Toward a Computational Historicism. Part 1: Discourse and Conceptual Topology

Poets are the unacknowledged legislators of the world.
– Percy Bysshe Shelley

… it is precisely because we are talking about ordinary language that we need to adopt a notation as different from ordinary language as possible, to keep us from getting lost in confusion between the object of description and the means of description.
¬–Sydney Lamb

Worlds within worlds – that’s how Tim Perper, my friend and colleague, described biology. At the smallest scale we have individual molecules, with DNA being of prime importance. At the largest scale we have the earth as a whole, with all living beings interacting in a single ecosystem over billions of years. In between we have cells, tissues, and organs of various sizes, autonomous organisms, populations of organisms on various scales from the invisible to continent-spanning, and interactions among populations of organisms on various scales.

Literature too is like that, from single figures and tropes, even single words (think of Joyce’s portmanteaus) through complete works of various sizes, from haiku to oral epics, from short stories through multi-volume novels, onto whole bodies of literature circulating locally, regionally, across continents and between them, from weeks and years to centuries and millennia. Somehow we as humanists and literary critics must comprehend it all. Breathtaking, no?

In this essay I sketch a potential computational historicism operating at multiple scales, both in time and textual extent. In the first part I consider network models on three scale: 1) topic models at the macroscale, 2) Moretti’s plot networks at the mesoscale, and 3) cognitive networks, taken from computational linguistics, at the microscale. I give examples of each and conclude by sketching relationships among them. I open the second part by presenting an account of abstraction given by David Hays in the early 1970s; in this model abstract concepts are defined over stories. I then move on to Hauser and Le-Khac on 19th Century novels, Stephen Greenblatt on self and person, and consider several texts, Amleth, Hamlet, The Winter’s Tale, Wuthering Heights, and Heart of Darkness.

Graphs and Networks

To the mathematician the image below depicts a topological object called a graph. Civilians tend to call such objects networks. The nodes or vertices, as they are called, are connected by arcs or edges.


Such graphs can be used to represent many different kinds of phenomena, a road map is an obvious example, a kinship tree is another, sentence structure is a third example. The point is that such graphs are signs of phenomena, notations. They are not the phenomena itself. Continue reading “Toward a Computational Historicism. Part 1: Discourse and Conceptual Topology”

Numerical vs. analytical modelling

Since its resurgence in the 90s Multi-agent models have been a close companion of evolutionary linguistics (which for me subsumes both the study of the evolution of Language with a capital L as well as language evolution, i.e. evolutionary approaches to language change). I’d probably go as far as saying that the early models, oozing with exciting emergent phenomena, actually helped in sparking this increased interest in the first place! But since multi-agent modelling is more of a ‘tool’ rather than a self-contained discipline, there don’t seem to be any guides on what makes a model ‘good’ or ‘bad’. Even more importantly, models are hardly ever reviewed or discussed on their own merits, but only in the context of specific papers and the specific claims that they are supposed to support.

This lack of discussion about models per se can make it difficult for non-specialist readers to evaluate whether a certain type of model is actually suitable to address the questions at hand, and whether the interpretation of the model’s results actually warrants the conclusions of the paper. At its worst this can render the modelling literature inaccessible to the non-modeller, which is clearly not the point. So I thought I’d share my 2 cents on the topic by scrutinising a few modelling papers and highlight some caveats, and hopefully also to serve as a guide to the aspiring modeller!

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Mathematical Modelling 101 – The Price Equation

So in this post I’m going to assume you know absolutely nothing about anything. If you know something about something this probably isn’t what you’re looking for. If you’re looking for something which will go into depth on how the price equation is derived this probably isn’t what you’re looking for either. If you simply want to know what the price equation does and how to use it at face value then welcome! You’ve found the right place.

The price equation is used to calculate how the average value of any variant can change within a population from generation to generation.

Here I will cover everything you need to know to understand the equation and slot in the right values:

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Mathematical Modelling 101 – Evolutionary Game Theory

Game Theory was fist applied to evolution by John Maynard-Smith and George Price in 1973. It differs from traditional game theory is that it focusses on dynamics of strategy change more than the properties of strategy equilibria, although equilibria still exist within EGT but are know as Evolutionary Stable Strategies as opposed to Nash Equilibria.


