Within the fall of 2017, Mehtaab Sawhney, then an undergraduate on the Massachusetts Institute of Expertise, joined a graduate studying group that got down to examine a single paper over a semester. However by the semester’s finish, Sawhney remembers, they determined to maneuver on, flummoxed by the proof’s complexity. “It was actually superb,” he mentioned. “It simply appeared fully on the market.”
The paper was by Peter Keevash of the College of Oxford. Its topic: mathematical objects known as designs.
The examine of designs will be traced again to 1850, when Thomas Kirkman, a vicar in a parish within the north of England who dabbled in arithmetic, posed a seemingly simple downside in {a magazine} known as the Woman’s and Gentleman’s Diary. Say 15 women stroll to highschool in rows of three daily for every week. Can you arrange them in order that over the course of these seven days, no two women ever discover themselves in the identical row greater than as soon as?
Quickly, mathematicians have been asking a extra normal model of Kirkman’s query: When you’ve got n parts in a set (our 15 schoolgirls), are you able to at all times kind them into teams of dimension ok (rows of three) so that each smaller set of dimension t (each pair of ladies) seems in precisely a kind of teams?
Such configurations, often called (n, ok, t) designs, have since been used to assist develop error-correcting codes, design experiments, check software program, and win sports activities brackets and lotteries.
However in addition they get exceedingly tough to assemble as ok and t develop bigger. Actually, mathematicians have but to discover a design with a worth of t better than 5. And so it got here as an incredible shock when, in 2014, Keevash showed that even for those who don’t know the best way to construct such designs, they always exist, as long as n is massive sufficient and satisfies some easy situations.
Now Keevash, Sawhney and Ashwin Sah, a graduate scholar at MIT, have proven that much more elusive objects, known as subspace designs, always exist as well. “They’ve proved the existence of objects whose existence is by no means apparent,” mentioned David Conlon, a mathematician on the California Institute of Expertise.
To take action, they needed to revamp Keevash’s unique method — which concerned an virtually magical mix of randomness and cautious development — to get it to work in a way more restrictive setting. And so Sawhney, now additionally pursuing his doctorate at MIT, discovered himself head to head with the paper that had stumped him just some years earlier. “It was actually, actually gratifying to completely perceive the methods, and to essentially undergo and work by means of them and develop them,” he mentioned.
‘Past What Is Past Our Creativeness’
For many years, mathematicians have translated issues about units and subsets — just like the design query — into issues about so-called vector areas and subspaces.
A vector house is a particular form of set whose parts — vectors — are associated to 1 one other in a way more inflexible means than a easy assortment of factors will be. Some extent tells you the place you’re. A vector tells you the way far you’ve moved, and in what course. They are often added and subtracted, made greater or smaller.
Think about the room you’re in. It incorporates an infinite variety of factors, and an infinite variety of vectors — ones stretching from the place you’re to each level within the room. All of these vectors will be constructed out of three elementary ones: a vector pointing horizontally in entrance of you, one other to your proper, and one other pointing up. By including these vectors, multiplying them by actual numbers, or doing a little mixture of the 2, you’ll be able to generate the three-dimensional vector house wherein you reside. (The variety of vectors wanted to generate the entire house is the dimension of the vector house.)
Numerous subspaces lie inside every vector house. Take simply the vectors pointing to your proper and in entrance of you. These outline a two-dimensional subspace — a flat airplane parallel to the ground.
Mathematicians typically work with finite vector areas and subspaces, the place vectors can’t level in each attainable course (and don’t have the identical notion of size). On this world, every vector house has solely a finite variety of vectors.
The subspace design downside offers with n-dimensional vector areas and their subspaces. In such vector areas — once more, as long as n is sufficiently massive and satisfies easy situations — are you able to discover a assortment of ok-dimensional subspaces such that any t-dimensional subspace is contained in precisely certainly one of them? Such an object known as an (n, ok, t) subspace design. It’s conceptually just like the extraordinary designs downside, nevertheless it includes preparations which can be rather more tightly constrained.
“It’s an necessary downside as a result of it’s one nook of a really deep analogy between units and subsets on the one hand, and vector areas and subspaces on the opposite,” mentioned Peter Cameron of the College of St. Andrews in Scotland.
