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Distractions and amusements, with a sandwich and coffee.

Without an after or a when.
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They serve as the form for The Outbreak Poems.

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`.

What would circles look like if `\pi`=22/7?

Imagine that the circle had a tiny loop at one of its points. The circumference of this loop would be added to the circumference of the circle, but the loop would be so small that we would never notice it.

This is reminiscent of how string theories describe higher dimensions—as tiny loops at each point in space, except in my example the loop is only at one point.

This idea originated with Klein, who explained the fourth dimension as a curled up circle of a very small radius. Another way in which this curling-up is used is to say that the fifth dimension is a curled up Planck length, as explained in this Imagining 10 Dimensions video.

If this idea is difficult to wrap your head around, you're not alone. We cannot think of additional dimensions in the regular spatial sence since we have no means of experiencing such phenomena. We can however imagine how flatlanders might explain the 3rd dimension, since we can perceive it. They would draw the curled up circles in their plane because they would not have the experience of drawing with perspective mimicking our 3rd dimension.

We would draw their explanation as shown on the right in the figure above, borrowing from our concept of the 3rd spatial dimension. Now imagine showing our explanation to a flatlander. They would not see the same thing as you—the circles would not intuitively imply the higher dimension to them.

This is analogous to why we cannot draw folded up dimensions. We are merely *solidlanders*—flatlanders in 3d space. Creatures that can perceive more spatial dimensions would use us as examples of diminished perceptual ability.

Did you notice the fallacy in the term *solidlander*? We refer to solids as objects that occupy the maximum number of spatial dimensions. There's no reason to think that creatures that perceive more dimensions wouldn't use this word the same way we do. We're solidlanders from our perspective and they're solidlanders from theirs.

Another way to imagine how a circle might look is a little more realistic. The theory of special relativity tells us that when we travel at speed relative to another object the dimensions of that object appear contracted to us in the direction of motion.

This contraction is always present, but essentially imperceptible unless we're travelling fast enough. For example, in order for a 1 meter object to appear contracted by the length of a hydrogen molecule (0.3 nm) we would have to be travelling at 7.3 km/s (Wolfram Alpha calculation)!

How fast would we have to be going to compress the circle sufficiently so that its circumference and radius ratio embody the `22/7` approximation of `\pi`? Pretty fast, it turns out. If we travel at just over 12,000 km/sec (0.04 times the speed of light, Wolfram Alpha calculation), the circle will compress as shown in the figure above, and the ratio of its circumference to the radius along direction of motion will make `\pi` appear to be `22/7`.

This compression in length would be barely perceptible to us. Below are both circles, shown overlapping, with `delta` being the extra length in radius required.

The value of `\delta`, which is 0.0008049179155 (if `r = 1`), can be calculated by considering the perimeter of an ellipse. The fact that `\delta` is small shouldn't be surprising since `22/7` is an excellent approximation of `\pi`, good to 0.04%.

Calculating the parameter of an ellipse is more complicated than calculating it for a circle because it uses something called an elliptic integral. This integral has no analytical solution and requires numerical approximation. Luckily, we have computers.

We can use the expression shown above for the perimeter of the ellipse to determine how much the circle needs to be deformed. Let's write `a = r + \delta` (original radius with slight deformation `\delta`) and `b=r`. Since `22/7 > \pi` we know that `\delta > 0`.

It remains to solve the equation below for a value of `\delta` that will yield a ratio of circumference to `r` of `2 \times 22/7`.

To make things simpler, let set `r=1`. Solving the equation numerically, I find $$\delta = 0.0008049179155$$

You can verify this solution at Wolfram Alpha.

After all this, we come full-circle to the meaning of full-circle.

You might ask why I didn't change the definition of `\pi` to `22/7` in the upper limit of the integral. After all, why not make the approximation exercise more faithful to the approximation?

It turns out that if I did that I would get `\delta=0`, which brings us back to the original circle. How is this possible?

Technically, this is because the integral returns the upper limit as its answer if the eccentricity is zero (i.e., `E(x,0)=x`).

Intuitively, this is because changing the upper limit of the integral actually redefines the angle of a full revolution. Now, full-circle isn't `2 \pi` radians, but `2 \times 22/7`. Given that the ratio of the circumference of a circle to its radius is exactly the size, in radians, of a full revolution, we don't need to change the shape of the circle if we're willing to change what a full revolution means.

*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 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.

I'm writing poetry daily to put my feelings into words more often during the COVID-19 outbreak.

Small hours of the world and me.

A poster full of epidemiological worry and statistics. Now updated with the genome of SARS-CoV-2 and COVID-19 case statistics as of 3 March 2020.

Bacterial and viral genomes of various diseases are drawn as paths with color encoding local GC content and curvature encoding local repeat content. Position of the genome encodes prevalence and mortality rate.

The deadly genomes collection has been updated with a posters of the genomes of SARS-CoV-2, the novel coronavirus that causes COVID-19.

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

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