#Margaret Wertheim

[celestialmazer]

Coral reefs inspired the crochet exhibition “Austrian Satellite Reef,” by Margaret and Christine Wertheim. It is on view at the Schlossmuseum Linz in Austria.Credit...David Payr for The New York Times

The Crochet Coral Reef Keeps Spawning, Hyperbolically

The long-running project, sometimes described as the environmental version of the AIDS quilt, thrives on convoluted math and a sea of volunteers.

By Siobhan Roberts

Published Jan. 15, 2024 Updated Jan. 16, 2024

Every year after the full moons in late October and November, Australia’s Great Barrier Reef begins its annual spawning — first the coral species inshore, where waters are warmer, then the offshore corals, the main event. Last year, this natural spectacle coincided with the woolly propagation of two new colonies of the Crochet Coral Reef, a long-running craft-science collaborative artwork now inhabiting the Schlossmuseum in Linz, Austria, and the Carnegie Museum of Art in Pittsburgh.

To date, nearly 25,000 crocheters (“reefers”) have created a worldwide archipelago of more than 50 reefs — both a paean to and a plea for these ecosystems, rainforests of the sea, which are threatened by climate change. The project also explores mathematical themes, since many living reef organisms biologically approximate the quirky curvature of hyperbolic geometry.

Within the realm of two dimensions, geometry deals with properties of points, lines, figures, surfaces: The Euclidean plane is flat and therefore displays zero curvature. By contrast, the surface of a sphere displays constant positive curvature; at all points, the surface bends inward toward itself. And a hyperbolic plane exhibits constant negative curvature; at all points, the surface curves away from itself. Reef life thrives on hyperbolism, so to speak; the curvy surface structure of coral maximizes nutrient intake, and nudibranchs propel through water with frilly flanges.

Christine Wertheim, a creator of the project and the artistic force behind it. Credit...David Payr for The New York Times

Margaret Wertheim, a science writer and twin sister to Christine, is in charge of the project’s scientific and mathematical components and its management. Credit...David Payr for The New York Times

In the artworks, marine morphologies are modeled — crocheted — with loopy verisimilitude. A bit like Monet’s water lilies, the crochet corals are abstract representations of nature, said Christine Wertheim, an artist and writer now retired from the California Institute of the Arts. Dr. Wertheim is the driving artistic force behind the project, which she created with Margaret Wertheim, her twin sister, a science writer who is in charge of scientific and mathematical components as well as management. The Wertheims, Australians who live together in Los Angeles, spun out the mother reef from their living room many moons ago, in 2005.

Crochet Coral Reef exhibitions typically have two main components: The Wertheims provide an anchor, of sorts, with works from their collection that they have crocheted over the years. They also incorporate pieces by select skilled international contributors. One is a “bleached reef,” evoking corals stressed by increases in ocean temperature; another, a “coral forest” made from yarn and plastic, laments the debris that pollutes reef systems.

Then in response to an open call, volunteers far and wide crochet a pageant of individual specimens that agglomerate in a “satellite reef,” staged by a local curatorial team with guidance from the Wertheims. The Wertheims liken this hive mind to a friendly iteration of the Borg from “Star Trek: Next Generation.” All contributors are credited.

The Linz satellite reef takes colorful inspiration from traditional Austrian craftswomanship, such as blue-and-white fabric (Blaudruck) or gold-and-black hats (Goldhauben). Credit...David Payr for The New York Times

The largest satellite reef thus far coalesced in 2022 at the Museum Frieder Burda in Baden-Baden, Germany, with some 40,000 coral pieces by about 4,000 contributors. The Wertheims call this the Sistine Chapel of crochet reefs (documented in a splashy exhibition catalog). But the show at the Linz Schlossmuseum, which is dedicated to natural science as well as art and culture, is reminiscent of the work of the painter Giuseppe Arcimboldo, whose collage portraits from depictions of fruits, vegetables and flowers are “fantastically heterogeneous, also very funny and clever,” Ms. Wertheim said.

The Linz satellite reef unites some 30,000 pieces by 2,000 crocheters. The disparate parts take colorful inspiration from traditional Austrian “craftswomanship,” as the exhibit text puts it, and there is a vast, glittery coral wall that gives a nod to the artist Gustav Klimt. In the Wertheims’ view, however, the crochet coral project is proof that it is not always lone geniuses who create great art, but also communities. In the art world, that is a radical idea, they noted, yet in science big collaborative projects and papers with thousands of authors are not unprecedented.

