Science Focus (issue 26)

Issue 026, 2024 SCIENCE FOCUS Lazarus Rising: The Attempted Resurrection of the Gastric Brooding Frog 拉撒路復活:絕種胃育蛙重生記 The Science Behind Cat Memes: Can Your Cat Haz Cheezburgerz? 貓咪迷因大解構:主子「可摸耳」 吃芝士漢堡? Movie Review: In Our Prime (2022) 影評:奇怪的數學家(2022) Masters of Transformation: Color-Changing Animals 偽裝大師:變色動物 The Shoelace Problem – What’s the Best Way to Lace Your Shoes? 鞋帶問題 — 怎樣穿鞋帶才是最佳 方法?

Dear Readers, Welcome to a bonus issue of Science Focus. Perhaps this will remind you of the joy of science, when you are kept busy by study trips, revision, or homework, during your Easter holiday. We focus on biology and mathematics this time. Although most of us have uniform skin colors that change little, some animals are far better at changing theirs, at short notice. We explore the color-changing secrets of chameleon and octopus. For cat lovers, we discuss the physiology and genetics of cats through memes. We also delve into the science and ethics behind animal cloning. Have you ever watched the movie Good Will Hunting? We bring you an equally captivating Korean movie that is worth adding to your playlist. Finally, for those of you who are puzzled by various ways to tie shoelaces, you will find a mathematical guide in this issue. We have just launched this year’s “Science in Lyrics” Writing Competition. For details, please visit our website by scanning the QR code on the back cover. Yours faithfully, Prof. Ho Yi Mak Editor-in-Chief 親愛的讀者: 歡迎閱讀額外出版的新一期《科言》!當你在復活節假期忙於參 加遊學團,勤於溫習和做功課的時候,希望本刊能令你重拾對科學的 喜悅。 今期我們主打生物和數學題材。雖然人類大多都擁有均勻而相對 恆定的膚色,但也有動物擅長於轉瞬間變色,所以我們將揭開變色龍和 八爪魚的變色秘密。各位貓癡也有福了,因為我們將從迷因解構貓咪的 生理和遺傳學。我們亦會探討複製動物背後的科學和道德問題。你有看 過電影《驕陽似我》嗎?今期我們會介紹另一套同樣值得你加入播放清 單的韓國電影。最後,對於被眾多鞋帶綁法弄得頭昏腦脹的你,我們將 會送上一份綁鞋帶的數學指南。 此外,今年的「歌詞與科學」寫作比賽現正接受報名,你可以掃瞄 本刊背頁的二維碼參閱《科言》網頁上的詳情。 主編 麥晧怡教授 敬上 Message from the Editor-in-Chief 主編的話 Copyright © 2024 HKUST E-mail: Homepage: Scientific Advisors 科學顧問 Prof. Yukinori Hirano平野恭敬教授 Prof. Ivan Ip 葉智皓教授 Editor-in-Chief 主編輯 Prof. Ho Yi Mak麥晧怡教授 Managing Editor 總編輯 Daniel Lau 劉劭行 Student Editorial Board學生編委 Editors 編輯 Sonia Choy 蔡蒨珩 Peace Foo 胡適之 Roshni Printer Aastha Shreeharsh Charlton Sullivan 蘇柏安 Helen Wong 王思齊 Social Media Editor 社交媒體編輯 Zoey Tsang 曾鈺榆 Graphic Designers 設計師 Ligeia Fu 付一乙 Evangeline Lei 雷雨晴 Coby Ngai 魏敏儀 Contents Science Focus Issue 026, 2024 What’s Happening in Hong Kong? 香港科技活動 Science Fiction: Voyage to the Edge of Imagination 1 科幻旅航 Black Holes: The Information Barrier 黑洞 ─ 信息的盡頭 Science Today 今日科學 Lazarus Rising: The Attempted Resurrection of the Gastric 2 Brooding Frog 拉撒路復活:絕種胃育蛙重生記 Amusing World of Science 趣味科學 The Science Behind Cat Memes: Can Your Cat Haz 6 Cheezburgerz? 貓咪迷因大解構:主子「可摸耳」吃芝士漢堡? Movie Review: In Our Prime (2022) 12 影評:奇怪的數學家(2022) Masters of Transformation: Color-Changing Animals 16 偽裝大師:變色動物 The Shoelace Problem – What’s the Best Way to 19 Lace Your Shoes? 鞋帶問題 — 怎樣穿鞋帶才是最佳方法?

What’s Happening in Hong Kong? 香港科技活動 Fun in Spring Science Activities 春日科學好節目 Any plans for this Spring? Check out these activities! 計劃好這個春天的好去處了嗎?不妨考慮以下活動! Science Fiction : Voyage to the Edge of Imagination 科幻旅航 Black Holes: The Information Barrier 黑洞 ─ 信息的盡頭 Are you a science fiction lover? The Science Museum has launched a special exhibition called "Science Fiction: Voyage to the Edge of Imagination." This immersive experience takes visitors on a journey through iconic science fiction exhibits, featuring a variety of films, literature, and art. With six immersive zones, including "Planet Mission" and "Bio Lab", visitors can explore significant themes within science fiction, such as space exploration, cyborgs, and future habitats. This cross-disciplinary exhibition should prompt visitors to reflect on the societal implications of advancing technology, and consider the opportunities and challenges of today and tomorrow through science fiction. The special exhibition at the Space Museum delves into the mysteries of black holes, revealing their myths and truths. In addition to the technologies used to "see" and "hear" black holes, visitors can also learn about the paradoxes and possibilities of these mysterious cosmic bodies. Is a black hole really a time machine? What will happen if you fall into a black hole? While we did not recommend you to find the answers by falling into an actual one a few issues ago, you can now do it in the exhibition through virtual reality goggles!. Period: Now – May 29, 2024 Venue: Special Exhibition Hall, Hong Kong Science Museum Admission fee: Extra entrance fee applies to this special exhibition. Please refer to the museum’s website for details. Period: Now – May 27, 2024 Venue: Foyer, Hong Kong Space Museum Admission fee: Free admission 展期: 現在至2024年5月29日 地點: 香港科學館特備展覽廳 入場費: 此專題展覽另設入場費,詳情請參閱科 學館網頁。 時間: 現在至 2024 年 5月27日 地點: 香港太空館大堂 入場費: 免費入場 你喜歡科幻故事嗎?科學館精心籌備了名為 「科幻旅航」的專題展覽,透過多件與科幻電影、 文學和藝術作品相關的展品,帶大家投身一段 奇妙的科幻旅程。展覽有「星際任務」和「生物 研究室」等的六個沉浸式展區,大家可以從中探 索多個科幻故事的熱門主題,例如太空探索、改 造人(cyborgs)和未來居所等等。這個跨領域 展覽希望促使大家思考先進科技為社會帶來的 影響,以及從科幻作品察看現在和未來的機遇和 挑戰。 這個太空館的專題展覽介紹關於黑洞的流 言和知識,解開其神秘面紗。大家除了可以認識 科學家用於「看見」和「聽見」黑洞的科技外,還 能了解更多關於黑洞的悖論和黑洞的各種可能 性。黑洞真的是時光機嗎?掉進黑洞後會發生甚 麼事?《科言》編採部之前曾勸告大家不要嘗試 親身掉進黑洞找答案,但現在你可以在展覽中透 過虛擬實境眼鏡實踐了! 1 MythBusters: Black Holes (Issue 019) 流言終結者:黑洞篇 (第十九期)

