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Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
WELCOME TO THE 5TH DIMENSION | This isn't meant to be understood — it's meant to be enjoyed.
Love music and science? Explore my collaboration with Max Cooper where we tell the story of infinities and animate the digits of π. Both tracks appear on Max's Yearning for the Infinite album.
Another collaboration with Max!

Max Cooper's Ascent — Making of the Music video

Enter the 5th dimension

Ascent answers the question: if you were living in a 5-dimensional room and projected digits of `\pi` onto its walls, what would you see?

1 · Press release

“Ascent” is chapter 9 of Max Cooper’s audio-visual masterpiece, “Unspoken Words” — a multi-platform project incorporating music, film, installation, live experience and digital art, exploring themes around the struggle to understa nd and express our internal state.

“Ascent” is an audio-visualisation of transcendence told through the lens of music, science and art. Max Cooper said about the inception of the theme:

“I was working on an installation project for a cathedral in Leuven, trying to communicate the idea and feeling of transcendence. I wanted to create this intense experience which I couldn’t put into words, but there was an ascending musical form which captured it”

Max commissioned scientist, artist and long-time collaborator, Martin Krzywinski to express the theme visually, interpreting the idea as an ascent into higher dimensions of spatial form, the resulting 5D hypercubes collapsed back down to the two dimensions of a screen.

“I discussed the idea with Martin [Krzywinski] to make associated visual ideas from the mathematics of form beyond our everyday, which delivered the message as directly and completely as I could.”

The “Ascent” NFT collection comprises five categories of works across a range of media and valuations. Black, Plasma, Viridis, Video and Public is available via Mesh Lab on Objkt on the Tezos blockchain.

2 · NFT posters

During the video walkthrough, you might have noticed that the camera is zoomed into only a portion of the full scene.

If you're wondering what everything looks like, these posters are for you. They represent the full scene — the camera is zoomed out to capture all the objects on the stage.

The posters are available as NFTs. These are 11,520 × 6,480 pixel lossless PNGs but the scene fits into the central 6,480 × 6,480 square.

Below I provide the print resolution (ppcm = pixels per centimeter, ppi = pixels per inch) for a square (6,480 × 6,480) image printed to fit onto common European and North American formats.

2.1 · European sizes


fmt
size
(mm)
size
(inch)

ppcm

ppi
A0
841 × 1,189
33.1 × 46.8
77
196
A1
594 × 841
23.4 × 33.1
109
277
A2
420 × 594
16.5 × 23.4
154
392
A3
297 × 420
11.7 × 16.5
218
554
A4
210 × 297
8.3 × 11.7
309
784
A5
148.5 × 210
5.8 × 8.3
436
1,108
A6
105 × 148.5
4.1 × 5.8
617
1,568

2.2 · North American sizes

size
(inch)
size
(mm)

ppi

ppcm
4 × 4
102 × 102
1,620
638
5 × 5
127 × 127
1,296
510
6 × 6
152 × 152
1,080
425
7 × 7
178 × 178
926
365
8 × 8
203 × 203
810
319
10 × 10
254 × 254
648
255
12 × 12
305 × 305
540
213
14 × 14
356 × 356
463
182
15 × 15
381 × 381
432
170
20 × 20
508 × 508
324
128
22 × 22
559 × 559
295
116
24 × 24
610 × 610
270
106
36 × 36
914 × 914
180
71
40 × 40
1,016 × 1,016
162
64
50 × 50
1,270 × 1,270
130
51

3 · The collections

Three sub-collections of still images — Black, Plasma, and Viridis — complete an expansive range of 90 vast still images. These stills depict the whole scene, often revealing what exists outside of the field of vision shown in the video piece at specific moments in time.

3.1 · The black-and-white collection

Black features 50 images with five editions, and one registered collector of each piece will be randomly selected and receive a unique one of one physical giclée print, printed on 300gsm minuet cotton rag using archival inks.

