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visualization + math

π Day 2024 Art Posters - A community garden of digits of π
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
2024 π DAY | 768 digits of `\pi` as a garden at night. Explore the gardens (BUY ARTWORK)

`\pi` Day 2019 Art Posters - Digits, internationally.


Pi Day 2019 Art Posters  - Digits, internationally.
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2021 π DAY | Good things grow for those who wait.' edition.

Pi Day 2019 Art Posters  - Digits, internationally.
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2019 π DAY | Hundreds of digits, hundreds of languages and a special kids' edition.

Pi Day 2019 Art Posters  - Digits, internationally.
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2018 π DAY | Street maps to new destinations.

Pi Day 2019 Art Posters  - Digits, internationally.
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2017 π DAY | Imagine the sky in a new way.


Pi Day 2019 Art Posters  - Digits, internationally.
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 π APPROXIMATION DAY | What would happen if about right was right.

Pi Day 2019 Art Posters  - Digits, internationally.
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 π DAY | These digits really fall for each other.

Pi Day 2019 Art Posters  - Digits, internationally.
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2015 π DAY | A transcendental experience.

Pi Day 2019 Art Posters  - Digits, internationally.
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 π APPROXIMATION DAY | Spirals into roughness.


Pi Day 2019 Art Posters  - Digits, internationally.
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 π DAY | Hypnotizes you into looking.

Pi Day 2019 Art Posters  - Digits, internationally.
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 π DAY | Come into the fold.

Pi Day 2019 Art Posters  - Digits, internationally.
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2013 π DAY | Where it started.

Pi Day 2019 Art Posters  - Digits, internationally.
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
CIRCULAR π ART | And other distractions.

On March 14th celebrate `\pi` Day. Hug `\pi`—find a way to do it.

For those who favour `\tau=2\pi` will have to postpone celebrations until July 26th. That's what you get for thinking that `\pi` is wrong. I sympathize with this position and have `\tau` day art too!

If you're not into details, you may opt to party on July 22nd, which is `\pi` approximation day (`\pi` ≈ 22/7). It's 20% more accurate that the official `\pi` day!

Finally, if you believe that `\pi = 3`, you should read why `\pi` is not equal to 3.

Most of the art is available for purchase as framed prints and, yes, even pillows. Sleep's never been more important — I take custom requests.

How many ages hence
Shall this our lofty scene be acted over
In states unborn and accents yet unknown!
—Willian Shakespeare (Julius Caesar, Act III, Scene 1)

Welcome to this year's celebration of `\pi` and mathematics.

The theme this year is typographical and pure—in contrast to last year's extremely elaborate computational art. This year is also the first time I have made a special kids' edition!

This year's poem is by Viorica Hrincu and it is about complications.

This year's `\pi` day song is Tshinanu by Kashtin.

If you enjoy art based on type, explore my other typographical works.

Tshinanu is written and performed by Kashtin in Innu-aimun, an Algonquian Cree language known by only about 10,000 people in Quebec and Labrador in Canada.

Perfect for listening to a language you probably don't understand.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Tshinanu by Kashtin. (listen)


Tshinanu

Tshinanu (What We All Are) Tshinanu ui tshissentetau Tshinanu tshinanu Tshinanu uauatetau Tshinanu tshmeshkananmenu Tshinanu u... u... u... Tshituassminut Tshinanu u... u... u... Tshinanu ui tshissentetau Tshinanu tshinanu Tshinanu uauatetau Tshinanu tshmeshkananmenu Tshinanu u... u... u... Tshituassminut Tshinanu u... u... u... Tshinanu ui tshissentetau Tshinanu tshinanu Tshinanu uauatetau Tshinanu tshmeshkananmenu Tshinanu u... u... u... Tshituassminut Tshinanu u... u... u... Tshinanu u... u... Shtapuenanu


—Tshinanu (What We Are), Kashtin


Tshinanu

Tshinanu (What We All Are) [English translation] All of us All of us Let us look at our way of life Our children Our grandfathers All of us All of us Let us look at our way of life Our rivers Our lands This is our reason


—Tshinanu (What We Are) [English translation], Kashtin
news + thoughts

Nasa to send our human genome discs to the Moon

Sat 23-03-2024

We'd like to say a ‘cosmic hello’: mathematics, culture, palaeontology, art and science, and ... human genomes.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
SANCTUARY PROJECT | A cosmic hello of art, science, and genomes. (details)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
SANCTUARY PROJECT | Benoit Faiveley, founder of the Sanctuary project gives the Sanctuary disc a visual check at CEA LeQ Grenoble (image: Vincent Thomas). (details)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
SANCTUARY PROJECT | Sanctuary team examines the Life disc at INRIA Paris Saclay (image: Benedict Redgrove) (details)

Comparing classifier performance with baselines

Sat 23-03-2024

All animals are equal, but some animals are more equal than others. —George Orwell

This month, we will illustrate the importance of establishing a baseline performance level.

