Science Focus (issue 022)

Issue 022, 2022 SCIENCE FOCUS Shuffle Playlist. Shuffle Playlist. Shuffle Playlist… 這個隨機播放清單……不太隨機! Lost Lessons – Succumbing to the Inescapable Food Coma 飯氣攻心—害我們上課睡著的惡作劇把戲? MythBusters: The Golden Ratio Around Us 流言終結者:黃金比例真是無處不在嗎? The Science of Ketchup: From Physics to Microbiology 茄汁的科學:從物理到微生物學 Transcending the Prizes: Jocelyn Bell Burnell 超越一切殊榮:Jocelyn Bell Burnell

Dear Readers, Welcome to a new issue of Science Focus. I hope you have overcome the inevitable disruption to your life and study due the latest wave of COVID infections. As always, our goal is to transport you to the wonderful world of scientific discoveries, as an alternative to traveling abroad. How many of you struggle to stay alert for school lessons, especially after lunch? We consider what goes on in the brain during a food coma and why such phenomenon may be advantageous to our ancestors. Speaking of lunch, how often do you have a plate of calamari with ketchup? Next time you do, please spare a thought on the rather intelligent squid. In some countries, experiments on cephalopods are highly regulated because of their well-developed nervous system that enables them to process and remember painful experiences. In another article, you may also learn why the physical and chemical properties of ketchup conspire against a smooth pour. For those of you who are interested in astronomy, have you heard of the name Jocelyn Bell Burnell? Her brilliant discovery of pulsars led not only to belated fame. She has used her professional influence and prize money to promote equality in science. A truly inspirational story. Finally, I wish all of you a healthy and happy summer. I hope to meet some of you in outreach activities, organized by the School of Science, online or in person. Before then, let’s stay connected via our Science Focus social media pages. Yours faithfully, Prof. Ho Yi Mak Editor-in-Chief 親愛的讀者: 歡迎閱讀最新一期《科言》。希望最近一波疫情在生活和學習上沒 有為大家帶來太大的不便。一如既往,我們會跨越時間地域帶大家進入 有趣的科學世界,暫且忘卻未能旅遊多時之苦。 除了在早上,你們試過在午飯後幾經掙扎才能提起精神上課嗎?我 們會探討在飯氣攻心時腦部發生的事情,以及飯氣攻心這個現象為甚 麼可能對我們的祖先帶來優勢。說到「食」,到訪西餐廳時你們會叫炸 魷魚圈配茄汁嗎?下次吃魷魚圈時,不妨花數秒想想那聰穎的魷魚;由 於頭足類動物的神經系統非常發達,使牠們能產生和記住疼痛感,因此 與頭足類動物相關的實驗在某些國家是受到嚴格規管的。在另一篇文 章中,你會學到為甚麼茄汁的物理和化學性質使我們永遠不能輕易倒出 它。對天文學有興趣的你聽過 Jocelyn Bell Burnell 的名字嗎?發現脈 衝星不僅為她帶來遲來的名聲,透過個人影響力和巨額獎金,她還深耕 細作致力促進科學上的平等,最終促成一個鼓舞人心的故事。 最後,我希望大家在夏日裡也能保持健康和心境愉快。希望能在理 學院舉辦的一些外展活動裡在線上或親身見到大家,但在這之前,讓我 們透過《科言》的社交平台保持聯繫吧! 主編 麥晧怡教授 敬上 Message from the Editor-in-Chief 主編的話 Copyright © 2022 HKUST E-mail: Homepage: Scientific Advisors 科學顧問 Prof. Jason Chan陳鈞傑教授 Prof. Stanley Lau 劉振鈞教授 Prof. Danny Leung 梁子宇教授 Prof. Tim Leung 梁承裕教授 Prof. Julie Semmelhack Prof. Yi Wang 王一教授 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 Kit Kan 簡迎曦 Dana Kim 金娥凜 Henry Lau 劉以軒 Sirius Lee 李揚 Lambert Leung 梁卓霖 Aastha Shreeharsh Graphic Designers 設計師 Tiffany Kwok 郭喬 Charley Lam 林曉薏 Cheuk Hei Tsang 曾卓希 Contents Science Focus Issue 022, 2022 What’s Happening in Hong Kong? 香港科技活動 HAYABUSA2~REBORN 1 隼鳥2號—星源再覓 Parade of the Five Planets – June 18-28, 2022 五星連珠— 2022年6月18至28日 Amusing World of Science 趣味科學 Shuffle Playlist. Shuffle Playlist. Shuffle Playlist… 2 這個隨機播放清單……不太隨機! Lost Lessons – Succumbing to the Inescapable Food Coma 6 飯氣攻心—害我們上課睡著的惡作劇把戲? MythBusters: The Golden Ratio Around Us 10 流言終結者:黃金比例真是無處不在嗎? The Science of Ketchup: From Physics to Microbiology 14 茄汁的科學:從物理到微生物學 Invade and Adapt – Genome Evolution via Transposable Elements 17 融為一體的不速之客—轉位子與基因組演化 Science in History 昔日科學 Transcending the Prizes: Jocelyn Bell Burnell 20 超越一切殊榮- Jocelyn Bell Burnell Science Today 今日科學 The Amazing Cephalopods 23 地球上的「外星智慧生物」:頭足類動物

