Infinity with Max Cooper — In Six Minutes
Great fleas have little fleas upon their backs to bite ’em,
And little fleas have lesser fleas, and so ad infinitum.
And the great fleas themselves, in turn, have greater fleas to go on;
While these again have greater still, and greater still, and so on.
—Augustus de Morgan
contents
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).
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.
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.
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.
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.
Cell Genomics cover
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.
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.
Science Advances cover
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.
More details about the design.
Kijima, Y. et al. A universal sequencing read interpreter (2023) Science Advances 9
Browse my gallery of cover designs.
Regression modeling of time-to-event data with censoring
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).
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
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
The video recently premiered on YouTube.
Renders of the full scene are available as NFTs.
Gene Cultures exhibit — art at the MIT Museum
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.
Annals of Oncology cover
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.
Pleasance E et al. Whole-genome and transcriptome analysis enhances precision cancer treatment options (2022) Annals of Oncology 33:939–949.
Browse my gallery of cover designs.