By Sonia Choy 蔡蒨珩 Lazarus Rising: The Attempted Resurrection of the Gastric Brooding Frog The arrival of Dolly, the first cloned mammal in 1996, marked an important page in human history. It was the first time humans were able to create a mammal in a laboratory. Pictures of Dolly made headlines across the world. But did you know that scientists also tried to use the same technology to bring extinct frogs back to life? The southern and northern gastric brooding frogs (Rheobatrachus silus and Rheobatrachus vitellinus) were discovered in 1972 and 1984 in Queensland, Australia respectively. Both being very small (about 30– 54 mm for the southern and 55–80 mm for the northern species) and living in a limited rainforest area (less than 1000 km2), they lived in streams of the Queensland mountain ranges [1, 2]. Like many native Australian species, the frogs were unique to the land down under, and possessed extremely unique characteristics. One such thing that caught headlines at that time was how they reproduce [3]. The mother swallows a number of eggs and stops producing acid in its stomach to allow the eggs to hatch into tadpoles, and later into frogs. It was suggested that a substance called prostaglandin E2 secreted by the tadpoles can inhibit the acid secretion of the mother [4]. Then the mother does not eat for six weeks and stops breathing through the lungs but the skin, as its bloated stomach has squeezed the lungs to collapse. Eventually, the mother gives birth to fully formed baby frogs via “propulsive vomiting”, much like a Russian doll. This dramatic method caught the attention of many, including zoologists who couldn’t believe this was true…until they saw it for themselves. Sadly, these frogs did not live very long, and by 1981, the southern breed had gone extinct in the wild; the northern breed was also extinct in 1985, within a year after its discovery. Mike Archer, a researcher from the University of New South Wales, had read about the frog and decided to 拉撒路復活: 絕種胃育蛙重生記 do something no one had seriously attempted before – to bring it back to life [3]. His plan was to use somatic cell nuclear transfer (SCNT) to transfer a somatic cell nucleus obtained from the frozen frog sample to a fresh egg of a reasonably close but existing relative, the barred frog (Mixophyes fasciolatus). With a full set of the southern gastric brooding frog’s DNA as the blueprint of life, they hoped the cell can divide and develop into a fullfledged individual. SCNT is divided into a few main steps. The first step was to use ultraviolet radiation to destroy the nuclear DNA of a donor egg [5]. Into this “empty” egg, scientists inserted a nucleus collected from the long frozen gastric brooding frog’s tissue sample. For the cell to divide and grow into an embryo, an electrical or chemical stimulation is usually given to activate the manipulated oocyte [6]. After many cell divisions, the embryo then underwent the crucial step of development, known as gastrulation, when cells in its exterior migrate internally – and there it stopped [3]. In the best-case scenario, the cell division and differentiation would continue further, to the point that we have a fully formed tadpole of the southern gastric brooding frog. Current technology is very far from even creating a southern gastric brooding frog tadpole, but Mike Archer’s great dream is to bring the frog back to life. This is partially for the potential medical benefits it may bring. As mentioned earlier in the article, female frogs temporarily stop the production of gastric acid after they swallow the egg and let it hatch. However, the species was extinct before scientists could further study them [7, 8]. If the cloning process is successful, this would lead to a better understanding of the southern gastric brooding frogs, and potentially help human patients suffering from too much or unwanted gastric acid. From acid reflux to ulcers and even more serious diseases, this

3 could be a potential, permanent cure. But Archer’s goal seemed simpler. Quote, “If we were responsible for the extinction of the species, deliberately or inadvertently, we have a moral responsibility or imperative to undo that if we can [3].” Over the last century, many species have gone extinct from human activities. Widespread deforestation and global warming have destroyed the habitats of many species, especially very rare ones that are endemic to Australia. Some, including Archer, believe that our responsibility is to restore these endangered species to their natural habitats, and undo the damage we have caused in the past. However, there are ethical issues surrounding this. First of all, extinction is part of nature’s cycle; species regularly fall on and off the earth all the time. By cloning the southern gastric brooding frog and bringing it back to life, we are upsetting Mother Nature. By Archer’s logic, if species died out by human behavior, then we should help restore those species back to the wild. The problem is that species go extinct due to a myriad of reasons; the Australian government, for example, lists the pathogenic fungus Batrachochytrium dendrobatidis as a possible extinction reason of the gastric brooding frogs [1, 2]. This is not to underplay the role of humans in destroying nature over the past century, but what is to say that the species definitely died only by human influence? In this case, why shouldn’t we just let nature take its course? Also, the world has changed since the southern gastric brooding frog went extinct. The current Queensland mountains are no doubt different from the ranges where the frog last thrived over 50 years ago. By sending them back into the wild after hatching in the laboratory, we may be sending them to a second death, as it is very likely that they will not survive for an extended period of time. In this case, what is the point of doing this? More fundamentally, which species should be brought back from extinction? Should humans be playing God? At least, most countries across the world agree that cloning should not be done in humans, making generating alternative organs from individuals currently impossible. Cloning technologies no doubt leave us with many unanswered questions. It is a tool that can be used, and misused; the very thin line between the two will continue to be discussed for some time.