What’s Happening in Hong Kong? 香港科技活動 Fun in Summer Science Activities 夏日科學好節目 Any plans for this summer? Check out these activities! 計劃好這個夏天的好去處了嗎?不妨考慮以下活動! HAYABUSA2~REBORN 隼鳥2號 — 星源再覓 Parade of the Five Planets June 18-28, 2022 五星連珠 2022年6月18至28日 Following the success of the space probe Hayabusa in 2010, its successor Hayabusa2 was launched in 2014 to collect soil samples from the asteroid Ryugu to study the birth of our solar system, which may hold the secret of the origin of life. It was also speculated that the samples might contain substances that are essential to life: water and organic matter. But things did not go as planned. What happened in its lone journey of 3.2 bi l l ion kilometers? Could Hayabusa2 eventually land smoothly on the unexpectedly rough terrain that it was not designed for? Visit the Space Museum and watch the show! Mercury, Venus, Mars, Jupiter and Saturn are five bright planets that are visible to the naked eye. It is uncommon for them to appear at once but here comes the chance – graced by the Moon, the five planets will do just that, from June 18 (Mon) to June 28, 2022 (Thu). While the planets seem to form a straight line in the sky, they don’t really align neatly to form a radius if we consider the top view of the solar system. The planets just coincidently cluster on the same side of the Sun that is visible on Earth – so it’s rather a trick of perspective. And don’t overthink – the world isn’t going to end in June and the next issue of Science Focus will be published as scheduled! Show period: Now – September 30, 2022 Time: 5:00 PMonMonday, Wednesday, Thursday and Friday (except public holiday) 11:00 AM, 3:30 PM and 8:00 PM on Saturday, Sunday and public holiday Venue: Space Theatre, Hong Kong SpaceMuseum Admission fee: Standard admission: $32 (stalls), $24 (front stalls) Concession admission: $16 (stalls), $12 (front stalls) Remark: Please refer to the museum’s website for more details. 映期:即日至 2022年9月30日 時間:星期一、三、四及五(公眾假期除外) 下午五時正 星期六、日及公眾假期上午十一時正、 下午三時三十分及八時正 地點:香港太空館天象廳 入場費:標準票:32 元(後座);24 元(前座) 優惠票:16 元(後座);12 元(前座) 備註:更多詳情請參閱太空館網頁。 隨著太空探測器隼鳥號在 2010 年任務成 功,它的繼任者隼鳥 2 號亦於 2014 年發射升 空,前往小行星龍宮採集土壤樣本,幫助我們解 開可能蘊藏生命起源奧秘的太陽系誕生之謎。 據當時估計,樣本可能會含有孕育生命必需的 物質:水和有機物。 但事情發展卻不如預期。究竟隼鳥 2 號在 32 億公里的孤獨旅程中出現了甚麼狀況?最後 又可以在超出其設計所容許的嶙峋地形上順利 降落嗎?快到太空館觀賞這套電影吧! 水星、金星、火星、木星和土星是肉眼能看 到的五顆行星,但五顆同時出現卻不是常見的現 象。現在機會來了! — 在月亮相伴下,五顆行星 會在 2022 年 6 月 18 日(一)至 28 日(四)連 成一線,上演「五星伴月」的戲碼。 雖然五顆行星會看似連成一直線,但並不會 一如我們所想的在太陽系軌道的鳥瞰圖中排列 成同心圓的半徑;它們只是湊巧地同時聚集在 太陽的同一邊,而又位於地球上能看見的角度, 因而在地球的天空上投影成一直線而已。不要想 多! — 世界不會在六月終結,而下期《科言》將 會如常出版! 1

sample, and we’re willing to jump to conclusions based on those patterns [3]. Shuffling in Real World: Fisher – Yates Shuffle vs. Naïve Method Take the Fisher–Yates shuffle [2], which shuffles a sequence randomly based on the input of other random number s . Let’s say there i s an ex i s t ing sequence of the numbers 1 to 10. First pick a random number from 1 to 10, called n, and remove the nth number in the existing sequence to begin a new sequence. For the next numbers, repeat this with any n from 1 to 9, from 1 to 8, and so on, until there are no numbers left in the existing sequence (see Figure 1). This sequence is totally random if the choices of n are also random, and in a moment, we’ll look at why this is true. We can think about the algorithm in terms of a deck of cards, removing random cards one at a time and stacking up the discarded cards in order to form a new deck. Comparing this with other ways to shuffle cards makes it obvious why Fisher–Yates is truly random. A “naïve” method is to take each card in sequence one at a time and swap it with another randomly chosen card, repeating for every card in the deck [4]. In other words, if we shuffle three cards (marked #1, #2, and #3) using our naïve method, we first swap the first card in the sequence with either the first (unchanged), second or third card. Then we shuffle the second card with either one of the three cards, and repeat the process until we go through every position in the sequence. The random choice at every stage is between three cards, so shuffling three times gives 3 x 3 x 3 = 33 = 27 By Peace Foo 胡適之 A coin comes up heads five times in a row. Two accidents happen on the same train line in one day. Or a shuffled playlist plays you the same artist three times running. Sometimes it seems like something other than coincidence is at work, but true randomness may not always feel that way to us. Statistically Independent Events: The Coin Doesn’t Remember! Let’s start with the coins. Many people expect a fair coin to alternate between heads and tails and will be surprised if the coin keeps coming up heads. When you first thought about it, you might have expected heads to come up half the time and tails half the time, so if heads have come up over half the time the coin should start landing on tails more often to compensate. This isn’t true, of course, because the coin can’t remember this! If you have a fair coin which has just landed on heads 99 times in a row, you can’t say that it’s more likely to land on tails next time because it’s a fair coin [1]. Since each toss has no effect on the next, we say that they are statistically independent events. If we toss a coin twice, and each toss has an equal chance of heads (H) or tails (T), there are four possible outcomes: HH, HT, TH, TT. Each outcome has the same chance (1/4) of happening, but the chances of one head and one tail in either order are 2/4 instead of 1/4. Three times, and we have eight possible outcomes: HHH, HHT, HTH, HTT, THH, TTH, THT, and TTT, each with 1/8 probabi l ity. In a ser ies of ten tosses, the results HTHTHTHTHT and HHTHTTTTHT and TTTTTTTTTT all have the same chance of occurring – one in 210, or 1/1024 – but you’ll probably remember the last one and not the others [2]. We read too much into patterns in a random Shuffle Playlist. Shuffle Playlist. Shuffle Playlist… 這個隨機播放清單…… 不太隨機!

