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Distractions and amusements, with a sandwich and coffee.

Trance opera—Spente le Stelle
• be dramatic
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They serve as the form for The Outbreak Poems.

Numbers are a lot of fun. They can start conversations—the interesting number paradox is a party favourite: every number must be interesting because the first number that wasn't would be very interesting! Of course, in the wrong company they can just as easily end conversations.

It is not yet known whether the digits of π are normal—determining this is an important problem in mathematics. In other words, is the distribution of digit frequencies in π uniform? Do each of the digits 0–9 appear exactly 1/10th of the time, does every two-digit string appear exactly 1/100th of the time and so on for every finite-length string^{1}?

^{1} One interesting finite-length string is the 6-digit Fenyman Point (...999999...) which appears at digit 762 in π. The Feynman Point was the subject of 2014 `\pi` Day art.

This question can be posed for different representations of π—in different bases. The distribution frequencies of 1/10, 1/100, and so on above refer to the representation of π in base 10. This is the way we're used to seeing numbers. However, if π is encoded as binary (base 2), would all the digits in 11.00100100001111... be normal? The table below shows the first several digits of π in each base from 2 to 16, as well as the natural logarithm base, `e`.

base, `b` | `\pi_b` | base, `b` | `\pi_b` |

2 | 11.00100100001111 | 10 | 3.14159265358979 |

3 | 10.01021101222201 | 11 | 3.16150702865A48 |

4 | 3.02100333122220 | 12 | 3.184809493B9186 |

5 | 3.03232214303343 | 13 | 3.1AC1049052A2C7 |

6 | 3.05033005141512 | 14 | 3.1DA75CDA813752 |

7 | 3.06636514320361 | 15 | 3.21CD1DC46C2B7A |

8 | 3.11037552421026 | 16 | 3.243F6A8885A300 |

`e` | 10.10100202000211 | ||

source: virtuescience.com |

Because the digits in the numbers are essentially random (this is a conjecture), the essence of the art is based on randomness.

A vexing consequence of π being normal is that, because it is non-terminating, π would contain *all* patterns. Any word you might think of, encoded into numbers in any way, would appear infinitely many times. The entire works of Shakespeare, too. As well, all his plays in which each sentence is reversed, or has one spelling mistake, or two! In fact, you would eventually find π within π, but only if you have infinite patience.

This is why any attempts to use the digits of `\pi` to infer meaning about anything is ridiculous. The exact opposite of what you find is also in `\pi`.

A number can be normal in one base, but another. For example, Stoneham's constant,

`\alpha_{2,3} = 1/2 + 1/(2^{3^1} 3^1) + 1/(2^{3^2} 3^2) + 1/(2^{3^3} 3^3) + ... + 1/(2^{3^k} 3^k) + ... `

is 0.54188368083150298507... in base 10 and 0.100010101011100011100011100... in base 2.

Stoneham's constant is provably normal in base 2. In some other bases, such 6, Stoneham's constant is provably not normal.

*Clear, concise, legible and compelling.*

The PDF template is a poster about making posters. It provides design, typography and data visualiation tips with minimum fuss. Follow its advice until you have developed enough design sobriety and experience to know when to go your own way.

*Realistic models of epidemics account for latency, loss of immunity, births and deaths.*

We continue with our discussion about epidemic models and show how births, deaths and loss of immunity can create epidemic waves—a periodic fluctuation in the fraction of population that is infected.

This column has an interactive supplemental component (download code) that allows you to explore epidemic waves and introduces the idea of the phase plane, a compact way to understand the evolution of an epidemic over its entire course.

Bjørnstad, O.N., Shea, K., Krzywinski, M. & Altman, N. (2020) Points of significance: The SEIRS model for infectious disease dynamics. *Nature Methods* **17**:557–558.

Bjørnstad, O.N., Shea, K., Krzywinski, M. & Altman, N. (2020) Points of significance: Modeling infectious epidemics. *Nature Methods* **17**:455–456.

*Shifting soundscapes, textures and rhythmic loops produced by laboratory machines.*

In commemoration of the 20th anniversary of Canada's Michael Smith Genome Sciences Centre, Segue was commissioned to create an original composition based on audio recordings from the GSC's laboratory equipment, robots and computers—to make “music” from the noise they produce.

*Genetic sequences of the coronavirus tell story of when the virus arrived in each country and where it came from.*

Our graphic in Scientific American's Graphic Science section in the June 2020 issue shows a phylogenetic tree based on a snapshot of the data model from Nextstrain as of 31 March 2020.

Our design on the cover of Nature Cancer's April 2020 issue shows mutation spectra of patients from the POG570 cohort of 570 individuals with advanced metastatic cancer.

The cover design accompanies our report in the issue Pleasance, E., Titmuss, E., Williamson, L. et al. (2020) Pan-cancer analysis of advanced patient tumors reveals interactions between therapy and genomic landscapes. *Nat Cancer* **1**:452–468.

*Every day sadder and sadder news of its increase. In the City died this week 7496; and of them, 6102 of the plague. But it is feared that the true number of the dead this week is near 10,000 ....*

—Samuel Pepys, 1665

This month, we begin a series of columns on epidemiological models. We start with the basic SIR model, which models the spread of an infection between three groups in a population: susceptible, infected and recovered.

We discuss conditions under which an outbreak occurs, estimates of spread characteristics and the effects that mitigation can play on disease trajectories. We show the trends that arise when "flattenting the curve" by decreasing `R_0`.

This column has an interactive supplemental component (download code) that allows you to explore how the model curves change with parameters such as infectious period, basic reproduction number and vaccination level.

Bjørnstad, O.N., Shea, K., Krzywinski, M. & Altman, N. (2020) Points of significance: Modeling infectious epidemics. *Nature Methods* **17**:455–456.