# Science Writing

Harlan Brothers in Cantor’s Paradise

Audioactive sequences and the playful genius of John Conway

“You don’t educate people by telling them useful things; you educate people by telling them interesting things” — John Horton Conway (1937–2020)

I was first exposed to the genius of John Conway through my work at the NSF-funded Yale Fractal Geometry Workshops...

Mathematics 8 min read

Harlan Brothers in Cantor’s Paradise

This mesmerizing spectacle of nature has been considered both a good omen and a harbinger of danger. The underlying physics help explain why.

“It was a beautiful sight, that electric fire playing around the mastheads and yardarms, and illuminating the whole ship with its pale light. It was like a fairy scene..."

Harlan Brothers in Cantor’s Paradise

Researchers Discover a Fractal Protein

Amazingly, cyanobacterium Synechococcus elongatus spontaneously forms Sierpinski triangles

It was nearly half-century ago that Benoit Mandelbrot first coined the term fractal to describe the broad family of self-similar shapes that repeat their pattern in either exactly or roughly the same fashion over a wide range of scales....

Science 7 min read

Harlan Brothers in Cantor’s Paradise

A Solution to the Problem of Deepfakes

Public key encryption holds an answer to the ever-expanding epidemic of disinformation and outright fakery

Technology 7 min read

Harlan Brothers in Cantor’s Paradise

Psychoacoustics, Shepard tones, and the logarithmic perception of pitch

“We adore chaos because we love to produce order.” — Maurits Cornelis Escher (1898 — 1972)

I recall having a blacklight poster of M.C. Escher’s “Other World” as a teenager. At the time, things couldn’t get too much cooler than the combination of blacklights AND Escher. If you’re unfamiliar with the piece, here’s the original woodcut print:

Science 10 min read

Harlan Brothers in Cantor’s Paradise

A serendipitous discovery by radio astronomer Nathan Cohen led to a new class of metamaterials

“The invisible and the non-existent look very much alike.” — Steven Weinberg (1933–2021)

Harlan Brothers in Cantor’s Paradise

Box-counting is an empirical technique we use to estimate the fractal dimension of an object, image, or set. It is based on a simple idea — cover the object with increasingly smaller boxes and then...

Harlan Brothers in Cantor’s Paradise

This elegant eighteenth century theorem gives a necessary and sufficient condition for proving primality

John Wilson was an English mathematician and judge who is best known for his formula for identifying prime numbers...

Prime Numbers 5 min read

Harlan Brothers in Cantor’s Paradise

Fractal Structure in John Coltrane’s Countdown

John Coltrane’s album Giant Steps, first recorded in 1959, stands out as one of the seminal recordings in jazz history. While it is best known for its title track “Giant Steps”, the third track, “Countdown,” is a similarly virtuosic performance over a challenging chord progression at a blistering pace...

Harlan Brothers in Cantor’s Paradise

More than two centuries separate The Art of Fugue, written by Johann Sebastian Bach, and the primitive computer printout of the first graphical representation of what is arguably the most famous fractal...

Harlan Brothers in Cantor’s Paradise

Alice: “Give me as many digits of π as you want. I will demonstrate how you can turn them into digits of e.” …

Harlan Brothers in Towards Data Science

Music is a rich source of multi-dimensional data. This data can take the symbolic form of a score, usually represented by MIDI values, or the form of an audio signal. For many years...

Music & Mathematics: Cosmic Twins

The connections between mathematics and music run deep. The subjects can be thought of as cosmic twins, born out of a tantalizing mixture of…