2014年10月21日 星期二

健康兩點靈-喝好水(3)

https://www.youtube.com/watch?v=Q4VcIt_gzNU

健康兩點靈-喝好水(3)

[小伍淨水]純水才是真正的好水


RO水 & 電解水

電解水與RO水有害

〈健康生活〉 你家淨水器 裝對了嗎?

http://news.ltn.com.tw/news/supplement/paper/823318

〈健康生活〉 你家淨水器 裝對了嗎?

2014-10-21
文/江守山
選購淨水設備前,建議消費者一定要對各種淨水過濾原理的成效有基本了解……
  • 市面上淨水設備,光是過濾方法就有電解、蒸餾、活性碳、逆滲透、紫外線等多種,讓人看得眼花撩亂。(資料照,記者侯千絹攝)
    市面上淨水設備,光是過濾方法就有電解、蒸餾、活性碳、逆滲透、紫外線等多種,讓人看得眼花撩亂。(資料照,記者侯千絹攝)
  • 江守山。(圖片提供/新自然主義)
    江守山。(圖片提供/新自然主義)
這些年來,隨著經濟發展,越來越多人肯在健康上花錢,市面上各種淨化水質的設備也就越賣越熱。
到底哪一種淨水設備最好呢?是很多人都想知道的。尤其市面上淨水設備,光是過濾方法就有電解、蒸餾、活性碳、逆滲透、紫外線等多種,讓人看得眼花撩亂。其實這些過濾方法看似複雜,但簡單來說就是濾心不同而已。
當然,不同的過濾方法,水質的過濾能力也有差異,因此在選購淨水設備前,建議消費者一定要對各種淨水過濾原理的成效有基本了解。

<喝得更安心>濾水補強 安裝有學問

對已裝設一般濾水器的人來說,一定想知道到底哪種過濾方式最好?如果要「補強」,該如何安裝,才能達到最好的過濾效果呢?
我個人認為,逆滲透是目前最好的淨化方式。舉例來說,不論藥廠做注射液、晶圓廠洗晶圓、洗腎室洗腎等需要純淨水的場合,都使用逆滲透系統。不過最好的逆滲透淨水系統,是過濾後不儲放而直接使用,以避免濾淨的水因為沒有抗菌力,而在儲水桶中長出大量細菌。
假如是有儲水桶的逆滲透系統,裝過濾水的儲水桶最好是不鏽鋼製,且不可以內含壓力球,否則已經淨化的水又會受到壓力球等塑化劑的二次污染。
至於補強過濾,建議可先查看水管進大樓或住家水塔前是否有裝設過濾器,其次是在自來水管線分裝到自家用水前裝設三鹵甲烷過濾器。因為台灣自來水不安全,部分原因是水管品質不良之故。據統計,台北市的水管漏水率是26.7%,遠遠高於巴黎的10%、東京的5.4%和柏林的4.3%,而且台灣本島的漏水率更超過35%,水管旁的泥沙、有機物也會進入水管,有機物遇到殘留的氯,就會形成更多三鹵甲烷。
所以要維持自來水乾淨,最好在進水塔前加裝過濾器,以去除泥沙等固態雜質,並在自家用水管線過濾三鹵甲烷和氯,最後才是在廚房裝設逆滲透淨水器,用以消除重金屬及荷爾蒙等有害物質。

<小資家庭看過來>沒裝濾水器 也可提升水質

如果真的沒有辦法安裝淨水設備,那又該怎麼辦?別擔心,只要掌握幾個小撇步,還是可以提升日常飲水品質︰
不要用清晨或假日後的第一道自來水︰在水管中靜置了一晚或一個週末的水,通常含鉛量最高,也沉積最多雜質,最好不要用。
自來水煮沸後打開鍋蓋多煮5分鐘︰根據日本的研究及環保署環境檢驗所實驗結果,自來水煮沸過程中,三鹵甲烷會先隨溫度增加而增加,並於煮沸到100℃時達到最高點,此後若打開鍋蓋繼續煮沸3到5分鐘,三鹵甲烷含量就會大幅減少。
所以在家中煮開水,建議應於煮沸後打開蓋子再煮沸5分鐘,不過要記得同時打開排油煙機或窗戶,以避免蒸散的三鹵甲烷又讓家人吸入。同理類推,如果是用有消氯功能的熱水瓶,記得「消氯鍵」也要在家中通風時才能按下。
最好晚上燒開水︰因為水管一整天已經被大量用水清洗乾淨了,所以晚上的水質最佳。

<達人小檔案>江守山

現任新光醫院腎臟科主治醫師。「腎臟病」年年登上國人十大死因排行榜,可說是台灣人的「新國病」!提醒大家工作緊張忙碌,就會在不知不覺中養成傷害腎臟的危險習慣,像是一忙就忘了上廁所、熬夜晚睡導致睡眠不足,還有飲食過度、飲食過量、運動不足導致血糖、血壓、血脂偏高,以及抽菸等等,每一項都是會嚴重影響腎臟健康的壞習慣。近日將出版《逆轉腎――腎臟科名醫江守山教你:喝對水、慎防毒、控三高》。

2014年8月28日 星期四

貢獻這所大學于宇宙的精神


人類的生存模式像病毒
自己無法生存
必須靠別的物種的努力過活
而且為了自己的生存,常常造成別的物種的滅絕

所有生物生存的過程
都只有取用需要的物品
只有人類還對地球取用想要的東西

文明的過程
就是分辨
什麼是需要
什麼是想要的
了解
得到需要的,必須付出什麼代價
得到想要的,必須付出什麼代價
然後在這個過程中
找到平衡點
找到和大自然共振的平衡點

找不到平衡點
病毒就會把自己也滅絕掉


2014年8月5日 星期二

行遍天下道路救援專線 0800-066-885


大潤發/大買家聯名卡之正、附卡
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及拖吊車兩側車身印有「高速公路局特約拖救車」字樣者。

高速公路救援說明
持卡人已登錄之車輛於高速公路上發生故障或事故時,須先向行遍天下道路救援專線0800-066-885申請救援,
基於安全考量或情況緊急已由其他高速公路合法拖吊公司拖救車(※)拖離現場時,請立即向0800-066-885道路救援服務專線申告,以免個人權益受損,服務中心人員將會告知其處理程序。
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※合法拖吊車:指拖吊車正前方印有「高速公路局特約拖救車」及五個阿拉伯數字、前擋風玻璃貼有高速公路梅花標誌拖吊服務證及拖吊車兩側車身印有「高速公路局特約拖救車」字樣者。
https://www.taishinbank.com.tw/TS/TS02/TS0201/TS020101/TS02010102/TSB011083

