resources
presentations
Let me tell you about something.
lunch break
Distractions and amusements, with a sandwich and coffee.
visualization + design
Pi Day Art Posters — March 14
download
numbers.tgz
1,000,000 digits of π, φ, e and ASN.
buy artwork
All the artwork can be purchased from Fine Art America.
transcend, don't repeat, yourself
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.
So let's explore what Pi looks like with something whimsical and pretty and colourful. Rational art of the highly irrational, a regime where beauty runs with her hair down and lets her "ribbons to flow confusedly." Robert Herrick says it well in Sweet Disorder,
I see a wild civility;—
Do more bewitch me, than when art
Is too precise in every part.
The posters explore the relationship between adjacent digits in Pi, which are encoded by color using the scheme shown above. The design appears to shimmer due to the luminance effect. In some versions of the poster, adjacent identical (or similar) digits are connected by lines.
The recipe for each poster is included and gives the color of the ith outer/inner circle. π[i] is used to represent the ith digit of π. For example, the recipe
π[i] / π[i+1]
generates a poster whose outer circle color encodes the ith digit and the inner circle color encodes the next digit (i+1). In this scheme, inner and outer circles of adjacent positions have the same color.
buy artwork
source and methods
The posters were generated automatically with a Perl script that generated SVG files. Post processing and layout was done in Illustrator. If you are interested in depicting your favourite number this way, let me know.
The design was inspired by the beautiful AIDS posters by Elena Miska.
love in Pi—you can find it here
I calculated Pi to 13,099,586 digits and then I found love.
It's fun to look for words in Pi. I wanted to know the first time that love appears in Pi. When encoded using the scheme a=0, b=1, ..., z=25, love is the digit 1114214. This digit appears first at position 13,099,586 (...892199163111142148187311392...). And, of course, infinitely many times after that.
buy artwork
buy artwork
buy artwork
If you use the scheme a=1, b=2, ..., z=26, then love becomes 1215225. This is first seen at 6,317,696 (...610311912912152256606850141...).
Because the digits of Pi never repeat and are distributed randomly (as far as we know), if you look long enough you'll find all the words in Pi infinitely many times.
700 digits (20 x 35)
π[i] / grey, 80% opacity
buy artwork
π[i] / π[i+1], 80% opacity
buy artwork
2,800 (40 x 70) digits
π[i] / grey, 80% opacity (equal neighbours connected)
buy artwork
π[i] / π[i+1], 80% opacity (equal neighbours connected)
buy artwork
— / π[i+1] (equal neighbours connected, unconnected digits not shown)
buy artwork
π[i] / π[i+1] (equal neighbours connected with line width proportional to difference in neighbour digits d∈{0,1,2}, unconnected digits not shown)
buy artwork
π[i] / π[i+1] (equal neighbours connected with line width proportional to difference in neighbour digits d∈{0..5}, unconnected digits not shown)
buy artwork
Pi (π): — / red (equal neighbours connected, unconnected digits not shown)
Phi (φ): — / white (equal neighbours connected, unconnected digits not shown)
e: — / grey (equal neighbours connected, unconnected digits not shown)
buy artwork
11,400 (80 x 140) digits
π[i] / grey, 80% opacity (equal neighbours connected)
buy artwork
π[i] / π[i+1], 80% opacity (equal neighbours connected)
buy artwork
π[i] / π[i+1] &>
π[i] / grey, 80% opacity (equal neighbours connected, unconnected digits not shown)
buy artwork
π[i] / π[i+1], 80% opacity (equal neighbours connected, unconnected digits not shown)
buy artwork
news + thoughts
Have data, will compare
In the March Points of Significance Nature Methods column, we continue our discussion of t-tests from November (Significance, P values and t-tests).
We look at what happens how uncertainty of two variables combines and how this impacts the increased uncertainty when two samples are compared and highlight the differences between the two-sample and paired t-tests.
When performing any statistical test, it's important to understand and satisfy its requirements. The t-test is very robust with respect to some of its assumptions, but not others. We explore which.
Krzywinski, M. & Altman, N. (2014) Points of Significance: Comparing Samples — Part I Nature Methods 11:215-216.
Krzywinski, M. & Altman, N. (2013) Points of Significance: Significance, P values and t-tests Nature Methods 10:1041-1042.
Circos at British Library Beautiful Science Exhibit
Beautiful Science explores how our understanding of ourselves and our planet has evolved alongside our ability to represent, graph and map the mass data of the time. The exhibit runs 20 February — 26 May 2014 and is free to the public. There is a good Nature blog writeup about it, a piece in The Guardian, and a great video that explains the the exhibit narrated by Johanna Kieniewicz, the curator.
I am privileged to contribute an information graphic to the exhibit in the Tree of Life section. The piece shows how sequence similarity varies across species as a function of evolutionary distance. The installation is a set of 6 30x30 cm backlit panels. They look terrific.
Think outside the bar—box plots
Quick, name three chart types. Line, bar and scatter come to mind. Perhaps you said pie too—tsk tsk. Nobody ever thinks of the box plot.
Box plots reveal details about data without overloading a figure with a full frequency distribution histogram. They're easy to compare and now easy to make with BoxPlotR (try it). In our fifth Points of Significance column, we take a break from the theory to explain this plot type and—I hope— convince you that they're worth thinking about.
The February issue of Nature Methods kicks the bar chart two more times: Dan Evanko's Kick the Bar Chart Habit editorial and a Points of View: Bar charts and box plots column by Mark Streit and Nils Gehlenborg.
Krzywinski, M. & Altman, N. (2014) Points of Significance: Visualizing samples with box plots Nature Methods 11:119-120.
Wired Data|Life 2013 talk
I recently presented at the Wired Data|Life 2013 conference, sharing my thoughts on The Art and Science of Data Visualization.
For specialists, visualizations should expose detail to allow for exploration and inspiration. For enthusiasts, they should provide context, integrate facts and inform. For the layperson, they should capture the essence of the topic, narrate a story and deligt.
Wired's Brandon Keim wrote up a short article about me and some of my work—Circle of Life: The Beautiful New Way to Visualize Biological Data.
Power and Sample Size
Experimental designs that lack power cannot reliably detect real effects. Power of statistical tests is largely unappreciated and many underpowered studies continue to be published.
This month, Naomi and I explain what power is, how it relates to Type I and Type II errors and sample size. By understanding the relationship between these quantities you can design a study that has both low false positive rate and high power.
Krzywinski, M. & Altman, N. (2013) Points of Significance: Power and Sample Size Nature Methods 10:1139-1140.
20 imperatives of science—limits of evidence
20 Tips for Interpreting Scientific Claims is a wonderful comment in Nature warning us about the limits of evidence.
I've made a poster (download hires PDF, PNG) of this list, grouping them into categories that are my own. Thrust this into everyone's hands, including your own.
Sutherland WJ, Spiegelhalter D & Burgman M (2013) Policy: Twenty tips for interpreting scientific claims. Nature 503:335–337.