Figure 1 An example of Fisher–Yates shuffle. 3 permutations. But as you may know, there are only 3 x 2 x 1 = 6 possible ways to mix up the order of those three cards: 123, 132, 213, 231, 312, 321. If you list all possible permutations resulting from the naïve method, you will find that the combinations 132, 213 and 231 come up five times, while 123, 312 and 321 come up only four times. Obviously, the result is biased. If you think intuitively, since 27 is not divisible by 6 (and nn or n > 2 is not divisible by n! in general), some of the possible permutations must happen more often than others (if all of them are equally likely to occur, the number of shuffles will be a multiple of 6). The chances are not equal, so the naïve method is not random. This is similar to the usual way to shuffle cards: In simple terms, we take an entire bunch of cards and swap it with another bunch of cards in the sequence. But these methods do not result in a random outcome, because the shuffled cards continue to circulate within the system. Contrast this with Fisher–Yates. Since a card is removed from consideration after each shuffle (and gets put into a new deck), the pool to be shuffled at each stage gets smaller, and for our three-card deck there wi l l be 3 x 2 x 1 = 6 permutations after three shuffles. Note that these permutations are calculated the same way as the possible ways of mixing up three cards: they both use the factorial function n! = n x (n - 1) … x 3 x 2 x 1, or 3! = 3 x 2 x 1 in this case which is equivalent to 3P3. They are essential ly the same algorithm in the sense that they are counted the exact same way. So the randomness behind the original selections of n is preserved throughout the permutations, and this is why we can guarantee Fisher– Yates is a fully random sequence provided n is chosen randomly. Creating a Less Random Playlist That Feels More “Random” Now let’s return to our random sequence 3-9-6-25-10-4-1-8-7 in Figure 1. We can call it a shuffled playlist of ten songs and say that songs 1, 4, 7, and 10 are by Adele (artist A), songs 2, 5, and 8 are by BTS (artist B), and songs 3, 6, and 9 are by Celine Dion (artist C). It looks like this: Celine Dion > Celine Dion > Celine Dion > BTS > BTS > Adele > Adele > Adele > BTS > Adele Which doesn’t look random at all! That’s because we focus on the unusual patterns of three Celine Dion and three Adele songs in a row. If you were like Spotify users between 2012 and 2014, you’d have rushed to complain [5] about all the times the shuffle algorithm played non-K-pop music over and over (assuming you also listened to K-pop before 2014). There were so many complaints, in fact, that Spotify retired the Fisher– Yates algorithm – yes, they originally used Fisher–Yates to shuffle playlists [6] – and introduced a new shuffling algorithm. Now, when you shuffle a playlist, different songs by the same artist and in the same genre are distributed roughly evenly across the list [7]. The Spotify engineers made the shuffle less random to convince you that it became more random. n Existing sequence New sequence 3 1 2 3 4 5 6 7 8 9 10 3 8 1 2 4 5 6 7 8 9 10 3 9 5 1 2 4 5 6 7 8 10 3 9 6 2 1 2 4 5 7 8 10 3 9 6 2 3 1 4 5 7 8 10 3 9 6 2 5 5 1 4 7 8 10 3 9 6 2 5 10 2 1 4 7 8 3 9 6 2 5 10 4 1 1 7 8 3 9 6 2 5 10 4 1 2 7 8 3 9 6 2 5 10 4 1 8 1 7 3 9 6 2 5 10 4 1 8 7

一枚硬幣連續擲出五次正面,同一條路線的列車在同一 天發生了兩宗意外,或是隨機播放清單連續給你三首由相同 歌手演唱的歌曲。這似乎並不是巧合,但真正的隨機也許未 如我們想像中的那樣。 統計上獨立的事件:硬幣並沒有記性! 讓我們先從硬幣說起。擲一枚公平的硬幣(fair coin)時, 很多人會預期正面和反面朝上的結果會交替出現,連續擲出 正面大概會使我們目瞪口呆。在沒有細想之下,你可能也會 估計正面和反面出現的次數會各佔一半,所以如果正面出現 的比例多於一半時,反面應該就將會出現得更頻密來補償 之前不均的結果 — 當然,這個想法是錯誤的,因為硬幣並 不會記得先前的結果!如果你有一枚公平的硬幣,它連續擲 出了 99 次正面朝上的結果,你不能說下次會有較大機會擲 出反面,因為它畢竟是一枚公平的硬幣 [1]。由於每次拋擲 對下次結果都沒有影響,我們稱這些為統計上獨立的事件。 如果我們擲兩次硬幣,每次正面或反面朝上的機會均 等,以下是四個可能的結果:正正、正反、反正和反反。每個 結果發生的機會都相同(1/4),但以任何次序出現一正一 反的機率為 2/4 而不是 1/4。擲三次的話會有八種可能:正 正正、正正反、正反正、正反反、反正正、反反正、反正反和 反反反,每種可能的機率均為 1/8。一連擲十次的話,正反 正反正反正反正反、正正反正反反反反正反和反反反反反 反反反反反三者的機率都一樣,均為 1/210 或 1/1024,可 是會令你留下深刻印象的肯定是最後一個組合而不是其他 [2]。我們太著迷於從隨機產生的結果中找規律,並會就此輕 率地下結論 [3]。 現實上的洗牌演算法:Fisher–Yates 洗牌法與天真法 讓我們先介紹 Fisher–Yates 洗牌法 [2],它根據另一組 隨機數字把序列隨機地打亂。假設現在有一組由數字 1 至 10 組成的序列。首先從 1 至 10 選一個隨機號碼叫n,然後 移除上述序列中第n個數字放到一組新序列裡。之後對序 列中餘下的數字重覆以上步驟,從 1 至 9、1 至 8 中選n,如 此類推,直至序列中的所有數字都被移除(見圖一)。 如果n的選擇是隨機的,那新序列也會是完全隨機的。 讓我們來看看為甚麼這個關係會成立。我們可以以一副卡牌 作比喻來理解這個演算法:每次隨機移除一張卡牌,並把移 除的卡牌疊起來組成一副新的卡組。 把這個演算法與其他洗牌方法作比較可以突顯為甚麼 Fisher–Yates 法是真正隨機。有一個「天真(naïve)」的方 法是每次在卡組中取出一張卡牌,然後與另一張隨機選擇的 卡牌交換位置,再對卡組中的每張卡重覆以上步驟 [4]。換 言之,如果我們用天真法洗一副有三張卡的卡組(卡牌上標 記了#1、#2 和 #3),第一步我們會把卡組中的第一張卡與 第一(不變)、第二或第三張卡的其中一張交換位置。然後 到第二張卡,我們又使它與三張卡的其中一張對換位置;重 覆以上過程直至卡組中的每一張卡都洗過一遍。 每一步我們都隨機從三張卡裡面選擇一張,因此三回合 一共可以帶來3 x 3 x 3 = 33 = 27 個排列(permutations) 結果。思路清晰的你大概已經意識到我們只有 3 x 2 x 1 = 6 種方式來排列三張卡牌:123, 132, 213, 231, 312 和 321。 如果你把從天真法每一步產生的可能排列逐一列出,你會 發現 132, 213 和 231 出現了五次,而 123, 312 和 321 只 出現四次,結果顯然是偏倚的。憑直覺也能得知因為 27 並 不能被 6 整除(基本上nn 或n > 2 都不能被n! 整除),所 以某些排列一定會比其他出現得更多(如果每個排列出現 的機會均等,排列結果的數目應是 6 的倍數)。由於機會不 均等,因此天真法並不隨機。 這與我們平時洗撲克牌的方式相似:簡單來說就是將卡 組中的一疊卡牌與另一疊互換位置;可是這些方法都不會產 生隨機的結果,因為洗過的卡牌都繼續在系統裡流轉。 跟 Fisher–Yates 法對比一下,由於每個回合都有一張 卡被移除(並調到新的卡組中),所以被考慮的卡牌會越來 越少,而在我們一副三張卡的例子裡,三回合只會帶來 3 x 2 x 1 = 6 個排列結果。計算這種排列結果數目的方法與計 算三張卡牌有多少個排列可能性的方法一樣:兩者都用到階 乘函數n! = n x (n – 1) … x 3 x 2 x 1;在我們的例子中是 3! = 3 x 2 x 1,亦等同3P3。兩者背後的計算思路基本上相同, 相同之處在於列出所有可能排列的方式。因此,n本身的隨 機性在洗牌中被得以保留;這也是為甚麼只要能確保n是 隨機選出的,就能保證 Fisher–Yates 法能提供一個完全隨 機的序列。 創造不太隨機但感覺隨機的播放清單 現在回到我們在圖一的隨機序列:3-9-6-2-5-10-41-8-7。它是我們共有十首歌的隨機播放清單:曲目一、 四、七、十是 Adele(藝人甲)的歌,曲目二、五、八是 BTS 防彈少年團(藝人乙)的歌,而曲目三、六、九是 Celine Dion(藝人丙)的歌。播放清單看來是這樣的: Celine Dion > Celine Dion > Celine Dion > BTS 防彈少 年團 > BTS 防彈少年團 > Adele > Adele > Adele > BTS 防彈少年團 > Adele 這樣的播放清單看起來一點兒也不隨機!這是因為我 們不經意地聚焦在連續三首 Celine Dion 和 Adele 的 歌這個不尋常的規律裡。假如你是 2012 至 2014 年的 Spotify 用家,你也許已經急不及待去投訴 [5] 這個不給你 聽 K-pop 的該死隨機播放清單(假設你在 2014 年前已經 在聽 K-pop)。那年 Spotify 實在收到太多投訴,使他們放 棄原來使用的Fisher–Yates演算法而引入新的演算法(對! 他們原本是用 Fisher–Yates 法來產生隨機播放清單 [6])。 現在選擇隨機播放時,演算法會確保由同一歌手演唱或屬 於同一種類的歌曲大致平均地分佈在播放清單中 [7]。 正是 Spotify 工程師把播放清單弄得不再隨機,來令你 相信它變得更加隨機。