2014年7月5日 星期六

學會和大自然共舞


交大物理所高文芳

辭典通常不是用來讀的,是用來查的,有疑問時,辭典就是好幫手。但是,小學生圖解科學辭典還想扮演:學童認識大自然的啓蒙導師。

物理就是大自然所有人、事、物的道理,有時候叫數學,有時候叫化學,有時候叫科學,連社會學的前身都叫做社會物理學。然而,現在大學物理系裡研究的,多半是實驗誤差在30%以下,比較簡單的部分。

以前,筆者覺得大自然最有趣的現象,就是這個繽紛多彩的世界,用眼睛看就很精彩,但是最不可思議的就是,這些令人目不暇給的彩色世界,竟然可以用簡單的數學公式來描繪。年長些,就開始覺得大自然更神奇的現象,就是這些看起來不會思考、沒有生命,也沒有讀過書的主角,不管是電子或光子,居然會聽從一些簡單數學公式的號令。叫他往東,幾乎所有大兵、小將都乖乖往東,不會亂跑,比自己的小孩還聽話。

一般科普讀物,尤其是要給學童看的自然讀物,如何遣詞用字是一門很大的學問。有一位文學家講過『板塊擠壓和地牛翻身』的故事。大意是,小一的學童不能理解板塊擠壓,地牛翻身就是地震成因的最好說法,不同的讀者,需要的教材自然不同。要作者寫一本大家都可以讀得懂的書既然很難,我們不妨換個角度,試著和作者一起寫這本書。

試著用小孩的角度和自己的小孩分享、一起成長、一起和大自然共舞。讀者心中有疑惑時,看到的如果是機會、是挑戰,年幼的學童很可能在努力解開心中的疑惑時,讓科學有機會展現另一種新鮮的風貌。

大自然的母語似乎是數學,而來自傳譯數學的困難,也常是造成閱讀障礙的原因。多數人很少留意的,是文字有一種神奇的魅力。同一句話,不同的人說,不同的人聽,都會產生令人驚訝的差異。如果聽者相信言者是出於善念,也樂於接受,一句平凡的話,也會被接收者無限上綱、感動地無以名狀。反之,反效果也會非常驚人。所以有人說,我們的語言很像一首詞義不夠精準的詩,因此讀詩的時候,要讀他的意境,不是表面的字義。

然而,沒有好的數學基礎真的就讀不好科學嗎?問了很多人,怎麼答案都不一樣?法拉第和高斯的故事,或許可以給我們一點啟示。

有人說法拉第的數學不好,所以他在面對電磁現象時,無法和高斯、馬克斯威這些大數學家一樣,靠高深的數學內功來欣賞、品味美麗的電磁世界。所以法拉第必須另闢捷徑:利用過人的想像力,將磁力線圖像化,讓數學的世界多了另一種精彩的面向。

懂越多數學,一定會讓你看到越多人看不到,而且非常精彩的視野。還無法理解這些數學前,一樣也可以駕馭自己的想像力,飽覽一些數學很難觸及,像詩一樣浪漫的彩色視界。

科普讀物的目的不是要講物理,而是要引領讀者對大自然的好奇心、誘導讀者自己找尋答案的趣味、啟發每個人不一樣的天賦,期待他們登峰造極,為人類開啟新的視野。像這本書的作者一樣,很多科普讀物的作者,都試圖用更精準、更適齡的『詩』,讓不同的讀者都能夠一起欣賞大自然的神奇。所以希望讀者閱讀時,能夠體會這些科普作家無比興奮的心情,期待大家一起探索、一起找出最適合自己解讀這個神奇世界的神方妙法。

有人說,太陽底下無鮮事。的確,天荒140億年,地老46億冬,大自然經過這麼多年的探索、演化,我們心中任何疑問,應該都能在天涯海角的某個角落裡找到答案。我們該做的,或許只是細心的觀察、謙虛的思索,學會讚美大自然、學會和大自然共舞。正在迷霧森林裡急著找出口的人類,或許可以在這個神奇的舞台上,舞出亮麗的身影。


畢竟,欣賞舞台劇的觀眾比演員更有深度時,這個世界一定可以更加美好。

2014年7月2日 星期三

傲慢 知識 生活

  學者搭船,與船夫閒聊。

「你有學過數學嗎?」學者問
「沒有。」
「啊!那你等於失去四分之一的生命。那學過哲學嗎?」
「也沒有。」
「那你等於失去一半的生命,多可惜啊!」

  忽然一陣狂風吹來,船將翻覆。
「你學過游泳嗎?」船夫問
「沒有。」學者惶恐的回答

「唉!那你將失去全部的生命了。」船夫感嘆的說......

  http://www.ltn.com.tw/

2014年5月21日 星期三

雨天車窗除霧什麼最給力? 洗潔精效果堪比除霧劑

http://big5.cntv.cn/gate/big5/xiamen.xmtv.cn/2013/12/16/ARTI1387156882175269.shtml


雨天車窗除霧什麼最給力? 洗潔精效果堪比除霧劑

發佈時間:2013年12月16日 09:22 | 來源:海峽導報

  據海峽導報報道(記者 香卉輝/文 吳曉平/圖)降溫了,下雨了!廈門冬天下雨,最頭痛的要數開車的市民,僅車窗擦霧氣就夠忙一路了,而且擦完沒幾分鐘又要重復勞動。

  如何才能讓車窗在冬季陰雨天也保持亮堂呢?昨日,導報記者一行來到廈門興日興車行,對市民常用的一些車窗除霧方式進行了對比實驗,如:空調、熱風、幹毛巾、汽車除霧劑、洗潔精等,結果發現家用洗潔精最實惠又實用,效果堪比專業除霧劑,而且可以保持一週以上時間。雨天開車出門,記得先用洗潔精擦擦車窗。

