Issue 031, 2025 SCIENCE FOCUS Beer, Student, and t-Distribution 啤酒、學生與t分佈 Prions: A Mysterious Infectious Agent 病原性蛋白顆粒：神秘的致病元兇 How Atomic Clocks Keep Almost Perfect Time 原子鐘如何精確計時？ The Magic of Euler’s Number e 歐拉數e的魔力 Q&A with HKUST Life Science Majors 讀生命科學的人：與科大學子對談
Dear Readers, I hope you have enjoyed a great start to the new school year. In addition to keeping up with the regular curriculum, you may also be busy with extracurricular activities that demand originality and teamwork. Perhaps the stories we share will serve as inspiration. Many of you must have done practice questions on statistics that involve the student’s t-distribution. Do you know its connection with beer brewing? How about the connection of Euler’s number (e) with the calculation of compound interest and radioisotope decay? Although we don’t carry an atomic clock with us all the time, it plays an indispensable role in letting Pokémon Go know exactly where we are. Finally, we share a tale that connects itchy sheep, cannibalism, and Nobel Prize. Read on to discover the medical mystery about prions. Some of you may be thinking about what to study after secondary school. In our ongoing series of articles that feature HKUST alumni, you will learn from four biologists on their paths of success. Hopefully, their stories will give you broader perspectives on university studies and beyond. I wish you the best in choosing your own path to success! Yours faithfully, Prof. Ho Yi Mak Editor-in-Chief 親愛的讀者： 希望大家在新學年伊始一切順利。在繼續恆常課程同時，你們可 能也忙著各樣需要發揮創意和團隊精神的課外活動，今期故事也許正 好能啟發大家。 你們當中很多人應該做過與學生t 分佈相關的統計題目，但你 知道它與釀造啤酒之間的關係嗎？你又知道歐拉數（e）如何被應用 於計算複利息和放射性衰變？儘管我們不會隨身攜帶原子鐘，但它在 Pokémon Go的定位功能中扮演著不可或缺的角色。最後，我們會分 享一個與羊搔癢症、食人習俗和諾貝爾獎相關的醫學故事，請閱讀後 文，並與我們一起拆解病原性蛋白顆粒的神秘面紗。 你們也許正在考慮中學畢業後的出路，在我們與科大校友的對談 系列中，你將會聽到四位主修生物學的舊生踏上成功之路的心路歷 程，希望他們的故事能擴闊你對大學及其後生涯發展的認知。衷心希 望大家能找到屬於自己的成功道路！ 主編 麥晧怡教授 敬上 Message from the Editor-in-Chief 主編的話 Copyright © 2025 HKUST E-mail: sciencefocus@ust.hk Homepage: https://sciencefocus.hkust.edu.hk Scientific Advisors 科學顧問 Prof. Tim Leung 梁承裕教授 Prof. Yi Wang 王一教授 Prof. Chi Wai Yu 余智偉教授 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 Sam Fan 樊潤璋 Roshni Printer Devandhira Wijaya Wangsa Helen Wong 王思齊 Jane Yang 楊靜悠 Daria Zaitseva Social Media Editors 社交媒體編輯 Audrey Chan 陳皚慧 Daisy Yeung 楊于葶 Graphic Designers 設計師 Jacky Lau 劉重信 Yerim Song 宋禮林 Winkie Wong 王穎琪 Constance Zhang 張粲璨 Contents Science Focus Issue 031, 2025 What’s Happening in Hong Kong? 香港科技活動 STARMAP to the Unseen Universe 1 星圖旅航 Geminid Meteor Shower — December 14–15, 2025 雙子座流星雨 ─ 2025 年 12 月 14 至 15 日 Science in History 昔日科學 Beer, Student, and t-Distribution 2 啤酒、學生與t分佈 Prions: A Mysterious Infectious Agent 7 病原性蛋白顆粒：神秘的致病元兇 Amusing World of Science 趣味科學 How Atomic Clocks Keep Almost Perfect Time 12 原子鐘如何精確計時？ The Magic of Euler’s Number e 16 歐拉數e的魔力 Who’s Who 科言人語 Q&A with HKUST Life Science Majors 20 讀生命科學的人：與科大學子對談
What’s Happening in Hong Kong? 香港科技活動 Fun in Fall Science Activities 秋日科學好節目 Any plans for this fall? Check out the following events! 計劃好這個秋天的課餘節目了嗎？不妨考慮以下活動！ STARMAP to the Unseen Universe 星圖旅航 This Sky Show invites audiences to embark on a captivating journey through the cosmos. This immersive experience spans 13.8 billion years of cosmic history, exploring the origins of the universe and venturing beyond our solar system. Audiences will witness the breathtaking beauty of the Milky Way, the formation of stars in the Orion Nebula, and the dramatic life cycles of stars, including supernova explosions and the mysterious nature of black holes. With stunning visuals and profound insights, STARMAP reveals the hidden complexities of the universe, inviting all to gaze at the stars with newfound wonder. 放映日期： 現在至2025年11月14日 時間： 下午三時半及八時正 （一、三至五） 下午二時正及六時半 （六、日及公眾假期） 地點： 香港太空館天象廳 入場費： 標準票：40 元（後座）；30 元（前座） 優惠票：20元（後座）；15 元（前座） 天象節目《星圖旅航》邀請觀眾踏上引人入 勝的宇宙之旅。這次沉浸式體驗將帶大家跨越 138億年的宇宙歷史，探索宇宙起源，並走出太 陽系探險。觀眾將見證銀河系的壯麗、獵戶座星 雲中恆星的形成，以及恆星戲劇性的生命週期， 包括超新星爆炸和神秘的黑洞等。透過壯觀的 視覺效果和深刻的講解，《星圖旅航》將揭示宇 宙隱秘的複雜性，從而邀請大家以全新角度凝 視星空。 Show Period: Now – November 14, 2025 Time: 3:30 PM and 8:00 PM (Mon, Wed to Fri) 2:00 PM and 6:30 PM (Sat, Sun and public holiday) Venue: Space Theatre, Hong Kong Space Museum Admission fee: Standard admission: $40 (stalls), $30 (front stalls) Concession admission: $20 (stalls), $15 (front stalls) This year, the Geminids are expected to peak on December 14 (Sun). The Hong Kong Space Museum has rated the local observation condition as “excellent.” You may observe the meteor shower during the entire night of December 14. Places with wide view of the sky and low light pollution are suitable for the observation, such as the East Dam of the High Island Reservoir, Tai Tau Chau in Shek O, and Tai Au Mun near HKUST. Please observe the “stargazing etiquette”— use a red light torch and don’t point it to others. To take photos of the starry sky, don’t forget to bring a tripod and a camera with a wide-angle lens! 今年雙子座流星雨的高峰期預計是12月 14日（日）。本地觀測條件被香港太空館評為「極 佳」，你可以在 14 日的整個晚上觀賞。 天空視野廣闊和光害較少的地方均適宜觀 測是次流星雨，本港的觀星熱點包括萬宜水庫 東壩、石澳大頭洲以及離科大不遠的大坳門等。 觀星時記得遵守「觀星禮儀」：使用紅光手電筒， 及不要把光照向其他觀星者。想嘗試天文攝影的 朋友記得攜帶三腳架和廣角鏡頭。 Geminid Meteor Shower December 14–15, 2025 雙子座流星雨 2025年12月14至15日 1