在1996 年,首隻複製哺乳類動物「多莉」的誕生標誌 著人類歷史上重要的一章,這是人類首次在實驗室合成哺 乳類動物。多莉的照片佔據了全世界報紙的頭條,但你知道 科學家亦曾經以同樣手法嘗試讓已絕種的青蛙重生嗎? 南部及北部胃育蛙(又稱胃育溪蟾,學名分別為 Rheobatrachus silus 和Rheobatrachus vitellinus)分 別於1972 及 1984 年在澳洲昆士蘭被首次發現。牠們體型 細小(南部品種身長只有30–54毫米,而北部品種也只有 55–80 毫米),居住在昆士蘭山脈的小溪中,出沒範圍僅限 在一片少於1000 km2 的熱帶雨林中 [1, 2]。像很多澳洲本 土物種一樣,胃育蛙僅在澳洲出現,而且擁有許多獨有的特 徵。 其中,引起傳媒廣泛報導的是胃育蛙的繁殖方式 [3]。母 蛙會吞下自己的卵,然後停止分泌胃酸,讓卵在胃裡孵化成 蝌蚪,再發育成青蛙。科學家認為由蝌蚪分泌的前列腺素 E2 可以抑制母蛙的胃酸分泌 [4]。在接下來的六週裡母蛙不會 進食,亦會停止用肺呼吸,轉而使用皮膚透氣,因為此時母 蛙鼓起的胃已把肺部擠壓得塌陷。最後,就像俄羅斯套娃一 樣,母蛙會透過嘔吐的方式誕下一群完全成形的小蛙。這種 戲劇性的產子方式引起了許多人注意,當中包括不少親眼看 見才相信的動物學家。遺憾的是,這些胃育蛙並沒有活很久: 南部胃育蛙於1981年在野外滅絕,而北部胃育蛙也在首次 發現後不足一年的 1985 年絕種。 新南威爾士大學研究員Mike Archer讀到關於胃育蛙 的資料後,決定做一件未有人認真嘗試過的事情:使胃育 蛙起死回生 [3]。他的計劃是使用體細胞核移植(somatic cell nuclear transfer / SCNT)技術,把從冷藏胃育蛙樣 本獲得的體細胞核轉移至其尚存近親 — 橫斑蟾屬青蛙 Mixophyes fasciolatus的活卵子內。研究團隊希望這顆含 有完整胃育蛙DNA的細胞能按遺傳物質上早已寫好的生 命藍圖,分裂並發育成發展完全的胃育蛙個體。 體細胞核移植可分為幾個主要步驟。第一步是用紫外線 破壞卵子的細胞核 DNA [5]。然後科學家從冷藏的胃育蛙組 織樣本取得細胞核,把其加入已去核的卵子中。為了讓細胞 分裂並發育成胚胎,研究人員通常還需要施以電擊或化學刺 激,以啟動被改造的卵細胞 [6]。經過多次細胞分裂後,胚胎 經歷早期發育裡被稱為原腸胚形成(gastrulation)的關鍵 步驟,這時胚胎外圍細胞移動至內層,然而實驗中的胚胎發 育就止步於此,未能再下一城 [3]。最理想的結局當然是細胞 分裂和分化繼續進行,直到發展出一隻完全成形的南方胃育 蛙蝌蚪。 雖然目前技術離能夠複製出南方胃育蛙蝌蚪還差很遠, 但Mike Archer的夢想是使胃育蛙重生。部分原因是為著 可能帶來的醫療益處。如前文所述,雌性胃育蛙能在吞下卵 後會暫停製造胃酸,讓卵孵化。然而,胃育蛙在科學家能進 一步研究之前就已經滅絕 [7, 8],如果能成功複製牠們,科 學家將能對南方胃育蛙有更深入的瞭解,並有可能從中找 到治療方法幫助過度分泌胃酸的病人。從胃酸倒流到消 化性潰瘍,甚至是更嚴重的疾病,研究都有可能會為相 關疾病提供根治方法。 然而 Archer 的動機也許更為簡單,如他所說: 「如果我們有意無意地使一個物種滅絕,在力所 能及的情況下,我們就有道德責任和義務將其 復原 [3]。」在過去這個世紀,人類活動使許多 物種滅絕,大規模砍林和全球暖化破壞了許

5 References 參考資料: [1] Department of Climate Change, Energy, the Environment and Water, Australia Government. (2023). Rheobatrachus silus — Southern Gastric-brooding Frog. Species Profile and Threats Database. public/ [2] Department of Climate Change, Energy, the Environment and Water, Australia Government. (2023). Rheobatrachus vitellinus — Northern Gastric-brooding Frog, Eungella Gastric-brooding Frog. Species Profile and Threats Database Profile. http:// pl?taxon_id=1910 [3] Yong, E. (2013, March 15). Resurrecting the Extinct Frog With a Stomach for a Womb. National Geographic. https://www. [4] Tyler, M. J., Shearman, D. J. C., Franco, R., O'Brien, P., Seamark, R. F., & Kelly, R. (1983). Inhibition of Gastric Acid Secretion in the Gastric Brooding Frog, Rheobatrachus silus. Science, 220(4597), 609–610. [5] TED. (2013, June 27). Michael Archer: How we'll resurrect the gastric brooding frog, the Tasmanian tiger [Video]. YouTube. [6] Gouveia, C., Huyser, C., Egli, D., & Pepper, M. S. (2020). Lessons Learned from Somatic Cell Nuclear Transfer. International Journal of Molecular Sciences, 21(7), 2314. https://doi. org/10.3390/ijms21072314 [7] UNSW. (2015, July 6). Back from the dead: Catastrophic Science [Video]. YouTube. [8] Wondracz, A. (2019, April 2). Mysterious frog that reproduces by regurgitating its young could hold the key to treating stomach ulcers...but it hasn't been seen in almost 40 years. Daily Mail. Gastric-brooding-frog-help-treat-stomach-ulcers.html 多物種的棲息地,尤其影響了許多澳洲獨有的罕見物種,因 此包括 Archer在內有些人認為我們有責任拯救這些瀕危 物種,將牠們帶回原來的棲息地,並盡可能彌補我們過去對 環境造成的破壞。 但這無疑會引申出一連串道德問題。首先,物種衰亡是 自然更替的一部分,地球上不斷會有新物種誕生,也會有現 存物種滅亡,而複製南方胃育蛙使牠其重生某程度上也是在 擾亂大自然生態。按照 Archer 的思路,如果物種因人類行 為滅絕,那我們就應該協助這些物種重返大自然。問題是使 物種滅絕的原因往往不止一個,例如澳洲政府就將致病真 菌Batrachochytrium dendrobatidis列入胃育蛙滅絕的 可能原因之一 [1, 2]。這裡不是想低估人類在過去一世紀對 大自然造成的破壞,但我們又怎能肯定一個物種是純粹因為 人類影響而滅絕呢?在這種情況下,順其自然又有何不可? 此外,自南方胃育蛙滅絕以來,環境已經變了很多。現 時的昆士蘭山脈無疑與 50 多年前胃育蛙茁壯成長的棲息地 不同。在實驗室孵化後將牠們送到野外,我們可能只是將牠 們送向第二次死亡,因為牠們很大機會無法在野外長時間存 活。在這種情況下,這樣做有甚麼意義嗎?更根本的是,哪 些物種應該被拯救,哪些不應?人類應該扮演上帝嗎?至少, 世界上大多數國家都同意不應該複製人類,使現在我們不能 透過製造複製人生產後備器官。 複製技術無疑為我們帶來了許多未能解答的道德問題; 它是可以一件被善用或誤用的工具,這一線之差將在未來一 段時間引起更多討論。

