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.
Convolutional neural networks
Nature uses only the longest threads to weave her patterns, so that each small piece of her fabric reveals the organization of the entire tapestry. – Richard Feynman
Following up on our Neural network primer column, this month we explore a different kind of network architecture: a convolutional network.
The convolutional network replaces the hidden layer of a fully connected network (FCN) with one or more filters (a kind of neuron that looks at the input within a narrow window).
Even through convolutional networks have far fewer neurons that an FCN, they can perform substantially better for certain kinds of problems, such as sequence motif detection.
Derry, A., Krzywinski, M & Altman, N. (2023) Points of significance: Convolutional neural networks. Nature Methods 20:.
Background reading
Derry, A., Krzywinski, M. & Altman, N. (2023) Points of significance: Neural network primer. Nature Methods 20:165–167.
Lever, J., Krzywinski, M. & Altman, N. (2016) Points of significance: Logistic regression. Nature Methods 13:541–542.
Neural network primer
Nature is often hidden, sometimes overcome, seldom extinguished. —Francis Bacon
In the first of a series of columns about neural networks, we introduce them with an intuitive approach that draws from our discussion about logistic regression.
Simple neural networks are just a chain of linear regressions. And, although neural network models can get very complicated, their essence can be understood in terms of relatively basic principles.
We show how neural network components (neurons) can be arranged in the network and discuss the ideas of hidden layers. Using a simple data set we show how even a 3-neuron neural network can already model relatively complicated data patterns.
Derry, A., Krzywinski, M & Altman, N. (2023) Points of significance: Neural network primer. Nature Methods 20:165–167.
Background reading
Lever, J., Krzywinski, M. & Altman, N. (2016) Points of significance: Logistic regression. Nature Methods 13:541–542.
Cell Genomics cover
Our cover on the 11 January 2023 Cell Genomics issue depicts the process of determining the parent-of-origin using differential methylation of alleles at imprinted regions (iDMRs) is imagined as a circuit.
Designed in collaboration with with Carlos Urzua.
Akbari, V. et al. Parent-of-origin detection and chromosome-scale haplotyping using long-read DNA methylation sequencing and Strand-seq (2023) Cell Genomics 3(1).
Browse my gallery of cover designs.
Science Advances cover
My cover design on the 6 January 2023 Science Advances issue depicts DNA sequencing read translation in high-dimensional space. The image showss 672 bases of sequencing barcodes generated by three different single-cell RNA sequencing platforms were encoded as oriented triangles on the faces of three 7-dimensional cubes.
More details about the design.
Kijima, Y. et al. A universal sequencing read interpreter (2023) Science Advances 9.
Browse my gallery of cover designs.
Regression modeling of time-to-event data with censoring
If you sit on the sofa for your entire life, you’re running a higher risk of getting heart disease and cancer. —Alex Honnold, American rock climber
In a follow-up to our Survival analysis — time-to-event data and censoring article, we look at how regression can be used to account for additional risk factors in survival analysis.
We explore accelerated failure time regression (AFTR) and the Cox Proportional Hazards model (Cox PH).
Dey, T., Lipsitz, S.R., Cooper, Z., Trinh, Q., Krzywinski, M & Altman, N. (2022) Points of significance: Regression modeling of time-to-event data with censoring. Nature Methods 19:1513–1515.
Music video for Max Cooper's Ascent
My 5-dimensional animation sets the visual stage for Max Cooper's Ascent from the album Unspoken Words. I have previously collaborated with Max on telling a story about infinity for his Yearning for the Infinite album.
I provide a walkthrough the video, describe the animation system I created to generate the frames, and show you all the keyframes
The video recently premiered on YouTube.
Renders of the full scene are available as NFTs.