Baselines are typically generated independently for each dataset using very simple models. Their role is to set the minimum level of acceptable performance and help with comparing relative improvements in performance of other models.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Comparing classifier performance with baselines. (read)

Unfortunately, baselines are often overlooked and, in the presence of a class imbalance5, must be established with care.

Megahed, F.M, Chen, Y-J., Jones-Farmer, A., Rigdon, S.E., Krzywinski, M. & Altman, N. (2024) Points of significance: Comparing classifier performance with baselines. Nat. Methods 20.

Happy 2024 π Day—
sunflowers ho!

Sat 09-03-2024

Celebrate π Day (March 14th) and dig into the digit garden. Let's grow something.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2024 π DAY | A garden of 1,000 digits of π. (details)

How Analyzing Cosmic Nothing Might Explain Everything

Thu 18-01-2024

Huge empty areas of the universe called voids could help solve the greatest mysteries in the cosmos.

My graphic accompanying How Analyzing Cosmic Nothing Might Explain Everything in the January 2024 issue of Scientific American depicts the entire Universe in a two-page spread — full of nothing.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
How Analyzing Cosmic Nothing Might Explain Everything. Text by Michael Lemonick (editor), art direction by Jen Christiansen (Senior Graphics Editor), source: SDSS

The graphic uses the latest data from SDSS 12 and is an update to my Superclusters and Voids poster.

Michael Lemonick (editor) explains on the graphic:

“Regions of relatively empty space called cosmic voids are everywhere in the universe, and scientists believe studying their size, shape and spread across the cosmos could help them understand dark matter, dark energy and other big mysteries.

To use voids in this way, astronomers must map these regions in detail—a project that is just beginning.

Shown here are voids discovered by the Sloan Digital Sky Survey (SDSS), along with a selection of 16 previously named voids. Scientists expect voids to be evenly distributed throughout space—the lack of voids in some regions on the globe simply reflects SDSS’s sky coverage.”

voids

Sofia Contarini, Alice Pisani, Nico Hamaus, Federico Marulli Lauro Moscardini & Marco Baldi (2023) Cosmological Constraints from the BOSS DR12 Void Size Function Astrophysical Journal 953:46.

Nico Hamaus, Alice Pisani, Jin-Ah Choi, Guilhem Lavaux, Benjamin D. Wandelt & Jochen Weller (2020) Journal of Cosmology and Astroparticle Physics 2020:023.

Sloan Digital Sky Survey Data Release 12

constellation figures

Alan MacRobert (Sky & Telescope), Paulina Rowicka/Martin Krzywinski (revisions & Microscopium)

stars

Hoffleit & Warren Jr. (1991) The Bright Star Catalog, 5th Revised Edition (Preliminary Version).

cosmology

H0 = 67.4 km/(Mpc·s), Ωm = 0.315, Ωv = 0.685. Planck collaboration Planck 2018 results. VI. Cosmological parameters (2018).

Error in predictor variables

Tue 02-01-2024

It is the mark of an educated mind to rest satisfied with the degree of precision that the nature of the subject admits and not to seek exactness where only an approximation is possible. —Aristotle

In regression, the predictors are (typically) assumed to have known values that are measured without error.

Practically, however, predictors are often measured with error. This has a profound (but predictable) effect on the estimates of relationships among variables – the so-called “error in variables” problem.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Error in predictor variables. (read)

Error in measuring the predictors is often ignored. In this column, we discuss when ignoring this error is harmless and when it can lead to large bias that can leads us to miss important effects.

Altman, N. & Krzywinski, M. (2024) Points of significance: Error in predictor variables. Nat. Methods 20.

Background reading

Altman, N. & Krzywinski, M. (2015) Points of significance: Simple linear regression. Nat. Methods 12:999–1000.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of significance: Logistic regression. Nat. Methods 13:541–542 (2016).

Das, K., Krzywinski, M. & Altman, N. (2019) Points of significance: Quantile regression. Nat. Methods 16:451–452.

Convolutional neural networks

Tue 02-01-2024

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).

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Convolutional neural networks. (read)

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 20:1269–1270.

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.

Martin Krzywinski | contact | Canada's Michael Smith Genome Sciences CentreBC Cancer Research CenterBC CancerPHSA
Google whack “vicissitudinal corporealization”
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