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visualization + math

Love music and science? Explore my collaboration with Max Cooper where we tell the story of infinities and animate the digits of π. Both tracks appear on Max's Yearning for the Infinite album.

The art of Pi (`\pi`), Phi (`\phi`) and `e`


Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2021 `\pi` reminds us that good things grow for those who wait.' edition.

Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2019 `\pi` has hundreds of digits, hundreds of languages and a special kids' edition.

Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2018 `\pi` day stitches street maps into new destinations.

Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2017 `\pi` day imagines the sky in a new way.


Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 `\pi` approximation day wonders what would happen if about right was right.

Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 `\pi` day sees digits really fall for each other.

Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2015 `\pi` day maps transcendentally.

Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` approx day spirals into roughness.


Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` day hypnotizes you into looking.

Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` day

Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2013 `\pi` day is where it started

Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Circular `\pi` art and other distractions

Like music with numbers? Here's a short list of some of my favourite songs that have numbers in their lyrics. Absolutely none of them is about bottles of beer.

music with numbers

1 — One Hundred Billion Sparks, Max Cooper | Imagine a neuron firing. Now imagine 100,000,000,000 neurons firing. This is the music for it.

2 — Numbers, Smoke City | This song is entirely composed of references to different numbers. The bonus? It's both in English and Portuguese. I love the way it ends—"Isn't it beautiful out here?".

Un
Un
Four
Five

Fifteen
Quinze
Seventeen
Seven

...

Tres
forty nine

Isn't it beautiful out here?
Isn't it beautiful out here?
Isn't it beautiful out here?

3 — 99 luftbaloons, Nena | The numerical classic.

Hast du etwas Zeit für mich
Dann singe ich ein Lied für dich
Von 99 Luftballons

4 — One, Aimee Mann | Beautiful mathematics of relationships using small numbers.

One is the lonliest number that you'll ever do. Two can be as bad as one, it's the lonliest number since the number one.

5 — Angels at My Door, Una | Long sequences of numbers.

58, 56, 54 angels at my door.
63, 62, 61, 60, 59, 58 angels at my gate.

6 — Tricky, Tricky, Royksopp | Number words about the fearful six from Norway.

Six afraid of seven 'cause seven, eight, nine
I'm about to lose it the second time

7 — Pt vs Ys, Yoshinori Sunahara | The first four numbers, in German, are this song's lyrics.

Eins, zwei, drei, vier.

8 — Der Kommissar, Falco | Unlike the previous song, this one starts with a German count (doesn't get to vier, though) and just gets better from there.

Two, three, four
Eins, zwei, drei
Na, es is nix dabei
Na, wenn ich euch erzähl' die G'schicht'

9 — 2wicky, Hooverphonic | The numbers likely reference the Prophet-600 and SH-101 synthesizers.

Prophet 60091.
Before we start you should know that you're not the only one who can hurt me.
SH10151.
This is the serial number of our orbital gun.
SH10151.
You better be sure before you leave me for another one.

10 — Straight to Number One, Touch and Go | Something to listen to after midnight.

Fingers, four, play, three, to number one.

11 — The Beat Experience, Pepe Deluxe | I am reminded of this song at too many academic seminars.

Here we are now, at the middle, of the fourth large part of this talk.
More and more I have the feeling that we are getting nowhere.
Slowly, as the talk goes on, we are getting nowhere.
And that is a pleasure.

It is not irritating where one is.
It is only irritating to think one would like to be somewhere else.
Here we are now, a little bit after the middle, of the fourth large part of this talk.

12 — Thousand Kisses Deep, Leonard Cohen | A list of songs that doesn't include one by Cohen is not worth reading. The sentiment of a thousand kisses is as old as lips existed. Catullus wrote to Lesbia "da mi basia mille, deinde centum, dein mille altera, dein secunda centum, deinde usque altera mille, deinde centum" [Give me a thousand kisses, then a hundred, then another thousand, then a second hundred, then yet another thousand, then a hundred.] Well, you get the idea.

And sometimes when the night is slow,
The wretched and the meek,
We gather up our hearts and go,
A Thousand Kisses Deep.

13 — Six Seven Times, Flunk | Curiously the product here is 42. This song is the answer to life.

You've got it all
Six seven times
You've got it all
Makes me feel so fine
And it's all there is

14 — 7 seconds, Youssou N'Dour | Dreamy references to a short period of time.

7 seconds away. Just as long as I stay. I'll be waiting.

15 — 100 Billion Stars, Lux | Something to relax to while you ponder insignificance.

16 — First Picture, Nikolaj Grandjean | First is the most memorable number.

I remember
The first picture
One million different shadows
Where we've been around the willows

17 — Millions of Millions, Music for a French Elevator | Very desirable. And I can't believe I transcribed the whole thing.

