GoKawiilIs math big or small?
Summary: When Illustrating a mathematical idea, the first thing you need to decide is the scale. Is this concept something you can hold in your hand, or something to wander around in? I will reflect on the scale of various analogies used by research mathematicians, such as Thurston’s train tracks and pictures of symplectic manifolds. Topologists use the metaphors of “geography” and “botany” to organize problems in their field. I will argue that geography and botany are flexible analogies, which give a natural scale for mathematical illustrations. Presented at: Rigorous Illustrations - Their creation and evaluation for mathematical research, IHP trimester on mathematical illustration 🔗 Link to file
The post below is a slightly extended version of my talk at IHP workshop on rigorous illustration. You can also watch the video.
Is math big or small?
Imagine a torus. This is not rhetorical, I want you to summon the mental image of a torus.
How big is your torus?
Why? Ive always struggled with this question. Every time you illustrate a torus, or indeed any mathematical idea, the first thing to decide is the scale. Scale is more than physical size. In this picture, the word “big” feels large because it dwarfs our friend by the I, whereas “small” feels small because its much smaller than the critter analyzing it. Scale is relative to the viewer.
Is math something to hold in your hand, or something to wander around it? To limit our scope, we’ll look at the scale of mathematical imagery used by researchers. I’m interested in those collective hallucinations which are embedded in the way the community conceptualizes mathematical ideas. In this post, we’ll go through several anecdotes of math, big and small, and discuss how the scale effects the illustrations.
Table of contents:
Train tracks
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