Great Tree, Great Axe巨樹與巨斧\tFrom what-if.xkcd.com

The Sea

If all the seas were combined into one sea， it would look pretty much like the Pacific Ocean， only a little bigger.

The Tree

Real trees can't grow taller than around 130 meters， thanks to physical limits on their ability to transport water. If they found a way around those limits， they'd face issues of fundamental physical strength; a kilometers-tall tree would crush3) itself.

Let's set aside4) these limits and imagine that we built a single standard tree out of all the material in all the world's trees. For our \"standard tree\"， we'll use the oak tree from the Sylva Foundation's5) OneOak project. The project extensively documents every detail of a single oak tree. As part of the project， the tree was cut down in 2010. Frankly， I'm not sure what to make of6) the whole thing， but it's as good a candidate as any for our model \"standard tree\".

The OneOak tree was 23.9 meters tall and weighed 14.385 tons. By comparison， one paper estimates that the world's forests have an aboveground7) plant mass of about 470 billion tons.

If—ignoring the physical constraints—we combined this mass into a single tree， modeled on the OneOak， the trunk would be two kilometers in diameter8). The upper branches would stretch about 75 kilometers above the surface—most of the way to space.

The Human

If we used the same approach to combine every living human into a single body—again， ignoring the obvious physical constraints—that person would be close to 3 kilometers tall. Proportionally9)， the person would have grown slightly less than the tree.

The Axe

How many axes are there in the world? Thanks to multiple meanings of the word \"axes\"， this is a hard problem to Google. Instead， let's try to get a reasonable guess through Fermi estimation10).

Since there's no central clearing house11) of axe-related information， I thought I'd try asking friends how many axes they had.

But this might miss a lot of axes; for example， some axes—like fire axes—are owned by organizations. To get a slightly fairer sample， I asked a bunch of friends around the country to estimate the number of axes and number of humans in their general vicinity12).

Some people were in houses with sheds， and had a 2:1 human-to-axe ratio. Other people were in large offices with hundreds of people and at best13) one or two fire axes. The average seemed to be around 50:1—much lower than I expected.

Of course， surveying random Internet-connected people who I know is hardly representative; rural people probably have more axes， while the very poor might not have any. But it also wouldn't make sense for there to be substantially14) more axes than people， if for no other reason than that humans can only really use one axe at a time.

But absent any other data， I'm guessing the ratio of humans to axes is probably somewhere between 50:1 and 5:1.

This means that our combined axe would be a little small for our combined person. It would be only a little over half a kilometer long—barely more than a flimsy15) hatchet16).

If an experienced axe user can chop down an eight-inch tree in 15 minutes， then chopping down our giant tree—if the rate is proportional to the axe size and square of the tree's diameter—would most likely take a few weeks of chopping.

巨海

如果所有的海洋都匯成一片海，那么這個新大洋會和太平洋沒什么兩樣，只不過大了一點而已。

巨樹

真實的樹木最高長不過130米左右，這是因為樹的水分輸送能力受到了物理限制。就算樹能設法突破這些限制，它們將面臨至關重要的物理力量問題：一棵幾千米高的樹會將自己壓垮。

讓我們把這些限制放在一邊，并假設我們用全世界所有樹木的所有部分合成一棵標準樹。我們會選用英國林木基金會“一棵橡樹”項目的那棵橡樹作為我們的“標準樹”。“一棵橡樹”項目詳細地記錄了一棵橡樹的各個細枝末節。按照該項目的計劃，這棵橡樹于2010年被砍伐。老實說，我沒太搞明白這整個項目，但用這棵橡樹作為我們的“標準樹”模型是再好不過了。

這棵橡樹高23.9米，重14.385噸。相比之下，根據一篇論文的估計，全世界所有森林地上部分的重量加起來約為4700億噸。

如果——忽略那些物理限制——我們將這4700億噸的樹木參照那棵橡樹的樣子合成一棵樹，那么這棵樹的樹樁直徑將達2000米，而上層枝葉將離地面約75千米，直沖太空。

巨人

假如我們用同樣的方法，將所有活著的人合成一個人——再次忽略那些顯而易見的物理限制——那么這個人將會有近3000米高。按比例來說，這個巨人會稍微不如那棵巨樹成長得茁壯。

巨斧

世界上有多少把斧頭？都怪“axes”這個單詞具有多重含義，我們難以通過谷歌搜索獲得答案。作為代替，讓我們盡力通過費米估算得到一個合理的估計值。

由于沒有與斧頭相關信息的中央統計機構，我想我應該試著問問朋友他們有多少把斧頭。

但是，這樣可能會遺漏很多斧頭。例如，有些斧頭——像消防斧這樣的斧頭——只有那些機構才擁有。為采集到一個稍微客觀一些的樣本，我請我在全國各地的一些朋友幫忙，讓他們估計一下他們那一帶的斧頭數量和居民數量。

