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# pi: beautiful

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

# visualization + design

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 $e$

2016 $\pi$ approximation day
2016 $\pi$ day
2015 $\pi$ day
2014 $\pi$ approx day
2014 $\pi$ day
2014 $\pi$ day
2013 $\pi$ day
Circular $\pi$ art

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.

All of the posters are listed in the posters section. Some also appear in the methods section, where I describe how they were made. Most of the circular art was made with Circos.

Circular and spiral art based on the digits of $\pi$, $\phi$ and $e$.

Some of the art shown here has been featured in a Numberphile video.

Progression and transition for the first 1,000 digits of $\pi$. Created with Circos. (PNG, BUY ARTWORK)
Progression and transition for the first 2,000 digits of $\pi$, $\phi$ and $e$. Created with Circos. (PNG, BUY ARTWORK)
Distribution of the first 13,689 digits of π. (PNG, BUY ARTWORK)

Progression and transition for the first 1,000 digits of $\pi$, $\phi$ and $e$. Created with Circos. (PNG, BUY ARTWORK)
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# Snellen Charts—Typography to Really Look at

Sat 18-02-2017

Another collection of typographical posters. These ones really ask you to look.

Snellen charts designed using physical constants, Braille and elemental abundances in the universe and human body.

The charts show a variety of interesting symbols and operators found in science and math. The design is in the style of a Snellen chart and typset with the Rockwell font.

# Essentials of Data Visualization—8-part video series

Fri 17-02-2017

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.

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.

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.

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

# 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.

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.

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.

# 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.

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.

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.

# 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.

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.