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visualization + design
The art of Pi (`\pi`), Phi (`\phi`) and `e`
Numbers are a lot of fun. They can start conversations—the interesting number paradox is a party favourite: every number must be interesting because the first number that wasn't would be very interesting! Of course, in the wrong company they can just as easily end conversations.
The art here is my attempt at transforming famous numbers in mathematics into pretty visual forms, start some of these conversations and awaken emotions for mathematics—other than dislike and confusion
Numerology is bogus, but art based on numbers can be beautiful. Proclus got it right when he said (as quoted by M. Kline in Mathematical Thought from Ancient to Modern Times)
Wherever there is number, there is beauty.
—Proclus Diadochus
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the numbers π, φ and e
The consequence of the interesting number paradox is that all numbers are interesting. But some are more interesting than others—how Orwellian!
All animals are equal, but some animals are more equal than others.
—George Orwell (Animal Farm)
Numbers such as `\pi` (or `\tau` if you're a revolutionary), `\phi`, `e`, `i = \sqrt{-1}`, and `0` have captivated imagination. Chances are at least one of them appears in the next physics equation you come across.
π φ e
= 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 ... = 1.61803 39887 49894 84820 45868 34365 63811 77203 09179 ... = 2.71828 18284 59045 23536 02874 71352 66249 77572 47093 ...
Of these three transcendental numbers, `\pi` (3.14159265...) is the most well known. It is the ratio of a circle's circumference to its diameter (`d = \pi r`) and appears in the formula for the area of the circle (`a = \pi r^2`).
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The Golden Ratio (`\phi`, 1.61803398...) is the attractive proportion of values `a > b` that satisfy `{a+b}/2 = a/b`, which solves to `a/b = {1 + \sqrt{5}}/2`.
The last of the three numbers, `e` (2.71828182...) is Euler's number and also known as the base of the natural logarithm. It, too, can be defined geometrically—it is the unique real number, `e`, for which the function `f(x) = e^x` has a tangent of slope 1 at `x=0`. Like `\pi`, `e` appears throughout mathematics. For example, `e` is central in the expression for the normal distribution as well as the definition of entropy. And if you've ever heard of someone talking about log plots ... well, there's `e` again!
Two of these numbers can be seen together in mathematics' most beautiful equation, the Euler identity: `e^{i\pi} = -1`. The tau-oists would argue that this is even prettier: `e^{i\tau} = 1`.
accidentally similar
Did you notice how the 13th digit of all three numbers is the same (9)? This accidental similarity generates its own number—the Accidental Similarity Number (ASN).
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news + thoughts
Cancer Cell cover
My cover design on the 11 April 2022 Cancer Cell issue depicts depicts cellular heterogeneity as a kaleidoscope generated from immunofluorescence staining of the glial and neuronal markers MBP and NeuN (respectively) in a GBM patient-derived explant.
LeBlanc VG et al. Single-cell landscapes of primary glioblastomas and matched explants and cell lines show variable retention of inter- and intratumor heterogeneity (2022) Cancer Cell 40:379–392.E9.
Browse my gallery of cover designs.
Nature Biotechnology cover
My cover design on the 4 April 2022 Nature Biotechnology issue is an impression of a phylogenetic tree of over 200 million sequences.
Konno N et al. Deep distributed computing to reconstruct extremely large lineage trees (2022) Nature Biotechnology 40:566–575.
Browse my gallery of cover designs.
Nature cover — Gene Genie
My cover design on the 17 March 2022 Nature issue depicts the evolutionary properties of sequences at the extremes of the evolvability spectrum.
Vaishnav ED et al. The evolution, evolvability and engineering of gene regulatory DNA (2022) Nature 603:455–463.
Browse my gallery of cover designs.
Happy 2022 `\pi` Day—
three one four: a number of notes
Celebrate `\pi` Day (March 14th) and finally hear what you've been missing.
“three one four: a number of notes” is a musical exploration of how we think about mathematics and how we feel about mathematics. It tells stories from the very beginning (314…) to the very (known) end of π (...264) as well as math (Wallis Product) and math jokes (Feynman Point), repetition (nn) and zeroes (null).
The album is scored for solo piano in the style of 20th century classical music – each piece has a distinct personality, drawn from styles of Boulez, Feldman, Glass, Ligeti, Monk, and Satie.
Each piece is accompanied by a piku (or πku), a poem whose syllable count is determined by a specific sequence of digits from π.
Check out art from previous years: 2013 `\pi` Day and 2014 `\pi` Day, 2015 `\pi` Day, 2016 `\pi` Day, 2017 `\pi` Day, 2018 `\pi` Day, 2019 `\pi` Day, 2020 `\pi` Day and 2021 `\pi` Day.
PNAS Cover — Earth BioGenome Project
My design appears on the 25 January 2022 PNAS issue.
The cover shows a view of Earth that captures the vision of the Earth BioGenome Project — understanding and conserving genetic diversity on a global scale. Continents from the Authagraph projection, which preserves areas and shapes, are represented as a double helix of 32,111 bases. Short sequences of 806 unique species, sequenced as part of EBP-affiliated projects, are mapped onto the double helix of the continent (or ocean) where the species is commonly found. The length of the sequence is the same for each species on a continent (or ocean) and the sequences are separated by short gaps. Individual bases of the sequence are colored by dots. Species appear along the path in alphabetical order (by Latin name) and the first base of the first species is identified by a small black triangle.
Lewin HA et al. The Earth BioGenome Project 2020: Starting the clock. (2022) PNAS 119(4) e2115635118.
The COVID charts — hospitalization rates
As part of the COVID Charts series, I fix a muddled and storyless graphic tweeted by Adrian Dix, Canada's Health Minister.
I show you how to fix color schemes to make them colorblind-accessible and effective in revealing patters, how to reduce redundancy in labels (a key but overlooked part of many visualizations) and how to extract a story out of a table to frame the narrative.
