Twenty — minutes — maybe — more.choose four wordsmore quotes
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 see a World in a grain of sand,
And Heaven in a wild flower,
Hold Infinity in the palm of your hand
And Eternity in an hour.
—William Blake

## 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.

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)
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)
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)
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)
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)
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

# Neural network primer

Mon 06-02-2023

Nature is often hidden, sometimes overcome, seldom extinguished. —Francis Bacon

In the first of a series of columns about neural networks, we introduce them with an intuitive approach that draws from our discussion about logistic regression.

Nature Methods Points of Significance column: Neural network primer. (read)

Simple neural networks are just a chain of linear regressions. And, although neural network models can get very complicated, their essence can be understood in terms of relatively basic principles.

We show how neural network components (neurons) can be arranged in the network and discuss the ideas of hidden layers. Using a simple data set we show how even a 3-neuron neural network can already model relatively complicated data patterns.

Derry, A., Krzywinski, M & Altman, N. (2023) Points of significance: Neural network primer. Nature Methods 20.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of significance: Logistic regression. Nature Methods 13:541–542.

# Cell Genomics cover

Mon 16-01-2023

Our cover on the 11 January 2023 Cell Genomics issue depicts the process of determining the parent-of-origin using differential methylation of alleles at imprinted regions (iDMRs) is imagined as a circuit.

Designed in collaboration with with Carlos Urzua.

Our Cell Genomics cover depicts parent-of-origin assignment as a circuit (volume 3, issue 1, 11 January 2023). (more)

Akbari, V. et al. Parent-of-origin detection and chromosome-scale haplotyping using long-read DNA methylation sequencing and Strand-seq (2023) Cell Genomics 3(1).

Browse my gallery of cover designs.

A catalogue of my journal and magazine cover designs. (more)

Thu 05-01-2023

My cover design on the 6 January 2023 Science Advances issue depicts DNA sequencing read translation in high-dimensional space. The image showss 672 bases of sequencing barcodes generated by three different single-cell RNA sequencing platforms were encoded as oriented triangles on the faces of three 7-dimensional cubes.

My Science Advances cover that encodes sequence onto hypercubes (volume 9, issue 1, 6 January 2023). (more)

Kijima, Y. et al. A universal sequencing read interpreter (2023) Science Advances 9.

Browse my gallery of cover designs.

A catalogue of my journal and magazine cover designs. (more)

# 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).

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

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.

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.