Within the 50 years since mathematicians began interested by this downside, they’ve discovered only one nontrivial example (although they know that extra normal sorts of subspace designs exist): In a 13-dimensional vector house, it’s attainable to cowl two-dimensional subspaces with three-dimensional ones precisely as soon as. The end result required a large computer-based proof, as a result of even for such small values of n, ok and t, you find yourself working with hundreds of thousands of subspaces. The complexity of such methods “isn’t simply past our creativeness; it’s past what’s past our creativeness,” mentioned Tuvi Etzion of the Technion in Israel, who helped uncover the instance.
However do subspace designs at all times exist, for any ok and t? Some mathematicians conjectured that, by and enormous, such objects are unattainable. Others, heartened by work accomplished through the years on designs, figured that “it might be onerous to show, but when there isn’t an apparent motive for them to not exist, then they need to exist,” Keevash mentioned.
In comparison with the designs realm, “for this downside, there was simply nothing,” Sah mentioned. “I suppose that prompts a little bit of curiosity at any time when that occurs.”
A Sponge for Errors
Sah and Sawhney met in 2017 as undergraduates at MIT (and ended up attending the identical studying group). Just a few months later, “they began working collectively and simply by no means stopped,” Conlon mentioned. “They’re producing high-quality analysis at a price the place I can’t even blink.”
The 2 younger mathematicians have been intrigued that it had been so onerous to write down down only one express instance of a subspace design, and so they noticed the issue as an ideal approach to discover the boundaries of necessary methods in combinatorics.
n","settings":{"socialLinks":[{"type":"facebook","label":"Facebook","url":"https://www.facebook.com/QuantaNews","__typename":"SocialMediaLink"},{"type":"twitter","label":"Twitter","url":"https://twitter.com/QuantaMagazine","__typename":"SocialMediaLink"},{"type":"youtube","label":"YouTube","url":"https://www.youtube.com/c/QuantaScienceChannel","__typename":"SocialMediaLink"},{"type":"instagram","label":"Instagram","url":"https://instagram.com/quantamag","__typename":"SocialMediaLink"},{"type":"rss","label":"RSS","url":"https://api.quantamagazine.org/feed/","__typename":"SocialMediaLink"}],"newsletterAction":"https://quantamagazine.us1.list-manage.com/subscribe/put up?u=0d6ddf7dc1a0b7297c8e06618&id=f0cb61321c","newsletterUrl":"http://us1.campaign-archive2.com/residence/?u=0d6ddf7dc1a0b7297c8e06618&id=f0cb61321c","sfNotice":"An editorially impartial publication supported by the Simons Basis.","commentsHeader":"
n","channels":[{"title":"The Joy of Why","slug":"the-joy-of-why","description":"The mathematician and author Steven Strogatz interviews leading researchers about the great scientific and mathematical questions of our time.","featured_image":{"alt":"","caption":"","url":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JoW_Quanta_2560x1440-1-1.jpg","width":2560,"height":1440,"sizes":{"thumbnail":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JoW_Quanta_2560x1440-1-1-520x293.jpg","square_small":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JoW_Quanta_2560x1440-1-1-160x160.jpg","square_large":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JoW_Quanta_2560x1440-1-1-520x520.jpg","medium":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JoW_Quanta_2560x1440-1-1-1720x968.jpg","medium_large":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JoW_Quanta_2560x1440-1-1-768x432.jpg","large":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JoW_Quanta_2560x1440-1-1.jpg","__typename":"ImageSizes"},"__typename":"Image"},"square_image":{"alt":"","caption":"","url":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