Chinese translation

Chinese translation

Note: until the multi-lingual support issue is resolved 1, I am putting the Chinese translation here.
Note2: this translation is not complete and far from perfect. Augustin is currently responsible for the translation, but his written Chinese is very, very poor, so a Chinese native speaker will need to do some serious proofreading. See issue: #428: Translate script in Chinese..

指數成長和倍增時間 (doubling time)

每一年2%,每一年3%,每一年7%,每一個時間單位的任何x%over time 就是(characterizes)指數成長。穩定(steady)的指數成長顯出(exhibits)一個固定(constant)倍增時間。這點很重要。

考慮一下(Consider)譬如說一個細菌在一個細菌培養基裡,它有一個一分鐘的倍增時間。 假設過了一分鐘,細菌有了八個單位。第二分鐘,長到十六個單位。第三分鐘,有三十二個。一直指數成長到第四分鐘有了六十四個。第五分鐘有128;第六分鐘有256;第七分鐘有512;1024;2048;4096在第十分鐘;超過八千在地十一分鐘;超過一萬一在第十二分鐘;這樣一直做下去。

每一個倍增等於所有前個倍增加起來的數量。

你可以很容易的計算倍增時間。這就是70除於成長比率的百分之多少(divide the percentage growth rate into 70)(2%,4%,7%,或 x%)。譬如說,70除於每一年2%等於倍增時間是35年。70除於每一年7%等於倍增時間是10年。70除於每一年10%等於倍增時間是7年。

當指數成長的過程成熟時,每一個新的倍增的數量變得超級的大,又長得越來越快。 For this thought exercise,只要28個倍增我們從八成長一直到二十億 (we went from 8 to more than 2 billion in a mere 28 doublings)。

在某一個階段(at some point),在培養基裡的細菌會突然互相吃或屋然自己到死 。。。???At some point, the bacteria in the growing medium suddenly eat or pollute themselves to death. 這生科(biology)叫做overshoot and collapse.

Stacking bills to the moon

現在考慮一下(consider)一張一千塊台幣的鈔票。它的厚度只有一釐米的十分之一。你想需要零點一釐米的幾個倍增才可以達到384,403公里,也就是月球和地球之間的平均距離?一疊鈔票。

甲) 超過一千個倍增?
乙) 500 到 1000 倍增?
丙) 100 到 500 倍增?
丁) 50 到 100 倍增?
或 戊) 少於 50 倍增?
一疊一千塊台幣,從地球到月球。

只要那張一釐米厚鈔票的42倍增,就能超過(well beyond)月球和地球之間的平均距離。並不需要那麼多次倍增 (That seems like not very many. [doublings])。

ㄌㄟ績了一端時間以後,指數成長很快的產生巨大的數目。 每一個倍增等於所有前個倍增加起來的數量 (After spooling up, doublings rapidly generate enormous numbers! The growth of any doubling equals the total of all the preceding growth! )

The lily pad

現在假設你和你的鄰居住在一個湖的旁邊。某一個人引入(introduce)一個百合稀罕的種類。這種百合可以每一天長大一倍。For this thought experiment, 假設那個湖大一致於第三十天他被百合完全覆蓋。(the lake is of such a size that it becomes completely covered on the 30th day) 對你和你的鄰居來說,這是一個一個非常嚴重的問題。

Realistically, at what percent coverage do you and your neighbors notice that you have a problem, a growing problem?
a) When you see the lake is more than 50% covered in lily pads?
b) 25% to 50% covered?
c) 12% to 25% covered?
or d) when you see the lake is 6% to 12% covered in lily pads?

Given exponential growth dynamic, your time remaining to respond if you noticed that you have a problem when you saw the lake was more than 50% covered, would be the last day.
If you noticed a problem at 25% to 50%, you would have 2 days.
If you noticed a problem at 12% to 25%, you have less than 3 days.
And if you noticed the problem early, say at 6% to 12% covered, you still would have no more than 4 days.

It takes 26 days growing exponentially before the lake is a mere 6% covered. Most of us would not recognize the problem until the lake is more than 50% covered. That would give us, as I said, less than 1 day to respond.