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# pi: fun

In Silico Flurries: Computing a world of snow. Scientific American. 23 December 2017

# visualization + design

The 2017 Pi Day art imagines the digits of Pi as a star catalogue with constellations of extinct animals and plants. The work is featured in the article Pi in the Sky at the Scientific American SA Visual blog.

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

2017 $\pi$ day
2016 $\pi$ approximation day
2016 $\pi$ day
2015 $\pi$ day
2014 $\pi$ approx day
2014 $\pi$ day
2013 $\pi$ day
Circular $\pi$ art

Like music with numbers? Here's a short list of some of my favourite songs that have numbers in their lyrics. Absolutely none of them is about bottles of beer.

## music with numbers

1 — Numbers, Smoke City | This song is entirely composed of references to different numbers. The bonus? It's both in English and Portuguese. I love the way it ends—"Isn't it beautiful out here?".

Un
Un
Four
Five

Fifteen
Quinze
Seventeen
Seven

...

Tres
forty nine

Isn't it beautiful out here?
Isn't it beautiful out here?
Isn't it beautiful out here?

2 — 99 luftbaloons, Nena | The numerical classic.

Hast du etwas Zeit für mich
Dann singe ich ein Lied für dich
Von 99 Luftballons

3 — One, Aimee Mann | Beautiful mathematics of relationships using small numbers.

One is the lonliest number that you'll ever do. Two can be as bad as one, it's the lonliest number since the number one.

4 — Angels at My Door, Una | Long sequences of numbers.

58, 56, 54 angels at my door.
63, 62, 61, 60, 59, 58 angels at my gate.

5 — Tricky, Tricky, Royksopp | Number words about the fearful six from Norway.

Six afraid of seven 'cause seven, eight, nine
I'm about to lose it the second time

6 — Pt vs Ys, Yoshinori Sunahara | The first four numbers, in German, are this song's lyrics.

Eins, zwei, drei, vier.

7 — Der Kommissar, Falco | Unlike the previous song, this one starts with a German count (doesn't get to vier, though) and just gets better from there.

Two, three, four
Eins, zwei, drei
Na, es is nix dabei
Na, wenn ich euch erzähl' die G'schicht'

8 — 2wicky, Hooverphonic | The numbers likely reference the Prophet-600 and SH-101 synthesizers.

Prophet 60091.
Before we start you should know that you're not the only one who can hurt me.
SH10151.
This is the serial number of our orbital gun.
SH10151.
You better be sure before you leave me for another one.

9 — Straight to Number One, Touch and Go | Something to listen to after midnight.

Fingers, four, play, three, to number one.

10 — The Beat Experience, Pepe Deluxe | I am reminded of this song at too many academic seminars.

Here we are now, at the middle, of the fourth large part of this talk.
More and more I have the feeling that we are getting nowhere.
Slowly, as the talk goes on, we are getting nowhere.
And that is a pleasure.

It is not irritating where one is.
It is only irritating to think one would like to be somewhere else.
Here we are now, a little bit after the middle, of the fourth large part of this talk.

11 — Thousand Kisses Deep, Leonard Cohen | A list of songs that doesn't include one by Cohen is not worth reading. The sentiment of a thousand kisses is as old as lips existed. Catullus wrote to Lesbia "da mi basia mille, deinde centum, dein mille altera, dein secunda centum, deinde usque altera mille, deinde centum" [Give me a thousand kisses, then a hundred, then another thousand, then a second hundred, then yet another thousand, then a hundred.] Well, you get the idea.

And sometimes when the night is slow,
The wretched and the meek,
We gather up our hearts and go,
A Thousand Kisses Deep.

12 — Six Seven Times, Flunk | Curiously the product here is 42. This song is the answer to life.

You've got it all
Six seven times
You've got it all
Makes me feel so fine
And it's all there is

13 — 7 seconds, Youssou N'Dour | Dreamy references to a short period of time.

7 seconds away. Just as long as I stay. I'll be waiting.

14 — 100 Billion Stars, Lux | Something to relax to while you ponder insignificance.

15 — First Picture, Nikolaj Grandjean | First is the most memorable number.

I remember
The first picture
Where we've been around the willows

16 — Millions of Millions, Music for a French Elevator | Very desirable. And I can't believe I transcribed the whole thing.