By Helen Wong 王思齊 Does project-based learning improve students’ academic performance? Which candidate is more likely to win in an election? Is a new drug effective in treating a certain disease? While these scenarios may seem unrelated, they all share a common thread: We need to collect information from samples or to make an inference about a population, whether it’s all students, all voters, or all patients. This process is formally known as statistical inference. Assuming the sampling process is random and unbiased, the quantities calculated from these samples, such as sample mean or sample variance, will vary from one sample to another. Thus, sample means obtained from different rounds of sampling follow a specific distribution. Without going into the rigorous mathematical proof, the central limit theorem tells us that the sampling distribution of the sample mean will be approximately normally distributed when the sample size is sufficiently large, even if the underlying population is not normally distributed. But what happens when our sample size is small and we have no idea about the population standard deviation? Today, we take for granted that in such cases, given that the underlying population is a normal distribution, the sampling distribution of sample mean follows the Student’s t-distribution, thanks to a brewer named William Sealy Gosset (1876–1937) [1–3]. Born in Canterbury, England, Gosset was educated at the University of Oxford, where he earned a firstclass degree in chemistry in 1899. Around this time, the Guinness brewery in Dublin recognized the need for rigorous quality control in beer production and began recruiting graduates from Oxford and Cambridge for this purpose. Gosset was among those selected. As an apprentice brewer, Gosset needed to evaluate how the quality of barley and hops might affect that of the beer. The quality of agricultural products is known to vary throughout a year, depending on factors such as climate and soil conditions. Therefore, Gosset’s goal was to maintain a consistently high quality of beer while also ensuring cost-effectiveness. This necessitated relying on small samples to draw conclusions that could inform the large-scale brewing process. By the early 20th century, the central limit theorem had been established, and many were familiar with using the normal distribution for statistical inference with large sample sizes. Gosset conducted experiments by sampling acidity values from beers produced under various conditions, such as using different batches of malted barley, to determine whether there were significant differences in mean acidity between these groups. Through his calculations, Gosset discovered that when the sample size was small, the sampling t分佈 啤酒、 學生 與 Beer, Student, t-Distribution and
3 distribution of the sample mean deviated noticeably from the normal distribution. This finding prompted his quest for a new distribution that would resemble the normal distribution but suitable for small sample observations. Despite achieving a first in the mathematical moderations examination during his time at Oxford, Gosset was clearly not a professional mathematician. The creation of the Student’s t-distribution was closely tied to his extensive correspondence with many of the leading statisticians of his time. Karl Pearson (footnote 1) was one of the key influences on Gosset’s career. Pearson introduced Gosset to nearly all the statistical methods known at the time and invited Gosset to visit his department at University College London from 1906 to 1907. During this period, Gosset worked on his small-sample problem and published the landmark paper “The Probable Error of a Mean” in the journal Biometrika [4], where Pearson served as editor, in 1908. Some curious readers may have noticed that the author of the paper is credited as “Student” rather than William Sealy Gosset. This was due to a policy at the Guinness brewery that prohibited staff from publishing under their own names or using any company data. To comply with this policy, Gosset adopted the pen name “Student,” which is believed to have been inspired by the cover of a notebook he was using at the time – The Student’s Science Notebook [5]. Yet Gosset himself did not coin the term “t-distribution.” In his 1908 paper, he still used the symbol z in his derivation of the sampling distribution of the sample mean for sample sizes ranging from 4 to 10. The symbol t was later introduced by Ronald Fisher (footnote 2), a legendary statistician and close friend of Gosset, in a 1925 paper [6]. In this work, Fisher fully derived the values of the Student’s t-distribution and demonstrated that it is a transformed normal distribution. The shape of the t-distribution changes depending on the sample size n, which is represented Figure 1 Normal distribution (pink) and t-distribution when the degree of freedom is 1 (blue). The t-distribution is flatter at the peak and has “thicker” tails compared to the normal distribution.
