Who should get vaccinated first?

Vaccination no doubt creates hope for a rapid recovery of our severely impacted economy and resumption of normal life from the long painful fight against the pandemic. The questions that concern most of us are which vaccine is more effective and whether the side effects are tolerable. Moreover, of greater interest to the policymakers is who should get vaccinated first, and which order of priority would result in the shortest time to herd immunity and/or the use of minimum resources. The point is that we don't have to vaccinate the weak or more vulnerable groups in order to protect them, but rather to vaccinate the spreaders in the community and hence protect the entire community. An elderly person could safely live in her nursing home if there were no infected caretakers or visitors!

In February 2021, Hong Kong government began offering free vaccine to the more vulnerable groups, including the elderly, medical and healthcare workers, and then teachers, taxi drivers, restaurant workers, etc., the rationale being the need for protection. However, taking a more scientific approach, the entire community is actually a network of people. Each individual has his or her own contacts. Some have more and some have less. An elderly person living in a nursing home under intermediate care would typically meet with three or four people (mostly caretakers or a couple of family visitors) daily. On the other hand, a cashier working in a convenience store could be in contact with hundreds of customers per day. In terms of the likelihood of spreading the virus, people having more contacts (technically called "degree" in a network) should more likely be the key spreaders.

A more effective approach may be to classify different groups according to the statistical average of the contact links per day. For instance, a taxi driver carries an average of 300 passengers a day; a restaurant waiter serves an average of 100 patrons a day; a teacher interacts with 50 students a day; and so on. Then, if we prioritize our order of vaccinating different groups in our community according to the average contact number of the groups, we should theoretically reach the nerd immunity state much quicker.

This is a research topic worth studying!

March 22, 2021

英式優雅

Harry 皇子和 Meghan 皇妃在 Oprah Winfrey 的一個電視訪問中，大說英國皇室的不是，言之鑿鑿，指控皇室成員種族歧視。英美媒體廣泛報導，網民加鹽加醋，煽動仇視皇室情緒，若處理不當，可釀成憲制危機。 事態嚴重，女皇也急忙發表聲明反駁，短短六十一字，優雅得體，但棉裡藏針，訓示兩個不肖子孫勿再造謠生事，毀皇室清譽。

女皇淡然一句「 recollections may vary」（記憶也許存在出入），彷彿指著 Harry 和 Meghan 說「你兩條友仔咪亂噏廿四」；然後再溫馨提醒他們這些家事「將 (應) 在家裡私下處理」（will be addressed by the family privately），也就是跟他們說「有嘢就返來講，唔好喺外面唱我」。英式英語之強乃在於器量的展現。雖然給 Harry 和 Meghan 公開罵了兩小時，身為他們祖母的英女皇還在聲明開端代表皇室「對他們過去幾年面對的挑戰表示痛心」(The whole family is saddened to learn the full extent of how challenging the last few years have been for Harry and Meghan.)，最後還說「Harry 和 Meghan 永遠是她至愛的家人」(will always be much loved family members.)，如此溫文大方，令人佩服！

若以當今中國特色語言來表達，Harry 和 Meghan 必定是「受外 (美) 國勢力操控惡意中傷皇室」，接受「別有用心的媒體訪問」，並「嚴重傷害英國人的人民感情」，英國全體人民必定「堅決反對」，要求 Harry 和 Meghan 「立刻停止抹黑以女皇為核心的英國皇室的錯誤行為」，英國將「追究到底」，要他們「付出沈重代價」，英國政府將保證「這些反英圖謀不會得逞」。

單憑表達不滿時所用的語言，可以反映一個人 (國家) 的器量和自信（也許說話的實際對象有異）， 同時也是軟實力的一種體現。英式英文，對比當今中國特色的中文，高下立見。

2021年3月18日

疫苗保護率的謬誤：統計學101

昨日，明報刊登了一篇以「稱有效率五成≠半數人有效 劉澤星：科興2/3接種者受保護」為題的報導*，引述負責審核新冠疫苗的顧問委員會召集人劉澤星先生指科興疫苗能有效保護三分之二的接種者。

按明報引述科興的數據，接種人數及接受安慰劑人數各約為5000人。前者當中85人受感染，後者168人受感染。劉先生基於 85：168（大概 1：2）的比例，推出 2/3 接種者受到保護！依照劉先生的算法，5000 這個參與者數目（採樣人數）並無任何意義！ 事實上，在某個群組所錄得的感染人數是受到許多因數影響，故需要增加採樣數目才能保證統計數字的可信性。況且，85和168是兩個群組的感染數字，很難理解如何單憑這兩個感染數字來推出疫苗的保護率。正式來說，在5000+5000 = 10000名參與者中，2/3感染者是沒有接種疫苗的。劉先生反過來說成 2/3接種者受到保護，肯定不正確。再加上，如果採樣數目不是5000，而是100萬的話，85和168、甚至1000的感染人數基本上沒有太大區別。從統計學角度看，採樣數目是非常重要的參數，絕對不能忽略。