Primordial bamboozlement

Scientifically, the Linz exhibition holds special symbolism since, as the narrative explains, the region was previously occupied by an “ancient primordial sea, filled with corals whose remains can still be found in the basins and Alps of Upper Austria.”

The mathematical dimension of the story intersects (from afar) with research by the applied mathematician Shankar Venkataramani and his students at the University of Arizona. They use idealized models to study hyperbolic surfaces in nature. “It’s all around us,” Dr. Venkataramani said — consider the ubiquity of curly kale. “The question is, Why is it all around us?” The textbook evolutionary benefit, he said, is that it helps optimize processes like circulation and nutrient absorption. His research group’s studies show additional advantages, such as affording a structural “sweet spot,” making organisms neither too rigid nor too flexible and allowing them “to move and change shape with a small energy budget.”

The Wertheim sisters share an appreciation for Dr. Seuss’ playful absurdity, which is a touchstone for the project. Credit...David Payr for The New York Times

When Margaret Wertheim, who studied math, physics and computer science at university, learned hyperbolic geometry, she found it “a bit bamboozling.” She took the principles more on faith than understanding. Yet through crocheting models, she said, “you really do learn in a very deep way what a hyperbolic structure is, and in a way that I think is very powerfully pedagogical.”

Feeling the frills

That the hyperbolic plane could be looped into existence with a crochet hook became apparent only a quarter-century ago. Daina Taimina, a mathematician now retired from Cornell University, made this discovery while preparing a geometry course. “I needed to feel it,” Dr. Taimina said. Investigations with the Wertheims in the early to mid-2000s planted a seed for their coral-reef project (and a chap book, “A Field Guide to Hyperbolic Space”) and for Dr. Taimina’s outreach workshops and shows (and a book of her own, “Crocheting Adventures With Hyperbolic Planes”).

Further back, in 1868, the Italian mathematician Eugenio Beltrami constructed a parchment model of the hyperbolic plane — and he rolled it into a negatively curved surface called a pseudosphere (as one does). A century later the mathematician William Thurston independently had a similar idea, using paper and tape.

Dr. Taimina encountered a crumbling paper version in 1997 at a workshop by David Henderson, a Cornell mathematician and her partner. Dr. Henderson had learned the model-making technique from Dr. Thurston. On the spot, Dr. Taimina set out to construct something more pliable and durable for her course. When she tried knitting, the result was too floppy, unwieldy. Crochet proved the perfect medium. Dr. Taimina devised a simple algorithm: Increase the number of stitches in the constant ratio N+1. For instance, say N=6: crochet six stitches, and on the seventh stitch, increase by crocheting two stitches into one; repeat, row upon row.

Eugenio Beltrami’s 19th-century parchment model of the hyperbolic plane, displaying constant negative curvature. Credit...Department of Mathematics, University of Pavia

Daina Taimina’s largest hyperbolic crochet model, using 4.8 miles of yarn and stretching more than two feet wide, earned a 2013 Guinness World Record. Credit...Daina Taimina

“You can experiment with different ratios, but not in the same model,” she cautioned in an article for “The Mathematical Intelligencer” that she wrote with Dr. Henderson. “You will get a hyperbolic plane only if you increase the number of stitches in the same ratio all the time.”

Dr. Taimina also joined Dr. Henderson, who died in 2018, as a co-author for revised editions of his book “Experiencing Geometry,” wherein he described his belief “that mathematics is a natural and deep part of human experience and that experiences of meaning in mathematics are accessible to everyone.”

The Wertheims adopted a similar vision with their Institute for Figuring, a nonprofit where projects are motivated by the belief that people can play with and aesthetically appreciate — and thereby acquire an understanding of — mathematical ideas.

With her science training, Margaret’s instinct had been to follow Dr. Taimina’s algorithm to the stitch. But Christine’s artistic sensibility was to break the rules and go wild. For instance, crochet a few rows, increasing every third stitch, and then switch to every fifth stitch, and then to every second stitch — the result is not perfectly hyperbolic, because the piece does not have regular curvature.

For the Wertheims, embracing that irregular frilliness was the moment their crochet reef project was born: The erratic algorithms begot a riotous taxonomy, a woological seascape of creatures that all the more closely emulated the geometrically aberrant curvatures of their real-life biological counterparts.