by the degrees of freedom (calculated as n – 1). With a smaller number of observations, the t-distribution is flatter at the peak and has “thicker” tails compared to the normal distribution (figure 1). As the sample size increases, especially when n exceeds 30, the t-distribution starts to resemble the normal distribution. Perhaps contrary to Gosset’s expectations, as reflected in his letter to Fisher, “you’re the only man that’s ever likely to use them!” the t-distribution has become one of the most famous statistical distributions. It is widely applied in both everyday life and academic research, and of course, a staple in statistics courses. So, the next time you encounter the Student’s t-distribution (or find yourself grappling with it in class), take a moment to appreciate the “Student” behind it, William Sealy Gosset, and the fascinating story of its creation. 專題研習是否能提升學生的學業表現？哪位候選人更有 可能在選舉中勝出？某種新藥對治療特定疾病是否有效？ 雖然這些情境看似毫無關聯，但它們都指向一個核 心概念：我們需要從樣本收集資訊，然後針對某個總體 （population）作出推論，總體可以是全體學生、全 體選民，也可以是全體病人。這過程被稱為「統計推論」 （statistical inference）。假設抽樣過程是隨機且無偏 的，從樣本中計算出的統計數值，如樣本平均值和樣本方 差等，在每次取樣皆會有所不同。 因此，從多次抽樣中得到的樣本平均值會遵循一個特 定的分佈。撇開嚴謹的數學證明不說，根據中心極限定理 （central limit theorem），當樣本量足夠大時，即使總 體並非正態分佈（normally distributed），樣本平均值 的抽樣分佈（sampling distribution of the sample mean）仍會近似正態分佈。 但如果樣本量很小，且我們對總體的標準差沒有頭緒 時，又該怎麼辦呢？今天我們早已習以為常：在這種情況 下，只要總體為正態分佈，樣本平均值的抽樣分佈就會遵 循學生t 分佈（註一）。這一重要發現要歸功於一位名叫 William Sealy Gosset（1876–1937）的釀酒師 [1–3]。 Gosset出生於英格蘭的坎特伯雷，1899 年於牛津 大學取得化學一級榮譽學位。當時，位於都柏林的健力士 （Guinness）啤酒廠意識到在釀酒過程中進行嚴格品質 控制的重要性，因而開始從牛津和劍橋大學招募畢業生， Gosset 便是其中之一。 1. Karl Pearson (1857–1936) was a British statistician and a key figure in the development of modern statistics [7]. His work laid the foundation for many statistical methods and concepts still in use today, including the Pearson correlation coefficient and the chi-squared distribution. Notably, Pearson founded the first university statistics department in the world at University College London in 1911. 2. Ronald Aylmer Fisher (1890–1962) was a British statistician and geneticist [8]. Hailed as “a genius who almost single-handedly created the foundations of modern statistical science,” Fisher’s contributions to statistics include the significance test, analysis of variance (ANOVA), and maximum likelihood estimation, among many others. In genetics, he is regarded as one of the three founding fathers of population genetics, a key component of the modern synthesis that combines Mendelian genetics with Darwin’s theory of evolution.
5 作為見習釀酒師，Gosset 的工作是評估大麥和啤酒 花的品質如何影響啤酒品質。農產品的品質會隨氣候和土 壤條件等因素而有所波動，因此 Gosset 的目標是在確保 成本效益的同時，將啤酒品質維持在高水平，這就需要從 小量樣本推論出大規模的釀造過程是否合乎標準。 20 世紀初已經存在中心極限定理，許多人已經熟悉在 樣本數量足夠大時使用正態分佈進行統計推論。Gosset 透過量度在不同條件下（例如使用不同批次的發芽大麥） 釀造出來啤酒的酸度值，以判斷不同批次啤酒是否在平均 酸度上存在顯著差異。 透過計算，Gosset 發現當樣本量較小時，樣本平均值 的抽樣分佈會明顯偏離正態分佈。這個發現促使他開始尋 找類似正態分佈，但適合小樣本量的新型分佈。 雖然 Gosset 曾在牛津大學的數學考試中取得優秀成 績，但他顯然並非專業數學家，因此學生t 分佈的誕生其 實有賴他與當時多位頂尖統計學家的緊密聯繫。 其中，Karl Pearson（註二）對Gosset的職業生涯 影響深遠。Pearson 向 Gosset 介紹了幾乎所有當時已知 的統計方法，並邀請他於 1906 至 1907 年訪問 Pearson 於倫敦大學學院所在的學系。在此期間，Gosset專注 研究小樣本問題，並於 1908 年在Pearson主編的 《Biometrika》期刊上發表了一篇劃時代的論文〈平均值 的可能誤差〉（The Probable Error of a Mean）[4]。 細心的讀者或許會注意到，這篇論文的作者署名是 「Student」（學生），而非 Gosset 的本名。這是因為健 圖一 正態分佈（粉紅）和自由度為1時的t分佈（藍）。與正態分 佈相比，t分佈的峰部較矮，尾部較「粗」。 力士啤酒廠有一項規定，禁止員工以本名或使用任何公 司數據發表論文。為了遵守這項政策，Gosset 選擇使用 筆名「Student」發表論文，據說靈感來自他當時使用的 筆記本封面標題《學生的科學筆記本》（The Student’s Science Notebook）[5]。 然而，「t 分佈」這個名稱並非出自 Gosset 本人。在 1908 年的論文中，Gosset 仍然使用符號z來推導樣本 量為4到10時樣本平均值的抽樣分佈。符號t 稍後由 傳奇統計學家兼Gosset好友Ronald Fisher（註三）於 1925 年的論文引入 [6]。Fisher在這篇著作中完整推導 出學生t 分佈的值，並證明了它是一種經轉換後的正態分 佈。t 分佈的形狀會隨樣本量n改變，而技術上樣本量會 以自由度（degree of freedom，即n – 1）表示。在樣 本量較小的情況下，相比起正態分佈，t 分佈的峰部會較 矮，尾部也較「粗」（圖一）。隨著樣本量增加，尤其當n 大於 30 時，t 分佈會開始變得接近正態分佈。
References 參考資料： [1] Brown, A. (2008). The strange origins of the Student’s t-test. Physiology News, Summer 2008, 13–16. https:// doi.org/10.36866/pn.71.13 [2] Pearson, E. S., Gosset, W. S., Plackett, R. L., & Barnard, G. A. (1990). Student: A statistical biography of William Sealy Gosset. Clarendon Press; Oxford University Press. [3] Trkulja, V., & Hrabač, P. (2020). The role of t test in beer brewing. Croatian Medical Journal, 61(1), 69–72. https://doi.org/10.3325/cmj.2020.61.69 [4] Student. (1908). The Probable Error of a Mean. Biometrika, 6(1), 1. https://doi.org/10.2307/2331554 [5] Ziliak, S. T. (2008). Retrospectives: Guinnessometrics: The Economic Foundation of “Student’s” t. Journal of Economic Perspectives, 22(4), 199–216. https://doi. org/10.1257/jep.22.4.199 [6] Fisher, R. A. (1925). Applications of Student’s distribution. Metron, 5, 90–104. [7] Magnello, M. E. (2014). Pearson, Karl: His Life and Contribution to Statistics. In Wiley StatsRef: Statistics Reference Online. John Wiley & Sons, Ltd. https://doi. org/10.1002/9781118445112.stat04822 [8] UCL. (2021, March 2). Ronald Aylmer Fisher (1890-1962). https://www.ucl.ac.uk/biosciences/gee/ucl-centrecomputational-biology/ronald-aylmer-fisher-1890-1962 Gosset 自己曾在寫給 Fisher 的信中評論道：「你很 可能是唯一一個會用這些東西的人！」