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Distractions and amusements, with a sandwich and coffee.

I'm not real and I deny I won't heal unless I cry.
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The never-repeating digits of `\pi` can be approximated by `22/7 = 3.142857`

to within 0.04%. These pages artistically and mathematically explore rational approximations to `\pi`. This 22/7 ratio is celebrated each year on July 22nd. If you like hand waving or back-of-envelope mathematics, this day is for you: `\pi` approximation day!

Want more math + art? Discover the Accidental Similarity Number. Find humor in my poster of the first 2,000 4s of `\pi`.

There are two kinds of `\pi` Approximation Day posters.

The first uses the Archimedean spiral for its design, which I've used before for other numerical art. The second packs warped circles, whose ratio of circumference to average diameter is `22/7` into what I call `\pi`-approximate circular packing.

In the Approximation Day poster, all `m/n` rational approximations to `\pi` are shown as circles on a spiral. The circle at the start of the spiral (top) corresponds to `m=1`. The circle at the center of the spiral corresponds to `m=10000`.

Each circle is colored by the accuracy of the best possible approximation `m/n` according to the color scheme below, which is the legend inset. For example, for `m=22` the best approximation has `n=7`.

The accuracy cutoffs were selected to assign roughly the same number of points to each category.

The location of the best approximations within each accuracy window is shown below.

A workshop in using the Circos Galaxy wrapper by Rasche and Hiltemann. Event organized by Australian Biocommons.

Galaxy wrapper training materials, Saskia Hiltemann, Helena Rasche, 2020 Visualisation with Circos (Galaxy Training Materials).

My webinar on fundamental concepts in data visualization and visual communication of scientific data and concepts. Event organized by Australian Biocommons.

*With one eye you are looking at the outside world, while with the other you are looking within yourself.*

—Amedeo Modigliani

Following up with our Markov Chain column and Hidden Markov model column, this month we look at how Markov models are trained using the example of biased coin.

We introduce the concepts of forward and backward probabilities and explicitly show how they are calculated in the training process using the Baum-Welch algorithm. We also discuss the value of ensemble models and the use of pseudocounts for cases where rare observations are expected but not necessarily seen.

Grewal, J., Krzywinski, M. & Altman, N. (2019) Points of significance: Markov models — training and evaluation of hidden Markov models. *Nature Methods* **17**:121–122.

Altman, N. & Krzywinski, M. (2019) Points of significance: Hidden Markov models. *Nature Methods* **16**:795–796.

Altman, N. & Krzywinski, M. (2019) Points of significance: Markov Chains. *Nature Methods* **16**:663–664.

*Science. Timeliness. Respect.*

Read about the design of the clothing, music, drinks and art for the Genome Sciences Center 20th Anniversary Celebration, held on 15 November 2019.

As part of the celebration and with the help of our engineering team, we framed 48 flow cells from the lab.

Each flow cell was accompanied by an interpretive plaque explaining the technology behind the flow cell and the sample information and sequence content.

*The scientific process works because all its output is empirically constrained.*

My chapter from The Aesthetics of Scientific Data Representation, More than Pretty Pictures, in which I discuss the principles of data visualization and connect them to the concept of "quality" introduced by Robert Pirsig in Zen and the Art of Motorcycle Maintenance.

Discover Cantor's transfinite numbers through my music video for the Aleph 2 track of Max Cooper's Yearning for the Infinite (album page, event page).

I discuss the math behind the video and the system I built to create the video.