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lunch break
Distractions and amusements, with a sandwich and coffee.
visualization + design
The art of Pi (`\pi`), Phi (`\phi`) and `e`
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 — One Hundred Billion Sparks, Max Cooper | Imagine a neuron firing. Now imagine 100,000,000,000 neurons firing. This is the music for it.
2 — 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?
3 — 99 luftbaloons, Nena | The numerical classic.
Hast du etwas Zeit für mich
Dann singe ich ein Lied für dich
Von 99 Luftballons
4 — 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.
5 — 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.
6 — 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
7 — Pt vs Ys, Yoshinori Sunahara | The first four numbers, in German, are this song's lyrics.
Eins, zwei, drei, vier.
8 — 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'
9 — 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.
10 — Straight to Number One, Touch and Go | Something to listen to after midnight.
Fingers, four, play, three, to number one.
11 — 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.
12 — 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.
13 — 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
14 — 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.
15 — 100 Billion Stars, Lux | Something to relax to while you ponder insignificance.
16 — First Picture, Nikolaj Grandjean | First is the most memorable number.
I remember
The first picture
One million different shadows
Where we've been around the willows
17 — 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
18 — 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.
19 — 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.
news + thoughts
Markov Chains
You can look back there to explain things,
but the explanation disappears.
You'll never find it there.
Things are not explained by the past.
They're explained by what happens now.
—Alan Watts
A Markov chain is a probabilistic model that is used to model how a system changes over time as a series of transitions between states. Each transition is assigned a probability that defines the chance of the system changing from one state to another.
Together with the states, these transitions probabilities define a stochastic model with the Markov property: transition probabilities only depend on the current state—the future is independent of the past if the present is known.
Once the transition probabilities are defined in matrix form, it is easy to predict the distribution of future states of the system. We cover concepts of aperiodicity, irreducibility, limiting and stationary distributions and absorption.
This column is the first part of a series and pairs particularly well with Alan Watts and Blond:ish.
Grewal, J., Krzywinski, M. & Altman, N. (2019) Points of significance: Markov Chains. Nature Methods 16:663–664.
1-bit zoomable gigapixel maps of Moon, Solar System and Sky
Places to go and nobody to see.
Exquisitely detailed maps of places on the Moon, comets and asteroids in the Solar System and stars, deep-sky objects and exoplanets in the northern and southern sky. All maps are zoomable.
Quantile regression
Quantile regression robustly estimates the typical and extreme values of a response.Quantile regression explores the effect of one or more predictors on quantiles of the response. It can answer questions such as "What is the weight of 90% of individuals of a given height?"
Unlike in traditional mean regression methods, no assumptions about the distribution of the response are required, which makes it practical, robust and amenable to skewed distributions.
Quantile regression is also very useful when extremes are interesting or when the response variance varies with the predictors.
Das, K., Krzywinski, M. & Altman, N. (2019) Points of significance: Quantile regression. Nature Methods 16:451–452.
Background reading
Altman, N. & Krzywinski, M. (2015) Points of significance: Simple linear regression. Nature Methods 12:999–1000.
Analyzing outliers: Robust methods to the rescue
Robust regression generates more reliable estimates by detecting and downweighting outliers.Outliers can degrade the fit of linear regression models when the estimation is performed using the ordinary least squares. The impact of outliers can be mitigated with methods that provide robust inference and greater reliability in the presence of anomalous values.
We discuss MM-estimation and show how it can be used to keep your fitting sane and reliable.
Greco, L., Luta, G., Krzywinski, M. & Altman, N. (2019) Points of significance: Analyzing outliers: Robust methods to the rescue. Nature Methods 16:275–276.
Background reading
Altman, N. & Krzywinski, M. (2016) Points of significance: Analyzing outliers: Influential or nuisance. Nature Methods 13:281–282.
Two-level factorial experiments
To find which experimental factors have an effect, simultaneously examine the difference between the high and low levels of each.Two-level factorial experiments, in which all combinations of multiple factor levels are used, efficiently estimate factor effects and detect interactions—desirable statistical qualities that can provide deep insight into a system.
They offer two benefits over the widely used one-factor-at-a-time (OFAT) experiments: efficiency and ability to detect interactions.
Since the number of factor combinations can quickly increase, one approach is to model only some of the factorial effects using empirically-validated assumptions of effect sparsity and effect hierarchy. Effect sparsity tells us that in factorial experiments most of the factorial terms are likely to be unimportant. Effect hierarchy tells us that low-order terms (e.g. main effects) tend to be larger than higher-order terms (e.g. two-factor or three-factor interactions).
Smucker, B., Krzywinski, M. & Altman, N. (2019) Points of significance: Two-level factorial experiments Nature Methods 16:211–212.
Background reading
Krzywinski, M. & Altman, N. (2014) Points of significance: Designing comparative experiments.. Nature Methods 11:597–598.
Happy 2019 `\pi` Day—
Digits, internationally
Celebrate `\pi` Day (March 14th) and set out on an exploration explore accents unknown (to you)!
This year is purely typographical, with something for everyone. Hundreds of digits and hundreds of languages.
A special kids' edition merges math with color and fat fonts.
Check out art from previous years: 2013 `\pi` Day and 2014 `\pi` Day, 2015 `\pi` Day, 2016 `\pi` Day, 2017 `\pi` Day and 2018 `\pi` Day.