/Jaki-King-General-Quanta_600.jpg","width":600,"height":600,"sizes":{"thumbnail":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/Jaki-King-General-Quanta_600-520x520.jpg","square_small":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/Jaki-King-General-Quanta_600-160x160.jpg","square_large":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/Jaki-King-General-Quanta_600-520x520.jpg","medium":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/Jaki-King-General-Quanta_600.jpg","medium_large":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/Jaki-King-General-Quanta_600.jpg","large":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/Jaki-King-General-Quanta_600.jpg","__typename":"ImageSizes"},"__typename":"Image"},"subscribe_itunes_link":"https://podcasts.apple.com/us/podcast/the-joy-of-why/id1608948873","subscribe_spotify_link":"https://open.spotify.com/show/2FoxHraQSKwxV2HgUfwLMp","subscribe_android_link":"https://podcasts.google.com/feed/aHR0cHM6Ly9hcGkucXVhbnRhbWFnYXppbmUub3JnL2ZlZWQvdGhlLWpveS1vZi13aHk","subscribe_stitcher_link":"https://www.stitcher.com/show/the-joy-of-why","__typename":"Channel"},{"title":"Quanta Science Podcast","slug":"quanta-podcast","description":"Susan Valot narrates in-depth news episodes based on Quanta Magazine's articles about mathematics, physics, biology and computer science. ","featured_image":{"alt":"text reads Quanta Science Podcast","caption":"","url":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2023/03/Lede-QSP-scaled.webp","width":2560,"height":1440,"sizes":{"thumbnail":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2023/03/Lede-QSP-520x293.webp","square_small":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2023/03/Lede-QSP-160x160.webp","square_large":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2023/03/Lede-QSP-520x520.webp","medium":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2023/03/Lede-QSP-1720x968.webp","medium_large":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2023/03/Lede-QSP-768x432.webp","large":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2023/03/Lede-QSP-scaled.webp","__typename":"ImageSizes"},"__typename":"Image"},"square_image":{"alt":"text reads Quanta Science Podcast","caption":"","url":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2023/03/Show_Cover-QSP-scaled.jpg","width":2560,"height":2560,"sizes":{"thumbnail":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2023/03/Show_Cover-QSP-520x520.jpg","square_small":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2023/03/Show_Cover-QSP-160x160.jpg","square_large":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2023/03/Show_Cover-QSP-520x520.jpg","medium":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2023/03/Show_Cover-QSP-1720x1720.jpg","medium_large":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2023/03/Show_Cover-QSP-768x768.jpg","large":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2023/03/Show_Cover-QSP-2880x2880.jpg","__typename":"ImageSizes"},"__typename":"Image"},"subscribe_itunes_link":"https://itunes.apple.com/us/podcast/quanta-science-podcast/id1021340531?mt=2&ls=1","subscribe_spotify_link":"https://open.spotify.com/show/7oKXOpbHzbICFUcJNbZ5wF?si=jdnj9sTHSD2bj4hDMFLKEA","subscribe_android_link":"https://podcasts.google.com/feed/aHR0cHM6Ly93d3cucXVhbnRhbWFnYXppbmUub3JnL2ZlZWQvcG9kY2FzdC8","subscribe_stitcher_link":"https://www.stitcher.com/podcast/quanta-magazine-2/quanta-magazine-podcast","__typename":"Channel"},{"title":"The Joy of x","slug":"the-joy-of-x","description":"The acclaimed mathematician and author Steven Strogatz interviews some of the world’s leading scientists about their lives and