. So I continued my reading on cancer. Finally, Leaf’s book came towards the end of the year based on a recommendation from Jacob Scott. It helped reinvigorate me after a summer away from the Moffitt Cancer Center.
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Cataloging a year of blogging

Happy Old New Year.

January 2016 is the the start of the 6th calendar year and the 41st month with updates to TheEGG. The reason for the large discrepancy between these two numbers is occasional months without activity. The past year was exceptional in this regard with the longest single silence on the blog between April 4th and October 26th. This means that the year saw only 29 new entries, 2 indexes cataloging 2014, a report on the EGT reading group, and an update on readership. This post is meant to organize the last year of activity for future reference, and to try to uncover common themes.

If you like lists and TL;DRs then this is for you.
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Abusing numbers and the importance of type checking

What would you say if I told you that I could count to infinity on my hands? Infinity is large, and I have a typical number of fingers. Surely, I must be joking. Well, let me guide you through my process. Since you can’t see me right now, you will have to imagine my hands. When I hold out the thumb on my left hand, that’s one, and when I hold up the thumb and the index finger, that’s two. Actually, we should be more rigorous, since you are imagining my fingers, it actually isn’t one and two, but i and 2i. This is why they call them imaginary numbers.

Let’s continue the process of extending my (imaginary) fingers from the leftmost digits towards the right. When I hold out my whole left hand and the pinky, ring, and middle fingers on my right hand, I have reached 8i.

But this doesn’t look like what I promised. For the final step, we need to remember the geometric interpretation of complex numbers. Multiplying by i is the same thing as rotating counter-clockwise by 90 degrees in the plane. So, let’s rotate our number by 90 degrees and arrive at \infty.

I just counted to infinity on my hands.

Of course, I can’t stop at a joke. I need to overanalyze it. There is something for scientists to learn from the error that makes this joke. The disregard for the type of objects and jumping between two different — and usually incompatible — ways of interpreting the same symbol is something that scientists, both modelers and experimentalists, have to worry about it.

Rigorous proof

If you want an actually funny joke of this type then I recommend the image of a ‘rigorous proof’ above that was tweeted by Moshe Vardi. My writen version was inspired by a variant on this theme mentioned on Reddit by jagr2808.

I will focus this post on the use of types from my experience with stoichiometry in physics. Units in physics allow us to perform sanity checks after long derivations, imagine idealized experiments, and can even suggest refinements of theory. These are all features that evolutionary game theory, and mathematical biology more broadly, could benefit from. And something to keep in mind as clinicians, biologists, and modelers join forces this week during the 5th annual IMO Workshop at the Moffitt Cancer Center.

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Pairing tools and problems: a lesson from the methods of mathematics and the Entscheidungsproblem

Three weeks ago it was my lot to present at the weekly integrated mathematical oncology department meeting. Given the informal setting, I decided to grab one gimmick and run with it. I titled my talk: ‘2’. It was an overview of two recent projects that I’ve been working on: double public goods for acid mediated tumour invasion, and edge
effects in game theoretic dynamics of solid tumours
. For the former, I considered two approximations: the limit as the number n of interaction partners is large and the limit as n = 1 — so there are two interacting parties. But the numerology didn’t stop there, my real goal was to highlight a duality between tools or techniques and the problems we apply them to or domains we use them in. As is popular at the IMO, the talk was live-tweeted with many unflattering photos and this great paraphrase (or was it a quote?) by David Basanta from my presentation’s opening:

Since I was rather sleep deprived from preparing my slides, I am not sure what I said exactly but I meant to say something like the following:

I don’t subscribe to the perspective that we should pick the best tool for the job. Instead, I try to pick the best tuple of job and tool given my personal tastes, competences, and intuitions. In doing so, I aim to push the tool slightly beyond its prior borders — usually with an incremental technical improvement — while also exploring a variant perspective — but hopefully still grounded in the local language — on some domain of interest. The job and tool march hand in hand.

In this post, I want to unpack this principle and follow it a little deeper into the philosophy of science. In the process, I will touch on the differences between endogenous and exogenous questions. I will draw some examples from my own work, by will rely primarily on methodological inspiration from pure math and the early days of theoretical computer science.

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Five motivations for theoretical computer science

There are some situations, perhaps lucky ones, where it is felt that an activity needs no external motivation or justification.  For the rest, it can be helpful to think of what the task at hand can be useful for. This of course doesn’t answer the larger question of what is worth doing, since it just distributes the burden somewhere else, but establishing these connections seems like a natural part of an answer to the larger question.

Along those lines, the following are five intellectual areas for whose study theoretical computer science concepts and their development can be useful – therefore, a curiosity about these areas can provide some motivation for learning about those cstheory concepts or developing them. They are arranged from the likely more obvious to most people to the less so: technology, mathematics, science, society, and philosophy. This post could also serve as an homage to delayed gratification (perhaps with some procrastination mixed in), having been finally written up more than three years after first discussing it with Artem.

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