5.50 million dollars, 2.6775 and very desirable 8 million dollars 5.6 million and 2.4 million 3.4 million and 2.9 million 1.2 would've amounted to 4 million 1.2 million 19.4 million 6.6 million 5.275 million 1.2 million 3-and-a-half million dollars 6.453 million 8 million 5.050 million 1.4 million close to a million dollars 933.5 million 3.8 million 5 million dollars 2-and-a-half million 600 million dollars can you shut the door? 3-and-a-half million dollars 2.5 million .050 million 572,750 thousand 5.050 million 3.8 million 3 million 150 thousand 8 million 419.5 million

17 — Love Potion #9, The Searchers | I started kissing everythying in sight.

It smelled like turpentine, it looked like Indian ink
I held my nose, I closed my eyes, I took a drink.

18 — 93 Million Miles, Luan Santana feat. John Kip | A little sticky, a little sweet but it makes up for the fact that much of it is in Portuguese.

But the absence of the light is a necessary part.

VIEW ALL

# Machine learning: supervised methods (SVM & kNN)

Thu 18-01-2018
Supervised learning algorithms extract general principles from observed examples guided by a specific prediction objective.

We examine two very common supervised machine learning methods: linear support vector machines (SVM) and k-nearest neighbors (kNN).

SVM is often less computationally demanding than kNN and is easier to interpret, but it can identify only a limited set of patterns. On the other hand, kNN can find very complex patterns, but its output is more challenging to interpret.

Nature Methods Points of Significance column: Machine learning: supervised methods (SVM & kNN). (read)

We illustrate SVM using a data set in which points fall into two categories, which are separated in SVM by a straight line "margin". SVM can be tuned using a parameter that influences the width and location of the margin, permitting points to fall within the margin or on the wrong side of the margin. We then show how kNN relaxes explicit boundary definitions, such as the straight line in SVM, and how kNN too can be tuned to create more robust classification.

Bzdok, D., Krzywinski, M. & Altman, N. (2018) Points of Significance: Machine learning: a primer. Nature Methods 15:5–6.

Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: a primer. Nature Methods 14:1119–1120.

# Human Versus Machine

Tue 16-01-2018
Balancing subjective design with objective optimization.

In a Nature graphics blog article, I present my process behind designing the stark black-and-white Nature 10 cover.

Nature 10, 18 December 2017

# Machine learning: a primer

Thu 18-01-2018
Machine learning extracts patterns from data without explicit instructions.

In this primer, we focus on essential ML principles— a modeling strategy to let the data speak for themselves, to the extent possible.

The benefits of ML arise from its use of a large number of tuning parameters or weights, which control the algorithm’s complexity and are estimated from the data using numerical optimization. Often ML algorithms are motivated by heuristics such as models of interacting neurons or natural evolution—even if the underlying mechanism of the biological system being studied is substantially different. The utility of ML algorithms is typically assessed empirically by how well extracted patterns generalize to new observations.

Nature Methods Points of Significance column: Machine learning: a primer. (read)

We present a data scenario in which we fit to a model with 5 predictors using polynomials and show what to expect from ML when noise and sample size vary. We also demonstrate the consequences of excluding an important predictor or including a spurious one.

Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: a primer. Nature Methods 14:1119–1120.

# Snowflake simulation

Tue 16-01-2018
Symmetric, beautiful and unique.

Just in time for the season, I've simulated a snow-pile of snowflakes based on the Gravner-Griffeath model.

A few of the beautiful snowflakes generated by the Gravner-Griffeath model. (explore)

The work is described as a wintertime tale in In Silico Flurries: Computing a world of snow and co-authored with Jake Lever in the Scientific American SA Blog.

Gravner, J. & Griffeath, D. (2007) Modeling Snow Crystal Growth II: A mesoscopic lattice map with plausible dynamics.

# Genes that make us sick

Wed 22-11-2017
Where disease hides in the genome.

My illustration of the location of genes in the human genome that are implicated in disease appears in The Objects that Power the Global Economy, a book by Quartz.

The location of genes implicated in disease in the human genome, shown here as a spiral. (more...)

# Ensemble methods: Bagging and random forests

Wed 22-11-2017
Many heads are better than one.

We introduce two common ensemble methods: bagging and random forests. Both of these methods repeat a statistical analysis on a bootstrap sample to improve the accuracy of the predictor. Our column shows these methods as applied to Classification and Regression Trees.

Nature Methods Points of Significance column: Ensemble methods: Bagging and random forests. (read)

For example, we can sample the space of values more finely when using bagging with regression trees because each sample has potentially different boundaries at which the tree splits.

Random forests generate a large number of trees by not only generating bootstrap samples but also randomly choosing which predictor variables are considered at each split in the tree.

Krzywinski, M. & Altman, N. (2017) Points of Significance: Ensemble methods: bagging and random forests. Nature Methods 14:933–934.