然而，讓 Gosset 始料不及的是t 分佈如今已成為最著名的統計分佈之一。 它被廣泛應用於日常生活和學術研究中，更不必說在統計 學課程中可以經常找到它的蹤影。因此，下次當你在遇到 學生t 分佈，或在課堂中被它搞得頭昏腦脹時，別忘了那 位真正的「學生」— William Sealy Gosset，以及背後 的精彩故事。 1. 編按：學生t 分佈（Student’s t-distribution）有時會根據讀音被翻譯 成「司徒頓t 分佈」。 2. Karl Pearson（1857–1936）是英國統計學家，也是推動現代統計學 發展的關鍵人物 [7]。他的工作為許多至今仍被廣泛使用的統計方法和 概念奠定了基礎，包括 Pearson 相關係數和卡方分佈。值得一提的是， Pearson 於1911 年在倫敦大學學院成立了全世界第一個統計學系。 3. Ronald Aylmer Fisher（1890–1962）是英國統計學和遺傳學家 [8]。 Fisher被譽為「幾乎以一己之力奠定現代統計科學基礎的天才」，他對統 計學的貢獻包括顯著性檢驗、變異數分析（ANOVA）和最大似然估計等。 在遺傳學方面，他被視為群體遺傳學的三位奠基人之一。群體遺傳學是結 合孟德爾遺傳學和達爾文演化論的現代演化綜論（modern synthesis） 的重要組成部分。
7 Prions: A Mysterious Infectious Agent 病原性蛋白顆粒： 神秘的致病元兇 By Daria Zaitseva What could possibly link a sheep illness called scrapie, a disease associated with cannibalism called Kuru, and a neurodegenerative disease called Creutzfeldt-Jakob disease? These fatal diseases occur in different species, and yet share a chilling commonality. More mysteriously, scientists could not identify the pathogen – neither virus nor bacteria were the culprit. Human’s knowledge at that time simply could not break the mystical curse. Let’s explore the mystery and see how one of the most obscure killers was discovered. Scrapie: Affected Sheep Uncontrollably Scratching Their Backs We begin in 18th-century England, where sheep farming was a cornerstone of the economy. But farmers soon faced a disturbing problem: Some sheep began scratching their backs against posts uncontrollably, then stopped feeding and became lame, and eventually turned emaciated and died [1]. The only way to prevent the spread of the disease was to isolate the sick animals from the flock. Nevertheless, without the ability to investigate further, this eerie disease was soon forgotten [1]. By the middle 20th century, scientists took a closer look [1]. They tried to identify the underlying pathogen. As the first step, they succeeded in experimentally transmitting the disease by inoculating the brain or spinal cord tissue from a diseased animal to a healthy one. The onset of disease can take as long as one to two years, so it left the scientists confused about the results of the experiment at first. Then, scientists attempted to identify the pathogen by treating tissue samples with different standard inactivation methods at the time, such as using a bacterial exclusion filter to remove, if any, bacteria. They also applied a dose of ionizing radiation that could disrupt, if any, nucleic acid (including DNA and RNA) in a separate experiment. However, the tissues remained infectious, so they realized the pathogen could be unusual this time. The only clues from brain dissections are the signature vacuoles – described as “soap bubbles” – in the cytoplasm of nerve cells, and the strange holes – called spongiform – in the sheep’s brains, giving the brain a sponge-like appearance. Kuru: A Mystical Curse Associated with Cannibalism As scrapie returned to the limelight, two medical doctors, Daniel Gajdusek and Vincent Zigas, reported firsthand in 1957 from Papua New Guinea a mysterious disease that
some believed was associated with cannibalism [1, 2]. Kuru was first discovered in the Fore tribe, with victims trembling, losing muscle control, laughing uncontrollably, and dying within months. The disease primarily affected women, with a female-male ratio of 14:1 in adults. In 1959, William Hadlow, an American veterinarian working on scrapie, happened to visit an exhibition on kuru in a medical museum in London [3]. He was shocked to find striking similarities between the two progressive degenerative diseases, from the signature “soap-bubbles” in the nerve cells, the extensive incubation period, to the failure in isolating a microbial agent [4]. After that, Hadlow wrote a letter to the editor of The Lancet, and also reached out to Gajdusek, drawing scientists’ attention to the high resemblance of the two diseases [5]. Later, Igor Klatzo, a neuropathologist who studied the brains of 12 kuru patients received from Gajdusek, also drew parallels between kuru and another human spongiform brain disease, Creutzfeldt-Jakob disease (CJD) [6]. In the next decade, scientists were able to experimentally transmit kuru and CJD to chimpanzee by inoculating infected human brain tissue, and later to laboratory rodents [1]. For kuru, we now understand that the disease spread through cannibalism: Female relatives would consume their relatives’ bodies as a mortuary practice “to free the spirit of the dead [7, 8],” during which they ingested the infected human brain concentrated with the