按基本數學邏輯，5000名接種者當中有 4915人未受感染，而5000名接受安慰劑的人士當中有 4832人未受感染，這也並不代表疫苗在接種者身上可提供 4915/5000 = 98.3% 的保護率，因為接受安慰劑的也有4832/5000 = 96.64%不受感染。我們只可以估算疫苗“相對”的保護率大概為50.43% （科興的50.66%應該是基於更準確的數字和統計方案）。

劉先生的2/3保護比例的說法有誤導公眾之嫌，必須予以修正。

2021年2月19日

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*「稱有效率五成≠半數人有效 劉澤星：科興2/3接種者受保護」— 明報 2020年2月18日

How time flies: Predicting when your life shall end

Every summer vacation in primary school was like a never ending holiday, and in my mind, still, the six years in primary school were very long, and definitely much longer than the seven years in secondary school. My memories of the days in the 2000s and 2010s are like yesterday, but those of my primary school days are much older history, disproportionally older! One thing for sure is that the perception of time duration gets shorter as one becomes older! In other words, time moves faster when you get older! So, depending on how old you are, your perception of a 10-year duration can be quite different!

The perceived absolute time also changes as one gets older! When you're young, you felt things that happened 40 years ago were like ancient history! But as you get older, things that happened 40 years ago seemed really not that long ago to you!

You probably still find the music of the 2010s pretty good. Way back, when you're a kid, your perception of the music that your mother loved was like ancient tune! The perception of time clearly changes as you grow older! That seems to be unavoidable, and you can do nothing to revert it. The question is not why, but how fast? Can we possibly work out how fast our perceived time shrinks? If you know the answer, you probably know how rapidly you age and perhaps also when your life shall end (disregarding accidental life-threatening events).

Taking another perspective, if our life ends at the time when our perceived time has shrunk to zero, or in practice shortened to a threshold point that life becomes almost meaningless, then one could possibly predict his own lifespan based on his own perception of time while he still lives and continues to age. This in theory should work!

Suppose your perceived time is Tperception while the actual time is T. A simple first order law that describes how rapidly your perceived time shrinks with time is:

Tperception = T exp( –T / τ )

where the parameter τ determines how fast (by how much) your perception of time would shrink over a fixed time lapse. Experience suggests that time perception shortens by half at the age of 25, around the time when one finishes college and gets to the real world. This means τ is roughly 37, because exp(–25/37) ≈ 0.5.

Hong Kong's average lifespan is 88 for women and 83 for men, say 85 for any average person. Thus, our perceived time has shortened to around 10% of the actual time at the end of our life, since exp(–85/37) = 0.1. We may say that if one perceives time as 90% shorter than it actually is, life is no longer meaningful!

If you know how rapidly your perception of time shortens, i.e., the value of τ, you should theoretically know when your life shall end.

January 16, 2021

問題翻譯 2.0

香港政府推出「抗疫基金」，為受COVID影響的企業和市民提供援助，「抗疫基金」英文竟然直譯為「Anti-Epidemic Fund」。不懂中文的朋友起初以為是為醫護界提供額外資源，務求儘快遏止病毒蔓延，又或者是為香港生物科技業界提供資金，加速研製疫苗。但香港並無研發疫苗的機構，大學也只是與某些內地和海外研究團隊合作而已，何來Anti-Epidemic 的 Fund？

Anti-Epidemic 明顯是「抗-疫」的直譯， 先有中，後譯英。問題是，有關政策局和行政部門精英雲集，竟無人察覺，讓如此垃圾翻譯出街，非常搞笑！美國類似基金叫「COVID-19 Relief Fund」，語義非常清晰，字眼是 relief，目標自然是為紓緩市民大眾因疫情所遭受的經濟困境而提供的援助。除了Anti-Epidemic 本身的意譯誤差，執行翻譯的官員的基本事實查證也欠妥，世衛在港府推出「抗疫基金」之前已老早宣布 COVID-19 成為全球大流行，本來的 Epidemic 已升級為 Pandemic，就算是誤譯也應該是 Anti-Pandemic Fund 才錯得對，現在乃錯上錯！

幾年前寫過兩篇關於香港的問題翻譯的博文1,2，主要是中譯的問題，是先英後中所牽涉的技術問題和文化差異產生的誤譯。現在剛剛相反，進化為問題翻譯 2.0！

2020年10月19日

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1 博士候選人：你幾時去參選？
2 從航機廣播看中國人的自信