# Crumbs

1. Adaptive dispersion via stochastic hill climbing
1. Description How to distribute $n$ vowels in an acoustic space so that the average vowel-to-vowel distance is maximized? In a classical paper, Liljencrants and Lindblom proposed numerically minimizing the energy function $$E = \sum_{i=1}^{n-1} \sum_{j=i+1}^{n} \frac{1}{(x_i - x_j)^2 + (y_i - y_j)^2}$$ where the $x_i$ stand for the first and the $y_i$ for the second formants (expressed in mel space, with second formants F3-corrected). In the paper, $E$ was minimized in a semi-guided manner by first distributing the $n$ vowels on a circle in the centre of the vowel space and then moving the vowels towards the periphery (defined by a model of the articulators) as long as $E$ was diminishing. ... read more
adaptive dispersion phonetics optimization c++ r
2. The problem of implementation and its relation to the philosophy of cognitive science
MA Thesis in Cognitive Science (2010, University of Helsinki). Open access Abstract According to certain arguments, computation is observer-relative either in the sense that many physical systems implement many computations (Hilary Putnam), or in the sense that almost all physical systems implement all computations (John Searle). If sound, these arguments have a potentially devastating consequence for the computational theory of mind: if arbitrary physical systems can be seen to implement arbitrary computations, the notion of computation seems to lose all explanatory power as far as brains and minds are concerned. ... read more
philosophy of mind computation
3. Plotting simplexes using R
In evolutionary game theory and related fields, one often needs to visualize the dynamics of three-dimensional systems, e.g. competition between three strategies $x_1$, $x_2$ and $x_3$ for which $x_1 + x_2 + x_3 = 1$. This is most conveniently done on a 2-simplex (ternary plot, de Finetti diagram), and the following code snippet defines a minimal way of visualizing data on a 2-simplex using R base graphics. The function takes a minimum of four arguments: x and y are vectors holding the $x_1$ and $x_2$ values (it is not necessary to input the remaining, third value, as $x_3 = 1 - x_1 - x_2$); label is a vector of length 3 giving labels for the vertices of the simplex. ... read more
visualization evolutionary game theory r
4. Evolutionary game theory
Some thoughts on evolutionary game theory and its applicability in diachronic linguistics, originally prepared for Postgridiots in 2014. PDF Abstract I review some basic concepts from Evolutionary Game Theory (EGT), a general mathematical framework for thinking about the competition and propagation of features or traits in arbitrary populations. While the origins of EGT lie in evolutionary biology, particularly in modelling individual contests in environments with limited resources, the framework has potential applications in fields as diverse as sociology, economics and linguistics, and adoption of the framework need not imply any sort of “biologism”, as I will argue. ... read more
evolutionary game theory
5. Fixing LaTeX math commas
If you use different fonts for text and math in your LaTeX documents (not generally recommended, but necessary if your favourite font does not come with mathematics support), you may have found yourself annoyed by having two differently shaped commas, one in text mode and the other in math mode. Here’s a demonstration with Times as the text font and Computer Modern as the math font: The vertices $(1,0,0)$, $(0,1,0)$, and $(0,0,1)$\dots A simple way of fixing this is to force math mode to use the text font comma. ... read more
latex fonts