5 References 參考資料: [1] Lieberman, D. A. (2012). Human Learning and Memory. Cambridge, UK: Cambridge University Press. doi:10.1017/ CBO9781139046978 [2] Cohen, B. (2020). The Hot Hand: The Mystery and Science of Streaks. New York, NY: Custom House. [3] Kahneman, D., & Tversky, A. (1972). Subjective Probability: A Judgment of Representativeness. Cognitive Psychology, 3, 430-454. doi:10.1016/0010-0285(72)90016-3. [4] Atwood, J. (2007, December 7). The danger of naïveté. Retrieved from [5] Lee, D. (2015, February 19). How random is random on your music player? BBC News. Retrieved from com/news/technology-31302312 [6] Feder, S. (2021, November 30). A brief history of shuffling your songs, from Apple to Adele. Popular Science. Retrieved from shuffle-play-history/ [7] Griffin, A. (2015, February 24). Why ‘random’ shuffle feels far from random. The Independent. Retrieved from n 原來序列 新序列 3 1 2 3 4 5 6 7 8 9 10 3 8 1 2 4 5 6 7 8 9 10 3 9 5 1 2 4 5 6 7 8 10 3 9 6 2 1 2 4 5 7 8 10 3 9 6 2 3 1 4 5 7 8 10 3 9 6 2 5 5 1 4 7 8 10 3 9 6 2 5 10 2 1 4 7 8 3 9 6 2 5 10 4 1 1 7 8 3 9 6 2 5 10 4 1 2 7 8 3 9 6 2 5 10 4 1 8 1 7 3 9 6 2 5 10 4 1 8 7 圖一 Fisher–Yates 洗牌法的一例

*Yawn* Oh no, your teacher stares at you. You rub your eyes, trying to focus on the differentiation problem your teacher asked you to solve. You start to think, is it the bowl of noodles I had for lunch? Why is it that a food coma hits us so hard every time after lunch? Common Misconception About Food Coma Traditional ly, it is bel ieved that sleepiness after a meal is due to the redistribution of blood flow. We think that blood rushes through the stomach and intestines to facilitate digestion, resulting in a reduction in blood and oxygen suppl ies to our brain and hence the induction of pos t -meal s leepi nes s , medical l y known as postprandial somnolence [1]. However, this is not the case. Blood redistribution theory fails because cerebral blood flow and brain oxygenation are known to be preferentially maintained under a wide range of physiological conditions [2]. They are strictly maintained even during exercise when much of the blood is diverted to muscles; and in fact, a study revealed that there was no measurable change in the blood flow to the brain in carotids after feeding [2]. Therefore, the intake of food wi l l probably not affect brain oxygenation and cerebral blood flow [2]. Lost Lessons – Succumbing to the Inescapable Food Coma 飯氣攻心- 害我們上課睡著的 惡作劇把戲? By Dana Kim 金娥凜