  空調除霧:速度快效果好

  缺點:維持時間短而且太冷

  空調除霧是所有車主最常用、最方便的方式。車行負責人陳劍海先用噴霧劑在車內噴灑熱氣,很快車子所有玻璃上都蒙上了一層霧氣。打開空調製冷的最低擋,1分鐘左右玻璃上的霧氣開始消失,所有玻璃完全除霧需要2分鐘左右,但此時,車內的導報記者已經凍得手腳冰涼。

  我們對著剛剛除去霧氣的車玻璃再次噴霧,玻璃立刻起霧。

  結果:速度快,效果好,但是在冬天十幾攝氏度的溫度下,對司機和乘客來説太冷,且維持時間短。

  防霧劑:效果好維持時間長

  缺點:需額外購買,成本較高

  導報記者在海西汽配城購買了一瓶車用“玻璃防霧劑”,價格30元。上面寫著採用“特殊原料製成,可在玻璃表面形成透明疏水離子膜,防止水珠霧氣凝結”。按照上面的使用説明,導報記者將其噴灑在已經起霧的擋風玻璃上,用布擦乾,玻璃立刻乾淨。

  用噴霧機在玻璃上再噴霧,十幾分鐘後依然沒有霧氣形成。

  結果:方便,效果好,維持時間長,但需額外購買,在普通汽車美容店賣50-80元,淘寶賣20多元。

  洗潔精:方便、維持時間長

  對比:成本低、性價比最高

  對於網上流傳説洗潔精除霧效果好,陳劍海透露,用洗潔精除霧也是他多年來自用的方法。導報記者將普通家用的洗潔精按照1:6加水稀釋,然後噴在幹毛巾上,在起霧的車玻璃上一擦,玻璃也立刻乾淨,效果與汽車防霧劑不相上下。

  “我最長紀錄曾經有半個月沒有起霧。”陳劍海説,不過要在沒有洗車和擦玻璃的情況下。洗潔精還能保持後視鏡淋雨後依然清晰。我們將洗潔精擦在車子後視鏡上,再用水去潑淋後視鏡,鏡面完全沒有水珠形成,而是形成一面水膜流下,看物體很清晰。“在普通雨天內可維持時間2天左右。”陳劍海説。

  結果:方便,效果好,維持時間長。無需額外購買,家裏的洗潔精擠一些兌點水就可以,成本幾乎可以忽略不計。

  專家解讀

  表面活性劑是關鍵

  實驗結果證實洗潔精的除霧功能確實很強大。按照大概1誜6的比例將洗潔精和水配比,裝進瓶子裏。在出行前,將車窗所有玻璃內側、後視鏡上全部用它擦拭一遍,你就可以不用擔心行程中霧氣影響視線了。

  為什麼洗潔精能起到防霧劑的作用,還能長時間維持不起霧?導報記者就此專門採訪了廈門一中的化學課楊老師,他告訴導報記者,主要原因就是洗潔精主要成分是表面活性劑。“表面活性劑有親水基團,又有親油基團。”楊老師解釋,當洗潔精均勻擦拭在玻璃上時,裏面的親水基團附著在玻璃表面,而親油基團有疏水作用,霧氣中的小水滴無法附著在上面,起到防霧的作用,且它沒有揮發性,所以能維持較久的時間。

2014年5月6日 星期二

亂打秀

美國:他想打誰,就打誰。

俄國:誰都不敢打他,但是他誰都敢打。

英國:美國打誰,他就打誰。

日本:誰打他,他就叫美國打誰。但是事實是:誰打他,美國就打誰。

中國:不管是誰,都當敵人亂打一通。

北韓:誰打他,他就打南韓。

台灣:誰都打他,當然像大部份民主國家一樣,也會自己也打自己。

2014年5月3日 星期六

Humboldt University Physics Institute

http://es.urbarama.com/project/humboldt-university-physics-institute


Humboldt University Physics Institute



The Humboldt University Physics Institute is part of the city planning of the town of Berlin and its scientific research site Adlershof. It is part of the newly planned buildings for the scientific research area of the Humboldt University. The Humboldt University is to complete and stimulate the privately financed part of the developing technological park. 
A master plan proposes a perpendicular street system for the area, which was developed without reference to the past airport site and its structural surroundings. Presently, the plastically formed building shells of the aerodynamic experimental buildings of the 1930's dominate the area. 

The building site chosen for the Physics Institute is the northern part of a street block on whose southern corner will also be build in the near future. The building integrates itself into the orthogonal system but remains at the same time a solitary body with four independent outer skins, each individually reflecting the different outside areas. Views and scenes show the internal structure and give the building a sense of transparency and plasticity. The internal separation through garden courtyards qualifies the setting, introducing autonomous botanically designed outside spaces. 

The inner organization follows the principle of central development with weblike hall and room connections. These reflect the actual and possibly changing user structure of the Physics Institute. The building offers easy orientation, short distances, and different combinations of its usable spaces. 

Because the site and structure of the building let not expect disturbing emissions, a one-layered building skin was planned. With the exception of the north facade, every outer part of the building got a passable facade area. These are easy-maintenance walk-ways equipped with different shading devices. All hall-ways have vegetative sun protection through overgrown steel and bamboo trellis, which are moun-ted along the walk-way of the facade. Every lounge has an outside-lying shading device. The outside walls are carried as light constructions over the supporting structure of reinforced concrete. 

The building concept focuses on escorting and influencing the development at Adlershof. The area will be, in opposition to the formulated city town-planning model, uncontrollably and discontinually evolving. Because of this, the concept offers an 'evolvable' building. In this way, the north facade will in the be-gin-ning form a build seal for the hu-ge open field of the former airport. Here, a homogenous, smooth outer skin with two sharply cut openings is planned. Even over a great distance the building contour is easy recognizable. The south side has a furlike overgrowth of ranking plants. In front of this side lies an undeveloped piece of land, which the thick 'plant-fur' is able to define and connect to the building. East and west si-de are given a permanent, three-dimensional surrounding. They are pervious and, at the inside, build up to multiple room layers. The building concept is structurally open and enables permanent chan-ge and new orientation of the inner structure and functionability.