The Black collection contains 50 assets. They are shown below downsampled to 1,000 × 1,000 pixels and cropped to a square format.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 01:29:01 FRAME 1897 [49] | ASCENT_Black_0011101101001 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 01:34:01 FRAME 2017 [50] | ASCENT_Black_0011111100001 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 01:06:01 FRAME 2545 [51] | ASCENT_Black_0100111110001 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 02:21:01 FRAME 2905 [52] | ASCENT_Black_0101101011001 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 02:25:01 FRAME 3001 [53] | ASCENT_Black_0101110111001 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 02:04:01 FRAME 3697 [54] | ASCENT_Black_0111001110001 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 02:06:01 FRAME 3745 [55] | ASCENT_Black_0111010100001 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 02:08:01 FRAME 3793 [56] | ASCENT_Black_0111011010001 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 02:15:19 FRAME 3979 [57] | ASCENT_Black_0111110001011 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 02:18:11 FRAME 4043 [58] | ASCENT_Black_0111111001011 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 02:23:03 FRAME 4155 [59] | ASCENT_Black_1000000111011 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 02:27:10 FRAME 4258 [60] | ASCENT_Black_1000010100010 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 03:31:21 FRAME 4365 [61] | ASCENT_Black_1000100001101 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 03:39:01 FRAME 4537 [62] | ASCENT_Black_1000110111001 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 03:45:01 FRAME 4681 [63] | ASCENT_Black_1001001001001 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 03:48:01 FRAME 4753 [64] | ASCENT_Black_1001010010001 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 03:04:01 FRAME 4897 [65] | ASCENT_Black_1001100100001 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 03:08:23 FRAME 5015 [66] | ASCENT_Black_1001110010111 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 03:09:13 FRAME 5029 [67] | ASCENT_Black_1001110100101 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 03:10:07 FRAME 5047 [68] | ASCENT_Black_1001110110111 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 03:11:02 FRAME 5066 [69] | ASCENT_Black_1001111001010 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 03:13:23 FRAME 5135 [70] | ASCENT_Black_1010000001111 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 03:15:23 FRAME 5183 [71] | ASCENT_Black_1010000111111 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 03:16:01 FRAME 5185 [72] | ASCENT_Black_1010001000001 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 03:18:02 FRAME 5234 [73] | ASCENT_Black_1010001110010 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 03:20:08 FRAME 5288 [74] | ASCENT_Black_1010010101000 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 03:22:23 FRAME 5351 [75] | ASCENT_Black_1010011100111 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 03:26:19 FRAME 5443 [76] | ASCENT_Black_1010101000011 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 03:28:23 FRAME 5495 [77] | ASCENT_Black_1010101110111 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 03:30:10 FRAME 5530 [78] | ASCENT_Black_1010110011010 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 03:31:23 FRAME 5567 [79] | ASCENT_Black_1010110111111 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 03:33:23 FRAME 5615 [80] | ASCENT_Black_1010111101111 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 03:34:13 FRAME 5629 [81] | ASCENT_Black_1010111111101 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 03:35:08 FRAME 5648 [82] | ASCENT_Black_1011000010000 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 03:36:10 FRAME 5674 [83] | ASCENT_Black_1011000101010 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 03:36:23 FRAME 5687 [84] | ASCENT_Black_1011000110111 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 04:40:11 FRAME 5771 [85] | ASCENT_Black_1011010001011 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 04:47:04 FRAME 5932 [86] | ASCENT_Black_1011100101100 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 04:05:23 FRAME 6143 [87] | ASCENT_Black_1011111111111 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 04:15:23 FRAME 6383 [88] | ASCENT_Black_1100011101111 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 04:19:10 FRAME 6466 [89] | ASCENT_Black_1100101000010 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 04:20:04 FRAME 6484 [90] | ASCENT_Black_1100101010100 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 04:21:16 FRAME 6520 [91] | ASCENT_Black_1100101111000 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 04:22:01 FRAME 6529 [92] | ASCENT_Black_1100110000001 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 04:23:23 FRAME 6575 [93] | ASCENT_Black_1100110101111 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 04:32:23 FRAME 6791 [94] | ASCENT_Black_1101010000111 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 04:34:02 FRAME 6818 [95] | ASCENT_Black_1101010100010 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 04:48:23 FRAME 7175 [96] | ASCENT_Black_1110000000111 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 05:01:21 FRAME 7245 [97] | ASCENT_Black_1110001001101 (BUY ARTWORK)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
MAX COOPER'S ASCENT NFT COLLECTION 05:09:23 FRAME 7439 [98] | ASCENT_Black_1110100001111 (BUY ARTWORK)
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”
{ 10.9.234.151 }