Since the dawn of the internet, cats have taken over our explore pages in the form of funny video compilations, heartwarming videos and of course: memes. Meme culture has guaranteed that cats can gain the same amount of worship and reverence now as they did in ancient Egypt. Some of these memes raised trivial yet interesting questions: Can Cats Have Cheeseburgers? This may be a seemingly silly question with a seemingly obvious answer; however, it may surprise you to know that it can prove beneficial to occasionally feed your cat hamburgers. As carnivorous animals, cats can have a variety of meats — making plain hamburgers a safe and welcome treat for them [1]. Feeding your cats burgers comes with its own set of “terms and conditions” though. Unfortunately, your cat cannot “haz cheezburgerz” (footnote 1) specifically. Contrary to popular belief that cats love milk, most adult cats are lactose intolerant [1] because they can no longer produce enough lactase to break down lactose after weaning. Therefore, it’s probably wise to skip the cheese and seasonings we add in our own hamburgers when you feed cats. Toppings such as onions and garlic can also harm their gastrointestinal tracts and damage red blood cells if consumed in large amounts. The oxidative compounds in onions can denature hemoglobin, causing anemia [1, 2]. …Or Maybe a Little Salami? As per the meme, a cat may as well have typed this out and, technically, it wouldn’t be wrong. While cats can have a little bit of salami, it shouldn’t become the staple of their diet. As a processed meat The Science Behind Cat Memes: Can Your Cat Haz Cheezburgerz? 貓咪迷因大解構: 主子「可摸耳」吃芝士漢堡? By Aastha Shreeharsh

with high sodium content, salami may exacerbate health risks and conditions relating to the heart and kidneys [1, 3]. As all uncooked meats do, salami too poses risks of Salmonella infection and trichinellosis (a disease caused by infection with Trichinella parasites). Kittens and pregnant cats should not be fed salami, as their immune systems are vulnerable to toxins and bacteria [3]. Are They Really Liquid Enough to “Sits” Where They “Fits”? We often ponder over unusual, inconsequential ideas and their meanings. Often, scientists are among those people pondering these questions. If you have ever wondered whether cats are truly liquid as you see yet another cat weasel its way into narrow crevices and hilariously small containers, you’re in luck. Researcher Marc-Antoine Fardin is one such scientist, who was awarded the Ig Nobel Prize in Physics (footnote 2) for answering this absurd question. Using rheology, the study of deformations and flows of matter, he found that, under certain conditions, cats may fit the definition of a liquid [4]. To determine the state of a material over a given time frame, rheologists look at the relationship between two time periods: the relaxation time and the experimental time. Aptly named, the relaxation time is the time taken by a material to modify its form to fit in a container; in this case, it would be the time taken by a cat to “fits” where it “sits”. Experimental time refers to the time elapsed since the deformation is observed; in this case, this could be the time the cat is observed since it first puts its paws in to “sits” in the fruit bowl. Finally, rheologists look at the ratio between the relaxation time and the experimental time — the Deborah number De: (where tc is the relaxation time and tp is the experimental time) When the Deborah number is less than 1, i.e. tp > tc, the material is considered relatively liquid. If you think carefully, by this definition, whether a material is perceived to be liquid or solid all depends on whether you observe it long enough for the deformation to take place. As Fardin puts it, “If you take a timelapse of a glacier on several years you will unmistakably see it flow down the mountain [5].” Similarly, a 7

waterfall can also appear “frozen” in a photo taken by a high speed camera. “For cats, the same principle holds,” Fardin remarked. “If you are observing a cat on a time longer than its relaxation time, it will be soft and adapt to its container, like a liquid would [5].” Why Is Grumpy Cat So Grumpy? Signalling the end of the weekend, Mondays typically serve as the herald of yet another week filled with classes, tests, and assignments galore; which is why this cat’s displeasure towards Monday seems relatable to us rather than unusual. However, if you were to look up Grumpy Cat memes on the internet, you’d very quickly see what earned her this nickname. With her piercing blue eyes forever narrowed in bemusement and a permanent scowl marring her face, Tardar Sauce, the star of the infamous Grumpy Cat meme, rose to fame as the poster child of grumpiness. Contrary to popular belief, Grumpy Cat’s surly expression is not caused by a morose disposition; rather, it is the direct result of an underbite due to a type of feline dwarfism known as achondroplasia [6]. Mutations in the UDP-glucose 6-dehydrogenase (UGDH) gene were suggested to cause this genetic disease [7, 8], leading to abnormal bone and cartilage development. This condition was speculated to have an autosomal dominant mode of inheritance. Homozygous mutants were not observed, likely because of its lethality at an early embryonic stage [7–9]. Although the resultant physical deformities may seem cute to us, they are also associated with spinal and degenerative joint problems [9], and a shortened lifespan [6]; yet breeders continue to breed cats afflicted with feline dwarfism to 自互聯網誕生以來,貓以層出不窮的方式佔據了我們社 交媒體的探索頁,有時是搞笑影片合輯,有時是窩心感人短 片,但不得不提的是:迷因!迷因文化確保貓受到的讚頌和 崇拜不亞於牠們在古埃及時期受到的膜拜,然而當中有些 迷因卻使我們不禁反思一些有趣小問題: 貓能吃芝士漢堡嗎? 這看似是答案非常 明顯的白痴問題,但你 可能不知道偶爾餵一下 主子吃漢堡包其實是 有益的。作為肉食性動 物,貓能吃不同種類的 肉,所以「簡單」的漢堡 包對貓來說是安全而 受歡迎的食物 [1];之 所以加上「簡單」是因 為有一些「注意事項」 我們不能忽略。 遺憾的是,你的主子並不能吃芝士漢堡(註一)。大眾對 貓的印象可能是認為牠們喜愛喝牛奶,然而牠們在戒奶後 並不能製造乳糖酶分解乳糖,所以成年貓大多是乳糖不耐 的 [1],因此我們不應將芝士和醬料加到給貓吃的漢堡中。 大量進食洋蔥、蒜頭等配料亦會對貓的消化道和紅血球造 成損害,尤其洋蔥中具氧化性的化合物能使血紅蛋白變性, 引致貧血 [1, 2]。 那少許莎樂美辣肉腸可以吧? 如這迷因所示,有主子可能曾因一時口腹之慾而在電 腦前偷偷回覆「可以」,技術上這不能說是錯的。儘管貓可 meet the high demand for unique-looking cats. Take this article as a sign: Adopt, don’t shop! 1 Editor’s note: The phrase “haz cheezburgerz” comes from LOLspeak – the vernacular associated with the LOLcats Internet memes that first became popular in 2007 [10]. LOLspeak embodies what made the LOLcats memes so popular – intentionally misspelled words that phonetically resemble the grammatically correct word (“cheezburger” for cheeseburger) and “purr-fect” puns that play on the fact that a cat is supposedly saying these phrases. 2 Ig Nobel Prize: An award that celebrates scientific research that “first makes people laugh, then think.”