Figure 1 The interactions between the four brain centers before and after ameal. 圖一 與餐後嗜睡相關的四個大腦中樞在進食前後的相互作用 7 Post-Meal Hormonal Change and Food Coma So, what could be the possible reasons behind food coma? With the postprandial increase in insulin level as an example, feeding can promote or inhibit the secret ion of a lot of hormones to maintain homeostasis. Such hormonal changes can al so reduce the desire for food intake by introducing a feeling of satiety. It has been suggested that the hormones involved may simultaneously affect the sleeping centers in the brain and contr ibute to food coma (footnote 1) [1, 2]. We will examine two (of the many) examples – melatonin and orexin. In addition to its role in regulating gastrointestinal motility [3], melatonin is commonly known as a hormone that regulates sleep-wake cycle – high levels of melatonin induce sleep. This has been shown by administrating melatonin to animals and humans in previous studies [2]. In fact, the gut increases the synthesis of melatonin considerably after meal consumption, so such increase is considered to be a contributing factor to food coma [2]. For orexin, it is known to be a hormone which promotes hunger, along with wakefulness, presumably through increasing the fi r ing rate of neurons in an arousal center in the hypothalamus [2], which was hypothesized to work by inhibiting the sleep centers [1]. Therefore, the reduction of orexin after a meal may contribute to the sleep-inducing effect by leaving off the inhibition of the sleep centers [2]. Consider the Bigger Picture: Interactions Between Brain Centers While some scientists incline to attribute the cause of food coma to the action of certain hormones, some take a further step back [1]. On top of the idea that the hunger-satiety axis modulates the sleep-wake axis, this view emphasizes the interaction between brain centers in the hypothalamus, and hormones are considered as just messengers that faci l itate communication between organs. As illustrated by the example of orexin above, there are four major centers in the hypothalamus that affect satiety and drowsiness. They can be simplified as the hunger, satiety, arousal and sleep centers. Hunger often comes with wakefulness; the hunger center is hypothesized to stimulate the arousal center and inhibit the sleep center. The arousal center itself works by inhibiting the sleep center, too. However, in the state of satiety, the satiety center inhibits the hunger center so everything in the pathway becomes the opposite and drowsiness occurs. The interactions are summarized in Figure 1. So, it is useful to understand what would lead to the feel ing of satiety, which intertwines with the occurrence of post-meal sleepiness. In fact, our body judges whether we should feel full by our energy level and by the physical conditions of the stomach [1]. To know whether we are replenished with energy after a meal, arcuate nucleus (ARC; footnote 2) in the hypothalamus detects the increase in the level of a blood-borne metabol ite, malonyl-CoA, whose level correlates with that of ATP (“energy”). Having combined other metabolic signals, ARC can stimulate the sat iety center and inhibit the hunger center through hormonal regulation. This contributes to the feelings of satiety and drowsiness. Meanwhile, our stomach should be stuffed with food for quite a whi le after eat ing. Vagus ner ve branches can sense the gast r ic di stens ion and delayed gastric emptying, which in turn lead to the release of some other gut hormones that stimulate the satiety center by their own actions and through vagal stimulation. This eventually yields the same feelings of being full and sleepy. Furthermore, this can account for the reason why solid food could induce greater drowsiness than liquid food, which is because solid food can cause greater gastric distension and further delay gastric emptying. Food Coma in the Light of Evolution So now, you may all be wondering – is it necessary for the satiety response to link to drowsiness? All it does it gets us into trouble for dozing off during class, right? True, but evolutionary biology suggests that there might be a reason behind post-meal sleepiness. To understand, we need to view this phenomenon in the Darwinian context – any subopt imal ef for t allocation can result in a selection disadvantage [4]. For a species to survive in natural selection, they must spend their limited energy and effort wisely. Speaking of these, some researchers speculated that digestion is a demanding metabolic process that requires focused effort and energy expenditure [2]. In response to that, our body may choose to temporarily lower its sensitivity to external stimuli to let our body