Patterns of change

Christine Wertheim noted that while crocheting, she could tell when a structure wanted to form another ruffle. “It’s interesting to feel that in your hands,” she said. Credit...David Payr for The New York Times

Another crochet-coral incarnation recently emerged from a pond of creativity organized by the Carnegie Museum of Art in Pittsburgh, a city known for its three rivers: The Allegheny and the Monongahela Rivers converge to form the Ohio, which empties into the Mississippi, which empties into the Gulf of Mexico, where coral spawns after July and August full moons. This show, organized by Alyssa Velazquez, a curatorial assistant of decorative arts and design, features only a satellite reef made by 281 community crocheters.

Ms. Velazquez noted that the Wertheims’ project takes inspiration from the fiber-art movement — advanced by mostly women, among them Sheila Hicks, Tau Lewis and Marie Watt — and then democratizes it. As (mostly) women gathered and interlocked loops of yarn, Ms. Velazquez observed the lines of conversations: memories of time spent at local waterways, recycling habits, the chance to crochet something other than baby bootees. At that, the enterprise represents “the creative potential for environmental dialogue and new ecological behaviors,” she said — invoking imaginative yet concrete patterns of change.

A version of this article appears in print on Jan. 16, 2024, Section D, Page 1 of the New York edition with the headline: Crochet Coral Reef Grows Hyperbolically.

More at This Is Colossal

https://www.thisiscolossal.com/2022/05/crochet-coral-reef-wertheim/

[dijetemjeseca]

Margaret and Christine Wertheim, Value and Transformation of Corals, 1.5 Degrees, Kunsthalle, Mannheim

[killy--chan]

Crochet Coral Reef by Christine and Margaret Wertheim

[stmichaelsministryofgnosis]

TechnoCalyps: Part III The Digital Messiah (2006)

Technocalyps is a three-part documentary series on the notion of transhumanism by Belgian visual artist and filmmaker Frank Theys.

The accelerating advances in genetics, brain research, artificial intelligence, bionics and nanotechnology seem to converge to one goal: to overcome human limits and create higher forms of intelligent life and to create transhuman life. Frank Theys conducts his enquiry into the scientific, ethical and metaphysical dimensions of these technological developments.

The film includes interviews by top scientists and thinkers on the subject worldwide, including Marvin Minsky, Ray Kurzweil, Hans Moravec, Terence McKenna, Bruce Sterling, Robert Anton Wilson, Margaret Wertheim, Rael, the Dalai Lama and many more.

St. Michael's Ministry of Gnosis serves as a sanctuary for literature, religion, scientific research, history, gnosis, and art. Our main practice is the collection and application of knowledge.

Official Telegram Channel for St. Michael's Ministry of Gnosis The uploaded content, opinions, and views expressed here do not reflect the opinions or views of St. Michael's Ministry of Gnosis. https://t.me/ministry0fgnosis

The Ministry of Gnosis Open Forum Telegram Channel serves as a platform for content sharing and civil discourse. Join today and help the community grow! https://t.me/ministry0fgnosisforum

If you enjoy our content, please consider making a donation @ https://buymeacoffee.com/ministrygnosis

[petitagite]

in ¨Value and Transformation of Corals"

by Margaret and Christine Wertheim

via pittsburghmercantile

[takahashicleaning]

ＴＥＤにて

マーガレット・ワーザイム： 珊瑚礁とかぎ針編み物��中に、ほのかに見えてくる美しき数学の世界観

（詳しくご覧になりたい場合は上記リンクからどうぞ）

マーガレット・ワーザイムは、数学者が発明したかぎ針編みの手法（あの手芸の編み方？）を用いて珊瑚礁を再現するプロジェクトを進めています。

チャールズダーウィンの生誕２００年を記念してということです。珊瑚礁の驚くべき側面を紹介し、珊瑚をつくり出す中で見られる双曲幾何学（非ユークリッド幾何学）の世界へと案内します。

これは、アインシュタインの一般相対性理論の基本となる数学でもあります。双曲幾何学（非ユークリッド幾何学）は、不思議でもあり日常に満ちあふれている現象でもあります。