Photography by: Werner Huthmacher

Source: Mies Arch Prize: http://www.miesarch.com/

2014年5月2日 星期五

Richard Feynman : I think I can safely say that nobody understands quantum mechanics.

http://en.wikiquote.org/wiki/Richard_Feynman

Uncertainty — the Quantum Mechanical View of Nature,” p. 127-128 I think I cansafely say that nobody understands


  1. FeynmanProbability and Uncertainty in Quantum Mechanics

    www.youtube.com/watch?v=kekayfI8Ii8

    翻譯這個網頁
    2010年11月8日 - Richard Feynman courtesy of the Cornell Messenger Lecture Archive. ... Probability and Uncertainty: The quantum mechanical view of nature.

Probability and Uncertainty - the Quantum Mechanical View of Nature
Chapter 6 of The Character of Physical Law
In the beginning of the history of experimental observation, or any other kind of observation on scientific things, it is intuition, which is really based on simple experience with everyday objects, that suggests reasonable explanations for things. But as we try to widen and make more consistent our description of what we see, as it gets wider and wider and we see a greater range of phenomena, the explanations become what we call laws instead of simple explanations. One odd characteristic is that they often seem to become more and more unreasonable and more and more intuitively far from obvious. To take an example, in the relativity theory the proposition is that if you think two things occur at the same time that is just your opinion, someone else could conclude that of those events one was before the other, and that therefore simultaneity is merely a subjective impression.
There is no reason why we should expect things to be otherwise, because the things of everyday experience involve large numbers of particles, or involve things moving very slowly, or involve other conditions that are special and represent in fact a limited experience with nature. It is a small section only of natural phenomena that one gets from direct experience. It is only through refined measurements and careful experimentation that we can have a wider vision. And then we see unexpected things: we see things that are far from what we would guess — far from what we could have imagined. Our imagination is stretched to the utmost, not, as in fiction, to imagine things which are not really there, but just to comprehend those things which are there. It is this kind of situation that I want to discuss.
Let us start with the history of light. At first light was assumed to behave very much like a shower of particles, of corpuscles, like rain, or like bullets from a gun. Then with further research it was clear that this was not right, that the light actually behaved like waves, like water waves for instance. Then in the twentieth century, on further research, it appeared again that light actually behaved in many ways like particles. In the photo-electric effect you could count these particles — they are called photons now. Electrons, when they were first discovered, behaved exactly like particles or bullets, very simply. Further research showed, from electron diffraction experiments for example, that they behaved like waves. As time went on there was a growing confusion about how these things really behaved — waves or particles, particles or waves? Everything looked like both.
This growing confusion was resolved in 1925 or 1926 with the advent of the correct equations for quantum mechanics. Now we know how the electrons and light behave. But what can I call it? If I say they behave like particles I give the wrong impression; also if I say they behave like waves. They behave in their own inimitable way, which technically could be called a quantum mechanical way. They behave in a way that is like nothing that you have ever seen before. Your experience with things that you have seen before is incomplete. The behaviour of things on a very tiny scale is simply different. An atom does not behave like a weight hanging on a spring and oscillating. Nor does it behave like a miniature representation of the solar system with little planets going around in orbits. Nor does it appear to be somewhat like a cloud or fog of some sort surrounding the nucleus. It behaves like nothing you have ever seen before.
There is one simplification at least. Electrons behave in this respect in exactly the same way as photons; they are both screwy, but in exactly the same way.
How they behave, therefore, takes a great deal of imagination to appreciate, because we are going to describe something which is different from anything you know about. In that respect at least this is perhaps the most difficult lecture of the series, in the sense that it is abstract, in the sense that it is not close to experience. I cannot avoid that. Were I to give a series of lectures on the character of physical law, and to leave out from this series the description of the actual behaviour of particles on a small scale, I would certainly not be doing the job. This thing is completely characteristic of all of the particles of nature, and of a universal character, so if you want to hear about the character of physical law it is essential to talk about this particular aspect.
It will be difficult. But the difficulty really is psychological and exists in the perpetual torment that results from your saying to yourself, 'But how can it be like that?' which is a reflection of uncontrolled but utterly vain desire to see it in terms of something familiar. I will not describe it in terms of an analogy with something familiar; I will simply describe it. There was a time when the newspapers said that only twelve men understood the theory of relativity. I do not believe there ever was such a time. There might have been a time when only one man did, because he was the only guy who caught on, before he wrote his paper. But after people read the paper a lot of people understood the theory of relativity in some way or other, certainly more than twelve.
"nobody understands quantum mechanics"
(6:50 in the youtube video) On the other hand, I think I can safely say that nobody understands quantum mechanics. So do not take the lecture too seriously, feeling that you really have to understand in terms of some model what I am going to describe, but just relax and enjoy it. I am going to tell you what nature behaves like. If you will simply admit that maybe she does behave like this, you will find her a delightful, entrancing thing. Do not keep saying to yourself, if you can possibly avoid it, 'But how can it be like that?' because you will get 'down the drain', into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.
So then, let me describe to you the behaviour of electrons or of photons in their typical quantum mechanical way. I am going to do this by a mixture of analogy and contrast.
If I made it pure analogy we would fail; it must be by analogy and contrast with things which are familiar to you. So I make it by analogy and contrast, first to the behaviour of particles, for which I will use bullets, and second to the behaviour of waves, for which I will use water waves. What I am going to do is to invent a particular experiment and first tell you what the situation would be in that experiment using particles, then what you would expect to happen if waves were involved, and finally what happens when there are actually electrons or photons in the system. I will take just this one experiment, which has been designed to contain all of the mystery of quantum mechanics, to put you up against the paradoxes and mysteries and peculiarities of nature one hundred per cent. Any other situation in quantum mechanics, it turns out, can always be explained by saying, 'You remember the case of the experiment with the two holes ? It's the same thing'. I am going to tell you about the experiment with the two holes. It does contain the general mystery; I am avoiding nothing; I am baring nature in her most elegant and difficult form.