* 呵欠 * 不得了,老師盯著你還未趕及合起的嘴。你擦了擦眼 睛,竭力把專注力放回老師叫你解的那道微分題目上。 你開始想:是不是中午吃的那碗麵在作祟?為甚麼每 次午餐後都必然飯氣攻心? 對於飯氣攻心的常見誤解 傳統上,人們相信餐後嗜睡是由於血流重新分配所 致,血液被認為會流向胃部及腸道以幫助消化,因此分 薄了供應至腦部的血液和氧,引發餐後嗜睡的現象 [1]。 然而這是錯誤的。血流改變理論不成立的原因是因為 身體已知會在大部分生理狀況下優先維持通往大腦的血 流和供氧量 [2],即使是運動期間當大部分血液都被送至 肌肉時,大腦的血流和供氧仍然會被嚴密地保持在適當 水平;而事實上,有研究指出在攝食後經頸動脈通往腦 部的血流並沒有錄得可量度的變化 [2],因此攝食並不太 可能會影響腦部供氧和大腦血流 [2]。 飯後的激素改變與飯氣攻心 那麼,我們又可以怎樣解釋飯氣攻心呢?以餐後胰島 素水平增加為例,進食可以增加或抑制體內一系列激素的 分泌,以維持體內平衡。這些激素水平的改變也可以透 過帶來飽足的感覺,減低我們對食物的慾望。有研究指 出當中涉及的激素可能同時影響腦部的睡眠中樞,導致飯 氣攻心的情況(註一)[1, 2]。以下我們會檢視(許多激 素當中的)兩個例子:褪黑激素(melatonin)和食慾素 (orexin)。 除了參與腸胃蠕動外 [3],褪黑激素亦眾所周知是一 種調節睡眠清醒周期(sleep-wake cycle)的激素,對 動物和人類施以褪黑激素的多項研究中已證明高褪黑激 素水平能引發睡意 [2]。事實上,餐後腸道會增加褪黑激 素的合成,這被認為是餐後嗜睡的成因之一 [2]。 至於食慾素,它是一種能同時引發飢餓感和令人保持 清醒的激素。據科學家推測,食慾素能增加下丘腦醒覺中 樞裡神經元的放電頻率 [2],使醒覺中樞能有效地抑制睡 眠中樞而令我們保持清醒 [1]。因此,餐後食慾素減少可 能會使睡眠中樞失去原來的抑制而引發睡意 [2]。 從宏觀角度看腦部中樞間的相互作用 有些科學家傾向把飯氣攻心的成因歸咎於某些激素的 作用,但亦有科學家退後一步從宏觀的角度看待這個問題 [1]。在飢餓—飽足軸(hunger-satiety axis)能調節睡 眠—清醒軸(sleep-wake axis)的概念之上,這種觀點 強調下丘腦裡面不同中樞間的相互作用,而激素的角色僅 被看成器官之間的訊息傳遞者而已。 正如上面食慾素的例子提及過,下丘腦裡面有四個影 響飽足感和睡意的主要中樞,簡單來說它們可以分為飢 餓、飽食、醒覺和睡眠中樞。飢餓通常伴隨著清醒;科學 家推測飢餓中樞能刺激醒覺中樞和抑制睡眠中樞,而醒覺 中樞本身亦能抑制睡眠中樞。可是當飽足時,飽食中樞會 抑制飢餓中樞,令機制內的相互作用都呈現相反效果而引 發睡意。圖一總結了以上提及的相互作用。 因此,了解甚麼會引起飽足感非常重要,因為它與餐後 嗜睡息息相關。事實上,我們身體會透過偵測我們的能量水 平和胃部的物理狀況來判斷我們是否應該感到飽足 [1]。 要知道我們在進食後能量是否得到補充,下丘腦內的弓 狀核(註二)會探測血液中代謝物丙二酰輔酶 A(malonylCoA)濃度的增加,而丙二酰輔酶 A 的水平正正與 ATP(即 「能量」)的水平相關。在同時考慮其他代謝訊號後,弓狀 核便能透過激素調節的方式刺激飽食中樞及抑制飢餓中 樞,給予我們飽足和睏倦的感覺。 與此同時,我們的胃部在飯後好一段時間都會被 食物填滿。迷走神經的分支能感覺到胃膨脹(gastric distension)和比平時所需時間較長的胃排空(gastric emptying),這會令身體分泌其他胃腸激素以直接或透過 迷走神經刺激的方式刺激飽食中樞,最終也會帶來飽足和 睏倦的感覺。除此之外,這也能解釋為甚麼固體食物比流質 食物更能引發睡意,這是因為固體食物能令胃部膨脹得更 大和逗留在胃部更久。 餐後嗜睡在進化上的意義 現在,你們也許在想:真的有必要把飽腹感連繫到睡意 “concentrate” on digestion by reducing energy and effort demands [2]. This could be the reason why we suddenly lose the vigor to hunt for extra calories. Another plaus ible reason i s that pos t -meal sleepiness may help consolidate what we learned from the circumstances that led to energy acquisition [2]. The brain is known to be plastic, or flexible, as neurons can rewi re themselves to enable more ef fect ive communication. This serves as the basis of learning and memory. It has been proposed that neuronal connections can be remodeled and strengthened during sleep [5], so sleep is long suspected to be a process that facilitates learning. With this concept in mind, post-meal sleep was suggested to subconsciously reinforce what you learn from the energy-acquiring experience before the meal – say, hunting. It prepares you for future opportunities to acquire energy [2]. So, food coma could actually give us an edge in natural selection! Unravel ing the Mystery Between Feeding Biology and Sleep Research studies on physiology and neuroscience have unveiled layers of mysteries of food coma by deciphering the functions of different hormones and brain parts. However, to this day, we are still unable to confirm why or how we get food coma confidently. Simi lar to many other scientific topics, l ike why we sleep, there are sti l l many unanswered questions regarding the potential link between feeding biology and sleep. 1 Editor’s note: Recall that one hormone can target multiple organs in hormonal coordination (cf. nervous coordination), so it is common for a hormone to performmultiple functions in different organs. 2 Nucleus: In the central nervous system, the word “nucleus” is used to describe a group of neurons that are located in a defined anatomical position.

9 1 編按:神經和激素協調的異同是課堂上老師會一再提及的重點:激素可以影 響多於一個器官。因此一種激素能在不同器官發揮不同功能其實也不太令人 意外。 2 神經核:「核」在這裡是形容在中樞神經系統中,處於解剖結構上同一位置的 一組神經元。 上嗎?那只是害我們在課堂上睡著的惡作劇把戲吧?或許 是的,但演化生物學告訴我們餐後嗜睡背後可能真的有其 重要性。 要明白箇中原因,我們要從達爾文主義分析餐後嗜睡這 個現象:要知道物種在分配有限的精力時,稍有差池都可能 導致物種在自然選擇中失利 [4]。換言之,如果一個物種要 在自然選擇中生存過來,就必須要明智地分配其有限的能 量和精力。 說到這些,有科學家猜測消化是耗費精力和能量的代謝 作用,所以身體可能選擇暫時降低對外界刺激的靈敏度,減 少對能量和精力的需求以專注於消化上 [2],這可能就是為 甚麼我們在餐後突然對尋找額外熱量意興闌珊的原因。 另一個可能的原因是餐後嗜睡有助鞏固我們在獲取 能量的活動中學到的東西 [2]。我們的腦部是可塑的,神 經元之間可以透過改變它們的接駁方式令溝通更為有 效,這正是學習和記憶背後的根據。科學家曾經提出神 經元間的連接可以在睡眠中被改變和鞏固 [5],因此睡眠 一直被猜測是有助學習的過程。有了這個概念,科學家 提出飯後睡眠有助我們在不自覺的情況下,鞏固我們在 餐前獲取能量的活動(例如打獵)中學到的東西,令我們 有更充分的準備去面對下次能夠獲取能量的機會 [2]。 所以,餐後嗜睡其實能在自然選擇中為我們帶來優勢。 解開攝食生物學與睡眠之間的謎 生理學和神經科學上的研究已透過闡釋 不同激素和大腦部分的功能揭示了飯氣攻心 的重重謎團,但直至今天,我們仍不能完全 肯定飯氣攻心背後的原因和原理。跟其他 許多科學問題,像是為甚麼我們需要睡覺 一樣,攝食生物學和睡眠之間的可能關係 確實有著很多尚待解答的問題。 References 參考資料: [[1] Kim SW, Lee BI. Metabolic state, neurohormones, and vagal stimulation, not increased serotonin, orchestrate postprandial drowsiness. Biosci Hypotheses. 2009;2(6):422427. doi:10.1016/j.bihy.2009.07.008 [2] Bazar KA, Yun AJ, Lee PY. Debunking a myth: neurohormonal and vagal modulation of sleep centers, not redistribution of blood flow, may account for postprandial somnolence. Med Hypotheses. 2004;63(5):778-782. doi:10.1016/j.mehy.2004.04.015 [3] Chen CQ, Fichna J, Bashashati M, Li YY, Storr M. Distribution, function and physiological role of melatonin in the lower gut. World J Gastroenterol. 2011;17(34):38883898. doi:10.3748/wjg.v17.i34.3888 [4] Gregory TR. Understanding Natural Selection: Essential Concepts and Common Misconceptions. Evolution (N Y). 2009;2(2):156-175. doi:10.1007/s12052-009-0128-1. [5] Frank MG, Issa NP, Stryker MP. Sleep enhances plasticity in the developing visual cortex. Neuron. 2001;30(1):275-287. doi:10.1016/s0896-6273(01)00279-3

