Mathematical Connections in the Silhouettes and Vortex

Silhouettes & Vortices

Mathematical Connections

If you are at the exhibit…

The story

Three human silhouettes portray a mathematician at three stages of life: a child creates music with her trumpet, a teenager rides across a swirling vortex of ideas on her self-built rocketboard, and an adult releases a cavalcade of written representations of math into the world. 

Look closely; what do you see?

Humans engage with mathematics in all sorts of ways on a daily basis. Looking at the silhouettes, can you think of ways that mathematics relates to…

  • making music?
  • surfing, skateboarding, or other sports?
  • the act of writing?
Focus on… the teenager’s banner

The banner streaming behind the rocketboarding teenager contains a hidden message inspired by the parachute of the Perseverance rover which landed on Mars in February 2021, at the time the Mathemalchemists were still planning and refining the installation.

Image: NASA/JPL-Caltech

The hidden messages use binary, or base 2, representations of numbers, which then correspond to letters via ASCII encoding.

Given the table below, can you decode the message on Mathemalchemy’s banner? (Hint: the third column represents the letter ‘r.’)

Table: Binary representations of numbers assigned to the alphabet according to the American Standard Code for Information Interchange (ASCII)

Silhouettes

Through the Silhouettes we wanted to make clear that mathematics is for all ages. Kids observe mathematical facts as they play (“Look – after turning this box, 3 rows of 4 chocolates look like 4 rows of 3 chocolates“).

The installation wants to celebrate mathematics at all levels, for everyone. We hope the three Silhouettes also provide a link between visitors and the Mathemalchemy world in front of them. Not everyone can project themselves into the role of Baker Arnold or Tortoise Tess; it may be easier to feel kinship with one of the three Human Silhouettes.

Cavalcade sheets mathematics theorem
Vortices

The Vortices in the sky are inspired by the vortices observed in the flow of a fluid around an obstacle. This phenomenon, which happens at large as well as at small scales, is also illustrated in the installation in the Mural and in the Cavalcade. Vortices of this type can be reproduced to high accuracy in simulations that compute numerical solutions of the Navier-Stokes equations. In this particular instance, they indicate that there is an obstacle (like a mute) in the opening of the Little Girl’s horn. (The flow past a true mute would likely have a different vortex sheet pattern, though.)

Teenager

The Teenager, surfing the vortices on her self-built rocket board, is holding a banner with a coded message. Can you decode it? The small picture in gray near the tip of the banner is a hint …

The support pole for the Teenager (she isn’t really being propelled on the vortex sheet by her rocket-board) provided a signposting opportunity, to different locations in the installation, and beyond. The Hilbert Hotel is a ways off, and of course infinity lies in all directions in the one-point compactification of our standard 3-dimensional Euclidean space.

Signpost
Unperceivable dimensions

A final note about “unperceivable dimensions”. This concept may seem fanciful, but such “hidden dimensions” are one ingredient of String Theory in theoretical physics, a powerful and mathematically very beautiful framework that unifies quantum mechanics and gravity; the extra dimensions in that setting are conjectured to be imperceptible at any scale where we can carry out experiments, so far.

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