work.","featured_image":{"alt":"","caption":"","url":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JoX_Spheres_1920x1080-1.jpg","width":1920,"height":1080,"sizes":{"thumbnail":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JoX_Spheres_1920x1080-1-520x293.jpg","square_small":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JoX_Spheres_1920x1080-1-160x160.jpg","square_large":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JoX_Spheres_1920x1080-1-520x520.jpg","medium":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JoX_Spheres_1920x1080-1-1720x968.jpg","medium_large":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JoX_Spheres_1920x1080-1-768x432.jpg","large":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JoX_Spheres_1920x1080-1.jpg","__typename":"ImageSizes"},"__typename":"Image"},"square_image":{"alt":"","caption":"","url":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JofX_podcast_logo-NEW-600.jpg","width":600,"height":600,"sizes":{"thumbnail":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JofX_podcast_logo-NEW-600-520x520.jpg","square_small":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JofX_podcast_logo-NEW-600-160x160.jpg","square_large":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JofX_podcast_logo-NEW-600-520x520.jpg","medium":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JofX_podcast_logo-NEW-600.jpg","medium_large":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JofX_podcast_logo-NEW-600.jpg","large":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JofX_podcast_logo-NEW-600.jpg","__typename":"ImageSizes"},"__typename":"Image"},"subscribe_itunes_link":"https://podcasts.apple.com/us/podcast/the-joy-of-x/id1495067186","subscribe_spotify_link":"https://open.spotify.com/show/5HcCtKPH5gnOjRiMtTdC07?si=lFzCzat9QfuPU3hWuYibxQ","subscribe_android_link":"https://podcasts.google.com/feed/aHR0cHM6Ly9hcGkucXVhbnRhbWFnYXppbmUub3JnL2ZlZWQvdGhlLWpveS1vZi14Lw","subscribe_stitcher_link":"https://www.stitcher.com/podcast/the-joy-of-x","__typename":"Channel"}],"editors":[{"name":"Bill Andrews - Senior Editor, CS, Columns","__typename":"Editor"},{"name":"Ben Brubaker - Staff CS Writer","__typename":"Editor"},{"name":"Matt Carlstrom - Senior Engagement Editor","__typename":"Editor"},{"name":"Jordana Cepelewicz - Senior Math Writer","__typename":"Editor"},{"name":"Nadia Drake - Senior Physics Editor","__typename":"Editor"},{"name":"Konstantin Kakaes - Senior Math Editor","__typename":"Editor"},{"name":"Thomas Lin - Editor in Chief","__typename":"Editor"},{"name":"Michael Moyer - Deputy Editor, Physics, Math, CS","__typename":"Editor"},{"name":"John Rennie - Deputy Editor, Biology, Podcasts","__typename":"Editor"},{"name":"Yasemin Saplakoglu - Staff Biology Writer","__typename":"Editor"},{"name":"Samuel Velasco - Art Director","__typename":"Editor"},{"name":"Charlie Wood - Staff Physics Writer","__typename":"Editor"},{"name":"Christopher Young - Director of Video","__typename":"Editor"}],"popularSearches":[{"term":"math","label":"Mathematics","__typename":"PopularSearch"},{"term":"physics","label":"Physics","__typename":"PopularSearch"},{"term":"black holes","label":"Black Holes","__typename":"PopularSearch"},{"term":"evolution","label":"Evolution","__typename":"PopularSearch"}],"searchTopics":[{"type":"Tag","label":"Podcasts","tag":{"name":"Quanta Podcast","slug":"quanta-podcast","term_id":"552","__typename":"Term"},"category":{"name":null,"slug":null,"term_id":null,"__typename":"Term"},"__typename":"SearchTopic"},{"type":"Tag","label":"Columns","tag":{"name":"Quantized