以吃少許辣肉腸,但這 不應成為其主食。辣肉 腸這類高鈉的加工肉類 可能增加心臟和腎臟的 健康風險及使健康惡化 [1, 3];像其他生肉一樣, 進食辣肉腸會帶來感 染沙門氏菌和旋毛蟲症 (由旋毛形線蟲屬寄生 蟲感染導致的疾病)的 風險,因此小貓和懷孕 貓隻不宜進食辣肉腸, 因為牠們的免疫系統未必足以抵禦毒素和細菌 [3]。 貓真的能鑽進所有狹小容器裡嗎? 我們也許經常為不尋常,但無關痛癢的小問題陷入沉 思,科學家通常都是其中一分子,而且沉思著類似的問題。 當你看見再有一隻貓把身軀鑽進狹縫或是細小容器的時候, 你是否也懷疑過貓到底是不是液體呢?如果你有這樣想過 的話,你走運了!研究員Marc-Antoine Fardin正是其中一 員,他因解答了這條可笑的問題而獲得搞笑諾貝爾物理獎(註 二)。流變學(rheology)是研究物體變形和流動的一個範 9

疇,從這個角度著手,他發現在特定條件下,貓也能符合液 體的定義 [4]。 要決定物料在特定時間裡的狀態,流變學家會觀察兩段 時間之間的關係:鬆弛時間(relaxation time)和實驗時間 (experimental time)。正如字面上的意思,鬆弛時間是物 料改變形狀以填滿容器的所需時間,在我們的例子裡就是 貓塞滿容器的所需時間。實驗時間則是指由開始觀察起計 的時間,這可能是從我們最先看到貓爪佔據水果盤一刻計 起。最後流變學家會計算鬆弛時間和實驗時間之間的比,即 是底波拉數(Deborah number / De): (tc 是鬆弛時間,而tp 是實驗時間。) 當底波拉數小於1,即是 tp > tc,物料就會相對地被視 為液態。如果你細心想想,根據這個定義,物料被我們認為 是液態還是固態,完全取決於觀察時間是否長得使我們能 看見變形過程。正如 Fardin 的解釋一樣:「如果你拍一條歷 時數年的冰川縮時短片,毫無疑問地你會看見冰川往山下流 動 [5]。」同樣地,在高速相機拍攝的照片裡,瀑布也能顯得 像被凝住了一樣。「套用在貓上也是同樣原理。」Fardin 評 論道,「如果你觀察貓的時間比其鬆弛時間長,貓就會像液 體一樣柔軟,亦能填滿容器 [5]。」 為甚麼不爽貓這麼不爽? 星期一標誌著美好週末的終結,面前等著大家的又是沒 完沒了的課堂、測驗和功課,這正是不爽貓(Grumpy Cat) 對星期一不爽的原因,相信大家都會有很深的共鳴。如果你 嘗試上網搜尋不爽貓迷因,很快你就會明白她為何得到這個 稱號。在半點疑惑下半開的銳利藍眼睛,怒瞪的殺氣劃破面 孔 — 不爽貓迷因裡的主角他他醬(Tardar Sauce)憑這副 惡形惡相成為互聯網上不爽的代表。 有別於大眾的理解,不爽貓的怒相並不是源自陰沉的性 格,而是由貓侏儒症導致的下顎前突所致,病名又稱為軟骨 發育不全(achondroplasia)[6]。尿苷二磷酸–葡萄糖 6– 脫氫酶(UDP-glucose 6-dehydrogenase / UGDH)基因 上的突變被認為是導致這個遺傳病的元兇 [7, 8],導致不正 常的骨骼及軟骨生長。科學家推測這個疾病是以常染色體 顯性模式(autosomal dominant mode of inheritance) 遺傳;此外科學家沒有觀察到顯性純合的個體,因為這些個