We start with bullets (fig. 28). Suppose that we have some source of bullets, a machine gun, and in front of it a plate with a hole for the bullets to come through, and this plate is armour plate. A long distance away we have a second plate which has two holes in it — that is the famous two-hole business. I am going to talk a lot about these holes, so I will call them hole No. 1 and hole No. 2. You can imagine round holes in three dimensions — the drawing is just a cross section. A long distance away again we have another screen which is just a backstop of some sort on which we can put in various places a detector, which in the case of bullets is a box of sand into which the bullets will be caught so that we can count them. I am going to do experiments in which I count how many bullets come into this detector or box of sand when the box is in different positions, and to describe that I will measure the distance of the box from somewhere, and call that distance 'x', and I will talk about what happens when you change 'x', which means only that you move the detector box up and down. First I would like to make a few modifications from real bullets, in three idealizations. The first is that the machine gun is very shaky and wobbly and the bullets go in various directions, not just exactly straight on; they can ricochet off the edges of the holes in the armour plate. Secondly, we should say, although this is not very important, that the bullets have all the same speed or energy. The most important idealization in which this situation differs from real bullets is that I want these bullets to be absolutely indestructible, so that what we find in the box is not pieces of lead, of some bullet that broke in half, but we get the whole bullet. Imagine indestructible bullets, or hard bullets and soft armour plate.
The first thing that we shall notice about bullets is that the things that arrive come in lumps. When the energy comes it is all in one bulletful, one bang. If you count the bullets, there are one, two, three, four bullets; the things come in lumps. They are of equal size, you suppose, in this case, and when a thing comes into the box it is either all in the box or it is not in the box. Moreover, if I put up two boxes I never get two bullets in the boxes at the same time, presuming that the gun is not going off too fast and I have enough time between them to see. Slow down the gun so it goes off very slowly, then look very quickly in the two boxes, and you will never get two bullets at the same time in the two boxes, because a bullet is a single identifiable lump.
Now what I am going to measure is how many bullets arrive on the average over a period of time. Say we wait an hour, and we count how many bullets are in the sand and average that. We take the number of bullets that arrive per hour, and we can call that the probability of arrival, because it just gives the chance that a bullet going through a slit arrives in the particular box. The number of bullets that arrive in the box will vary of course as I vary 'x'. On the diagram I have plotted horizontally the number of bullets that I get if I hold the box in each position for an hour. I shall get a curve that will look more or less like curve N12 because when the box is behind one of the holes it gets a lot of bullets, and if it is a little out of line it does not get as many, they have to bounce off the edges of the holes, and eventually the curve disappears. The curve looks like curve N12, and the number that we get in an hour when both holes are open I will call N12, which merely means the number which arrive through hole No. 1 and hole No. 2.
I must remind you that the number that I have plotted does not come in lumps. It can have any size it wants. It can be two and a half bullets in an hour, in spite of the fact that bullets come in lumps. All I mean by two and a half bullets per hour is that if you run for ten hours you will get twenty-five bullets, so on the average it is two and a half bullets. I am sure you are all familiar with the joke about the average family in the United States seeming to have two and a half children. It does not mean that there is a half child in any family — children come in lumps. Nevertheless, when you take the average number per family it can be any number whatsoever, and in the same way this number N12, which is the number of bullets that arrive in the container per hour, on the average, need not be an integer. What we measure is the probability of arrival, which is a technical term for the average number that arrive in a given length of time.
Finally, if we analyse the curve N12 we can interpret it very nicely as the sum of two curves, one which will represent what I will call N1, the number which will come if hole No. 2 is closed by another piece of armour plate in front, and N2, the number which will come through hole No. 2 alone, if hole No. 1 is closed. We discover now a very important law, which is that the number that arrive with both holes open is the number that arrive by coming through hole No. 1, plus the number that come through hole No. 2. This proposition, the fact that all you have to do is to add these together, I call `no interference'.
N12 = N1 + N2 (no interference).
That is for bullets, and now we have done with bullets we begin again, this time with water waves (fig. 29).
The source is now a big mass of stuff which is being shaken up and down in the water. The armour plate becomes a long line of barges or jetties with a gap in the water in between. Perhaps it would be better to do it with ripples than with big ocean waves; it sounds more sensible. I wiggle my finger up and down to make waves, and I have a little piece of wood as a barrier with a hole for the ripples to come through. Then I have a second barrier with two holes, and finally a detector. What do I do with the detector? What the detector detects is how much the water is jiggling. For instance, I put a cork in the water and measure how it moves up and down, and what I am going to measure in fact is the energy of the agitation of the cork, which is exactly proportional to the energy carried by the waves. One other thing: the jiggling is made very regular and perfect so that the waves are all the same space from one another. One thing that is important for water waves is that the thing we are measuring can have any size at all. We are measuring the intensity of the waves, or the energy in the cork, and if the waves are very quiet, if my finger is only jiggling a little, then there will be very little motion of the cork. No matter how much it is, it is proportional. It can have any size; it does not come in lumps; it is not all there or nothing.
What we are going to measure is the intensity of the waves, or, to be precise, the energy generated by the waves at a point. What happens if we measure this intensity, which I will call 'I' to remind you that it is an intensity and not a number of particles of any kind? The curve I12, that is when both holes are open, is shown in the diagram (fig. 29). It is an interesting, complicated looking curve. If we put the detector in different places we get an intensity which varies very rapidly in a peculiar manner. You are probably familiar with the reason for that. The reason is that the ripples as they come have crests and troughs spreading from hole No. 1, and they have crests and troughs spreading from hole No. 2. If we are at a place which is exactly in between the two holes, so that the two waves arrive at the same time, the crests will come on top of each other and there will be plenty of jiggling. We have a lot of jiggling right in dead centre. On the other hand if I move the detector to some point further from hole No. 2 than hole No. 1, it takes a little longer for the waves to come from 2 than from 1, and when a crest is arriving from 1 the crest has not quite reached there yet from hole 2, in fact it is a trough from 2, so that the water tries to move up and it tries to move down, from the influences of the waves coming from the two holes, and the net result is that it does not move at all, or practically not at all. So we have a low bump at that place. Then if it moves still further over we get enough delay so that crests come together from both holes, although one crest is in fact a whole wave behind, and so you get a big one again, then a small one, a big one, a small one... depending upon the way the crests and troughs 'interfere'. The word interference again is used in science in a funny way. We can have what we call constructive interference, as when both waves interfere to make the intensity stronger. The important thing is that I12 is not the same as I1 plus I2, and we say it shows constructive and destructive interference. We can find out what I1 and I2 look like by closing hole No. 2 to find I1, and closing hole No. 1 to find I2. The intensity that we get if one hole is closed is simply the waves from one hole, with no interference, and the curves are shown in fig. 2. You will notice that I1 is the same as N1, and I2 the same as N2 and yet I12 is quite different from N12.