トポロジーにも関連していくような楕円的幾何学および双曲的幾何学は、ユークリッド幾何学の平行線定理に疑問を提案した結果誕生しました。

古代エジプトの土地の測量から始まった幾何学は、ギリシャ時代に発展し、ユークリッドの「原論」という書籍にまとめられます。

しかし、「平行線の公理」のみが未解決の問題でした。その二千年来の謎を１９世紀になり思いがけない形で解決されたのです。

ハンガリーのボヤイ親子、ロシアのロバチェフスキー、ドイツのガウスにより同時期に独立して「非ユークリッド幾何学」として誕生しました。

カオス理論にも貢献しているポアンカレの他に、ドイツのリーマンもモデルを構築しています。

さらに、コロンブス以前では、地球の表面は、平らであると感じるのは、極く自然であるにもかかわらず、まるいと考えるのもトポロジー的、非ユークリッド幾何学的な発想です。

次元に関してはこの場合、数学的な次元を前提としています。

次元のコンパクト化の説明の前に、数学的な次元の重要性について、さて、一般相対性理論をカルツァは、電磁気力に応用していきます。

当時は、それが重力以外に考えられる唯一の力でした。つまり、電気や、磁石の引き付けなどを引き起こす力のことです。 ここで空間と時間が歪むこと以外に、もしも次元が歪むことで電磁気力が働くかもしれないことに気づきます。

1926年にオスカークラインも、知覚で見えない次元がある可能性を示します。5 次元化して電磁気力も幾何学として表せるようにしたカルツァ・クライン理論というものです。

カルツァが3次元ではなく、4次元の宇宙における歪みと曲がりを説明する方程��を書き出した時、彼はアインシュタインがすでに３次元で導き出していた方程式を見出しました。それらは、重力を説明するための方程式です。

でも、カルツァは次元がひとつ増えたことによるもうひとつの方程式も見つけました。その方程式を見てみるとそれは正に科学者たちが長年の間。電磁力を表すために使ってきた方程式でした。驚くべきことです。それが、こつぜんと計算結果に現れてきたのです。

こうして、数学的な次元は、空間の量子化を数値的に表現できるようになっていくキッカケになりました。

その後のカルツァ・クライン理論は、無限に存在する次元の形状の一部をカラビ・ヤウ多様体として表現できました。

例えば、手を振って大きな弧を描く時、手のひらは3つの広がった次元の中ではなく、巻き上げられた次元の中を突っ切っています。

もちろん、巻き上げられた次元はとても小さいので、体を動かす間に、こうした次元を1サイクルして出発点に戻ることが繰り返され、その回数は、膨大な数にのぼります。このように次元の広がりが小さいと言う事は、手のような大きな物体が動く余地があまりないと言うことです。

それは結局、平均化されてしまい腕を振った時でも、私たちは巻き上げられたこのような次元を横断し膨大に旅したことに全く気づいていません。

これは、結び目の不変量にも関連しています。

まず初めに、円周を3次元ユークリッド空間に埋め込んだものを「結び目」と定義していることから始まります。

結び目理論においては、変形して移り合う「結び目」は、同じ「結び目」とみなして「結び目」を研究する。

「結び目」を研究するひもの結び方はいろいろあるので、様々なタイプの「結び目」がある。では、「結び目」のタイプはどのようにして区別すれば良いのであろうか？

「結び目」に対して定められる値で、「結び目」を変形することに関して不変であるようなものを「不変量」と言う。結び目理論は、トポロジー(位相幾何学)の一分野である。

1980年代に、数理物理的手法が、低次元トポロジーに導入されて、3次元トポロジーにおいては「結び目」と3次元多様体の膨大な数の不変量(量子不変量)が発見された。

これによって、4次元トポロジーには、ゲージ理論がもたらされることになりました。これらからゲージ場の数学的根拠として、活用されることになっていきます。

量子不変量は、数理物理に由来する量子群や共形場理論やチャーンサイモンズ理論を背景として、様々な代数構造を用いて構成される量子不変量やこれに関連するトピックを研究する研究領域を量子トポロジーと呼ばれています。

