Mathematics and Statistics

Applied Mathematics, Geometry and Topology, Analysis, Mathematical Modeling, Statistical Modeling, Game Theory, Operations, Biostatistics, Epidemiology, GIS, Image Processing

Game landscapes: from fitness scalars to fitness functions

Theory, Evolution, and Games Group bloggers Biology and Life Sciences, Mathematics and Statistics, Technology and Engineering
My biology writing focuses heavily on fitness landscapes and evolutionary games. On the surface, these might seem fundamentally different from each other, with their only common feature being that they are both about evolution. But there are many ways that we can interconnect these two approaches. The most popular connection is to view these models as two different extremes in terms of time-scale. When we are looking at evolution on short time-scales, we are primarily…

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Learning Without Excitement

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
It’s not fun to do. Right now, there’s nothing stopping you from teaching yourself advanced mathematics, a new language, design, the details of theatre, or any other subject. The resources available to you are vast and often, free. So why don’t we all spend our time learning? Simple: there’s no point to it. No, I’m not saying that learning how to code is pointless. Rather, I’m saying that, without any need to code, it’s difficult…

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Heuristics Lead to Rigour

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
As you learn more ideas in mathematics, it’s easy to start feeling like certain ideas are “below” you. This often comes in the form of saying that ideas are “trivial”, as if they shouldn’t take up any of your time. This can be exacerbated further in mathematics by the idea of rigour. Once we learn that not all proofs are equal, it can be tempting to say, “Okay, I get this proof, but that’s not…

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Colour, psychophysics, and the scientific vs. manifest image of reality

Theory, Evolution, and Games Group bloggers Biology and Life Sciences, Mathematics and Statistics, Technology and Engineering
Recently on TheEGG, I’ve been writing a lot about the differences between effective (or phenomenological) and reductive theories. Usually, I’ve confined this writing to evolutionary biology; especially the tension between effective and reductive theories in the biology of microscopic systems. For why this matters to evolutionary game theory, see Kaznatcheev (2017, 2018). But I don’t think that microscopic systems are the funnest place to see this interplay. The funnest place to see this is in…

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Knowledge From Repetition

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
When I’m sitting in class and listening to the professor, I get frustrated when they go over a concept once and then continue on as if everything is clear. I think to myself, “Do they really expect us to understand a concept from just one example?” And yet, I realize that I do the same thing when I’m working with a student. This is a bit disconcerting, and it reminds me that teaching is a…

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I Could Be Wrong

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
As a physics student, I’m taught over and over again that science is about checking to see where we have made incorrect assumptions. The goal of science is to correct our assumptions about the world, and find better descriptions for what is going on. Of course, this is a distilled version of the goal of science (and I imagine some would disagree), but my point is that science aims to perform a consistency check on…

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Constant-sum games as a way from non-cell autonomous processes to constant tumour growth rate

Theory, Evolution, and Games Group bloggers Biology and Life Sciences, Mathematics and Statistics, Technology and Engineering
A lot of thinking in cancer biology seems to be focused on cell-autonomous processes. This is the (overly) reductive view that key properties of cells, such as fitness, are intrinsic to the cells themselves and not a function of their interaction with other cells in the tumour. As far as starting points go, this is reasonable. But in many cases, we can start to go beyond this cell-autonomous starting point and consider non-cell-autonomous processes. This…

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Where Does It Belong In The Web?

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
If you look at a typical mathematics class, you will find that they follow a similar rhythm. First, students are presented with a definition. A few examples of how that definition applies might be given, and then the rest of the class is spent proving results based on this definition. It’s a familiar recipe, and it works well for transmitting information. If you asked students to give a presentation on the topic, I would predict…

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Being Good At Mathematics

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
“How did you get so good?” This is a question I’m asked from time to time with respect to mathematics and physics. People see the kinds of grades I get, and they want to know what my secret is. I presume they think I have a method, or at least some explanation as to why I get great grades at school. When I hear this question, I often have to hold myself back from ranting…

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