他們有些住在帶牲口棚的房子里，這些地方人與斧的比例為2:1。其他人則在可容納數百人的辦公大樓里，這些地方最多只有一兩把消防斧。這樣看起來人與斧的平均比例約為50:1，遠遠低于我的預期。

當然，隨機調查的這些我認識的網友難具代表性；農村居民可能擁有更多的斧頭，而太窮的人家可能連一把斧頭也沒有。但斧頭數量也不會大大超過人口數量，這不合情理，只因為我們每次真的只能用一把斧頭。

不過，由于沒有任何其他數據，我在想人與斧頭的比例很可能在50:1到5:1之間。

這就是說，合成的這把巨斧對合成的這位巨人來說會有點小，長度可能僅500米出頭——充其量只是一把不算結實的小斧頭。

假如一位嫻熟的伐木工砍倒一棵8英寸(編注：約20厘米)粗的樹需要15分鐘，那么砍倒我們這棵巨樹——如果砍伐速度與斧頭大小和樹干直徑的平方成正比的話——很可能要花幾個星期的時間。1.splish-splash: 水花四濺聲

2.Mother Goose: 《鵝媽媽童謠》，是英國民間的童謠集。這些民間童謠流傳時間相當久，總數約有八百多首，包括幽默故事、游戲歌曲、兒歌、謎語、字母歌、繞口令等。

3.crush [kr#652;#643;] vt. 壓斷

4.set aside: 把……置于一旁，不顧

5.Sylva Foundation: 林木基金會，英國的一個慈善機構，旨在復興英國的林業文化，推動和提升森林的可持續管理。

6.make of: 理解；解釋

7.aboveground: 在地面上的

8.diameter [da#618;#712;#230;m#618;t#601;(r)] n. 直徑

9.proportionally [pr#601;#712;p#596;#720;#643;#601;nli] adv. 按比例地

10.Fermi estimation: 費米估算，以美國物理學家恩利克·費米(Enrico Fermi， 1901~1954)命名，是在科學研究中用來做量綱分析、估算和清晰地驗證一個假設的估算問題，比如“芝加哥有多少鋼琴調琴師？”，這是費米提出的一個經典的費米問題。

11.clearing house: 信息交換所；信息交換機構

The Sea

If all the seas were combined into one sea， it would look pretty much like the Pacific Ocean， only a little bigger.

The Tree

Real trees can't grow taller than around 130 meters， thanks to physical limits on their ability to transport water. If they found a way around those limits， they'd face issues of fundamental physical strength; a kilometers-tall tree would crush3) itself.

Let's set aside4) these limits and imagine that we built a single standard tree out of all the material in all the world's trees. For our \"standard tree\"， we'll use the oak tree from the Sylva Foundation's5) OneOak project. The project extensively documents every detail of a single oak tree. As part of the project， the tree was cut down in 2010. Frankly， I'm not sure what to make of6) the whole thing， but it's as good a candidate as any for our model \"standard tree\".

The OneOak tree was 23.9 meters tall and weighed 14.385 tons. By comparison， one paper estimates that the world's forests have an aboveground7) plant mass of about 470 billion tons.

If—ignoring the physical constraints—we combined this mass into a single tree， modeled on the OneOak， the trunk would be two kilometers in diameter8). The upper branches would stretch about 75 kilometers above the surface—most of the way to space.

The Human

If we used the same approach to combine every living human into a single body—again， ignoring the obvious physical constraints—that person would be close to 3 kilometers tall. Proportionally9)， the person would have grown slightly less than the tree.

The Axe

How many axes are there in the world? Thanks to multiple meanings of the word \"axes\"， this is a hard problem to Google. Instead， let's try to get a reasonable guess through Fermi estimation10).

Since there's no central clearing house11) of axe-related information， I thought I'd try asking friends how many axes they had.

But this might miss a lot of axes; for example， some axes—like fire axes—are owned by organizations. To get a slightly fairer sample， I asked a bunch of friends around the country to estimate the number of axes and number of humans in their general vicinity12).

Some people were in houses with sheds， and had a 2:1 human-to-axe ratio. Other people were in large offices with hundreds of people and at best13) one or two fire axes. The average seemed to be around 50:1—much lower than I expected.

Of course， surveying random Internet-connected people who I know is hardly representative; rural people probably have more axes， while the very poor might not have any. But it also wouldn't make sense for there to be substantially14) more axes than people， if for no other reason than that humans can only really use one axe at a time.