古典的な結び目理論においては、個々の結び目の特性を個別に研究する研究が中心であったが、量子トポロジーでは多くの「結び目の集合」を研究対象としています。

1980年代に結び目の不変量が大量に発見される発端になったのは、1914年にジョーンズ多項式と言う結び目不変量が発見され���ことにあります。

その後、統計物理で知られていたヤンバクスター方程式の多数の解、つまり「R行列」を用いて大量の結び目不変量が発見されました。

さらに、1980年代後半に量子群が、発見されたことにより、それらの大量の不変量は、量子不変量として整理されて理解されるようになりました。

1990年代には、これらの大量の量子不変量を統一的に扱って、研究する2つの手法が開発されました。

これは、次元のコンパクト化への始まりになります。

1つは、コンセビッチ不変量と言う1つの巨大な不変量に、すべての量子不変量を統一する方法。

もう一つは、バシリエフ不変量と言う「共通の性質」で不変量を特徴づける方法があります。

ゲージ対称性、アイソスピン、クォーク理論、ヒッグス粒子など。

さらに、数理物理に由来する量子群や共形場理論、チャーンサイモンズ理論もあります。

そして、スーパーストリング理論や量子化学の「変分法」にも応用されている。

自分の周りのローカルな狭い範囲では平らであるのに、グローバルにはまるくなっていることを見抜いて、その視野は、ユニバーサルであるとさえ言えます。宇宙にもトポロジー的な考えが、宇宙を語るキーワードになります。

しかし、一般生活の範囲ではバランスも大切です。

＜おすすめサイト＞

メリアン・バンジェス：込み入ったデザインの美しさ

ジム・サイモンズ：ウォールストリートを制した天才数学者

アーサーベンジャミン：フィボナッチ数の魅力

ＴＥＤにも登場したブライアングリーンがSuper String Theory(スーパーストリング理論)をわかりやすく紹介してくれる

コニフォールド転移とオートファジーとの偶然の一致について2016

ノーベル賞受賞者のジェームズ・ワトソン：DNA構造解明にいたるまで

キャリー マリス：危険な感染症に対する次世代の治療法について

＜提供＞

東京都北区神谷の高橋クリーニングプレゼント

独自サービス展開中！服の高橋クリーニング店は職人による手仕上げ。お手頃50ですよ。往復送料、曲Song購入可。詳細は、今すぐ電話。東京都内限定。北部、東部、渋谷区周囲。地元周辺区もＯＫです

東京都北区神谷の高橋クリーニング店Facebook版

[clansocreations]

@yesdangerpls OH OH OH SPEAKING OF CROCHET.

We saw an exhibition of crochet coral reef (in an Austrian museum of natural sciences) and there were like diagrams on how it works and like it's really amazing.

The two women who started this amazing project are a mathematician and an artist and I think that tells you all you need to know

Why art belongs in STEM / STEAM

[artbookdap]

TOMORROW! Saturday, December 10 at 3 PM, @artbookhwla Bookstore presents a special book signing event with Margaret Wertheim, celebrating 'Value and Transformation of Corals.' Wertheim will be in conversation with a special guest, to be announced, with book signing to follow. Pre-order a copy signed by Margaret and register for the event via linkinbio!⁠ ⁠ ARTBOOK AT HAUSER & WIRTH LOS ANGELES BOOKSTORE⁠ Margaret Wertheim: 'Value and Transformation of Corals'⁠ Saturday, December 10, 2022: 3 PM PST⁠ 917 East 3rd Street⁠ Los Angeles, CA 90013⁠ Phone: 213-988-7413⁠ ⁠ @wienand_verlag @crochetcoralreef #crochetcoralreef #margaretwertheim 🪸🪡 https://www.instagram.com/p/Cl-A9pUu44d/?igshid=NGJjMDIxMWI=

[knithacker]

Op-Ed: Art imitates life — not even a plastic crocheted coral artwork can stand up to climate change: 👉 https://buff.ly/3x9UeRq via Los Angeles Times

[art2catch]

I think with those hidden door narratives in stories it’s like this: 

If you go through a portal, it’s fantasy. If something else enters through the portal, it’s horror.

embroidered and crocheted art by J.J.

[exhaled-spirals]

When it comes to the very big and the extremely small, physical reality appears to be not one thing, but two. Where quantum theory describes the subatomic realm as a domain of individual quanta, all jitterbug and jumps, general relativity depicts happenings on the cosmological scale as a stately waltz of smooth flowing space-time. General relativity is like Strauss — deep, dignified and graceful. Quantum theory, like jazz, is disconnected, syncopated, and dazzlingly modern.

Margaret Wertheim, “Physic’s Pangolin” in Aeon Magazine

[stmichaelsministryofgnosis]

Technocalyps: Part II Preparing for the Singularity (2006)

Technocalyps is a three-part documentary series on the notion of transhumanism by Belgian visual artist and filmmaker Frank Theys.

The accelerating advances in genetics, brain research, artificial intelligence, bionics and nanotechnology seem to converge to one goal: to overcome human limits and create higher forms of intelligent life and to create transhuman life. Frank Theys conducts his enquiry into the scientific, ethical and metaphysical dimensions of these technological developments.

