Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - contact me Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca on Twitter Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Lumondo Photography Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Pi Art Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Hilbertonians - Creatures on the Hilbert Curve
In your hiding, you're alone. Kept your treasures with my bones.Coeur de Piratecrawl somewhere bettermore quotes

similarity: fun


EMBO Practical Course: Bioinformatics and Genome Analysis, 5–17 June 2017.


visualization + design

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The 2016 Pi Day art imagines the digits of Pi as physical masses collapsing under gravity and is featured in the articles The Gravity of Pi and The Boundless Beauty of Pi at the Scientific American SA Visual blog.

The art of Pi (`\pi`), Phi (`\phi`) and `e`


Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 `\pi` approximation day

Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 `\pi` day

Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2015 `\pi` day

Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` approx day

Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` day

Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` day

Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2013 `\pi` day

Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Circular `\pi` art

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

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Like music with numbers? Try Angels at My Door (Una), Pt vs Ys (Yoshinori Sunahara), 2wicky (Hooverphonic), One (Aimee Mann), Straight to Number One (Touch and Go), 99 luftbaloons (Nena).

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


Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
2,258 digits of `\phi`, 3,855 digits of `e` and 3,628 digits of `\pi` in 6 level treemaps. Uniform line thickness. Bauhaus prime colors in Piet Mondrian style. (2015 `\pi` day posters, BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
All art posters are available for purchase.
I take custom requests.

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`).


Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
2,258 digits of `\phi`, 3,855 digits of `e` and 3,628 digits of `\pi` in 6 level treemaps. Uniform line thickness. Bauhaus prime colors in Piet Mondrian style. (2016 `\pi` day posters, BUY ARTWORK)

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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news + thoughts

Essentials of Data Visualization—8-part video series

Mon 16-01-2017
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca

In collaboration with the Phil Poronnik and Kim Bell-Anderson at the University of Sydney, I'm delighted to share with you our 8-part video series project about thinking about drawing data and communicating science.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Essentials of Data Visualization: Thinking about drawing data and communicating science.

We've created 8 videos, each focusing on a different essential idea in data visualization: encoding, shapes, color, uncertainty, design, drawing missing or unobserved data, labels and process.

The videos were designed as teaching materials. Each video comes with a slide deck and exercises.

P values and the search for significance

Mon 16-01-2017
Little P value
What are you trying to say
Of significance?
—Steve Ziliak

We've written about P values before and warned readers about common misconceptions about them, which are so rife that the American Statistical Association itself has a long statement about them.

This month is our first of a two-part article about P values. Here we look at 'P value hacking' and 'data dredging', which are questionable practices that invalidate the correct interpretation of P values.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: P values and the search for significance. (read)

We also illustrate how P values can lead us astray by asking "What is the smallest P value we can expect if the null hypothesis is true but we have done many tests, either explicitly or implicitly?"

Incidentally, this is our first column in which the standfirst is a haiku.

Altman, N. & Krzywinski, M. (2017) Points of Significance: P values and the search for significance. Nature Methods 14:3–4.

Background reading

Krzywinski, M. & Altman, N. (2013) Points of significance: Significance, P values and t–tests. Nature Methods 10:1041–1042.

...more about the Points of Significance column

Intuitive Design

Thu 03-11-2016

Appeal to intuition when designing with value judgments in mind.

Figure clarity and concision are improved when the selection of shapes and colors is grounded in the Gestalt principles, which describe how we visually perceive and organize information.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
One of the Gestalt principles tells us that the magenta and green shapes will be perceived as as two groups, overriding the fact that the shapes within the group might be different. What the principle does not tell us is how the reader is likely to value each group. (read)

The Gestalt principles are value free. For example, they tell us how we group objects but do not speak to any meaning that we might intuitively infer from visual characteristics.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of View column: Intuitive Design. (read)

This month, we discuss how appealing to such intuitions—related to shapes, colors and spatial orientation— can help us add information to a figure as well as anticipate and encourage useful interpretations.

Krzywinski, M. (2016) Points of View: Intuitive Design. Nature Methods 13:895.

...more about the Points of View column

Regularization

Fri 04-11-2016

Constraining the magnitude of parameters of a model can control its complexity.

This month we continue our discussion about model selection and evaluation and address how to choose a model that avoids both overfitting and underfitting.

Ideally, we want to avoid having either an underfitted model, which is usually a poor fit to the training data, or an overfitted model, which is a good fit to the training data but not to new data.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Regularization (read)

Regularization is a process that penalizes the magnitude of model parameters. This is done by not only minimizing the SSE, `\mathrm{SSE} = \sum_i (y_i - \hat{y}_i)^2 `, as is done normally in a fit, but adding to this minimized quantity the sum of the mode's squared parameters, `\mathrm{SSE} + \lambda \sum_i \hat{\beta}^2_i`.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Regularization. Nature Methods 13:803-804.

Background reading

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Model Selection and Overfitting. Nature Methods 13:703-704.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Classifier evaluation. Nature Methods 13:603-604.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Logistic regression. Nature Methods 13:541-542.

...more about the Points of Significance column

Model Selection and Overfitting

Fri 04-11-2016

With four parameters I can fit an elephant and with five I can make him wiggle his trunk. —John von Neumann.

By increasing the complexity of a model, it is easy to make it fit to data perfectly. Does this mean that the model is perfectly suitable? No.

When a model has a relatively large number of parameters, it is likely to be influenced by the noise in the data, which varies across observations, as much as any underlying trend, which remains the same. Such a model is overfitted—it matches training data well but does not generalize to new observations.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Model Selection and Overfitting (read)

We discuss the use of training, validation and testing data sets and how they can be used, with methods such as cross-validation, to avoid overfitting.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Model Selection and Overfitting. Nature Methods 13:703-704.

Background reading

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Classifier evaluation. Nature Methods 13:603-604.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Logistic regression. Nature Methods 13:541-542.

...more about the Points of Significance column

Classifier Evaluation

Tue 13-09-2016

It is important to understand both what a classification metric expresses and what it hides.

We examine various metrics use to assess the performance of a classifier. We show that a single metric is insufficient to capture performance—for any metric, a variety of scenarios yield the same value.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Classifier Evaluation (read)

We also discuss ROC and AUC curves and how their interpretation changes based on class balance.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Classifier evaluation. Nature Methods 13:603-604.

Background reading

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Logistic regression. Nature Methods 13:541-542.

...more about the Points of Significance column