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Pi Day 2022 — three one four: a number of notes — A musical journey into the digits of Pi
On March 14th celebrate `\pi` Day. Hug `\pi`—find a way to do it.
For those who favour `\tau=2\pi` will have to postpone celebrations until July 26th. That's what you get for thinking that `\pi` is wrong. I sympathize with this position and have `\tau` day art too!
If you're not into details, you may opt to party on July 22nd, which is `\pi` approximation day (`\pi` ≈ 22/7). It's 20% more accurate that the official `\pi` day!
Finally, if you believe that `\pi = 3`, you should read why `\pi` is not equal to 3.
3 There you go
1 Straight
4 Number me not
1 Scales
5 There is more of me
9 To forget than you can remember
—Emma Beauxis-Aussalet (314... piku)
Welcome to 2022 Pi Day: a celebration of `\pi` and mathematics (and music).
Buy the Album
The "three one four: a number of notes" album is available on Bandcamp, Spotify and Tidal.
Numberphile Podcast
Greg and I discuss the album on the Numberphile podcast.
Download the score
The album is fully scored for solo piano.
Artwork
The artwork for the album is the Wallis Sieve. It is a fractal whose area is `\pi/4`.
The sieve is generated by starting with a black square and dividing it into a grid of 3 × 3 squares and removing the middle square. On the second iteration, each of the squares is further divided into a grid of 5 × 5 squares, and the middle in each grid is removed. As this process continues (at iteration `n` we divide each square into `(2n+1)^2` smaller squares and remove the middle one), the black area (what remains after the middle squares are removed) approaches `\pi/4`.
The Wallis Sieve is said to "round the square" because by removing progressively smaller squares, we've rounded the big square into a quarter circle.
You can download a very high resolution level 5 Wallis Sieve. For normal viewing, the first three levels are visible and the fourth appears as dots. The fifth level is essentially invisible and, unless you're looking to zoom in interactively, there's little point in dividing futher.
Musical Influences
The album is inspired by 20th century classical music. Each track is a tribute to an influential composer from the era.
The methods section has detailed notes from Greg, the composer.
track 1 — 314... : the mid-century multiple serialists
Pierre Boulez (Piano Sonatas No. 1 and No. 2)
Karlheinz Stockhausen (Klavierstücke I-XVII)
Gyorgy Ligeti (Musica Ricercata 1–11)
Steve Reich (Piano phase score and visualization | Clapping Music Electric Counterpoint)
Phillip Glass (Mad Rush, String Quartet No. 3)
Erik Satie (Gnossienne No. 3, 3 Gymnopedies and 6 Gnossiennes)
Morton Feldman (Piano Pieces | Triadic Memories for the Piano | Intermissions for Piano)
Wynton Kelly (On Green Dolphin St. | Autumn Leaves | If I Should Lose You)
Bud Powell (Wail)
Thelonious Monk (Underground)
track 2 — Feynman Point
track 3 — Wallis Product
track 4 — nn
track 5 — null
track 6 — ...264 : Bebop jazz
Propensity score weighting
It is not certain that everything is uncertain. —Blaise Pascal
We have already explored how we can mitigate bias caused by confounding variables in observational studies using propensity score (PS) matching (PSM) and propensity score weighting (PSW). However, any statistical model is only as good as its assumptions and, if it is specified incorrectly, it can itself produce biased estimates of the treatment effect.
This month, we explore double robustness, a powerful statistical concept that provides a valuable “safety net” against the risk of an incorrect model. It offers two opportunities, instead of just one, to obtain a valid estimate of the treatment effect — making it possible to draw credible causal inferences from observational data without having to depend on a single set of modeling assumptions.
Kurz, C.F., Krzywinski, M. & Altman, N. (2026) Points of significance: Double Robustness. Nat. Methods 23:868–869.
Nature Biotechnology cover
My cover design on the 7 April 2026 Nature Biotechnology issue shows the dendrogram that represents a cluster of uniquely expressed (or downregulated) genes in human naive stem cells induced from such cells. Within each dendrogram block, the genomic barcode sequence (sampled from Supplementary Table 1) is depicted with a Code 39 barcode. The highlighted barcode is one of those used for cell isolation.
Ishiguro S. et al. A multi-kingdom genetic barcoding system for precise clone isolation (2026) Nature Biotechnology 44:616–629.
Browse my gallery of cover designs.
Happy 2026 π Day—
Art for the 5%
Celebrate π Day (March 14th) and enjoy the art — but only if you're part of the 5%.
Go ahead, see what you can't see.
Ishihara's Tests for Colour Deficiency
Authentic and accurate images of Ishihara's test plates photographed (and lovingly color-corrected) from the 38-plate Ishihara's Tests for Colour Deficiency.
I also provide the position, size, and color of each circle on each test plate.
Symmetric alternatives to the ordinary least squares regression
What immortal hand or eye, could frame thy fearful symmetry? — William Blake, "The Tyger"
This month, we look at symmetric regression, which, unlike simple linear regression, it is reversible — remaining unaltered when the variables are swapped.
Simple linear regression can summarize the linear relationship between two variables `X` and `Y` — for example, when `Y` is considered the response (dependent) and `X` the predictor (independent) variable.
However, there are times when we are not interested (or able) to distinguish between dependent and independent variables — either because they have the same importance or the same role. This is where symmetric regression can help.
Luca Greco, George Luta, Martin Krzywinski & Naomi Altman (2025) Points of significance: Symmetric alternatives to the ordinary least squares regression. Nat. Methods 22:1610–1612.
Beyond Belief Campaign BRCA Art
Fuelled by philanthropy, findings into the workings of BRCA1 and BRCA2 genes have led to groundbreaking research and lifesaving innovations to care for families facing cancer.
This set of 100 one-of-a-kind prints explore the structure of these genes. Each artwork is unique — if you put them all together, you get the full sequence of the BRCA1 and BRCA2 proteins.