As a matter of fact, the mathematics of the curve I12 is rather interesting. What is true is that the height of the water, which we will call h, when both holes are open is equal to the height that you would get from No. 1 open, plus the height that you would get from No. 2 open. Thus, if it is a trough the height from No. 2 is negative and cancels out the height from No. 1. You can represent it by talking about the height of the water, but it turns out that the intensity in any case, for instance when both holes are open, is not the same as the height but is proportional to the square of the height. It is because of the fact that we are dealing with squares that we get these very interesting curves.
h12 = h1 + h2
I12 ≠ I1 + I2 (Interference)
I12 = (h12)2
I1 = (h1)2
I2 = (h2)2
That was water. Now we start again, this time with electrons (fig. 30).
The source is a filament, the barriers tungsten plates, these are holes in the tungsten plate, and for a detector we have any electrical system which is sufficiently sensitive to pick up the charge of an electron arriving with whatever energy the source has. If you would prefer it, we could use photons with black paper instead of the tungsten plate — in fact black paper is not very good because the fibres do not make sharp holes, so we would have to have something better — and for a detector a photo-multiplier capable of detecting the individual photons arriving. What happens with either case? I will discuss only the electron case, since the case with photons is exactly the same.
First, what we receive in the electrical detector, with a sufficiently powerful amplifier behind it, are clicks, lumps, absolute lumps. When the click comes it is a certain size, and the size is always the same. If you turn the source weaker the clicks come further apart, but it is the same sized click. If you turn it up they come so fast that they jam the amplifier. You have to turn it down enough so, that there are not too many clicks for the machinery that you are using for the detector. Next, if you put another detector in a different place and listen to both of them you will never get two clicks at the same time, at least if the source is weak enough and the precision with which you measure the time is good enough. If you cut down the intensity of the source so that the electrons come few and far between, they never give a click in both detectors at once. That means that the thing which is coming comes in lumps — it has a definite size, and it only comes to one place at a time. Right, so electrons, or photons, come in lumps. Therefore what we can do is the same thing as we did for bullets: we can measure the probability of arrival. What we do is hold the detector in various places — actually if we wanted to although it is expensive, we could put detectors all over at the same time and make the whole curve simultaneously — but we hold the detector in each place, say for an hour, and we measure at the end of the hour how many electrons came, and we average it. What do we get for the number of electrons that arrive? The same kind of N12 as with bullets? Figure 30 shows what we get for N12, that is what we get with both holes open. That is the phenomenon of nature, that she produces the curve which is the same as you would get for the interference of waves. She produces this curve for what? Not for the energy in a wave but for the probability of arrival of one of these lumps.
The mathematics is simple. You change I to N, so you have to change h to something else, which is new — it is not the height of anything — so we invent an 'a', which we call a probability amplitude, because we do not know what it means. In this case a1 is the probability amplitude to arrive from hole No. 1, and a2 the probability amplitude to arrive from hole No. 2. To get the total probability amplitude to arrive you add the two together and square it. This is a direct imitation of what happens with the waves, because we have to get the same curve out so we use the same mathematics. I should check on one point though, about the interference. I did not say what happens if we close one of the holes. Let us try to analyse this interesting curve by presuming that the electrons came through one hole or through the other. We close one hole, and measure how many come through hole No. 1, and we get the simple curve N1. Or we can close the other hole and measure how many come through hole No. 2, and we get the N2 curve. But these two added together do not give the same as N1 + N2; it does show interference. In fact the mathematics is given by this funny formula that the probability of arrival is the square of an amplitude which itself is the sum of two pieces, N12 = (a1+ a2)2. The question is how it can come about that when the electrons go through hole No. 1 they will be distributed one way, when they go through hole No. 2 they will be distributed another way, and yet when both holes are open you do not get the sum of the two. For instance, if I hold the detector at the point q with both holes open I get practically nothing, yet if I close one of the holes I get plenty, and if I close the other hole I get something. I leave both holes open and I get nothing; I let them come through both holes and they do not come any more. Or take the point at the centre; you can show that that is higher than the sum of the two single hole curves. You might think that if you were clever enough you could argue that they have some way of going around through the holes back and forth, or they do something complicated, or one splits in half and goes through the two holes, or something similar, in order to explain this phenomenon. Nobody, however, has succeeded in producing an explanation that is satisfactory, because the mathematics in the end are so very simple, the curve is so very simple (fig. 30).
I will summarize, then, by saying that electrons arrive in lumps, like particles, but the probability of arrival of these lumps is determined as the intensity of waves would be. It is in this sense that the electron behaves sometimes like a particle and sometimes like a wave. It behaves in two different ways at the same time (fig. 31).
That is all there is to say. I could give a mathematical description to figure out the probability of arrival of electrons under any circumstances, and that would in principle be the end of the lecture — except that there are a number of subtleties involved in the fact that nature works this way. There are a number of peculiar things, and I would like to discuss those peculiarities because they may not be self-evident at this point.
To discuss the subtleties, we begin by discussing a proposition which we would have thought reasonable, since these things are lumps. Since what comes is always one complete lump, in this case an electron, it is obviously reasonable to assume that either an electron goes through hole No. 1 or it goes through hole No. 2. It seems very obvious that it cannot do anything else if it is a lump. I am going to discuss this proposition, so I have to give it a name; I will call it `proposition A'.
Now we have already discussed a little what happens with proposition A. If it were true that an electron either goes through hole No. 1 or through hole No. 2, then the total number to arrive would have to be analysable as the sum of two contributions. The total number which arrive will be the number that come via hole 1, plus the number that come via hole 2. Since the resulting curve cannot be easily analysed as the sum of two pieces in such a nice manner, and since the experiments which determine how many would arrive if only one hole or the other were open do not give the result that the total is the sum of the two parts, it is obvious that we should conclude that this proposition is false. If it is not true that the electron either comes through hole No. 1 or hole No. 2, maybe it divides itself in half temporarily or something. So proposition A is false. That is logic. Unfortunately, or otherwise, we can test logic by experiment. We have to find out whether it is true or not that the electrons come through either hole 1 or hole 2, or maybe they go round through both holes and get temporarily split up, or something.