But absent any other data， I'm guessing the ratio of humans to axes is probably somewhere between 50:1 and 5:1.

This means that our combined axe would be a little small for our combined person. It would be only a little over half a kilometer long—barely more than a flimsy15) hatchet16).

If an experienced axe user can chop down an eight-inch tree in 15 minutes， then chopping down our giant tree—if the rate is proportional to the axe size and square of the tree's diameter—would most likely take a few weeks of chopping.

巨海

如果所有的海洋都匯成一片海，那么這個新大洋會和太平洋沒什么兩樣，只不過大了一點而已。

巨樹

真實的樹木最高長不過130米左右，這是因為樹的水分輸送能力受到了物理限制。就算樹能設法突破這些限制，它們將面臨至關重要的物理力量問題：一棵幾千米高的樹會將自己壓垮。

讓我們把這些限制放在一邊，并假設我們用全世界所有樹木的所有部分合成一棵標準樹。我們會選用英國林木基金會“一棵橡樹”項目的那棵橡樹作為我們的“標準樹”?！耙豢孟饦洹表椖吭敿毜赜涗浟艘豢孟饦涞母鱾€細枝末節。按照該項目的計劃，這棵橡樹于2010年被砍伐。老實說，我沒太搞明白這整個項目，但用這棵橡樹作為我們的“標準樹”模型是再好不過了。

這棵橡樹高23.9米，重14.385噸。相比之下，根據一篇論文的估計，全世界所有森林地上部分的重量加起來約為4700億噸。

如果——忽略那些物理限制——我們將這4700億噸的樹木參照那棵橡樹的樣子合成一棵樹，那么這棵樹的樹樁直徑將達2000米，而上層枝葉將離地面約75千米，直沖太空。

巨人

假如我們用同樣的方法，將所有活著的人合成一個人——再次忽略那些顯而易見的物理限制——那么這個人將會有近3000米高。按比例來說，這個巨人會稍微不如那棵巨樹成長得茁壯。

巨斧

世界上有多少把斧頭？都怪“axes”這個單詞具有多重含義，我們難以通過谷歌搜索獲得答案。作為代替，讓我們盡力通過費米估算得到一個合理的估計值。

由于沒有與斧頭相關信息的中央統計機構，我想我應該試著問問朋友他們有多少把斧頭。

但是，這樣可能會遺漏很多斧頭。例如，有些斧頭——像消防斧這樣的斧頭——只有那些機構才擁有。為采集到一個稍微客觀一些的樣本，我請我在全國各地的一些朋友幫忙，讓他們估計一下他們那一帶的斧頭數量和居民數量。

他們有些住在帶牲口棚的房子里，這些地方人與斧的比例為2:1。其他人則在可容納數百人的辦公大樓里，這些地方最多只有一兩把消防斧。這樣看起來人與斧的平均比例約為50:1，遠遠低于我的預期。

當然，隨機調查的這些我認識的網友難具代表性；農村居民可能擁有更多的斧頭，而太窮的人家可能連一把斧頭也沒有。但斧頭數量也不會大大超過人口數量，這不合情理，只因為我們每次真的只能用一把斧頭。

不過，由于沒有任何其他數據，我在想人與斧頭的比例很可能在50:1到5:1之間。

這就是說，合成的這把巨斧對合成的這位巨人來說會有點小，長度可能僅500米出頭——充其量只是一把不算結實的小斧頭。

假如一位嫻熟的伐木工砍倒一棵8英寸(編注：約20厘米)粗的樹需要15分鐘，那么砍倒我們這棵巨樹——如果砍伐速度與斧頭大小和樹干直徑的平方成正比的話——很可能要花幾個星期的時間。DThe Fall

The tree would weigh between 1% and 10% as much as the Chicxulub asteroid17) that killed the dinosaurs. It would strike the ocean with much less speed than the Chicxulub asteroid， and the energy release would be much less substantial. However， it would still be moving at kilometers per second， and would be able to displace a gigantic18) amount of water.

The Chicxulub impact created a giant tsunami19). There have been some beautiful simulations20) of the Chicxulub tsunami. The exact details of the tsunami depend on a lot of factors， but it seems safe to say that waves at least tens or hundreds of meters high would inundate21) every coastline and destroy virtually every coastal city and many farther inland.