1 編按:此處英語原文為源自LOL 語(LOLspeak)的「haz cheezburgerz」, 貓咪迷因(LOLcat memes)由2007年開始在網上爆紅 [10],LOL語是貓 咪迷因上的調皮文字,亦是貓咪迷因爆紅的原因,當中包括發音相近但故意 串錯的詞彙(以「cheezburger」代替「cheeseburger」),也有模仿貓說話 的雙關語(例如「purr-fect」,「purr」是貓獨特的低沉咕嚕聲)。 2 搞笑諾貝爾獎:一個獎項以表揚「首先令人發笑,繼而發人深省」的科學研究。 體大概在胚胎發育初期就已經死亡 [7–9]。雖然疾病導致的 殘缺外表看來非常可愛,但疾病有可能為個體帶來脊柱和關 節退化問題 [9],亦可能縮短個體壽命 [6],然而商人仍然繼 續透過配種繁殖受疾病折磨的侏儒貓,以應對市場對長相 獨特貓隻的需求。所以,這篇文章亦希望呼籲大家:領養代 替購買。 References 參考資料: [1] Belvoir Media Group, Cornell University College of Veterinary Medicine Feline Health Center. Feeding Human Foods: The Facts. CatWatch. https://www. [2] Yuyama M. Oxidative Compounds in Onion (Allium cepa L. Onion). Isolation and Demonstration of Their Oxidative Damage to Erythrocytes. Japanese Journal of Veterinary Research. 1989;37(2):144. dspace/bitstream/2115/3186/1/KJ00002377289.pdf [3] Lesser J. Can Cats Eat Salami? The Spruce Pets. https:// beef%2C%20and,safe%20to%20offer%20your%20cat. [4] Fardin MA. Answering the question that won me the Ig Nobel prize: Are cats liquid? The Conversation. https:// [5] Devlin H. Solid and liquid cats, didgeridoos and cheese disgust scoop Ig Nobel awards. The Guardian. https:// [6] Metych M. Dwarfism in Cats: It’s Only Cute ‘til Someone Gets Hurt. Encyclopaedia Britannica. https://www. [7] Struck AK, Braun M, Detering KA, et al. A structural UGDH variant associated with standard Munchkin cats. BMC Genetics. 2020;21(1):67. doi:10.1186/s12863-020-00875-x [8] Anderson LM, Fox DB, Chesney KL, Coates JR, Torres BT, Lyons LA. Skeletal Manifestations of Heritable Disproportionate Dwarfism in Cats as Determined by Radiography and Magnetic Resonance Imaging. Veterinary and Comparative Orthopaedics and Traumatology. 2021;34(5):327-337. doi:10.1055/s-00411730355 [9] British Small Animal Veterinary Association. Cat Breeds – Trophies With Hidden Problems? Journal of Small Animal Practice. 2008;49(10):7-9. [10] Gawne L, Vaughan J. I can haz language play: The construction of language and identity in LOLspeak. Proceedings of the 42nd Australian Linguistic Society Conference – 2011. 2012;97-122. 11

Directed by Park Dong-hoon, the movie opens with high school student Han Jiwoo (Kim Dong-hwi) and his struggles with mathematics. He crosses paths with security guard Lee Hak-sung (Choi Min-sik), a North Korean defector and reclusive mathematician whose story is gradually revealed throughout the movie, and ends up asking him for help in preparation for a tough exam. Hak-sung agrees to teach him – to appreciate math, rather than to cram. The movie then tracks their growing relationship (which the actors portray very well), the involvement of Ji-woo’s friend Park Bo-ram (Jo Yun-Seo), the impact of the exam and Hak-sung’s proof of the Riemann hypothesis (in reality still unsolved to this day). On the whole its setup has been compared to the 1997 film Good Will Hunting, which also features an anonymous but mathematically gifted university worker, but it has a strong story of its own and avoids rehashing the same plot. Without spoiling the movie, let’s see whether its plot makes sense in reality! Who Was the Old Man in Hak-sung's Flashback? At the end of Hak-sung’s first lesson he calls Jiwoo an “epsilon”. The memory that explains this is centered on Hak-sung’s childhood meeting with Paul Erdős, one of the most productive and eccentric mathematicians of the 20th century, who also independently proved the prime number theorem [1]. Erdős traveled around the world with only one suitcase of clothes, collaborating with so many different colleagues that mathematicians still use the “Erdős number” to track the network of people he worked with. He was also famous for his odd vocabulary, where he called women “bosses”, men “slaves”, lectures “sermons”, and nonmathematicians “trivial beings” [2]. (Hak-sung also calls Ji-woo a “trivial being” in the same scene.) Children were called “epsilons” because in calculus an epsilon represents a positive but very small number. Erdős met many “epsilons” throughout his life. According to his biographer, Paul Hoffman, Erdős “made it his mission to seek out child prodigies all over the world” and encourage them with further problems [3]. He met the 10-year-old Terence Tao at the 1985 International Mathematical Olympiad (IMO), very By Peace Foo 胡適之 Movie Review: In Our Prime (2022) 影評: 奇怪的數學家 (2022)

13 similar to Hak-sung’s memory of Erdős meeting him at the 1982 IMO. Erdős had already been teaching children gifted in mathematics as early as the 1960s: “[László] Lovász only started doing serious mathematics late in life, said Erdős, ‘at the ripe old age of nearly seventeen. When Lovász was still an epsilon, in the first year of high school, he and … a fellow mathematician courted the same boss-child, also a mathematician and not a bad one as bosses go. The two slave children asked her to choose. She chose Lovász,’ and they got married. But the love story could be improved upon, Erdős noted, by having the boss-child answer: ‘I will choose the one who proves the Riemann Hypothesis.’ [3]” Did North Korea Actually Participate in the IMO? In the segment announcing the proposed proof of the Riemann hypothesis, the mathematician Oh Jung-nam tells viewers that he once represented South Korea at the IMO alongside Hak-sung, who represented North Korea. In reality, North Korea has participated in the IMO, but they did not begin doing so until 1990 and did not participate between 1993 and 2006. They were disqualified for suspected cheating in 1991 and 2010 [4, 5]. South Korea began participating in 1988 and has attended every IMO since then [6]. So neither Jungnam nor Hak-sung could have gone to the IMO in 1982 as the movie shows. But it is quite likely that both would have done well based on the overall performance of the Koreas at the IMO: South Korea has the fourth most gold medals and North Korea has the 23rd, out of 120 participating countries in IMO history [7], although it is worth mentioning that North Korea has not participated as often as South Korea and the two countries often perform similarly well in individual tournaments. What About the Nobel Prize? Another newscaster heard that Hak-sung could be awarded a Nobel Prize for his proof of the Riemann hypothesis. This is not accurate. There is no Nobel Prize for mathematics; the most prestigious prize is the Fields Medal, which is only awarded to mathematicians 40 years old or under. The best estimate for Hak-sung’s age is 45–50 years old, so he would not get the prize. However, he would certainly be awarded the Abel Prize, established in 2001 and often described as a mathematics' equivalent to the Nobel Prize, as well as receiving the Clay Institute’s prize of one million US dollars for a successful solution to the Riemann hypothesis, one of their Millennium Problems. (Out of the seven problems, only one has been solved, the Poincaré conjecture, which we wrote about in Issue 019. Remarking that “Everybody understood that if the proof is correct then no other recognition is needed,” Grigory Perelman, another “hermit mathematician” like Hak-sung, refused both the prize money, and the Fields Medal.) Is the “π Song” Real? A review claims that the highlight of the movie is the scene where Hak-sung plays the “π song” to “convince [Ji-woo] that math is of ethereal beauty” [8]. With the digits of π written out in front of him, Haksung says that he will “play π” by assigning the digit 1 to the note C, 2 to D, and so on. He tells Bo-ram to accompany the melody that this produces. This is not a new way to represent the digits of π and many examples can be found on YouTube [9, 10]. The opening of the song in the movie does correspond to the first 14 digits of π: 3.1415 92 65358 97 As the accompaniment begins, aside from repeating this block, Hak-sung also weaves extra notes into his part of the song that do not correspond to digits of π. Then after the first glissando, he plays a simple repeating pattern of the next 14 digits: 9323 846 2643 383 But he does not follow it exactly throughout. In fact his part corresponds to the sequence: 9323 846 2643 383 9323 846 5 The song dresses these 28 digits of π up with a piano accompaniment. It does not necessarily present many digits of π in order, and is more of an interpretative art piece, though a very beautiful one that matches the tone the director wants to communicate in the movie. By itself π would not make

