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data visualization + art

Aleph 2 — official music video

MAX COOPER'S ALEPH 2 | From Max Cooper's album Yearning for the Infinite. Music by Max Cooper. Animation by Martin Krzywinski.

Aleph 2 — live at the Barbican in London

MAX COOPER'S ALEPH 2 | From Max Cooper's album Yearning for the Infinite. Music by Max Cooper. Animation by Martin Krzywinski.
My animation of 5 dimensions sets the stage for Max Cooper's track Ascent from his new album Unspoken Words.
Another mathy collaboration with Max!

Infinity with Max Cooper — In Six Minutes

To Infinity and beyond!
—Buzz Lightyear

1 · The story of infinity in 6 minutes

In collaboration with Max Cooper, we tell a story about infinity in 6 minutes (and 34 seconds).

What's the story about? Natural numbers, integers, rationals, reals, power sets and the cardinality of the continuum — a real visual parade of numbers.

But math is a serious matter — so we include two of Cantor's diagnoal proofs in the video. Watch as we show that the size of the set of rational numbers is the same as the set of natural numbers (making them countable) but that the size of the set of real numbers is larger (making them uncountable).

2 · Aleph 2 — Yearning for the Infinite

In science one tries to tell people,
in such a way as to be understood by everyone,
something that no one ever knew before.
But in poetry, it’s the exact opposite.
—Paul Dirac, Mathematical Circles Adieu by H. Eves [quoted]

The style of Aleph 2 is that of a low-fi terminal. We used the Classic Console font by Csaba Széll, which I extended to include more set theory symbols (download extended font).

The animation was closely synchronized to the music, all the while trying to avoid looking too much like something from the Matrix movie.

3 · Video walkthrough

To help you interpret what you are seeing, I walk you through the video and introduce you some advanced concepts of set theory. This way, next time you see an equation like `|\mathbb{R}| = | \mathbb{P}(\mathbb{N}) | = 2^{\aleph_0}`, you'll sprout a smile of joy.

Yearning for the Infinite - Max Cooper and Martin Krzywinski - Visualization of Infinity and Pi / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
We begin counting the natural numbers, whose cardinality is `|\mathbb{N}| = \aleph_0`. Screenshot from Max Cooper's Aleph 2 (Yearning for the Infinite). (Max Cooper/Martin Krzywinski)
Yearning for the Infinite - Max Cooper and Martin Krzywinski - Visualization of Infinity and Pi / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
A bijection between the naturals and integers demonstrating that both have the same cardinality. Screenshot from Max Cooper's Aleph 2 (Yearning for the Infinite). (Max Cooper/Martin Krzywinski)
Yearning for the Infinite - Max Cooper and Martin Krzywinski - Visualization of Infinity and Pi / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
A bijection between the naturals and rationals. We traversing the table of rationals in a zig-zag manner. Screenshot from Max Cooper's Aleph 2 (Yearning for the Infinite). (Max Cooper/Martin Krzywinski)
Yearning for the Infinite - Max Cooper and Martin Krzywinski - Visualization of Infinity and Pi / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
We alter the digits on the diagonal to create a real that is nowhere in the list. Screenshot from Max Cooper's Aleph 2 (Yearning for the Infinite). (Max Cooper/Martin Krzywinski)
Yearning for the Infinite - Max Cooper and Martin Krzywinski - Visualization of Infinity and Pi / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Power set elements of naturals (left) and reals (right). The size of these sets is separated by one step in the hierarchy of Aleph numbers, if the Continuum Hypothesis is true. Screenshot from Max Cooper's Aleph 2 (Yearning for the Infinite). (Max Cooper/Martin Krzywinski)
Yearning for the Infinite - Max Cooper and Martin Krzywinski - Visualization of Infinity and Pi / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Aleph remains. Screenshot from Max Cooper's Aleph 2 (Yearning for the Infinite). (Max Cooper/Martin Krzywinski)

These pages describe the system I build to generate the animation and the mathematics behind infinity, including sets, cardinality, countability, $\aleph$ and the Continuum Hypothesis.

I also present the animation system I built for the video, which was coded from scratch.

4 · My other collaborations with Max

If you like infinity, you might like dimensions too.

Check out my video for Max Cooper's Ascent, which animates 5-dimensional cubes doing their confusing things.

My animation of 5 dimensions sets the stage for Max Cooper's track Ascent from his new album Unspoken Words.
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