In other words， the Mother Goose poem in John's question probably wouldn't wipe out the human race， but it would probably be the deadliest single disaster in our species' history. Even by the ghastly22) standards of old children's fairy tales， that's pretty bad.巨樹之倒

這棵巨樹的重量為導致恐龍滅亡的希克蘇魯伯小行星重量的1%~10%。巨樹倒向海洋的速度要比?？颂K魯伯小行星撞向海洋的速度小很多，而且釋放的能量也要少很多。不過，巨樹的倒落速度仍將達到數千米每秒，并會激起滔天的海浪。

?？颂K魯伯小行星的撞擊引發了一場巨大的海嘯，對于這場海嘯已有一些精彩的模擬。雖然海嘯的各項具體情況取決于多種因素，但有一點似乎可以肯定——最少高達幾十米或幾百米的海浪將淹沒所有海岸，并將摧毀幾乎所有的沿海城市和許多更遠一些的內陸地區。

換句話說，約翰提出的關于《鵝媽媽童謠》里那首詩的問題可能不會造成人類滅亡，但卻可能是人類歷史上最致命的一次災難。即便是按照古老的兒童童話故事的恐怖程度來衡量，這場災難也夠可怕的。In closing， I offer my favorite piece of axe-related legal trivia23): Lawyer Kevin Underhill， of the legal blog Lowering the Bar， highlighted the wonderful 1998 case People v. Foranyic24). In this case， he writes， appeals court ruled25) \"that there was probable cause for police to detain26) someone they see riding a bike at 3 a.m.， carrying an axe\".

So if you're two miles tall and heading toward the coast to cut down the world's only tree ... watch out for cops.

最后，我要提一下我最喜歡的一段關于斧頭的法律小插曲：法律博客“降低律師門檻”的博主凱文·昂德希爾律師專門強調了這起精彩絕倫的1998年福倫伊克公訴案。他寫道，在該案中，上訴法院判定“若是發現有人在凌晨3:00攜帶一把斧頭騎自行車，警方有可以成立的理由拘留當事人”。

因此，如果你身高兩英里(編注：約3000米)，正要到海邊去砍倒世上唯一的一棵樹……可得小心警察。In closing， I offer my favorite piece of axe-related legal trivia23): Lawyer Kevin Underhill， of the legal blog Lowering the Bar， highlighted the wonderful 1998 case People v. Foranyic24). In this case， he writes， appeals court ruled25) \"that there was probable cause for police to detain26) someone they see riding a bike at 3 a.m.， carrying an axe\".

So if you're two miles tall and heading toward the coast to cut down the world's only tree ... watch out for cops.

最后，我要提一下我最喜歡的一段關于斧頭的法律小插曲：法律博客“降低律師門檻”的博主凱文·昂德希爾律師專門強調了這起精彩絕倫的1998年福倫伊克公訴案。他寫道，在該案中，上訴法院判定“若是發現有人在凌晨3:00攜帶一把斧頭騎自行車，警方有可以成立的理由拘留當事人”。

因此，如果你身高兩英里(編注：約3000米)，正要到海邊去砍倒世上唯一的一棵樹……可得小心警察。12.vicinity [v#601;#712;s#618;n#601;ti] n. 附近

13.at best: 至多，充其量

14.substantially [s#601;b#712;st#230;n#643;#601;li] adv. 大量地

15.flimsy [#712;fl#618;mzi] adj. 脆弱的；易損壞的；劣質的

16.hatchet [#712;h#230;t#643;#618;t] n. 短柄小斧

17.Chicxulub asteroid: ?？颂K魯伯小行星，其直徑至少有10千米，在6500萬年前撞擊了今天墨西哥境內的希克蘇魯伯地區，形成了一個撞擊隕石坑，即?？颂K魯伯隕石坑(Chicxulub crater)。

18.gigantic [d#658;a#618;#712;ɡ#230;nt#618;k] adj. 巨大的，龐大的

19.tsunami [tsu#720;#712;nɑ#720;mi] n. 海嘯

20.simulation [#716;s#618;mju#712;le#618;#643;n] n. 模擬；模仿

21.inundate [#712;#618;n#652;nde#618;t] vt. 淹沒

22.ghastly [#712;ɡɑ#720;stli] adj. 可怕的；恐怖的

23.trivia [#712;tr#618;vi#601;] n. 小事；瑣事

24.People v. Foranyic: 福倫伊克公訴案。被告福倫伊克(全名Robert Francis Foranyic)凌晨3:00拿著斧子、騎著車子在路上，一名警察覺得福倫伊克可能會進行犯罪活動因而將其逮捕。福倫伊克進行了上訴，不過法院最后判定該警察的行為是合理且合法的。

25.rule [ru#720;l] vt. 裁決；裁定

26.detain [d#618;#712;te#618;n] vt. 拘留；扣押