resources
visualizations
presentations
lunch break
Distractions and amusements, with a sandwich and coffee.
visualization + design
`\pi` Approximation Day Art Posters
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!
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.
news + thoughts
`k` index: a weightlighting and Crossfit performance measure
Similar to the `h` index in publishing, the `k` index is a measure of fitness performance.
To achieve a `k` index for a movement you must perform `k` unbroken reps at `k`% 1RM.
The expected value for the `k` index is probably somewhere in the range of `k = 26` to `k=35`, with higher values progressively more difficult to achieve.
In my `k` index introduction article I provide detailed explanation, rep scheme table and WOD example.
Dark Matter of the English Language—the unwords
I've applied the char-rnn recurrent neural network to generate new words, names of drugs and countries.
The effect is intriguing and facetious—yes, those are real words.
But these are not: necronology, abobionalism, gabdologist, and nonerify.
These places only exist in the mind: Conchar and Pobacia, Hzuuland, New Kain, Rabibus and Megee Islands, Sentip and Sitina, Sinistan and Urzenia.
And these are the imaginary afflictions of the imagination: ictophobia, myconomascophobia, and talmatomania.
And these, of the body: ophalosis, icabulosis, mediatopathy and bellotalgia.
Want to name your baby? Or someone else's baby? Try Ginavietta Xilly Anganelel or Ferandulde Hommanloco Kictortick.
When taking new therapeutics, never mix salivac and labromine. And don't forget that abadarone is best taken on an empty stomach.
And nothing increases the chance of getting that grant funded than proposing the study of a new –ome! We really need someone to looking into the femome and manome.
Dark Matter of the Genome—the nullomers
An exploration of things that are missing in the human genome. The nullomers.
Julia Herold, Stefan Kurtz and Robert Giegerich. Efficient computation of absent words in genomic sequences. BMC Bioinformatics (2008) 9:167
Clustering
Clustering finds patterns in data—whether they are there or not.We've already seen how data can be grouped into classes in our series on classifiers. In this column, we look at how data can be grouped by similarity in an unsupervised way.
We look at two common clustering approaches: `k`-means and hierarchical clustering. All clustering methods share the same approach: they first calculate similarity and then use it to group objects into clusters. The details of the methods, and outputs, vary widely.
Altman, N. & Krzywinski, M. (2017) Points of Significance: Clustering. Nature Methods 14:545–546.
Background reading
Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Logistic regression. Nature Methods 13:541-542.
Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Classifier evaluation. Nature Methods 13:603-604.
What's wrong with pie charts?
In this redesign of a pie chart figure from a Nature Medicine article [1], I look at how to organize and present a large number of categories.
I first discuss some of the benefits of a pie chart—there are few and specific—and its shortcomings—there are few but fundamental.
I then walk through the redesign process by showing how the tumor categories can be shown more clearly if they are first aggregated into a small number groups.
(bottom left) Figure 2b from Zehir et al. Mutational landscape of metastatic cancer revealed from prospective clinical sequencing of 10,000 patients. (2017) Nature Medicine doi:10.1038/nm.4333
Tabular Data
Tabulating the number of objects in categories of interest dates back to the earliest records of commerce and population censuses.After 30 columns, this is our first one without a single figure. Sometimes a table is all you need.
In this column, we discuss nominal categorical data, in which data points are assigned to categories in which there is no implied order. We introduce one-way and two-way tables and the `\chi^2` and Fisher's exact tests.
Altman, N. & Krzywinski, M. (2017) Points of Significance: Tabular data. Nature Methods 14:329–330.