infectious agent. Creutzfeldt-Jakob Disease: Lessons to Scientists So, what was the infectious agent? Stanley Prusiner, an American neurologist and biochemist, recalled the bizarre observation in his CJD patients: There was no immune response elicited – no fever, no increase in white blood cell count, and no humoral immune response – meaning that whatever caused the disease might not be a foreign agent [9]. With his biochemistry background, Prusiner decided to approach the problem differently by attempting to purify the infectious agent from affected mice inoculated with scrapie agent [9]. After harvesting and blending the spleens and brains of the mice, the homogenate was centrifuged for different times and speeds to separate constituents with different densities. After testing the infectivity of each sample, a highly infectious fraction was recovered despite the removal of over 98% of proteins and polynucleotides. With this cleaner sample, scientists demonstrated that infectivity could be reduced by procedures that hydrolyze or modify proteins, eventually leading to the discovery that the culprit wasn’t a microbe at all, but a misfolded protein. Prion: The Misfolded Protein Proteins are essentially amino acid chains, which are folded into precise shapes to function properly. Despite the lack of knowledge about its precise function, prion (PRNP) gene encodes normal prion protein which is active in the brain [10]. However, the amino acid chain somehow misfolds, and these deformed proteins, usually referred to as “prions”
9 (derived from “proteinaceous infectious particles”), can damage nerve cells [11]. Even worse, they can convert the normal prion protein into more prions, enabling them to multiply exponentially within the body and transmit among individuals through ingestion of affected tissue or direct contact of body fluid. Some prion diseases, such as fatal familial insomnia, are heritable; mutations in PRNP gene which can induce the formation of the abnormal protein were identified in those cases [12]. Prion accumulation then destroys brain tissue, creating the sponge-like holes seen in scrapie, kuru, and CJD. Unlike most other pathogens, such as bacteria or viruses, prions have no DNA – so perhaps they are not “programmed” to infect the host, but rather a tragic mistake of nature, simply a mistake in the folding process. Yet, they cause incurable, fatal diseases across species. Conclusion The history of prions is a testament to the power of scientific curiosity, perseverance, and collaboration. What began as a radical and controversial idea challenged a fundamental biological dogma and ultimately reshaped the understanding of multiple fields. As scientists continue to confront new mysteries in biology and medicine, this story serves as an inspiration: Truth is not always obvious, but with rigor, collaboration, and intellectual courage, even the most unconventional ideas can shed light on the darkest of nature’s secrets. 究竟在羊類發現的「羊搔癢症」、與食人習俗有關的 「庫魯病」，以及一種叫「克雅二氏症」的神經退化疾病 之間有甚麼關係？雖然這些致命疾病出現在不同物種中， 但它們卻有可怕的共通之處。更神秘的是，科學家無法確 定病原體，致病元兇既不是病毒，也不是細菌。當時人類 的認知無法破解這個神秘詛咒。讓我們探討這個謎團，了 解如何找出這個難以捉摸的致命元兇。 羊搔癢症：受感染的羊不受控制地抓撓背部 故事開始於18世紀的英國，那時牧羊業是經濟的基 礎。然而農民不久就面臨一個令人憂慮的問題：一些羊開 始不受控制地借柱子抓撓背部，隨後停止進食，變得一瘸 一拐，最終消瘦不堪並死亡 [1]。避免疾病傳播的唯一方 法是將病羊隔離。由於缺乏進一步調查的能力，這種怪 異的疾病很快已被遺忘 [1]。 到了20世紀中葉，科學家進行更深入的研究，嘗試 找出病原體 [1]。首先，他們成功透過將病羊的腦或脊髓 組織接種到健康羊隻身上，從而人工傳播疾病。由於潛伏 期可以長達一至兩年，這一點曾讓科學家對實驗是否成 功感到困惑。隨後，科學家嘗試透過使用當時多種能使病 原體失去活性的標準方法處理樣本組織，例如使用除菌 濾膜去除可能存在的細菌等，試圖識別病原體。在另外的 實驗中，他們還以能破壞核酸（包括 DNA 和 RNA）的電 離輻射劑量處理樣本組織，嘗試破壞當中可能含有的核 酸。可是組織依然具傳染性，使他們意識到這次的病原體 可能前所未見。腦部解剖獲得的唯一線索是神經元細胞 質出現被形容為「肥皂泡」的空泡，以及大腦中的奇怪空 洞，使大腦看起來呈海綿狀。
庫魯病：與食人習俗有關的神秘詛咒 在羊搔癢症重新成為科學家關注議題的同時， Daniel Gajdusek 和Vincent Zigas兩 位 醫 生 於 1957年從巴布亞新幾內亞第一身報告了一種被認為與 食人習俗相關的神秘疾病 [1, 2]。庫魯病首次發現於法 雷部落，患者不僅會顫抖和喪失控制肌肉的能力，還會 失控地大笑，並在幾個月內死亡。這種疾病主要影響女 性，成年患者中女性與男性之比為 14:1。 在1959年，研究羊搔癢症的美國獸醫William Hadlow 碰巧在倫敦的醫學博物館參觀一個關於庫魯病 的展覽 [3]。他驚訝地意識到這兩種進行性退化疾病之 間有著明顯的相似之處，例如神經元中的標誌性「肥皂 泡」、長潛伏期，以及無法識別致病微生物等 [4]。 此後，Hadlow 向《刺針》（The Lancet）的編輯 寫信，又主動聯絡 Gajdusek，希望喚起科學界關注這 兩種疾病的高度相似性 [5]。隨後，神經病理學家Igor Klatzo 從 Gajdusek 取得 12 個庫魯病患者的腦部樣 本，在仔細檢視後，發現庫魯病與另一種人類海綿狀腦 病 ─ 克雅二氏症亦有著相似之處 [6]。隨後十年，科學 家成功透過接種受感染的人腦組織，將庫魯病和克雅二 氏症在實驗中傳給黑猩猩和小鼠 [1]。 至於庫魯病，我們現在知道它是透過食人行為傳播的： 女性會在喪葬儀式中進食親屬的遺體以「釋放死者的靈 魂」[7, 8]，過程中攝取了含高濃度致病因子的人腦組織。 克雅二氏症：給科學家的啟示 那麼，致病因子究竟是甚麼？美國神經學家和生物化 學家Stanley Prusiner回憶起他在其克雅二氏症病人 中觀察到的反常現象：疫病並沒有引發免疫反應。患者 沒有發燒，白血球數量沒有增加，也沒有觸發體液免疫 反應，意味著引起疾病的可能不是外來的病原體 [9]。 Prusiner 憑藉自己的生物化學背景，決定以一個不 同的方式著手。他嘗試從接種了羊搔癢症致病組織的小 鼠中提取致病因子 [9]。在收集並攪勻小鼠的脾臟和腦 部後，用離心機以不同時間和轉速處理所得的勻漿，把 成分按密度分離。在測試每個樣本的傳染性後，他發現 一個保留了具高度傳染性的樣本，當中超過 98% 的蛋白 質和多核苷酸已被去除。有了這個更乾淨的樣本，科學 家證明致病樣本的傳染性可以透過水解或修飾蛋白質減 少，最終發現罪魁禍首根本不是微生物，而是錯誤折疊的 蛋白質。 病原性蛋白顆粒：錯誤折疊的蛋白質 蛋白質本質上是氨基酸鏈，它們需要被折疊成正確 的形狀才能運作。普里昂蛋白基因編碼著正常的普里昂 蛋白，儘管我們對其功能尚未清楚了解，但已知普里昂蛋 白活躍於大腦 [10]。然而，其氨基酸鏈在相關疾病中不 知為何被錯誤折疊，產生的畸形蛋白稱為「病原性蛋白 顆粒」，能損害神經細胞 [11]。更糟的是，它們能將正常 的普里昂蛋白轉換為病原性蛋白顆粒，使它們在體內的 數量呈指數級增長，並能透過攝取受影響組織或體液接 觸在個體間傳播。也有些病原性蛋白顆粒疾病具遺傳性， 例如致死性家族失眠症等；在這些病症中，已知一些普
