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The art of Pi (`\pi`), Phi (`\phi`) and `e`
This section contains various art work based on `\pi`, `\phi` and `e` that I created over the years.
Some of the numerical art reveals interesting and unexpected observations. For example, the sequence 999999 in π at digit 762 called the Feynman Point. Or that if you calculate π to 13,099,586 digits you will find love.
`\pi` day art and `\pi` approximation day art is kept separate.
For some time I have been thinking about creating minimalist typographical art based on the digits of `\pi`. The `i`-ness `\pi` project was one of my first forays into this kind of art.
the `i`-ness of `\pi`
In the `i`-ness of `\pi` poster shown above, the average is mapped onto a color and the standard deviation onto size.
the `i`-ness of `\phi` and `e`
Compare the `i`-ness of `\pi` to that of the other famous transcendental number, `e`, and the mysterious but attractive Golden Ratio, `phi`.
the 4-ness of `\pi`
These posters show the difference between each digit and 4,
Spring and fall color themes of the posters are also available.
curiously humorous variant
I assure you—`\pi` has a lot of 4s. Why, in the first 19,528 digits there are 2,000 of them! That's a lot. Here they are.
If you stare at them long enough, they even appear to move. Amazing.
Symmetric alternatives to the ordinary least squares regression
What immortal hand or eye, could frame thy fearful symmetry? — William Blake, "The Tyger"
This month, we look at symmetric regression, which, unlike simple linear regression, it is reversible — remaining unaltered when the variables are swapped.
Simple linear regression can summarize the linear relationship between two variables `X` and `Y` — for example, when `Y` is considered the response (dependent) and `X` the predictor (independent) variable.
However, there are times when we are not interested (or able) to distinguish between dependent and independent variables — either because they have the same importance or the same role. This is where symmetric regression can help.
Luca Greco, George Luta, Martin Krzywinski & Naomi Altman (2025) Points of significance: Symmetric alternatives to the ordinary least squares regression. Nat. Methods 22:1610–1612.
Beyond Belief Campaign BRCA Art
Fuelled by philanthropy, findings into the workings of BRCA1 and BRCA2 genes have led to groundbreaking research and lifesaving innovations to care for families facing cancer.
This set of 100 one-of-a-kind prints explore the structure of these genes. Each artwork is unique — if you put them all together, you get the full sequence of the BRCA1 and BRCA2 proteins.
Propensity score weighting
The needs of the many outweigh the needs of the few. —Mr. Spock (Star Trek II)
This month, we explore a related and powerful technique to address bias: propensity score weighting (PSW), which applies weights to each subject instead of matching (or discarding) them.
Kurz, C.F., Krzywinski, M. & Altman, N. (2025) Points of significance: Propensity score weighting. Nat. Methods 22:638–640.
Happy 2025 π Day—
TTCAGT: a sequence of digits
Celebrate π Day (March 14th) and sequence digits like its 1999. Let's call some peaks.
Crafting 10 Years of Statistics Explanations: Points of Significance
I don’t have good luck in the match points. —Rafael Nadal, Spanish tennis player
Points of Significance is an ongoing series of short articles about statistics in Nature Methods that started in 2013. Its aim is to provide clear explanations of essential concepts in statistics for a nonspecialist audience. The articles favor heuristic explanations and make extensive use of simulated examples and graphical explanations, while maintaining mathematical rigor.
Topics range from basic, but often misunderstood, such as uncertainty and P-values, to relatively advanced, but often neglected, such as the error-in-variables problem and the curse of dimensionality. More recent articles have focused on timely topics such as modeling of epidemics, machine learning, and neural networks.
In this article, we discuss the evolution of topics and details behind some of the story arcs, our approach to crafting statistical explanations and narratives, and our use of figures and numerical simulations as props for building understanding.
Altman, N. & Krzywinski, M. (2025) Crafting 10 Years of Statistics Explanations: Points of Significance. Annual Review of Statistics and Its Application 12:69–87.
Propensity score matching
I don’t have good luck in the match points. —Rafael Nadal, Spanish tennis player
In many experimental designs, we need to keep in mind the possibility of confounding variables, which may give rise to bias in the estimate of the treatment effect.
If the control and experimental groups aren't matched (or, roughly, similar enough), this bias can arise.
Sometimes this can be dealt with by randomizing, which on average can balance this effect out. When randomization is not possible, propensity score matching is an excellent strategy to match control and experimental groups.
Kurz, C.F., Krzywinski, M. & Altman, N. (2024) Points of significance: Propensity score matching. Nat. Methods 21:1770–1772.