All we have to do is watch them. And to watch them we need light. So we put behind the holes a source of very intense light. Light is scattered by electrons, bounced off them, so if the light is strong enough you can see electrons as they go by. We stand back, then, and we look to see whether when an electron is counted we see, or have seen the moment before the electron is counted, a flash behind hole 1 or a flash behind hole 2, or maybe a sort of half flash in each place at the same time. We are going to find out now how it goes, by looking. We turn on the light and look, and lo, we discover that every time there is a count at the detector we see either a flash behind No. 1 or a flash behind No. 2. What we find is that the electron comes one hundred per cent, complete, through hole 1 or through hole 2 — when we look. A paradox!
Let us squeeze nature into some kind of a difficulty here. I will show you what we are going to do. We are going to keep the light on and we are going to watch and count how many electrons come through. We will make two columns, one for hole No. 1 and one for hole No. 2, and as each electron arrives at the detector we will note in the appropriate column which hole it came through. What does the column for hole No. 1 look like when we add it all together for different positions of the detector? If I watch behind hole No. 1 what do I see? I see the curve N1 (fig. 30). That column is distributed just as we thought when we closed hole 2, much the same way whether we are looking or not. If we close hole 2 we get the same distribution in those that arrive as if we were watching hole No. 1; likewise the number that have arrived via hole No. 2 is also a simple curve N2. Now look, the total number which arrive has to be the total number. It has to be the sum of the number N1 plus the number N2; because each one that comes through has been checked off in either column 1 or column 2. The total number which arrive absolutely has to be the sum of these two. It has to be distributed as N1 + N2. But I said it was distributed as the curve N12. No, it is distributed as N1 + N2. It really is, of course; it has to be and it is. If we mark with a prime the results when a light is lit, then we find that N1', is practically the same as N1, without the light, and N2' is almost the same as N2. But the number N12', that we see when the light is on and both holes are open is equal to the number that we see through hole 1 plus the number that we see through hole 2. This is the result that we get when the light is on. We get a different answer whether I turn on the light or not. If I have the light turned on, the distribution is the curve N1 + N2. If I turn off the light, the distribution is N12. Turn on the light and it is N1 + N2 again. So you see, nature has squeezed out! We could say, then, that the light affects the result. If the light is on you get a different answer from that when the light is off. You can say too that light affects the behaviour of electrons. If you talk about the motion of the electrons through the experiment, which is a little inaccurate, you can say that the light affects the motion, so that those which might have arrived at the maximum have somehow been deviated or kicked by the light and arrive at the minimum instead, thus smoothing the curve to produce the simple N1 + N2 curve.
Electrons are very delicate. When you are looking at a baseball and you shine a light on it, it does not make any difference, the baseball still goes the same way. But when you shine a light on an electron it knocks him about a bit, and instead of doing one thing he does another, because you have turned the light on and it is so strong. Suppose we try turning it weaker and weaker, until it is very dim, then use very careful detectors that can see very dim lights, and look with a dim light. As the light gets dimmer and dimmer you cannot expect the very very weak light to affect the electron so completely as to change the pattern a hundred per cent from N12 to N1+ N2. As the light gets weaker and weaker, somehow it should get more and more like no light at all. How then does one curve turn into another? But of course light is not like a wave of water. Light also comes in particle-like character, called photons, and as you turn down the intensity of the light you are not turning down the effect, you are turning down the number of photons that are coming out of the source. As I turn down the light I am getting fewer and fewer photons. The least I can scatter from an electron is one photon, and if I have too few photons sometimes the electron will get through when there is no photon coming by, in which case I will not see it. A very weak light, therefore, does not mean a small disturbance, it just means a few photons. The result is that with a very weak light I have to invent a third column under the title 'didn't see'. When the light is very strong there are few in there, and when the light is very weak most of them end in there. So there are three columns, hole 1, hole 2, and didn't see. You can guess what happens. The ones I do see are distributed according to the curve N1 + N2. The ones I do not see are distributed as the curve N12. As I turn the light weaker and weaker I see less and less and a greater and greater fraction are not seen. The actual curve in any case is a mixture of the two curves, so as the light gets weaker it gets more and more like N12 in a continuous fashion.
I am not able here to discuss a large number of different ways which you might suggest to find out which hole the electron went through. It always turns out, however, that it is impossible to arrange the light in any way so that you can tell through which hole the thing is going without disturbing the pattern of arrival of the electrons, without destroying the interference. Not only light, but anything else — whatever you use, in principle it is impossible to do it. You can, if you want, invent many ways to tell which hole the electron is going through, and then it turns out that it is going through one or the other. But if you try to make that instrument so that at the same time it does not disturb the motion of the electron, then what happens is that you can no longer tell which hole it goes through and you get the complicated result again.
Heisenberg noticed, when he discovered the laws of quantum mechanics, that the new laws of nature that he had discovered could only be consistent if there were some basic limitation to our experimental abilities that had not been previously recognized. In other words, you cannot experimentally be as delicate as you wish. Heisenberg proposed his uncertainty principle which, stated in terms of our own experiment, is the following. (He stated it in another way, but they are exactly equivalent, and you can get from one to the other.) 'It is impossible to design any apparatus whatsoever to determine through which hole the electron passes that will not at the same time disturb the electron enough to destroy the interference pattern'. No one has found a way around this. I am sure you are itching with inventions of methods of detecting which hole the electron went through; but if each one of them is analysed carefully you will find out that there is something the matter with it. You may think you could do it without disturbing the electron, but it turns out there is always something the matter, and you can always account for the difference in the patterns by the disturbance of the instruments used to determine through which hole the electron comes.
This is a basic characteristic of nature, and tells us something about everything. If a new particle is found tomorrow, the kaon — actually the kaon has already been found, but to give it a name let us call it that — and I use kaons to interact with electrons to determine which hole the electron is going through, I already know, ahead of time — I hope — enough about the behaviour of a new particle to say that it cannot be of such a type that I could tell through which hole the electron would go without at the same time producing a disturbance on the electron and changing the pattern from interference to no interference. The uncertainty principle can therefore be used as a general principle to guess ahead at many of the characteristics of unknown objects. They are limited in their likely character.
Let us return to our proposition A — 'Electrons must go either through one hole or another'. Is it true or not? Physicists have a way of avoiding the pitfalls which exist. They make their rules of thinking as follows. If you have an apparatus which is capable of telling which hole the electron goes through (and you can have such an apparatus), then you can say that it either goes through one hole or the other. It does; it always is going through one hole or the other — when you look. But when you have no apparatus to determine through which hole the thing goes, then you cannot say that it either goes through one hole or the other. (You can always say it — provided you stop thinking immediately and make no deductions from it. Physicists prefer not to say it, rather than to stop thinking at the moment.) To conclude that it goes either through one hole or the other when you are not looking is to produce an error in prediction. That is the logical tight-rope on which we have to walk if we wish to interpret nature.