The film includes interviews by top scientists and thinkers on the subject worldwide, including Marvin Minsky, Ray Kurzweil, Hans Moravec, Terence McKenna, Bruce Sterling, Robert Anton Wilson, Margaret Wertheim, Rael, the Dalai Lama and many more.

St. Michael's Ministry of Gnosis serves as a sanctuary for literature, religion, scientific research, history, gnosis, and art. Our main practice is the collection and application of knowledge.

Official Telegram Channel for St. Michael's Ministry of Gnosis The uploaded content, opinions, and views expressed here do not reflect the opinions or views of St. Michael's Ministry of Gnosis. https://t.me/ministry0fgnosis

The Ministry of Gnosis Open Forum Telegram Channel serves as a platform for content sharing and civil discourse. Join today and help the community grow! https://t.me/ministry0fgnosisforum

If you enjoy our content, please consider making a donation @ https://buymeacoffee.com/ministrygnosis

[nettculture]

Incredible crocheted coral reefs from Los Angeles based sisters Margaret and Christine Wertheim at https://www.margaretwertheim.com/ & https://crochetcoralreef.org "Pod World Hyperbolic", from the Coral Reef Project by Margaret and Christine Wertheim and the Institute For Figuring, at the Biennale Arte 2019, Photo by Francesco Galli, courtesy La Biennale di Venezia

[tendertools]

“Relativity says we live in four dimensions. String theory says it’s 10. What are ‘dimensions’ and how do they affect reality?“

[podkins]

I loved this TED Talk by crochet artist Margaret Wertheim. Check it above, and the blurb below.

Snowflakes, fractals, the patterns on a leaf -- there's beauty to be found at the intersection of nature and physics, beauty and math. Science writer Margaret Wertheim (along with her twin sister, Christine) founded the Institute for Figuring to advance the aesthetic appreciation of scientific concepts, from the natural physics of snowflakes and fractals to human constructs such as Islamic mosaics, string figures and weaving. 

The IFF's latest project is perhaps its most beguilingly strange -- a coral reef constructed entirely by crochet hook, a project that takes advantage of the happy congruence between the mathematical phenomena modeled perfectly by the creatures of the reef,  and repetitive tasks such as crocheting -- which, as it turns out, is perfectly adapted to model hyperbolic space. It is easy to sink into the kaleidoscopic, dripping beauty of the yarn-modeled reef, but the aim of the reef project is twofold: to draw attention to distressed coral reefs around the world, dying in droves from changing ocean saline levels, overfishing, and a myriad of threats; and to display a flavor of math that was previously almost impossible to picture. By modeling these complex equations in physical space, this technique can help mathematicians see patterns and make breakthroughs.

“Margaret Wertheim might technically fall under the oh-so-banal title of a science communicator. But this fiery Australian native has roamed far beyond the standard definition of one who just talks about science.” — Kristin Abkemeier, Inkling Magazine

For more via TED Talks https://www.ted.com/speakers/margaret_wertheim

[rachelcrummeyrachelcrummey]

“We have built a world of rectilinearity: the rooms we inhabit, the skyscrapers we work in, the grid-like arrangement of our streets and the freeways we travel on our way to work speak to us in straight lines.

People have learned to play by Euclidean rules because 2,000 years of geometrical training have engraved the grid in our minds. But in the early nineteenth century, mathematicians became aware of another kind of space in which lines cavorted in strange and seemingly aberrant formations. This suggested the existence of a new geometry. To everyone at the time,hyperbolic space seemed pathological, because it didn’t conform to one of Euclid’s most cherished principles, the so-called parallel postulate. In this sense, it contradicted millenia of mathematical wisdom and, frankly, it offended common sense.

But eons before the dawning of mathematical awareness, nature had exploited this supposedly forbidden form, realizing it throughout the vegetable and marine kingdoms. Outside our boxes, the natural world teems with swooping, curling, crenellated forms, from the fluted surfaces of lettuces and fungi to the frilled skirts of nudibranchs and sea slugs and anemones. Nature just loves hyperbolic structures.

What is also fascinating is that although physicists had long thought the space of our universemust necessarily conform to Euclid’s ideals, data coming from telescopic studies of the early universe suggest the cosmological whole may possibly be a hyperbolic form.”

Margaret Wertheim, full interview here