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).
This year I've done something very different — a surprise for both the ear and eye. Working with Gregory Coles, we've composed an album based on the mathematics of `\pi`.
The album is called “three one four: a number of digits” . It is a sixteen minute musical exploration of the digits of `\pi`. Experience this famous number from its beginning (Track 1 314…) to its very (known) end (Track 6 ...264), as well as the math (Track 3 Wallis Product) and jokes (Track 2 Feynman Point) behind it and aspects of its digits, such as repetition (Track 4 nn) and zeroes (Track 5 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 and Stockhausen (314…), Ligeti (Feynman Point), Reich and Glass (Wallis Product), Satie (nn), Feldman (null), Powell and Monk (...264).
Each piece is accompanied by a piku (or πku), a poem whose syllable count is determined by a specific sequence of digits from π. I came up with the concept of a piku for 2020 Pi Day.
9 We know we can never have it all
2 Never
4 But yet can we
2 Ever
6 In endless scarcity
4 Have just enough?
—Emma Beauxis-Aussalet (...264 piku)
The piku collection were written by Emma Beauxis-Aussalet set of piku and each piku follows a syllable count that closely matches the theme of its track.
Our album was the theme of a Numberphile Podcast “The First and Last Digits of Pi” and appeared in Nature Briefing for March 14, 2022.
I sit down with the composer of the album, Gregory Coles, and start the conversation about turning mathematics into music. Our attempt was to find a compelling balance between `\pi` and the heart of a musician.
We go through the list of tracks on the album and give you a sense of what to expect.
what to listen to first?
geek out on music theory and scores
If you're a music geek, you'll love our detailed discussion of the music theory behind each track and a thorough score analysis.
download score
The entire album is arranged for solo piano and lovingly engraved. You can download the full score.
Propensity score matching
I don’t have good luck in the match points. —Rafael Nadal, Spanish tennis player
In many experimental designs, we need to keep in mind the possibility of confounding variables, which may give rise to bias in the estimate of the treatment effect.
If the control and experimental groups aren't matched (or, roughly, similar enough), this bias can arise.
Sometimes this can be dealt with by randomizing, which on average can balance this effect out. When randomization is not possible, propensity score matching is an excellent strategy to match control and experimental groups.
Kurz, C.F., Krzywinski, M. & Altman, N. (2024) Points of significance: Propensity score matching. Nat. Methods 21:1770–1772.
Nasa to send our human genome discs to the Moon
We'd like to say a ‘cosmic hello’: mathematics, culture, palaeontology, art and science, and ... human genomes.
Comparing classifier performance with baselines
All animals are equal, but some animals are more equal than others. —George Orwell
This month, we will illustrate the importance of establishing a baseline performance level.
Baselines are typically generated independently for each dataset using very simple models. Their role is to set the minimum level of acceptable performance and help with comparing relative improvements in performance of other models.
Unfortunately, baselines are often overlooked and, in the presence of a class imbalance, must be established with care.
Megahed, F.M, Chen, Y-J., Jones-Farmer, A., Rigdon, S.E., Krzywinski, M. & Altman, N. (2024) Points of significance: Comparing classifier performance with baselines. Nat. Methods 21:546–548.
Happy 2024 π Day—
sunflowers ho!
Celebrate π Day (March 14th) and dig into the digit garden. Let's grow something.
How Analyzing Cosmic Nothing Might Explain Everything
Huge empty areas of the universe called voids could help solve the greatest mysteries in the cosmos.
My graphic accompanying How Analyzing Cosmic Nothing Might Explain Everything in the January 2024 issue of Scientific American depicts the entire Universe in a two-page spread — full of nothing.
The graphic uses the latest data from SDSS 12 and is an update to my Superclusters and Voids poster.
Michael Lemonick (editor) explains on the graphic:
“Regions of relatively empty space called cosmic voids are everywhere in the universe, and scientists believe studying their size, shape and spread across the cosmos could help them understand dark matter, dark energy and other big mysteries.
To use voids in this way, astronomers must map these regions in detail—a project that is just beginning.
Shown here are voids discovered by the Sloan Digital Sky Survey (SDSS), along with a selection of 16 previously named voids. Scientists expect voids to be evenly distributed throughout space—the lack of voids in some regions on the globe simply reflects SDSS’s sky coverage.”
voids
Sofia Contarini, Alice Pisani, Nico Hamaus, Federico Marulli Lauro Moscardini & Marco Baldi (2023) Cosmological Constraints from the BOSS DR12 Void Size Function Astrophysical Journal 953:46.
Nico Hamaus, Alice Pisani, Jin-Ah Choi, Guilhem Lavaux, Benjamin D. Wandelt & Jochen Weller (2020) Journal of Cosmology and Astroparticle Physics 2020:023.
Sloan Digital Sky Survey Data Release 12
Alan MacRobert (Sky & Telescope), Paulina Rowicka/Martin Krzywinski (revisions & Microscopium)
Hoffleit & Warren Jr. (1991) The Bright Star Catalog, 5th Revised Edition (Preliminary Version).
H0 = 67.4 km/(Mpc·s), Ωm = 0.315, Ωv = 0.685. Planck collaboration Planck 2018 results. VI. Cosmological parameters (2018).
constellation figures
stars
cosmology
Error in predictor variables
It is the mark of an educated mind to rest satisfied with the degree of precision that the nature of the subject admits and not to seek exactness where only an approximation is possible. —Aristotle
In regression, the predictors are (typically) assumed to have known values that are measured without error.
Practically, however, predictors are often measured with error. This has a profound (but predictable) effect on the estimates of relationships among variables – the so-called “error in variables” problem.
Error in measuring the predictors is often ignored. In this column, we discuss when ignoring this error is harmless and when it can lead to large bias that can leads us to miss important effects.
Altman, N. & Krzywinski, M. (2024) Points of significance: Error in predictor variables. Nat. Methods 21:4–6.
Background reading
Altman, N. & Krzywinski, M. (2015) Points of significance: Simple linear regression. Nat. Methods 12:999–1000.
Lever, J., Krzywinski, M. & Altman, N. (2016) Points of significance: Logistic regression. Nat. Methods 13:541–542 (2016).
Das, K., Krzywinski, M. & Altman, N. (2019) Points of significance: Quantile regression. Nat. Methods 16:451–452.