Yoga for Mathematicians
The 9th Heidelberg Laureate Forum marked a return to the city of Heidelberg after two years online. The key features of the forum were back: the in-person lectures and panels, the boat trip, the dinner in the castle, the saxophone quartet playing “In The Mood”. But in the era of the ‘new normal” there were two key additions to the daily routine. First was the daily COVID test, and second were the warm-up sessions.
The warm-up sessions were introduced during the forum’s online years so people could mark the start of the day and prepare themselves mentally and physically. This new tradition continued at the 2022 Heidelberg Laureate Forum, with delegates being guided through yoga and mindfulness each morning by a lovely yogi named Andreas.
As a journalist, I decided to join the warm-up session one morning and make notes about what the experience was like. And I did! But as a mathematician, I thought it would be far funner to see what maths I could find in the yoga poses. This is what I discovered.
(Full disclaimer: I am not a yoga expert, and every photo you see is my first attempt at each pose. But that adds to the comedic value, right?)
The Graph Plots
Some yoga poses mimic graph plots!
The simplest of these is the mountain pose (Tadasana in Sanskrit), or as I like to call it \(x = 0\).
Another fairly basic pose is s the imaginatively names Wide-Legged Standing Forward Bend (Prasarita Padottanasana), also known as \(y = – |x|\) (and yes, this is an excuse for me to show off my fabulous HLF t-shirt)
Those fancying a bit of an ab workout can also try their hand at \(y = |x|\), otherwise known as the boat pose (or Navasana in Sanskrit).
No list of mathematic yoga poses would be complete without mentioning the triangle pose. Know as Trikonasana in Sanskrit (with Trikona translating as “three corners”). I don’t even need to shoehorn this pose into being mathematical.
Our next pose forms the circle, or unknot if you’d rather. This is the camel pose (Ustrasana).
Another shape that can be made is an oblong, or rectangle. One way to do this is via the Utthita Hasta Padangusthasana pose, in English known as the Extended Hand-to-Big-Toe pose.
But wait! This is the king dancer pose, or Natarajasana and it’s topologically equivalent to the above pose. Despite this, it would be impossible for me to move from one pose to another without letting go, because I’ve actually swapped which foot I’m holding. Reflections that are not superimposable, like this, are known as “chiral” in both chemistry and topology.
Every mathematician loves a good sequence, and yoga does not disappoint. There are not one, not two, but THREE warrior poses (or Virabhadrasana in Sanskrit).
The final three poses I’d like to share are wonderfully mathematical, as I genuinely did use mathematics to be able to do them.
First is the wheel pose, or Urdhva Dhanurasana in Sanskrit. The mathematics behind making this pose work is that, as you may have noticed, I took my socks off. This was to increase the coefficient of friction between my feet and the floor, so that I didn’t slip.
The next pose is known as Bakasana in Sanskrit: the crow pose. The key physics behind this is ensuring that your centre of mass is between your two hands. To do this, you sometimes have to tilt further forward than your intuition would lead you to believe.
A bit of a stretch
Okay, so maybe I used a bit of poetic licence with some of these poses, but that’s the wonderful thing about maths – if you look hard enough you can notice it everywhere and have a lot of fun doing it! What’s more, I think that for many people, the state of calm focus that is reached by meditation is very similar to the feeling of “flow” one can get when deep in a mathematical problem. Maybe maths and yoga aren’t so different after all!