The wor ld we l ive in i s a big place – a vast expanse of land and sea, in an even bigger cosmic web known as the universe, much of which remains a mystery to us. Making sense of our place in the universe has always been a comfort to humanity in the face of the unknown. The most significant way we do this is by seeking patterns. One such example is the golden ratio. Denoted by the Greek letter phi (φ), the golden ratio is an irrational number – an unending number with infinite digits that cannot be expressed as a ratio of two integers, just like π – that has caught the attention of mathematicians, biologists, artists, and architects across the world throughout history [1]. You may be wondering exactly what the golden ratio is and what makes it so special. In order to understand it, let’s assume a variable x, which represents the length of a line segment. The line segment is then divided into two parts, one longer than the other. The length of the longer part is normalized to one and that of the remaining part becomes x – 1, as illustrated in Figure 1. So, what would the ratio between x and the longer part be, such that it is equal to that between the longer and shorter parts? To find the value of such a “divine proportion” x, we can create a quadratic equation from the relationship above: By solving the equat ion and reject ing the negative solution, we can get x equals to , approximately 1.618 – this value is the golden ratio. Another famous mathematical concept you may have heard of, the Fibonacci numbers (Fn) forming the Fibonacci sequence, is also closely related to this ratio. Each number in this sequence is the sum of its two predecessors: 0, 1, 1, 2, 3, 5 and so on. The limit of the ratio between each number and its predecessor is, as you can probably tell, the golden ratio, φ. In other words, the higher the Fibonacci numbers, the closer the ratio is to φ. Often linked to the “beauty of proportion” [2], φ appears in various areas of nature and was said to have inspired artists and architects for centuries. For instance, phyl lotaxis (arrangement of leaves around the stem) of certain plants was discovered to be related to the golden ratio. While the angle between successive leaves or leaf pairs can be 90 degrees (decussate pattern) or 180 degrees (distichous pattern), spiral phyllotaxis with an angle close to the golden angle, approximately 137.5 degrees ( foot note 1; f i g u r e 2 ) , i s also prevalent in plants [3]. It i s not hard to imagine that such recurrent encounters with this ratio in nature have probably intrigued and awed ancient Greeks and us, as we can identify the incorporation of the ratio into the Parthenon and da Vinci’s The Last Supper [1]. The frequent appearance of the golden ratio in artwork begs the question: Is the golden Figure 1 Division of a line segment of length x into two parts. By Aastha Shreeharsh MYTHBUSTERS : The Golden Figure 2 Spiral phyllotaxis. (Leaves at consecutive vertical levels are pseudo-colored differently from red to purple.)

11 ratio really a solution to our pursuit of beauty? Much to our surprise, this might just be our wishful thinking. It may be overthinking that has led us to identify its seemingly overwhelming presence in nature. The human brain loves seeking patterns, so much that perhaps it “favors” the emergence of φ in many of these instances, even when there is no concrete evidence to support the notion [1]. The most compelling case of this myth is the look of nautilus shells. Naut i l us i s a sea creatu re f rom the same animal class, Cephalopoda, as squids and octopi. Unlike other cephalopods, its home is a beautiful, chambered shel l with a spi ral. These spi rals are known as logarithmic spirals or growth spirals – spirals that keep growing further apart from the innermost curves as illustrated in Figure 3. Nautilus shells are said to be the prime example of the appearance of φ in the natural world, with their logarithmic spirals s u g g e s t e d t o h a v e a n aspect rat io equivalent to the golden ratio – a deeply held belief that is so popular in no small part due to literature such as Dan Brown’s Da Vinci Code, renowned sci ent i s t s and academic institutions like the Smithsonian (footnote 2) perpetuating this “fact” [2]. Yet , i f you w e r e t o e v e r inspect a nautilus shell for yourself in real life, you may find the aspect ratio actually closer to 4:3 (1.333) than φ (1.618). When this myth of every nautilus shell having the golden ratio is thought about more deeply, isn’t it kind of odd to think that every single nautilus shell in existence would have the same ratio? It would be more believable if this ratio is varied, even by a few decimal numbers, in different specimens, right? That’s precisely the same thought a cer tain researcher by the name of Christopher Bartlett had. He went so far as to surmise that even the 4:3 ratio is not an accurate aspect ratio for most nautilus shells. When 80 shells were examined from the Smithsonian collections, the average ratio came out to be 1.310. All shells had varying ratios with slightly different number; making it absolutely wrong to state that all these spirals somehow have the same measurement, say, 1.6 – a value much closer to the actual value of φ than 1.310 [2]. Why did so many scientists and educators believe this myth then? Well, as covered in this article before, the way humans survive and interpret the world is through seeking out patterns. Sometimes we do this subconsciously against our better judgement, which leads to flawed speculations such as the fantasy of the golden ratio being all around us; however, another great thing about humanity is our insatiable curiosity, which helps us not only create these myths but debunk them just as well. Figure 3 Logarithmic spiral of nautilus. 1 The golden angle: Imagine that we want to divide a circle into two sectors in the golden ratio. After setting up a quadratic equation with the smaller and larger central angles as x degrees and (360 – x) degrees respectively, you will be able to get the golden angle x, which is approximately 137.5 degrees. 2 The Smithsonian Institution: A large museum, education and research complex in Washington, D.C. in the US. 流言終結者:黃金比例真是無處不在嗎? Ratio Around Us

