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
listen; there's a hell of a good universe next door: let's go.e.e. cummingsgo theremore quotes

3.14: 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.

`\pi` Day 2016 Art Posters


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

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

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2015 `\pi` day

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` approx day

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` day

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` day

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2013 `\pi` day

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

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.

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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
All art posters are available for purchase.
I take custom requests.

This year's `\pi` day art collection celebrates not only the digit but also one of the fundamental forces in nature: gravity.

In February of 2016, for the first time, gravitational waves were detected at the Laser Interferometer Gravitational-Wave Observatory (LIGO).

The signal in the detector was sonified—a process by which any data can be encoded into sound to provide hints at patterns and structure that we might otherwise miss—and we finally heard what two black holes sound like. A buzz and chirp.

The art is featured in the Gravity of Pi article on the Scientific American SA Visual blog.

this year's theme music

All the art was processed while listening to Roses by Coeur de Pirate, a brilliant female French-Canadian songwriter, who sounds like a mix of Patricia Kaas and Lhasa. The lyrics Oublie-moi (Forget me) are fitting with this year's theme of gravity.

Mais laisse-moi tomber, laisse-nous tomber
Laisse la nuit trembler en moi
Laisse-moi tomber, laisse nous tomber
Cette fois

But let me fall, let us fall
Let the night tremble in me
Let me fall, let us fall
This time

The Einstein-`\pi` connection

The number `\pi` appears in the fundamental equation of general relativity, which relates gravity (left side) to energy and momentum (right side).

`R_{\mu \nu} - \tfrac{1}{2} Rg_{\mu\nu} = 8 \pi G T_{\mu \nu}`

The reason why `\pi` appears has to do with the need to include the surface area of the sphere, `4 \pi r^2` in the mathematics. This is very nicely described in Sean Carrol's article Einstein and `\pi`.

The gravity of `\pi`

Let's make the digits of `\pi` into masses, throw them into space, and watch gravity make them collide and orbit each other. Read about the details of the simulation and look at the posters.


Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
The first 14 digits of `\pi` generate various orbits as the digits are assigned mass and subject to gravity. (BUY ARTWORK)

As the number of digits is increased, more elaborate patterns arise. Here is one simulation using 100 digits.


Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Things can get a little crazy with mor digits. Here, 153 digits are used. (BUY ARTWORK)

How about 1000 digits? In this simulation the masses are similar and they all collide within the circle.


Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
The first 1000 digits of `\pi` collapse into a single mass. (BUY ARTWORK)

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
The first 3 digits of `\pi` collapse into a single mass. 49 times. (BUY ARTWORK)

VIEW ALL

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