Imagine a situation in which 2 members of a species come into conflict over a resource. Within this conflict each animal has the optional to ‘fight’, ‘display’ or ‘run away’. There are 2 strategies within this species, either the Dove strategy or the Hawk strategy. In the Dave strategy, upon meeting someone also adopting the Dove strategy both “Doves” display and share the resource or upon meeting a “Hawk” the Dove runs away. Adopting the Hawk strategy entails always fighting. So upon meeting a Dove the Hawk will fight and the Dove will run away and the Hawk will take all of the resource, and upon meeting another Hawk, both will fight and one will win out. On average across many interactions with other Hawks, the payoff gained ends up being (v/2)-c where v=value of resource and c=cost.

Dove Hawk
Dove v/2, v/2 v, 0
Hawk 0, v (v-c)/2, (v-c)/2

The question to ask of this game is, given values v and c, which strategy will evolutionarily win out?

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Mathematical Modelling 101 – Intro to Game Theory

This post is going to just be a very brief introduction to what Game Theory is, how it works and some basic terminology. In later posts I will get more advanced and cover how it can be applied to Cultural Evolution.

What is Game Theory?

Game theory is a branch of applied mathematics most commonly used in Economics. However, it can be very successfully applied to other social sciences as well as Evolutionary Biology. It gives both descriptive answers (what people do) and prescriptive answers (what people should do) in a given game.

Why is this relevant?

Game Theory is a very good tool in predicting outcomes, not only in the very simple games covered in this post, but also in predicting the outcomes of evolutionary strategies and of predicting outcomes for signalling games which can inform us on human and animal communicative strategies.  Running iterated games over populations can introduce interesting qualifications to these very simple ideas as well and explain some things which may, at first, appear maladaptive, as such is a very useful tool in bypassing our intuitions. It is of these things that the next few posts will explore.

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Selection on Fertility and Viability

So in my previous post on mathematical modelling I looked at viability selection and how it can be expressed using relatively simple mathematics. What I didn’t mention was fertility. My reasoning largely being because the post was already getting unwieldy large for a blog, and, from now on, I’m going to limit the length on these math-based posts. I personally find I get more out of small, bite-sized chunks of information that are easily digestible, than overloading myself by trying understand too many concepts all at once. With that said, I’ll now look at what happens when the two zygote types, V(A) and V(B), differ in their fertility.

A good place to start is by defining the average number of zygotes produced by each type as z(A) and z(B). We can then plug these into a modified version of the recursion equation I used in the earlier post:

So now we can consider both fertility and viability selection. Furthermore, this can be combined to give us W(A) = V(A)z(A) and W(B) = V(B)z(B):

Remember, , is simply the the average the fitness in the population, which can be used in the following difference equation:

That’s it for now. The next post will look at the long-term consequences of these processes.

Reference: McElreath & Boyd (2007). Mathematical Models of Social Evolution: A guide for the perplexed. University of Chicago Press. Amazon link.

Mathematical Modelling 101: Introduction & Viability Selection

I think the best place to start would be to state the following: Do not fear math. I spent far too long dodging equations and, when that wasn’t possible, freezing in a state of absolute confusion when faced with something like:

By the end of this post, you’ll hopefully be able to understand the above is not just a bunch of jibberish. Now before we get into the nitty gritty of the subject, I think a clarification of my assumptions is in order:

  1. That you’ll have a basic understanding of evolutionary biology. If not, then may I suggest Evolution as a very good, and highly comprehensive, introductory text. Failing that, you can always pop over to the wikipedia page.
  2. Although these posts will refer to evolutionary biology, my background is in linguistics and socio-cultural evolution — and as such, I will tend to default to the position of explaining these latter areas.
  3. It might sound insulting, but you’ll also need a basic understanding of math. You’ll be surprised by the number of people who, despite being very bright, lack even an elementary grasp of the fundamentals. A good place to start is with Kahn Academy’s wonderful online resource:
  4. Having said that, I’m not really expecting anything beyond algebra level math, and I’ll do my best to try and clarify any confusions in the comments section. Also, I’m hardly a math guru, so I welcome anyone with a solid background in math to provide any hints, tips or suggestions, and, in the event I’m plain wrong, point out any mistakes.

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