latest news

Distractions and amusements, with a sandwich and coffee.

Drive, driven. Gave, given.
•
• Give me a number of games.
• more quotes

On March 14th celebrate `\pi` Day. Hug `\pi`—find a way to do it.

For those who favour `\tau=2\pi` will have to postpone celebrations until July 26th. That's what you get for thinking that `\pi` is wrong. I sympathize with this position and have `\tau` day art too!

If you're not into details, you may opt to party on July 22nd, which is `\pi` approximation day (`\pi` ≈ 22/7). It's 20% more accurate that the official `\pi` day!

Finally, if you believe that `\pi = 3`, you should read why `\pi` is not equal to 3.

This year's `\pi` day art collection celebrates not only the digit but also one of the fundamental forces in nature: gravity.

In February of 2016, for the first time, gravitational waves were detected at the Laser Interferometer Gravitational-Wave Observatory (LIGO).

The signal in the detector was sonified—a process by which any data can be encoded into sound to provide hints at patterns and structure that we might otherwise miss—and we finally heard what two black holes sound like. A buzz and chirp.

The art is featured in the Gravity of Pi article on the Scientific American SA Visual blog.

All the art was processed while listening to Roses by Coeur de Pirate, a brilliant female French-Canadian songwriter, who sounds like a mix of Patricia Kaas and Lhasa. The lyrics Oublie-moi (Forget me) are fitting with this year's theme of gravity.

Mais laisse-moi tomber, laisse-nous tomber

Laisse la nuit trembler en moi

Laisse-moi tomber, laisse nous tomber

Cette fois

But let me fall, let us fall

Let the night tremble in me

Let me fall, let us fall

This time

The art is generated by running a simulation of gravity in which digits of `\pi` are each assigned a mass and allowed to collide eand orbit each other.

The mathematical details of the simulation can be found in the code section.

A simulation starts with taking `n` digits of `\pi` and arranging them uniformly around a circle. The mass of each digit, `d_i` (e.g. 3), is given by `(1+d)^k` where `k` is a mass power parameter between 0.01 and 1. For example, if `k=0.42` then the mass of 3 is `(1+3)^{0.42} = 1.79`.

The figure below shows the evolution of a simulation with `n=3` digits and `k=1`. The digits 3 and 4 collide to form the digit `3+4 = 7` and immediately collides with 1 to form `7+1=8`. With only one mass left in the system, the simulation stops.

When masses have initial velocities, the patterns quickly start to get interesting. In the figure above, the masses are initalized with zero velocity. As soon as the simulation, each mass immediately starts to move directly towards the center of mass of the other two masses.

When the initial velocity is non-zero, such as in the figure below, the masses don't immediately collapse towards one another. The masses first travel with their initial velocity but immediately the gravitational force imparts acceleration that alters this velocity. In the examples below, only those simulations in which the masses collapsed within a time cutoff are shown.

Depending on the initial velocities, some systems collapse very quickly, which doesn't make for interesting patterns.

For example, the simulations above evolved over 100,000 steps and in some cases the masses collapsed within 10,000 steps. In the figure below, I require that the system evolves for at least 15,000 steps before collapsing. Lovely doddles, don't you think?

When a simulation is repeated with different initial conditions, the set of outcomes is called an ensemble.

Below, I repeat the simulation 100 times with `n=3` and `k=0.2`, each time with slightly different initial velocity. The velocities have their `x`- and `y`-components normally distributed with zero mean and a fixed variance. Each of the four ensembles has its simulations evolve over progressively more time steps: 5,000, 7,500, 10,000, and 20,000.

You can see that with 5,000 steps the masses don't yet have a chance to collide. After 7,500, there have been collisions in a small number of systems. The blue mass corresponds to the 3 colliding with 4 and the green mass to 1 colliding with 4. After 10,000, even more collisions are seen and in 3 cases we see total collapse (all three digits collided). After 20,000,

The value of `k` greatly impacts the outcome of the simulation. When `k` is very small, all the digits have essentially the same mass. For example, when `k=0.01` the 0 has a mass of 1 and 9 has a mass of 1.02.

When `k` is large, the difference in masses is much greater. For example, for `k=2` the lightest mass is `(1+0)^2=1` and the heaviest `(1+9)^2=10`. Because the acceleration of a mass is proportional to the mass that is attracting it, in a pair of masses the light mass will accelerate faster.

As the number of digits is increased, the pattern of collapse doesn't qualitatively change.

I ran a large number of simulations. For various values of `n` and `k`, I repeated the simulation several times to sample different intial velocities.

Below is a great example of how a stable orbital pattern of a pair of masses can be disrupted by the presence of another mass. You can see on the left that once the light red mass moves away from the orange/green pair, they settle into a stable pattern.

The figure below shows one of my favourite patterns. As the digits collide, three masses remain, which leave the system. They remain under each other's gravitational influence, but are moving too quickly to return to the canvas within the time of the simulation.

Use this fun inteactive gravity simulator if you want to drop your own masses and watch them orbit.

The Sanctuary Project is a Lunar vault of science and art. It includes two fully sequenced human genomes, sequenced and assembled by us at Canada's Michael Smith Genome Sciences Centre.

The first disc includes a song composed by Flunk for the (eventual) trip to the Moon.

But how do you send sound to space? I describe the inspiration, process and art behind the work.

A forest of digits

Celebrate `\pi` Day (March 14th) and finally see the digits through the forest.

This year is full of botanical whimsy. A Lindenmayer system forest – deterministic but always changing. Feel free to stop and pick the flowers from the ground.

And things can get crazy in the forest.

Check out art from previous years: 2013 `\pi` Day and 2014 `\pi` Day, 2015 `\pi` Day, 2016 `\pi` Day, 2017 `\pi` Day, 2018 `\pi` Day and 2019 `\pi` Day.

*All that glitters is not gold. —W. Shakespeare*

The sensitivity and specificity of a test do not necessarily correspond to its error rate. This becomes critically important when testing for a rare condition — a test with 99% sensitivity and specificity has an even chance of being wrong when the condition prevalence is 1%.

We discuss the positive predictive value (PPV) and how practices such as screen can increase it.

Altman, N. & Krzywinski, M. (2021) Points of significance: Testing for rare conditions. *Nature Methods* **18**:224–225.

*We demand rigidly defined areas of doubt and uncertainty! —D. Adams*

A popular notion about experiments is that it's good to keep variability in subjects low to limit the influence of confounding factors. This is called standardization.

Unfortunately, although standardization increases power, it can induce unrealistically low variability and lead to results that do not generalize to the population of interest. And, in fact, may be irreproducible.

Not paying attention to these details and thinking (or hoping) that standardization is always good is the "standardization fallacy". In this column, we look at how standardization can be balanced with heterogenization to avoid this thorny issue.

Voelkl, B., Würbel, H., Krzywinski, M. & Altman, N. (2021) Points of significance: Standardization fallacy. *Nature Methods* **18**:5–6.

*Clear, concise, legible and compelling.*

Making a scientific graphical abstract? Refer to my practical design guidelines and redesign examples to improve organization, design and clarity of your graphical abstracts.

An in-depth look at my process of reacting to a bad figure — how I design a poster and tell data stories.