當中相鄰葉片或葉片對的角度是與黃金角度接近的 137.5 度(註一;圖二)[3]。不難想像我們在大自然中一次又一次 地與這個比例的相遇,大概已經勾起古希臘人和我們對它的 興趣和敬畏之情,這從巴特農神殿的建築融合了黃金比例和 達文西的〈最後的晚餐〉中就能看到端倪 [1]。黃金比例接 二連三出地現在不同作品中,使人不禁問道:在人類追求美 感的探索中,黃金比例真的是構成美的其中一個的因素嗎? 令人意外的是,這也許只是我們一廂情願,是過分猜想 令我們認為它在大自然中無所不在。人類腦袋天生喜愛尋找 規律,喜愛得即使沒有實質證據支持也寧願相信 φ 出現不 同情境中 [1]。關於這個誤會最具說服力的例子是鸚鵡螺外 殼的外觀。 鸚鵡螺是一種海洋生物,與魷魚和八爪魚都屬於頭足綱 的動物。與其他頭足綱動物不同,鸚鵡螺居住在分成多個腔 室的漂亮螺旋外殼中。牠們外殼的螺旋曲線被稱為對數螺 線或成長螺線,就是如圖三所示不斷從最內層曲線向外成 長的螺旋。 鸚鵡螺外殼對數螺線的長闊比被認為與黃金比例相符, 因此亦被公認是自然界中出現 φ 的著名例子。人們之所以 會有這個根深蒂固的概念,要多得包括 Dan Brown 的《達 文西密碼》等文學作品及史密森尼學會(The Smithsonian Institution;註二)等學術機構和其他知名科學家錯誤地宣 揚這件「事實」[2]。 然而,如果你有機會親身檢視鸚鵡螺外殼,你會發 現它的長闊比與其說是接近 φ (1.618),其實更接近 4:3 (1.333)。如果再一次認真思考「每個鸚鵡螺外殼都符合黃 我們居住的世界浩瀚無垠 — 遼闊的陸地和海洋,亦只 是宇宙的一小部分。透過嘗試理解我們所身處的世界,對 人類而言是一種在未知中的慰藉。我們透過從事物中找出 規律來認識世界,黃金比例就是其中一個例子。 在數學上,黃金比例以希臘字母 φ 表示。它是一個無理 數,與 π 一樣有著無限個小數位,並且不能被表達成兩個 整數之比。在歷史長河中,黃金比例這個無理數吸引了世界 上不少數學家、生物學家、藝術家和建築師的目光 [1]。你 或許現在就想知道黃金比例究竟是甚麼,以及它為何如此 獨特;在搞清楚這一切之前,讓我們先設x為一線段的長 度,然後把這線段一分為二,當中一段比另一段長。如圖 一所示,設較長一段的長度為 1,而餘下部分為x – 1。 那麼,如果x與較長一段之比和較長一段與較短一段之 比相同,前者之比需為甚麼? 要找出這個「神聖比例」x的值,我們可以藉上述關係 推導出一條二元方程。 透過解方程並捨去負數解後,我們可以得出x等於 ,大約是 1.618 – 這就是黃金比例的值。你可能聽過 另一個與黃金比例相關的著名數學概念 – 斐波那契數 (Fibonacci numbers (Fn)),數列中的每個數均為其前兩 者之和:0, 1, 1, 2, 3, 5……聰明的你也許已經察覺到,每個 斐波那契數與數列中前一個數之比的極限(limit)正是黃 金比例 φ。換言之,隨著數列中的數字越來越大,前後兩者 之比會越接近 φ。 人們經常把φ與美學扯上關係,稱之為「比例之美」[2]。 φ出現在大自然的不同領域中,還據說在過去數千年啟發了 不少藝術家和建築師。譬如說某些植物的葉序(葉片圍繞莖 部生長的排列形態)與黃金分割相關,在相鄰葉片或葉片對 之間的角度可以呈 90 度(稱為十字或交互形態)或 180 度 (二列形態)的同時,螺旋葉序也是在植物中非常普遍的, 圖一 把長度為 x 的線段分成兩部分 圖二 螺旋葉序(低至高的葉片依次以紅至紫的「假色(pseudo color)」表示。) MYTHBUSTERS : The Golden

13 金比例」這個流言的話,你不覺得世間上所有鸚鵡螺外殼都 擁有一模一樣比例的想法有點奇怪嗎?相反,如果每個樣本 之間都有著些微差異,即使是小數點後數個位也好,這不是 會更為合理嗎? 這正是一位名叫 Christopher Bartlett 的研究員所抱 持的想法,他甚至推測 4:3 也不能準確地描述大多數鸚鵡 螺外殼的比例。在檢查史密森尼學會館藏的 80 個外殼後, 他最終發現平均比例是 1.310。另外,全部外殼的比例都有 著些微差異,因此所有外殼均擁有 1.6 之類相同比例的說 法顯然是錯的,而 1.310 本身也比 1.6 離 φ 的準確值更 遠 [2]。 那為甚麼有這麼多科學家和教育工作者相信這個流言 呢?嗯,像前面提到的一樣,人類的生存之道以及對自然萬 物之理的詮釋一向有賴觀察規律,有時潛意識對尋找規律 的固執會勝過我們的理性判斷,以致出現黃金比例無處不 在等的美麗錯覺;然而,人性的另一個優點是我們有著無窮 的好奇心,使我們不但能創造流言,亦能破解流言。 1 黃金角度:假設我們要把一個圓形以黃金比例分成兩個扇形,在設大小扇形 的圓心角分別為x和 (360 – x) 度後,便可以設一道二元方程。解方程後會得 出黃金角度x約為 137.5 度。 2 史密森尼學會:集博物館、教育及研究機構於一身,位處美國華盛頓特區的 大型綜合學術組織。 References 參考資料: [1] Iosa, M., Morone, G., & Paolucci, S. (2018). Phi in physiology, Psychology and Biomechanics: The golden ratio between myth and science. BioSystems, 165, 31–39. doi:10.1016/j.biosystems.2018.01.001 [2] Bartlett, C. (2018). Nautilus Spirals and the Meta-Golden Ratio Chi. Nexus Network Journal, 21, 641–656. https://doi. org/10.1007/s00004-018-0419-3 [3] Strauss, S., Lempe, J., Prusinkiewicz, P., Tsiantis, M., & Smith, R. S. (2020). Phyllotaxis: is the golden angle optimal for light capture?. The New Phytologist, 225(1), 499–510. doi:10.1111/ nph.16040 流言終結者:黃金比例真是無處不在嗎? Ratio Around Us 圖三 鸚鵡螺的對數螺線