Columns","slug":"quantized","term_id":"551","__typename":"Term"},"category":{"name":null,"slug":null,"term_id":null,"__typename":"Term"},"__typename":"SearchTopic"},{"type":"Series","label":"Series","tag":{"name":null,"slug":null,"term_id":null,"__typename":"Term"},"category":{"name":null,"slug":null,"term_id":null,"__typename":"Term"},"__typename":"SearchTopic"},{"type":"Category","label":"Interviews","tag":{"name":"Q&A","slug":"qa","term_id":"567","__typename":"Term"},"category":{"name":"Q&A","slug":"qa","term_id":"176","__typename":"Term"},"__typename":"SearchTopic"},{"type":"Category","label":"Multimedia","tag":{"name":null,"slug":null,"term_id":null,"__typename":"Term"},"category":{"name":"Multimedia","slug":"multimedia","term_id":"43","__typename":"Term"},"__typename":"SearchTopic"},{"type":"Category","label":"Puzzles","tag":{"name":"puzzles","slug":"puzzles","term_id":"542","__typename":"Term"},"category":{"name":"Puzzles","slug":"puzzles","term_id":"546","__typename":"Term"},"__typename":"SearchTopic"},{"type":"Category","label":"Blog Posts","tag":{"name":null,"slug":null,"term_id":null,"__typename":"Term"},"category":{"name":"Abstractions blog","slug":"abstractions","term_id":"619","__typename":"Term"},"__typename":"SearchTopic"},{"type":"news","label":"News Articles","tag":{"name":null,"slug":null,"term_id":null,"__typename":"Term"},"category":{"name":null,"slug":null,"term_id":null,"__typename":"Term"},"__typename":"SearchTopic"},{"type":"videos","label":"Videos","tag":{"name":null,"slug":null,"term_id":null,"__typename":"Term"},"category":{"name":null,"slug":null,"term_id":null,"__typename":"Term"},"__typename":"SearchTopic"}],"searchSections":[{"name":"Mathematics","slug":"mathematics","term_id":"188","__typename":"Term"},{"name":"Physics","slug":"physics","term_id":"189","__typename":"Term"},{"name":"Biology","slug":"biology","term_id":"191","__typename":"Term"},{"name":"Computer Science","slug":"computer-science","term_id":"190","__typename":"Term"}],"searchAuthors":[{"id":"38171","name":"Adam Becker","__typename":"AuthorList"},{"id":"28087","name":"Adam Mann","__typename":"AuthorList"},{"id":"29794","name":"Alex Kontorovich","__typename":"AuthorList"},{"id":"53037","name":"Alex Stone","__typename":"AuthorList"},{"id":"39302","name":"Alexander Hellemans","__typename":"AuthorList"},{"id":"56","name":"Alla Katsnelson","__typename":"AuthorList"},{"id":"47249","name":"Allison Parshall","__typename":"AuthorList"},{"id":"29458","name":"Allison Whitten","__typename":"AuthorList"},{"id":"73","name":"Amanda Gefter","__typename":"AuthorList"},{"id":"39164","name":"Ana Kova","__typename":"AuthorList"},{"id":"59","name":"Andreas von Bubnoff","__typename":"AuthorList"},{"id":"8728","name":"Anil Ananthaswamy","__typename":"AuthorList"},{"id":"11648","name":"Ann Finkbeiner","__typename":"AuthorList"},{"id":"50964","name":"Anna Funk","__typename":"AuthorList"},{"id":"50172","name":"Anna Gibbs","__typename":"AuthorList"},{"id":"51678","name":"Anna Kramer","__typename":"AuthorList"},{"id":"42689","name":"Annie Melchor","__typename":"AuthorList"},{"id":"95","name":"Ariel Bleicher","__typename":"AuthorList"},{"id":"52094","name":"Arleen Santana","__typename":"AuthorList"},{"id":"15493","name":"Ashley Smart","__typename":"AuthorList"},{"id":"450","name":"Ashley Yeager","__typename":"AuthorList"},{"id":"36490","name":"Ben Brubaker","__typename":"AuthorList"},{"id":"16315","name":"Bill Andrews","__typename":"AuthorList"},{"id":"2752","name":"Bob Henderson","__typename":"AuthorList"},{"id":"15492","name":"Brendan Z. Foster","__typename":"AuthorList"},{"id":"68","name":"Brooke Borel","__typename":"AuthorList"},{"id":"62","name":"Carl Zimmer","__typename":"AuthorList"},{"id":"13684","name":"Caroline Lee","__typename":"AuthorList"},{"id":"13691","name":"Caroline Lee","__typename":"AuthorList"},{"id":"50","name":"Carrie Arnold","__typename":"AuthorList"},{"id":"15142","name":"Chanda Prescod-Weinstein","__typename":"AuthorList"},{"id":"8084","name":"Charlie Wood","__typename":"AuthorList"},{"id":"742","name":"Christie Wilcox","__typename":"AuthorList"},{"id":"51630","name":"Christopher W. Young","__typename":"AuthorList"},{"id":"11543","name":"Claudia Dreifus","__typename":"AuthorList"},{"id":"57","name":"Courtney Humphries","__typename":"AuthorList"},{"id":"7262","name":"Dalmeet