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lunch break
Distractions and amusements, with a sandwich and coffee.
visualization + design
The art of Pi (`\pi`), Phi (`\phi`) and `e`
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.
The art here is my attempt at transforming famous numbers in mathematics into pretty visual forms, start some of these conversations and awaken emotions for mathematics—other than dislike and confusion
Numerology is bogus, but art based on numbers can be beautiful. Proclus got it right when he said (as quoted by M. Kline in Mathematical Thought from Ancient to Modern Times)
Wherever there is number, there is beauty.
—Proclus Diadochus
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the numbers π, φ and e
The consequence of the interesting number paradox is that all numbers are interesting. But some are more interesting than others—how Orwellian!
All animals are equal, but some animals are more equal than others.
—George Orwell (Animal Farm)
Numbers such as `\pi` (or `\tau` if you're a revolutionary), `\phi`, `e`, `i = \sqrt{-1}`, and `0` have captivated imagination. Chances are at least one of them appears in the next physics equation you come across.
π φ e
= 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 ... = 1.61803 39887 49894 84820 45868 34365 63811 77203 09179 ... = 2.71828 18284 59045 23536 02874 71352 66249 77572 47093 ...
Of these three transcendental numbers, `\pi` (3.14159265...) is the most well known. It is the ratio of a circle's circumference to its diameter (`d = \pi r`) and appears in the formula for the area of the circle (`a = \pi r^2`).
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The Golden Ratio (`\phi`, 1.61803398...) is the attractive proportion of values `a > b` that satisfy `{a+b}/2 = a/b`, which solves to `a/b = {1 + \sqrt{5}}/2`.
The last of the three numbers, `e` (2.71828182...) is Euler's number and also known as the base of the natural logarithm. It, too, can be defined geometrically—it is the unique real number, `e`, for which the function `f(x) = e^x` has a tangent of slope 1 at `x=0`. Like `\pi`, `e` appears throughout mathematics. For example, `e` is central in the expression for the normal distribution as well as the definition of entropy. And if you've ever heard of someone talking about log plots ... well, there's `e` again!
Two of these numbers can be seen together in mathematics' most beautiful equation, the Euler identity: `e^{i\pi} = -1`. The tau-oists would argue that this is even prettier: `e^{i\tau} = 1`.
accidentally similar
Did you notice how the 13th digit of all three numbers is the same (9)? This accidental similarity generates its own number—the Accidental Similarity Number (ASN).
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`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.