References 參考資料： [1] Brown, P., & Bradley, R. (1998). 1755 and all that: a historical primer of transmissible spongiform encephalopathy. BMJ, 317(7174), 1688–1692. https://doi. org/10.1136/bmj.317.7174.1688 [2] Gajdusek, D. C., & Zigas, V. (1957). Degenerative Disease of the Central Nervous System in New Guinea. New England Journal of Medicine, 257(20), 974–978. https://doi.org/nejm195711142572005 [3] Hadlow, W. J. (2008). Kuru likened to scrapie: the story remembered. Philosophical Transactions of the Royal Society of London B: Biological Sciences, 363(1510), 3644. https://doi.org/10.1098/rstb.2008.4013 [4] Hadlow, W. J. (1959). Scrapie and Kuru. Lancet, 274(7097), 289–290. [5] Liberski, P. P., Gajos, A., Sikorska, B., & Lindenbaum, S. (2019). Kuru, the First Human Prion Disease. Viruses, 11(3), 232. https://doi.org/10.3390/v11030232 [6] Liberski, P. P., Sikorska, B., Lindenbaum, S., Goldfarb, L. G., McLean, C., Hainfellner, J. A., & Brown, P. (2012). Kuru: Genes, Cannibals and Neuropathology. Journal of Neuropathology and Experimental Neurology, 71(2), 92–103. https://doi.org/10.1097/NEN.0b013e3182444efd [7] Quinn, L., Whitfield, J., Alpers, M. P., Campbell, T., Hummerich, H., Pomat, W., Siba, P., Koki, G., Moltke, I., Collinge, J., Hellenthal, G., & Mead, S. (2024). Population structure and migration in the Eastern Highlands of Papua New Guinea, a region impacted by the kuru epidemic. American Journal of Human Genetics, 111(4), 668–679. https://doi.org/10.1016/ j.ajhg.2024.02.011 [8] Alpers M. P. (2008). The epidemiology of kuru: monitoring the epidemic from its peak to its end. Philosophical Transactions of the Royal Society of London B: Biological Sciences, 363(1510), 3707–3713. https://doi.org/10.1098/rstb.2008.0071 [9] Prusiner, S. B. (1998). Prions. Proceedings of the National Academy of Sciences of the United States of America, 95(23), 13363–13383. https://doi.org/10.1073/ pnas.95.23.13363 [10] National Library of Medicine. (2024, June 28). PRNP gene: prion protein (Kanno blood group). MedlinePlus. https://medlineplus.gov/genetics/gene/prnp/ [11] Ramanan, V. K. (2025, February 14). Transmissible Spongiform Encephalopathies. National Institute of Neurological Disorders and Stroke. https://www.ninds. nih.gov/health-information/disorders/transmissiblespongiform-encephalopathies [12] Bernardi, L., & Bruni, A. C. (2019). Mutations in Prion Protein Gene: Pathogenic Mechanisms in C-Terminal vs. N-Terminal Domain, a Review. International Journal of Molecular Sciences, 20(14), 3606. https://doi. org/10.3390/ijms20143606 11 里昂蛋白基因上的突變能引發異常蛋白形成 [12]。 病原性蛋白顆粒的積聚能破壞腦部組織，產生出現 於羊搔癢症、庫魯病和克雅二氏症的海綿狀空洞。與細 菌或病毒等大多數病原體不同，病原性蛋白顆粒並沒有 DNA，所以或許它們感染宿主的背後並不受任何「指令」 指使，而僅為折疊過程中的錯誤，導致這場悲劇。儘管如 此，它們為多個物種帶來無法治癒的致命疾病。 結論 病原性蛋白顆粒的故事見證了科學好奇心、堅持不懈 和合作的力量。最初一個具爭議的假設挑戰了生物學的 基礎法則，儘管看似違反常理，但最終重塑了多個領域 的認知。隨著科學家繼續面對生物學及醫學上的謎團， 這個故事提醒我們：真相並非總是顯而易見，但透過嚴 謹研究、相互合作和敢於挑戰常理的勇氣，即使是最非 比尋常的想法，也能照亮自然中最黑暗的秘密。
How Atomic Keep 原子鐘 Why Do We Need Perfect Time? Every time you launch Pokémon Go or other games that require the Global Position System (GPS), your phone’s GPS determines coordinates and shows your location. What if your avatar is teleporting across town or refusing to register the two kilometers you’ve walked to hatch an egg – frustrating, right? That’s exactly what happens when GPS timing drifts even for a small error. Radio signals travel at the speed of light, which is approximately 3 × 108 m/s. To determine the distance between you and a GPS satellite, the travel time of the radio signal emitted by the satellite to you is needed. By the simple velocity formula, we know that an uncertainty of just one nanosecond (10-9 seconds) in a clock corresponds to about 30 cm of range error [1], so a timing drift can misplace your avatar enough to miss a rare resource in game. Without atomic-level precision, our smartphones’ “blue dot” on the map could drift wildly from reality. Nature of Time Let’s start with a fundamental question: What is time? Philosophers have long debated whether time “flows” like a river – an ever-moving present that carries us from past to future – or whether all moments exist equally, with past, present, and future represented as slices in a four-dimensional space, and many other competing perspectives [2]. While no one knows what exactly time is, one pragmatic point of view is that we can define the length of time by counting some repeatable, periodic processes. The most common periodic processes are sunrise and sunset, caused by Earth’s rotation. We can also use gravity-driven swinging pendulums, which provide a near-constant oscillation