劇情簡介 這套電影由朴東勳執導,以高中生韓智宇(金東輝 飾) 學習數學的煩惱揭開序幕。韓智宇遇上當保安糊口的脫北 退隱數學家李學成(崔岷植 飾),後者的身世隨故事的推 進逐步揭曉,韓智宇最後請求李學成教他應付艱深的數學 考試。李學成同意,但只答應教他欣賞數學,而不會操練試 題。故事之後描述二人逐漸變得熟絡的關係(演員對此演 繹得恰到好處!)、韓智宇朋友朴寶藍(趙尹瑞 飾)的加 入、那場考試帶來的影響,以及李學成解開黎曼猜想 (Riemann hypothesis)的證明(在現實上黎曼猜 想尚未被證實)。有人把故事劇情與在1997年上映 的電影《驕陽似我》(Good Will Hunting)作對比, 皆因兩者同樣涉及默默無名但極具數學天份的大學工 友,但《奇怪的數學家》本身就是獨樹一格的原創故事, 因此並不會令觀眾有舊調重彈之感。就讓我們在避免透 露劇情的情況下,看看劇情在現實世界是否合理吧! 李學成回憶中的老人是誰? 李學成在第一堂課結束時稱韓智宇為 「epsilon」,這關乎李 學成在 童年時與 Paul Erdős會面的一段回憶。Paul Erdős是20世紀 其中一個最多產的古怪數學家,曾獨立證明質數定 理(prime number theorem)[1]。Erdős帶著一 箱衣服就環遊世界跟不同數學家合作,協作者多至數學界 現在還用「Erdős數」來追蹤任何一個數學家與他的淵源。 使Erdős 聞名的還有他自創的奇怪詞彙,例如他稱女性為 「老闆」,男性為「奴隸」,講課為「講道」,以及非數學家為 「凡人」[2]。(李學成在同一幕也稱韓智宇為「凡人」。)小 孩被稱為「epsilon」的原因是因為 epsilon 在微積分裡代 表一個非常小的正數。 Erdős 一 生 遇 過 不 少「epsilon」。傳 記 作 者 Paul Hoffman 寫到 Erdős「致力尋找世界各地的天才兒童」, 並以超越他們程度的數學問題激勵他們 [3]。他在1985年 國際數學奧林匹克(IMO)就遇上當時只有十歲的陶哲軒, 這呼應李學成回憶中 Erdős 在 1982 年 IMO 跟他會面的 情景。 其實Erdős 早於1960 年代就開始教導數學資優兒童: 「[László]Lovász在較遲的時候才開始認真接觸數 學,Erdős 形容為『在十七歲左右的成熟之年。當 Lovász 仍是個 epsilon,讀第一年高中的時候,他與……一位熱愛 數學的同輩追求著同一個小老闆,那老闆亦是數學同好, 以老闆來說算是學得不錯。兩個小奴隸著她在兩人中選一 個,她選了 Lovász。』然後兩人就結婚了。但 Erdős認為他 們的愛情故事可以錦上添花,例如小老闆可以回答:『我會 選能證明黎曼猜想的那位。』[3]」 北韓事實上有參與過 IMO 嗎? 在公佈黎曼猜想證明擬定稿的一段,數學家吳正南告 訴觀眾他曾代表南韓,與北韓代表李學成在 IMO 碰頭。 現實上北韓的確有參加過 IMO,他們由1990 年起才 開始參加,其後在 1993至 2006 年間均缺席比賽;另外他 們在1991和2010年因懷疑作弊被取消資格 [4, 5]。另一 方面南韓由1988 年起到現在依然是 IMO 從未缺席的常 客 [6]。由此可見,電影中無論是吳正南或李學成都不可能 出現在 1982 年的 IMO 裡,但按兩韓的整體往績推論,兩 者如果參賽的話也很可能會有不錯的表現:南韓是總金牌 數目排名第四的國家,而北韓則在 IMO歷史上 120 個參 賽國家中排行第23 [7],雖然值得留意的是北韓的參賽次 數並不如南韓多,而兩國在單次對賽中通常都旗鼓相當。 那諾貝爾獎呢? 另一個主播聽說李學成可能會因成功證明黎曼猜想而 獲頒諾貝爾獎,然而這是不可能的。諾貝爾並不設數學獎, 數學界最頂尖的獎項是菲爾茲獎(Fields Medal),但那 只頒予 40 歲或以下數學家,李學成怎樣看也有 45至 50 歲,因此他也不會獲頒菲爾茲獎。但他應該會獲頒在 2001 年創立的阿貝爾獎(Abel Prize),那亦是一個經常被形 容為相當於諾貝爾獎的數學獎項;亦會因成功解決黎曼猜 想而獲得克雷研究所(Clay Institute)的100萬美元獎 金,因為那是研究所其中一道懸賞的千禧年難題。(在他們 much of a song anyway, since there is perhaps nothing mathematically special about its pattern of decimal digits. What has turned this essentially random pattern into a proper piece of music is the application of the human imagination. Nevertheless, it’s a very fitting song for a movie that celebrates the advancement of mathematics. So much of this subject began as either a useless curiosity, like a dead butterfly pinned on a card, or a narrow solution to a narrow real-world problem; it is our imagination that propels individual parts of mathematics beyond either of these labels, and gives it the power and scope that makes it beautiful. If you are a serious math lover who wants to know more about the Riemann hypothesis and analytic number theory, please find the additional content on our website. What is the Riemann Hypothesis?