This proposition that I am talking about is general. It is not just for two holes, but is a general proposition which can be stated this way. The probability of any event in an ideal experiment — that is just an experiment in which everything is specified as well as it can be — is the square of something, which in this case I have called 'a', the probability amplitude. When an event can occur in several alternative ways, the probability amplitude, this 'a' number, is the sum of the 'a's for each of the various alternatives. If an experiment is performed which is capable of determining which alternative is taken, the probability of the event is changed; it is then the sum of the probabilities for each alternative. That is, you lose the interference.
The question now is, how does it really work ? What machinery is actually producing this thing? Nobody knows any machinery. Nobody can give you a deeper explanation of this phenomenon than I have given; that is, a description of it. They can give you a wider explanation, in the sense that they can do more examples to show how it is impossible to tell which hole the electron goes through and not at the same time destroy the interference pattern. They can give a wider class of experiments than just the two slit interference experiment. But that is just repeating the same thing to drive it in. It is not any deeper; it is only wider. The mathematics can be made more precise; you can mention that they are complex numbers instead of real numbers, and a couple of other minor points which have nothing to do with the main idea. But the deep mystery is what I have described, and no one can go any deeper today.
What we have calculated so far is the probability of arrival of an electron. The question is whether there is any way to determine where an individual electron really arrives? Of course we are not averse to using the theory of probability, that is calculating odds, when a situation is very complicated. We throw up a dice into the air, and with the various resistances, and atoms, and all the complicated business, we are perfectly willing to allow that we do not know enough details to make a definite prediction; so we calculate the odds that the thing will come this way or that way. But here what we are proposing, is it not, is that there is probability all the way back: that in the fundamental laws of physics there are odds.
Suppose that I have an experiment so set up that with the light out I get the interference situation. Then I say that even with the light on I cannot predict through which hole an electron will go. I only know that each time I look it will be one hole or the other; there is no way to predict ahead of time which hole it will be. The future, in other words, is unpredictable. It is impossible to predict in any way, from any information ahead of time, through which hole the thing will go, or which hole it will be seen behind. That means that physics has, in a way, given up, if the original purpose was — and everybody thought it was — to know enough so that given the circumstances we can predict what will happen next. Here are the circumstances: electron source, strong light source, tungsten plate with two holes: tell me, behind which hole shall I see the electron? One theory is that the reason you cannot tell through which hole you are going to see the electron is that it is determined by some very complicated things back at the source: it has internal wheels, internal gears, and so forth, to determine which hole it goes through; it is fifty-fifty probability, because, like a die, it is set at random; physics is incomplete, and if we get a complete enough physics then we shall be able to predict through which hole it goes. That is called the hidden variable theory. That theory cannot be true; it is not due to lack of detailed knowledge that we cannot make a prediction.
I said that if I did not turn on the light I should get the interference pattern. If I have a circumstance in which I get that interference pattern, then it is impossible to analyse it in terms of saying it goes through hole 1 or hole 2, because that interference curve is so simple, mathematically a completely different thing from the contribution of the two other curves as probabilities. If it had been possible for us to determine through which hole the electron was going to go if we had the light on, then whether we have the light on or off is nothing to do with it. Whatever gears there are at the source, which we observed, and which permitted us to tell whether the thing was going to go through 1 or 2, we could have observed with the light off, and therefore we could have told with the light off through which hole each electron was going to go. But if we could do this, the resulting curve would have to be represented as the sum of those that go through hole 1 and those that go through hole 2, and it is not. It must then be impossible to have any information ahead of time about which hole the electron is going to go through, whether the light is on or off, in any circumstance when the experiment is set up so that it can produce the interference with the light off. It is not our ignorance of the internal gears, of the internal complications, that makes nature appear to have probability in it. It seems to be somehow intrinsic. Someone has said it this way — 'Nature herself does not even know which way the electron is going to go'.
the same conditionsdo not always produce the same results
A philosopher once said 'It is necessary for the very existence of science that the same conditions always produce the same results'. Well, they do not. You set up the circumstances, with the same conditions every time, and you cannot predict behind which hole you will see the electron. Yet science goes on in spite of it — although the same conditions do not always produce the same results. That makes us unhappy, that we cannot predict exactly what will happen. Incidentally, you could think up a circumstance in which it is very dangerous and serious, and man must know, and still you cannot predict. For instance we could cook up — we'd better not, but we could — a scheme by which we set up a photo cell, and one electron to go through, and if we see it behind hole No. 1 we set off the atomic bomb and start World War III, whereas if we see it behind hole No. 2 we make peace feelers and delay the war a little longer. 
the future is unpredictable
Then the future of man would be dependent on something which no amount of science can predict. The future is unpredictable.
What is necessary 'for the very existence of science', and what the characteristics of nature are, are not to be determined by pompous preconditions, they are determined always by the material with which we work, by nature herself. We look, and we see what we find, and we cannot say ahead of time successfully what it is going to look like. The most reasonable possibilities often turn out not to be the situation. If science is to progress, what we need is the ability to experiment, honesty in reporting results — the results must be reported without somebody saying what they would like the results to have been — and finally — an important thing — the intelligence to interpret the results. An important point about this intelligence is that it should not be sure ahead of time what must be. It can be prejudiced and say 'That is very unlikely; I don't like that'. Prejudice is different from absolute certainty. I do not mean absolute prejudice — just bias. As long as you are only biased it does not make any difference, because if your bias is wrong a perpetual accumulation of experiments will perpetually annoy you until they cannot be disregarded any longer. They can only be disregarded if you are absolutely sure ahead of time of some precondition that science has to have. In fact it is necessary for the very existence of science that minds exist which do not allow that nature must satisfy some preconceived conditions, like those of our philosopher.

See also The Distinction of Past and Future