period and form the basis of early mechanical clocks. Albeit less notably, even your body counts: You wake up refreshed and feel sleepy at night, which marks one full day (assuming your circadian rhythm stays on track). However, given that the Earth does not rotate at a perfectly uniform speed, and that the duration of one swing is slightly different from pendulum to pendulum due to manufacturing error [3], a new definition of time is needed. In 1927, a Canadian engineer, Warren Marrison, found that quartz crystals vibrate at a remarkably consistent frequency under an electric field [3]. When carefully cut into a proper shape and size, a standard quartz crystal in a clock vibrates at 32,768 Hz [3, 4]. By counting the duration for which 32,768 oscillations take, we can define that one second has passed. Core of Cesium-Beam Atomic Clock However, from 10 seconds per year for a mechanical clock to only one second in three
13 By Sam Fan 樊潤璋 Clocks Almost Perfect Time 如何精確計時？ years for a quartz clock [3], there was still room for improvement for the timekeeping accuracy. As a result, scientists developed more advanced timekeeping technologies. Cesium-beam clocks are just one member of the atomic clock family: Others include rubidium-beam standards, hydrogen masers, compact chip-scale clocks, and the newest optical lattice clocks. Cesium-beam designs remain the most widely used standard worldwide. In fact, the Hong Kong Observatory has been relying on cesium-beam atomic clocks to provide official time service since 1980, with an accuracy kept within 0.01 microsecond (10-8 seconds) per day [5]. At its core, the clock does not “tick” atoms but counts the cycles of a microwave signal precisely locked to an atomic reference. The cesium atoms act as a built-in tuning fork; cesium only resonate to the frequency at 9,192,631,770 Hz within the microwave band to change between two very slightly different energy states. This happens when cesium atoms pass through a microwave cavity [6]. If the microwave frequency is above or below 9,192,631,770 Hz, fewer atoms undergo a change in energy levels. The irregularity can be detected, and the oscillator will be steered back onto the exact cesium resonance frequency, ensuring the microwave oscillator stays locked to atomic standard. Once the oscillator is held exactly at the resonance frequency, every single cycle becomes one “tick” of the clock. By simply tallying 9,192,631,770 of these ticks, the device measures one second [6, 7]. Since this shift in energy levels is a fundamental property of cesium atoms, every clock built anywhere with cesium atoms can reproduce the same resonance frequency of 9,192,631,770 Hz signal, ensuring that time is uniform around the world. Importance of Time Synchronization Every GPS satellite carries multiple atomic clocks and broadcasts signals with an accurate timestamp of when the signal is emitted, so that receivers on the ground can determine their distance to the satellite by multiplying the signal’s travel time and the speed of light [8]. Without the cesium or rubidium standards, minute timing drifts would quickly lead to substantial positional errors in just a few minutes due to the cumulative time error of the onboard clock. Summary In just a few decades, we’ve gone from pendulums and quartz crystals to atomic clocks and optical lattices that keep time to within a quintillionth of a second (10-18 seconds), so precise that they can sense minuscule shifts in Earth’s gravity or hunt for hints of dark matter in the cosmos [9]. Although the principles behind atomic precision may seem complicated, the technologies they enable are integral to our daily lives. Every time we check our phones, play a game, look up our location, or simply glance at the clock, we tap into nature’s steady rhythms.
為何需要精確計時？ 當你每次打開Pokémon Go或其他需要全球 定位系統（Global Position System / GPS）的遊戲時， 你手機的 GPS都會確定你所在的座標並顯示你的位置。 假如你的角色突然在地圖上「瞬間移動」，或是遊戲不承 認你已走完孵蛋所需的兩公里路程時，無力感隨即會在刹 那間湧現，GPS時間出現些微誤差都會導致這些問題發 生。 無線電訊號以光速傳播，大約是每秒3 × 108 米。要得 知你與GPS衛星之間的距離，系統需要知道衛星發出的 無線電訊號到達你所在位置的所需時間。依照最簡單的速 度公式，我們知道時鐘只要出現一納秒（10-9 秒）誤差，就 會導致大約30厘米的範圍誤差 [1]。因此，即使是極小的 時間偏差，也可能讓你的角色錯過遊戲中的稀有資源。沒 有原子等級的精準度，手機地圖上的「藍點」就可能大幅偏 離現實位置。 時間的本質 我們可以從一個基本問題作為起點：甚麼是時間？長 久以來，哲學家爭論時間是否像河流般「流動」：是不斷前 進的現在將我們由過往帶到未來；抑或所有時刻平等地存 在，過去、現在與未來只是四維空間中的一幀幀片段。當 然還有其他各種不同觀點 [2]。雖然沒有人能確定時間究 竟是甚麼，但從實際角度來說，我們可以透過數算一些可 重複、具週期性的現象來定義時間的長度。 最常見的週期性現象是因地球自轉而產生的日出日落。 我們也能利用由重力驅動的鐘擺，它能提供幾乎恆定的 擺動週期，從而成為早期機械鐘的基礎。另外， 儘管你可能不自覺，但甚至你的身體 也在「計時」：你在早上精神飽滿， 晚上感到困倦，以此完成一天的 循環（假設你的生理時鐘沒有偏 差）。不過地球的自轉速度並不 完全恆定，不同鐘擺也會因製造 誤差導致擺動週期略有不同 [3]，因 此我們需要一個全新的時間定義。1927 年，加拿大工程師Warren Marrison發現石英晶體在電 場下會以極穩定的頻率振動 [3]。當被切割成適當形狀與 大小時，時鐘裡的標準石英晶體會以 32,768 赫茲的頻率 振動 [3, 4]。只要計算32,768次振動所需的時間，我們就 可以定義一秒。 銫原子鐘的結構 然而，從機械鐘每年可能出現 10 秒誤差，到石英鐘三 年只會出現一秒誤差 [3]，精準度依然有進步空間，於是科 學家發展出更先進的計時技術。銫原子鐘是原子鐘家族的 一員，其他還包括銣原子鐘、氫原子鐘、晶片級原子鐘，以 及最新的光晶格鐘。銫原子鐘仍是全球最常用的設計，而 事實上，香港天文台自1980 年起就以銫原子鐘提供授時 服務，精準度可維持在每天 0.01微秒（10-8 秒）以內 [5]。 銫原子鐘的內部並非藉原子「滴答滴答」擺動計時， 而是精確地數算鎖定於銫原子基準的微波訊號週期。銫 原子就像內建的音叉，只對 9,192,631,770 赫茲的微波頻 率產生共振，而在兩個能量狀態之間轉換。這個過程發生
