π Day 2026 Art Posters - Art for the 5%
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.
Nature’s first green is gold,
Her hardest hue to hold.
— Robert Frost (Nothing Gold Can Stay)
Welcome to this year's celebration of `\pi` and mathematics.
The theme this year is a homage to Shinobu Ishihara (1879–1963) and embodies the Japanese saying "To show something, hide something.".
This year, the digits of `\pi` are discernable only by people with colorblindness. It's the only test where a negative is a positive!
This year's `\pi` poem is Nothing Gold Can Stay by Robert Frost.
This year's `\pi` day song is Colors by Laleh.
contents
If you can't see anything, you're ok.
If you can see something, you're not ok.
Mostly.
It's because you have a piercing stare.
People with normal color vision will always see more information than people affected by colour blindness. Depending on your committment, patters will reveal themselves to you eventually.
This year's art is for the 5% of you (men) out there that have colour deficiency due to shortage (or lack of) M-cones. This 5% makes up most of the population (about 8%) affected by some kind of colour deficiency.
That's a number that's not zero — it deserves its own art.
Colour blindness makes it difficult to distinguish certain colours and to buy clothes or choose matching curtains.
Depending on the degree of deficiency, your experience may vary from merely having trouble to being completely insensitive to colour differences.
Color pairs that give you troubles are called confusion colours (duh). Another term for them is metameric colours, but that's not as fun to say.
For example, if you have deuteranopia, you cannot distinguish the three colour pairs (among many others) and Spock becomes invisible.
If you have deuteranomaly (partial deficit), you may still see Spock but with some amount of difficulty.
I have a lot of resources about colour blindness. Take a look at my colour palettes for colour blindness and a deep dive into the math of colour blindness, on which this year's `\pi` Day art is based.
Ishihara's Tests for Colour Deficiency are drawings of numbers (and other shapes) that make use of confusion colours to test for colour deficiency.
I've spent quite a bit of time photographing these plates and providing an authentic and colour-accurate set of images for each plate.
If you've seen Ishihara's test plates, you've probably seen one of the vanishing plates.
On these plates, the number of obvious to someone with normal vision but not visible to someone with colour blindness.
The choice of colours on transformation plates is relatively easy to understand — confusion colours are used for both the background and the digit.
In Ishihara's 38-plate book, there are 4 mysterious “hidden” plates.
These are truly vexing — they hide the digit from someone with normal vision but make it visible to someone with colour blindness.
This year's `\pi` Day art is inspired by these plates.
This year's art pays respects to Ishihara's Tests for Colour Deficiency and the Japanese adage “To show something, hide something.”.
What did you see? Hint: it's `\pi` day.
If you have normal vision, there's a small chance that you saw something.
If you have deuteranopia, there's a large chance that you saw something.
The effect is subtle. We all see what we want to see.
In the pattern is the symbol for `\pi` (surprise!). The dots that make up the digit (a few spill outside too) are colored with colors largely sampled from a line of confusion — a set of colors that look identical to someone with colour blindness.
The background of the art is made up of colors sampled from a different line of confusion.
This is what the whole thing looks like to a normal eye and a deuteranope.
Confused yet? Read about the method behind the art and look at the posters.
There is a variety of posters (and postcards) that will hurt your eyes.
Here's one of them — a 50 cm × 70 cm test where a positive is a negative.
Happy 2026 π Day—
Art for the 5%
Celebrate π Day (March 14th) and enjoy the art — but only if you're part of the 5%.
Go ahead, see what you can't see.
Ishihara's Tests for Colour Deficiency
Authentic and accurate images of Ishihara's test plates photographed (and lovingly color-corrected) from the 38-plate Ishihara's Tests for Colour Deficiency.
I also provide the position, size, and color of each circle on each test plate.
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.
Understanding p-values and significance
P-values combined with estimates of effect size are used to assess the importance of experimental results. However, their interpretation can be invalidated by selection bias when testing multiple hypotheses, fitting multiple models or even informally selecting results that seem interesting after observing the data.
We offer an introduction to principled uses of p-values (targeted at the non-specialist) and identify questionable practices to be avoided.
Altman, N. & Krzywinski, M. (2024) Understanding p-values and significance. Laboratory Animals 58:443–446.
Depicting variability and uncertainty using intervals and error bars
Variability is inherent in most biological systems due to differences among members of the population. Two types of variation are commonly observed in studies: differences among samples and the “error” in estimating a population parameter (e.g. mean) from a sample. While these concepts are fundamentally very different, the associated variation is often expressed using similar notation—an interval that represents a range of values with a lower and upper bound.
In this article we discuss how common intervals are used (and misused).
Altman, N. & Krzywinski, M. (2024) Depicting variability and uncertainty using intervals and error bars. Laboratory Animals 58:453–456.