Singh Chawla","__typename":"AuthorList"},{"id":"70","name":"Dan Falk","__typename":"AuthorList"},{"id":"19918","name":"Dana Najjar","__typename":"AuthorList"},{"id":"13695","name":"Daniel Garisto","__typename":"AuthorList"},{"id":"32676","name":"Daniel S. Freed","__typename":"AuthorList"},{"id":"13724","name":"David H. Freedman","__typename":"AuthorList"},{"id":"26310","name":"David S. Richeson","__typename":"AuthorList"},{"id":"30207","name":"David Tse","__typename":"AuthorList"},{"id":"19266","name":"Devin Powell","__typename":"AuthorList"},{"id":"13251","name":"Diana Kwon","__typename":"AuthorList"},{"id":"17000","name":"Elena Renken","__typename":"AuthorList"},{"id":"17149","name":"Elizabeth Landau","__typename":"AuthorList"},{"id":"5279","name":"Elizabeth Preston","__typename":"AuthorList"},{"id":"58","name":"Elizabeth Svoboda","__typename":"AuthorList"},{"id":"32612","name":"Ellen Horne","__typename":"AuthorList"},{"id":"53047","name":"Elliot Lichtman","__typename":"AuthorList"},{"id":"27534","name":"Emily Buder","__typename":"AuthorList"},{"id":"25173","name":"Emily Levesque","__typename":"AuthorList"},{"id":"64","name":"Emily Singer","__typename":"AuthorList"},{"id":"47","name":"Erica Klarreich","__typename":"AuthorList"},{"id":"14784","name":"Erika K. Carlson","__typename":"AuthorList"},{"id":"98","name":"Esther Landhuis","__typename":"AuthorList"},{"id":"5830","name":"Eva Silverstein","__typename":"AuthorList"},{"id":"6793","name":"Evelyn Lamb","__typename":"AuthorList"},{"id":"75","name":"Ferris Jabr","__typename":"AuthorList"},{"id":"52","name":"Frank Wilczek","__typename":"AuthorList"},{"id":"69","name":"Gabriel Popkin","__typename":"AuthorList"},{"id":"77","name":"George Musser","__typename":"AuthorList"},{"id":"19092","name":"Grant Sanderson","__typename":"AuthorList"},{"id":"20557","name":"Howard Lee","__typename":"AuthorList"},{"id":"66","name":"Ingrid Daubechies","__typename":"AuthorList"},{"id":"46418","name":"Ingrid Wickelgren","__typename":"AuthorList"},{"id":"85","name":"Ivan Amato","__typename":"AuthorList"},{"id":"37141","name":"Jake Buehler","__typename":"AuthorList"},{"id":"44758","name":"James Dinneen","__typename":"AuthorList"},{"id":"49403","name":"James R. Riordon","__typename":"AuthorList"},{"id":"12170","name":"Janna Levin","__typename":"AuthorList"},{"id":"32","name":"Jeanette Kazmierczak","__typename":"AuthorList"},{"id":"51","name":"Jennifer Ouellette","__typename":"AuthorList"},{"id":"44787","name":"Joanna Thompson","__typename":"AuthorList"},{"id":"50541","name":"John M. Beggs","__typename":"AuthorList"},{"id":"72","name":"John Pavlus","__typename":"AuthorList"},{"id":"16475","name":"John Preskill","__typename":"AuthorList"},{"id":"91","name":"John Rennie","__typename":"AuthorList"},{"id":"10351","name":"Jonathan Lambert","__typename":"AuthorList"},{"id":"31716","name":"Jonathan O'Callaghan","__typename":"AuthorList"},{"id":"1241","name":"Jordana Cepelewicz","__typename":"AuthorList"},{"id":"8463","name":"Joshua Roebke","__typename":"AuthorList"},{"id":"49","name":"Joshua Sokol","__typename":"AuthorList"},{"id":"16815","name":"jye","__typename":"AuthorList"},{"id":"67","name":"K.C. Cole","__typename":"AuthorList"},{"id":"37462","name":"Karmela Padavic-Callaghan","__typename":"AuthorList"},{"id":"87","name":"Kat McGowan","__typename":"AuthorList"},{"id":"36139","name":"Katarina Zimmer","__typename":"AuthorList"},{"id":"20556","name":"Katherine Harmon Courage","__typename":"AuthorList"},{"id":"90","name":"Katia Moskvitch","__typename":"AuthorList"},{"id":"39551","name":"Katie McCormick","__typename":"AuthorList"},{"id":"27374","name":"Kelsey Houston-Edwards","__typename":"AuthorList"},{"id":"40","name":"Kevin Hartnett","__typename":"AuthorList"},{"id":"47633","name":"Konstantin Kakaes","__typename":"AuthorList"},{"id":"45758","name":"Kristina Armitage","__typename":"AuthorList"},{"id":"38413","name":"Lakshmi