References 參考資料： [1] Tavella P, Petit G. Precise time scales and navigation systems: mutual benefits of timekeeping and positioning. Satell Navig. 2020;1. doi:10.1186/s43020020-00012-0 [2] Emery N, Markosian N, Sullivan M. Time. Stanford Encyclopedia of Philosophy. Updated November 24, 2020. https://plato.stanford.edu/entries/time/ [3] Smithsonian National Museum of American History. Splitting Seconds. On Time: How America Had Learned to Live by the Clock. https:// americanhistory.si.edu/ontime/expanding/seconds. html [4] Lombardi MA. The Accuracy and Stability of Quartz Watches. Horological Journal. 2008. https://tsapps. nist.gov/publication/get_pdf.cfm?pub_id=50647 [5] Chee SC. Network Time Service – Past and Future. Hong Kong Observatory. Updated April, 2022. https://www.hko.gov.hk/en/education/astronomyand-time/time-service/00669-Network-TimeService-Past-and-Future.html [6] Hebra AJ. The Physics of Metrology: All about Instruments: From Trundle Wheels to Atomic Clocks. Springer Vienna; 2010. doi:10.1007/978-3-211-78381-8 [7] Audoin C, Guinot B. The Measurement of Time: Time, Frequency and the Atomic Clock. Cambridge University Press; 2001. [8] Federal Aviation Administration. Satellite navigation - GPS - How it works. https://www.faa.gov/about/ office_org/headquarters_offices/ato/service_units/ techops/navservices/gnss/gps/howitworks [9] Lea R. Atomic clocks on Earth could reveal secrets about dark matter across the universe. Space.com. Updated September 2, 2023. https://www.space. com/ultra-precise-atomic-clocks-investigate-darkmatter-earth 15 於銫原子通過微波空腔時 [6]，如果空腔中的微波頻率偏 離這個值，會令較少銫原子轉換能量狀態。我們可以在偵 測到偏離的情況下校正微波共振器，以確保共振器始終 鎖定在銫的共振頻率上。只要共振器固定在這個頻率，它 發出的每個微波訊號週期就成為一次「滴答」。當數到第 9,192,631,770次時，原子鐘就會記錄一秒過去 [6, 7]。 由於這種能量狀態的轉換是銫原子的基本性 質，所以無論銫原子鐘在哪裡製造，都能有著相同的 9,192,631,770 赫茲共振頻率，因而確保計時標準全球通 用。 時間同步的重要性 每顆 GPS 衛星都搭載多台原子鐘，並廣播帶有精準時 間戳記的訊號，讓地面接收器能透過「訊號傳播時間×光 速」計算出其與衛星的距離 [8]。如果沒有銫或銣的時間 標準，衛星時鐘在幾分鐘內累積的微小時間誤差，就已經 能導致巨大的定位偏差。 總結 短短幾十年間，我們已經從鐘擺與石英晶體，發展到原 子鐘，以及能將誤差控制在百京分之一秒（10-18 秒）的光 晶格鐘，精準到足以感應地球引力的微小變化，甚至用來 搜尋宇宙中的暗物質 [9]。雖然原子鐘背後的原理看似複 雜，但當中所使用的技術卻已融入日常生活。每當我們查 看手機、玩遊戲、定位，或只是看時鐘時，其實我們都在借 助大自然的律動。
Euler’s Nu The Magic of What Is Euler’s Number? Have you ever come across a number that seems to connect math, science, and the world around us? One of the most fascinating is Euler’s number, written as e, a special constant approximately equal to 2.718, central to countless natural and scientific phenomena. It’s the foundation of the natural logarithm, a tool that helps us understand how things grow or shrink over time. From bacteria multiplying in a lab to stars fading in the sky, e appears in countless natural processes [1]. Surprisingly, this number was first uncovered not in a science lab but in a puzzle about money. Let’s explore how e came to be and why it’s so extraordinary. By Jane Yang 楊靜悠 A Mathematical Gem Discovered in Finance The story of e begins in the 1600s with Jacob Bernoulli, a mathematician curious about how small changes add up [2, 3]. Imagine you have $1.00, and you’re offered an unrealistic 100% annual growth rate. If this growth is added once at the year’s end, your $1.00 doubles to $2.00. But what if the growth is calculated more often? Suppose it’s added twice a year. Every six months, you gain 50%, so your $1.00 grows to $1.00 × 1.5 × 1.5 = $2.25 by year’s end. If it’s calculated four times a year, each period adds 25%, turning your $1.00 into $1.00 × 1.25 × 1.25 × 1.25 × 1.25 = $2.44. Monthly calculations yield $1.00 × (1 + 1/12)^12, about $2.61. The pattern is clear: More frequent additions mean a larger result. Here’s the exciting part. What if the growth is calculated every day, every minute, or even every second? The formula becomes $1.00 × (1 + 1/n)^n, where n is the number of times the growth is added. As n grows larger — approaching infinitely frequent additions — the result doesn’t climb endlessly but settles around 2.718281828459045… . This number is e! Bernoulli discovered this constant, revealing a mathematical gem that would resonate far beyond his original question. The Power of e in Our World Why is e so important? Named after Leonhard Euler, who further explored its properties in the 1700s, this number became a universal key to understanding exponential change, appearing in fields like biology, physics, medicine, and engineering. Its unique properties make it ideal for describing processes that speed up or slow down, like a snowball growing larger
ebookshelf.hkust.edu.hkRkJQdWJsaXNoZXIy NDk5Njg=