5.50 million dollars, 2.6775 and very desirable 8 million dollars 5.6 million and 2.4 million 3.4 million and 2.9 million 1.2 would've amounted to 4 million 1.2 million 19.4 million 6.6 million 5.275 million 1.2 million 3-and-a-half million dollars 6.453 million 8 million 5.050 million 1.4 million close to a million dollars 933.5 million 3.8 million 5 million dollars 2-and-a-half million 600 million dollars can you shut the door? 3-and-a-half million dollars 2.5 million .050 million 572,750 thousand 5.050 million 3.8 million 3 million 150 thousand 8 million 419.5 million

18 — Love Potion #9, The Searchers | I started kissing everythying in sight.

It smelled like turpentine, it looked like Indian ink
I held my nose, I closed my eyes, I took a drink.

19 — 93 Million Miles, Luan Santana feat. John Kip | A little sticky, a little sweet but it makes up for the fact that much of it is in Portuguese.

But the absence of the light is a necessary part.

news + thoughts

Regression modeling of time-to-event data with censoring

Mon 21-11-2022

If you sit on the sofa for your entire life, you’re running a higher risk of getting heart disease and cancer. —Alex Honnold, American rock climber

In a follow-up to our Survival analysis — time-to-event data and censoring article, we look at how regression can be used to account for additional risk factors in survival analysis.

We explore accelerated failure time regression (AFTR) and the Cox Proportional Hazards model (Cox PH).

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Regression modeling of time-to-event data with censoring. (read)

Dey, T., Lipsitz, S.R., Cooper, Z., Trinh, Q., Krzywinski, M & Altman, N. (2022) Points of significance: Regression modeling of time-to-event data with censoring. Nature Methods 19.

Music video for Max Cooper's Ascent

Tue 25-10-2022

My 5-dimensional animation sets the visual stage for Max Cooper's Ascent from the album Unspoken Words. I have previously collaborated with Max on telling a story about infinity for his Yearning for the Infinite album.

I provide a walkthrough the video, describe the animation system I created to generate the frames, and show you all the keyframes

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Frame 4897 from the music video of Max Cooper's Asent.

The video recently premiered on YouTube.

Renders of the full scene are available as NFTs.

Gene Cultures exhibit — art at the MIT Museum

Tue 25-10-2022

I am more than my genome and my genome is more than me.

The MIT Museum reopened at its new location on 2nd October 2022. The new Gene Cultures exhibit featured my visualization of the human genome, which walks through the size and organization of the genome and some of the important structures.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
My art at the MIT Museum Gene Cultures exhibit tells shows the scale and structure of the human genome. Pay no attention to the pink chicken.

Annals of Oncology cover

Wed 14-09-2022

My cover design on the 1 September 2022 Annals of Oncology issue shows 570 individual cases of difficult-to-treat cancers. Each case shows the number and type of actionable genomic alterations that were detected and the length of therapies that resulted from the analysis.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
An organic arrangement of 570 individual cases of difficult-to-treat cancers showing genomic changes and therapies. Apperas on Annals of Oncology cover (volume 33, issue 9, 1 September 2022).

Pleasance E et al. Whole-genome and transcriptome analysis enhances precision cancer treatment options (2022) Annals of Oncology 33:939–949.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
My Annals of Oncology 570 cancer cohort cover (volume 33, issue 9, 1 September 2022). (more)

Browse my gallery of cover designs.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
A catalogue of my journal and magazine cover designs. (more)

Survival analysis—time-to-event data and censoring

Fri 05-08-2022

Love's the only engine of survival. —L. Cohen

We begin a series on survival analysis in the context of its two key complications: skew (which calls for the use of probability distributions, such as the Weibull, that can accomodate skew) and censoring (required because we almost always fail to observe the event in question for all subjects).

We discuss right, left and interval censoring and how mishandling censoring can lead to bias and loss of sensitivity in tests that probe for differences in survival times.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Survival analysis—time-to-event data and censoring. (read)

Dey, T., Lipsitz, S.R., Cooper, Z., Trinh, Q., Krzywinski, M & Altman, N. (2022) Points of significance: Survival analysis—time-to-event data and censoring. Nature Methods 19:906–908.

3,117,275,501 Bases, 0 Gaps

Sun 21-08-2022

See How Scientists Put Together the Complete Human Genome.

My graphic in Scientific American's Graphic Science section in the August 2022 issue shows the full history of the human genome assembly — from its humble shotgun beginnings to the gapless telomere-to-telomere assembly.

Read about the process and methods behind the creation of the graphic.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
3,117,275,501 Bases, 0 Gaps. Text by Clara Moskowitz (Senior Editor), art direction by Jen Christiansen (Senior Graphics Editor), source: UCSC Genome Browser.

See all my Scientific American Graphic Science visualizations.


© 1999–2022 Martin Krzywinski | contact | Canada's Michael Smith Genome Sciences CentreBC Cancer Research CenterBC CancerPHSA