Chandrasekaran","__typename":"AuthorList"},{"id":"12570","name":"Laura Poppick","__typename":"AuthorList"},{"id":"38699","name":"Leila Sloman","__typename":"AuthorList"},{"id":"23451","name":"Liam Drew","__typename":"AuthorList"},{"id":"79","name":"Liz Kruesi","__typename":"AuthorList"},{"id":"38","name":"Lucy Reading-Ikkanda","__typename":"AuthorList"},{"id":"47180","name":"Lyndie Chiou","__typename":"AuthorList"},{"id":"60","name":"Maggie McKee","__typename":"AuthorList"},{"id":"2333","name":"Mallory Locklear","__typename":"AuthorList"},{"id":"3569","name":"Marcus Woo","__typename":"AuthorList"},{"id":"414","name":"Mark Kim-Mulgrew","__typename":"AuthorList"},{"id":"50807","name":"Marta Zaraska","__typename":"AuthorList"},{"id":"20495","name":"Matt Carlstrom","__typename":"AuthorList"},{"id":"47830","name":"Matt von Hippel","__typename":"AuthorList"},{"id":"17147","name":"Matthew Hutson","__typename":"AuthorList"},{"id":"30953","name":"Max G. Levy","__typename":"AuthorList"},{"id":"32437","name":"Max Kozlov","__typename":"AuthorList"},{"id":"38705","name":"mcho","__typename":"AuthorList"},{"id":"40613","name":"Melanie Mitchell","__typename":"AuthorList"},{"id":"7186","name":"Melinda Wenner Moyer","__typename":"AuthorList"},{"id":"14093","name":"Michael Harris","__typename":"AuthorList"},{"id":"34","name":"Michael Kranz","__typename":"AuthorList"},{"id":"23","name":"Michael Moyer","__typename":"AuthorList"},{"id":"74","name":"Michael Nielsen","__typename":"AuthorList"},{"id":"19093","name":"Michele Bannister","__typename":"AuthorList"},{"id":"50861","name":"Mike Orcutt","__typename":"AuthorList"},{"id":"1472","name":"Moira Chas","__typename":"AuthorList"},{"id":"6476","name":"Monique Brouillette","__typename":"AuthorList"},{"id":"42264","name":"Mordechai Rorvig","__typename":"AuthorList"},{"id":"52093","name":"Nadia Drake","__typename":"AuthorList"},{"id":"10","name":"Natalie Wolchover","__typename":"AuthorList"},{"id":"37605","name":"Nick Thieme","__typename":"AuthorList"},{"id":"43298","name":"Nicole Yunger Halpern","__typename":"AuthorList"},{"id":"37428","name":"Nima Arkani-Hamed","__typename":"AuthorList"},{"id":"19962","name":"Nola Taylor Tillman","__typename":"AuthorList"},{"id":"51434","name":"Nona McKenna","__typename":"AuthorList"},{"id":"24","name":"Olena Shmahalo","__typename":"AuthorList"},{"id":"1816","name":"Patrick Honner","__typename":"AuthorList"},{"id":"84","name":"Peter Byrne","__typename":"AuthorList"},{"id":"55","name":"Philip Ball","__typename":"AuthorList"},{"id":"50804","name":"Polly Stryker","__typename":"AuthorList"},{"id":"31","name":"Pradeep Mutalik","__typename":"AuthorList"},{"id":"24011","name":"Puja Changoiwala","__typename":"AuthorList"},{"id":"100","name":"Quanta Magazine","__typename":"AuthorList"},{"id":"2784","name":"R. Douglas Fields","__typename":"AuthorList"},{"id":"26114","name":"Rachel Crowell","__typename":"AuthorList"},{"id":"9412","name":"Raleigh McElvery","__typename":"AuthorList"},{"id":"820","name":"Ramin Skibba","__typename":"AuthorList"},{"id":"1666","name":"Rebecca Boyle","__typename":"AuthorList"},{"id":"20950","name":"Richard Masland","__typename":"AuthorList"},{"id":"48","name":"Robbert Dijkgraaf","__typename":"AuthorList"},{"id":"80","name":"Roberta Kwok","__typename":"AuthorList"},{"id":"15681","name":"Robin George Andrews","__typename":"AuthorList"},{"id":"51187","name":"Robin Lloyd","__typename":"AuthorList"},{"id":"24577","name":"Rodrigo Pérez Ortega","__typename":"AuthorList"},{"id":"78","name":"Sabine Hossenfelder","__typename":"AuthorList"},{"id":"23845","name":"Samuel Velasco","__typename":"AuthorList"},{"id":"83","name":"Sarah Lewin","__typename":"AuthorList"},{"id":"35441","name":"Scott Aaronson","__typename":"AuthorList"},{"id":"76","name":"Sean B. Carroll","__typename":"AuthorList"},{"id":"15680","name":"Sean