By Helen Wong 王思齊 15 References 參考資料: [1] Stewart, I. (2013). The Great Mathematical Problems. Profile Books. [2] Monroe, H., & Scott, P. (2004). Paul Erdős. Australian Mathematics Teacher, 60(2), 14-16. [3] Hoffman, P. (1998). The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth. Fourth Estate. [4] International Mathematical Olympiad. (n.d.). Democratic People's Republic of Korea. http://www. [5] Berg, A. (2021). Statistical Analysis of the International Mathematical Olympiad. Math Intelligencer, 43, 105112. [6] International Mathematical Olympiad. (n.d.). Republic of Korea. r.aspx?code=KOR [7] International Mathematical Olympiad. (n.d.). Results: Cumulative results by country. http://www.imo-official. org/results_country.aspx?column=awards&order=desc [8] Kim, B. (2022, February 23). (Movie Review) Mathematics no longer difficult in 'In Our Prime'. Odyssey. php?ncode=179561410240172 [9] Blake, M. (2011, February 13). What Pi sounds like [Video]. YouTube. watch?v=WQdLDMLrYIA [10] aSongScout. (2011, March 27). Song from π! [Video]. YouTube. watch?v=OMq9he-5HUU 列出的七道難題中只有一道被成功解開,那就是我們在第 十九期提及過的龐加萊猜想(Poincaré conjecture)。成功 解決難題的Grigory Perelman跟李學成一樣都是極其低調 的退隱數學家,他堅拒接受獎金和菲爾茲獎,並解釋道:「所 有人都明白如果證明正確就不需要額外的嘉許。」) 「π歌」是真的嗎? 其中一個影評認為整套電影最精彩的部分是李學成演 奏「π歌」來「說服[韓智宇]數學擁有非凡的美」的一幕 [8]。 李學成把 π 的值詳列在面前,說自己會把數字1 彈作音符 C,2作D並如此類推地演奏 π,又著朴寶藍奏出伴奏旋律。 這其實並不是甚麼新鮮事,在 YouTube 上也能找到不少 例子 [9, 10]。 電影中歌曲的開首的確對應 π 的頭 14 位數字: 3.1415 92 65358 97 然而隨著伴奏開始,李學成除了重覆以上部分還加入了與 π數值無關的額外音符。在第一個滑音之後,他重覆彈奏 之後的14位數字: 9323 846 2643 383 但他也沒有完全依照數值來彈,事實上他彈的是: 9323 846 2643 383 9323 846 5 歌曲基本上就是把π的28位數字以鋼琴伴奏潤飾, 並沒有順序演奏出π的值,反而更像一闋經重新詮釋的藝 術品,當中美麗的旋律正與導演想在戲中表達的格調吻合; 但無論如何π本身也不太可能構成一首歌的主體,因為小 數點後的值在數學上也許並沒有任何特別之處,能把這串 基本上是隨機的數字轉化成像樣的音樂多多少少只是我們 活用了自己的想像而已。 儘管如此,這音樂卻能奏出電影想帶出的訊息:到 底是甚麼驅使數學發展呢?不少數學始 於無用的好奇,一開始只像把一隻 垂死蝴蝶釘在卡紙上孤芳自賞 的一門藝術,又或是解決 現實上某個專門問題的專 門答案,但正是我們的想 像使數學突破界限,在各 個層面上融會貫通,為蘸 上數學更美麗的色彩。 如果你是數學狂迷,想更 深入了解黎曼猜想和解析 數論(analytic number theory),請參閱《科言》網 頁上的附加內容。 甚麼是黎曼猜想?

Introduction Amidst the myriad of phenomena that animals exhibit – from mimicry, hibernation, to bioluminescence – one of the most fascinating is the ability of some animals to change their colors in the blink of an eye. As a result, they can hide from predators, communicate with peers, intimidate when threatened, and regulate body temperature. How Do Animals Change Color? The process by which animals change color involves specialized cells called chromatophores. Located in the skin, they are colored cells that contain pigments or photonic structures [1]. Pigments absorb specific wavelengths of visible light and reflect those that are not absorbed, resulting in the colors we see. There are various types of pigment-containing chromatophores, named according to their color: melanophores for black or dark brown, cyanophores for blue, xanthophores for yellow chromatophores, and so on. In addition to pigmentary colors, there are structural colors created by a different mechanism. Iridophores in fish, amphibians and reptiles are made up of transparent guanine nanocrystals [2] that function to interfere with the light reflected off the skin at certain frequencies [3]. Iridophores can also produce iridescence, in which the color appears to change depending on the viewing angle [1]. Chameleons Chameleons are commonly known for being the representatives of color-changing animals. While most animals can change their color by controlling the dispersion and aggregation of chromatophores, chameleons have an additional level of control with two overlaying sets of iridophores [2]. The upper layer contains regularly arranged guanine nanocrystals. For panther chameleons, they can change their skin color by increasing the distance between these tiny crystals to manipulate the interference of light, leading to the reflection of longer wavelengths from blue to red. In the background of yellow xanthophores, the skin color of a male panther chameleon can thus change from green to yellow or orange when it is excited in male contests or courtship. The lower layer contains disordered guanine crystals of high reflectivity in the near-infrared region (700–1,400nm). It provides passive thermal protection to chameleons by reflecting direct and indirect “heat radiations” from the sun back into the environment, thus lowering their body temperature in the dry and sunny habitat. Mimic Octopus While chameleons have been the fascination of scientists for decades, the mimic octopus takes the art of adaptation to complex new heights. Among the diverse species of octopus, Thaumoctopus mimicus stands out for its remarkable mimicry skills, through a combination of sophisticated body movements and dynamic skin patterning [4]. The color-changing properties of the mimic octopus is enabled by the fine control over its chromatophores and iridophores [1]. Surrounded by radial muscles, their chromatophores Masters of Transformation: 偽裝大師:變色動物 Color-Changing