Carroll","__typename":"AuthorList"},{"id":"7239","name":"Shannon Hall","__typename":"AuthorList"},{"id":"44197","name":"Sheon Han","__typename":"AuthorList"},{"id":"65","name":"Siobhan Roberts","__typename":"AuthorList"},{"id":"5944","name":"Sophia Chen","__typename":"AuthorList"},{"id":"61","name":"Steph Yin","__typename":"AuthorList"},{"id":"63","name":"Stephanie Bucklin","__typename":"AuthorList"},{"id":"26311","name":"Stephanie DeMarco","__typename":"AuthorList"},{"id":"71","name":"Stephen Ornes","__typename":"AuthorList"},{"id":"17148","name":"Steve Nadis","__typename":"AuthorList"},{"id":"13356","name":"Steven Strogatz","__typename":"AuthorList"},{"id":"17150","name":"Susan D'Agostino","__typename":"AuthorList"},{"id":"39768","name":"Tamar Lichter Blanks","__typename":"AuthorList"},{"id":"2960","name":"Tara C. Smith","__typename":"AuthorList"},{"id":"52224","name":"Theo Nicitopoulos","__typename":"AuthorList"},{"id":"14785","name":"Thomas Lewton","__typename":"AuthorList"},{"id":"3","name":"Thomas Lin","__typename":"AuthorList"},{"id":"54","name":"Tim Vernimmen","__typename":"AuthorList"},{"id":"88","name":"Tom Siegfried","__typename":"AuthorList"},{"id":"12964","name":"Vanessa Schipani","__typename":"AuthorList"},{"id":"53","name":"Veronique Greenwood","__typename":"AuthorList"},{"id":"86","name":"Virginia Hughes","__typename":"AuthorList"},{"id":"3244","name":"Viviane Callier","__typename":"AuthorList"},{"id":"89","name":"Wynne Parry","__typename":"AuthorList"},{"id":"15913","name":"XiaoZhi Lim","__typename":"AuthorList"},{"id":"42263","name":"Yasemin Saplakoglu","__typename":"AuthorList"},{"id":"45757","name":"Zack Savitsky","__typename":"AuthorList"}],"adBehavior":"in all places","adUrl":"https://www.simonsfoundation.org/","adImageHome":"https://d2r55xnwy6nx47.cloudfront.internet/uploads/2021/11/SF_HP_520x684_C.png","adImageArticle":"https://d2r55xnwy6nx47.cloudfront.internet/uploads/2021/11/SF_article_320percentE2percent80percent8ApercentC3percent97percentE2percent80percent8A550_C.png","adImageTablet":"https://d2r55xnwy6nx47.cloudfront.internet/uploads/2021/11/SF_newslettertablet_1780x500_C.png","adImageMobile":"https://d2r55xnwy6nx47.cloudfront.internet/uploads/2021/11/SF_HP_520x684_C.png","trackingScripts":"rnrnrnrnrnrnrnrn"},"theme":{"web page":{"accent":"#ff8600","textual content":"#1a1a1a","background":"white"},"header":{"kind":"default","gradient":{"coloration":"white"},"strong":{"major":"#1a1a1a","secondary":"#999999","hover":"#ff8600"},"clear":{"major":"white","secondary":"white","hover":"#ff8600"}}},"redirect":null,"fallbackImage":{"alt":"","caption":"","url":"https://d2r55xnwy6nx47.cloudfront.internet/uploads/2017/04/default.gif","width":1200,"peak":600,"sizes":{"thumbnail":"https://d2r55xnwy6nx47.cloudfront.internet/uploads/2017/04/default-520x260.gif","square_small":"https://d2r55xnwy6nx47.cloudfront.internet/uploads/2017/04/default-160x160.gif","square_large":"https://d2r55xnwy6nx47.cloudfront.internet/uploads/2017/04/default-520x520.gif","medium":"https://d2r55xnwy6nx47.cloudfront.internet/uploads/2017/04/default.gif","medium_large":"https://d2r55xnwy6nx47.cloudfront.internet/uploads/2017/04/default-768x384.gif","massive":"https://d2r55xnwy6nx47.cloudfront.internet/uploads/2017/04/default.gif","__typename":"ImageSizes"},"__typename":"Picture"}},"modals":{"loginModal":false,"signUpModal":false,"forgotPasswordModal":false,"resetPasswordModal":false,"lightboxModal":false,"callback":null,"props":null},"podcast":{"id":null,"taking part in":false,"length":0,"currentTime":0},"person":{"loggedIn":false,"savedArticleIDs":[],"userEmail":"","editor":false},"feedback":{"open":false},"cookies":{"acceptedCookie":false}},
env: {
APP_URL: 'https://www.quantamagazine.org',
NODE_ENV: 'manufacturing',
WP_URL: 'https://api.quantamagazine.org',
HAS_GOOGLE_ID: true,
HAS_FACEBOOK_ID: true,
},
}
Discussion about this post