《那些古怪又讓人憂心的問題》第12期:摩爾鼴鼠
MOLE OF MOLES
Q. What would happen if you were to gather a mole (unit of measurement) of moles (the small furry critter) in one place?
Q．如果你把一摩爾的鼴鼠放到一起會發生什麼？--肖恩.賴斯A. THINGS GET A BIT gruesome. First, some definitions.
A．有點可怕。首先我們要弄清一些定義。
A mole is a unit. It's not a typical unit, though. It's really just a number-like "dozen" or "billion." If you have a mole of something, it means you have 602,214,129,000,000,000,000,000 of them (usually written 6.022 × 1023). It's such a big number1 because it's used for counting numbers of molecules, which there are a lot of.
摩爾是一個計量單位，而不是典型的那些單位。它其實就是一個數字，就像"一打"或"十億"那樣。如果你有1摩爾的某種東西，那麼這意味着你有602214129000000000000000個（通常寫成6.022×1023）這種東西。這個數字無比巨大2，因爲它就是用來計算分子數的，而分子可是有許許多多的。A mole is also a type of burrowing mammal. There are a handful of types of moles, and some of them are truly horrifying.2 So what would a mole of moles-602,214,129,000,000,000,000,000 animals-look like?
"Mole"也可以指一種會打洞的哺乳生物：鼴鼠。鼴鼠的種類有許多，其中有一些看上去非常嚇人。那麼一摩爾（602214129000000000000000只）鼴鼠放到一起會是什麼樣的呢？First, let's start with wild approximations. This is an example of what might go through my head before I even pick up a calculator, when I'm just trying to get a sense of the quantities-the kind of calculation where 10, 1, and 0.1 are all close enough that we can consider them equal:
首先我們先從一些狂野的近似聯想開始。很多時候我在拿起計算器進行計算之前，都會先在腦中想一想，這次就是一個例子，我想對這個數量有一個大致的概念。在這麼大的數字面前，10和1與0.1之間的區別已經微乎其微，我們可以近似地把它們認爲都是相等的。A mole (the animal) is small enough for me to pick up and throw.[citation needed ] Anything I can throw weighs 1 pound. One pound is 1 kilogram. The number 602,214,129,000,000,000,000,000 looks about twice as long as a trillion, which means it's about a trillion trillion. I happen to remember that a trillion trillion kilograms is how much a planet weighs. . . . if anyone asks, I did not tell you it was okay to do math like this.
鼴鼠的體形很小，我可以很輕鬆地把它們拿起來再扔出去。任何我能扔出去的東西重量都是1磅。1磅就是1千克。602214129000000000000000這個數字看起來有一萬億的2倍長，所以它大約有一億億億這麼多。我恰好記得一顆行星的質量也差不多是這麼重。如果任何人提起這種計算方法，千萬別說是我教你的。That's enough to tell us that we're talking about a pile of moles on the scale of a planet. It's a pretty rough estimate, since it could be off by a factor of thousands in either direction.
這也就意味着1摩爾鼴鼠的大小已經能和行星的大小相媲美了。這個估算相當粗略，可能多算或者少算了幾千倍。Let's get some better numbers.
讓我們用一些精確些的數字。An eastern mole (Scalopus aquaticus) weighs about 75 grams, which means a mole of moles weighs:
一隻東部鼴鼠（拉丁學名：Scalopus aquaticus）重約75克，也就是說一摩爾的鼴鼠重：That's a little over half the mass of our moon.
這比半個月球還要重一些。Mammals are largely water. A kilogram of water takes up a liter of volume, so if the moles weigh 4.52 × 1022 kilograms, they take up about 4.52 × 1022 liters of volume. You might notice that we're ignoring the pockets of space between the moles. In a moment, you'll see why.
哺乳生物體內很大一部分是水。1千克的水體積爲1立方米，所以那麼多的鼴鼠的體積大約爲4.52×1022立方米。你可能發現了我們這裏忽略了鼴鼠間的空隙，稍後你就會知道爲什麼要這麼做。The cube root of 4.52 × 1022 liters is 3562 kilometers, which means we're talking about a sphere with a radius of 2210 kilometers, or a cube 2213 miles on each edge.
4.52×1022立方米的立方根是3562千米，也就意味着這麼多鼴鼠能堆成半徑2210千米的一個球，或邊長2213英里（1英里≈1.6千米）的立方體。If these moles were released onto the Earth's surface, they'd fill it up to 80 kilometers deep-just about to the (former) edge of space: This smothering ocean of high-pressure meat would wipe out most life on the planet, which could-to reddit's horror-threaten the integrity of the DNS system. So doing this on Earth is definitely not an option.
果這些鼴鼠被釋放到地球表面，它們堆起來能夠達到80千米高，差不多已經到了（之前定義的）外太空的最低高度。這個嚇人的高壓肉柱會抹掉這個星球上絕大多數的生命，這會威脅到域名解析系統的完整性，所以在地球上這麼幹是萬萬不行的。Instead, let's gather the moles in interplanetary space. Gravitational attraction would pull them into a sphere. Meat doesn't compress very well, so it would undergo only a little bit of gravitational contraction, and we'd end up with a mole planet slightly larger than the Moon.
相反，我們可以把鼴鼠都堆在星際空間中。在重力的作用下，它們會慢慢聚集成一個球體。肉不怎麼能被壓縮，所以這個大肉球只會因重力作用而縮小一點，最後我們將看到一個比月球稍大一些的鼴鼠星。The moles would have a surface gravity of about one-sixteenth of Earth's-similar to that of Pluto. The planet would start off uniformly lukewarm-probably a bit over room temperature-and the gravitational contraction would heat the deep interior by a handful of degrees.
鼴鼠星表面的重力加速度約爲地球的十六分之一，和冥王星差不多。起初整個星球的溫度都很均勻，差不多比室溫高一些，隨後重力收縮會使內部的溫度上升幾攝氏度。But this is where it gets weird.
之後事情就變得奇怪起來。The mole planet would be a giant sphere of meat. It would have a lot of latent energy (there are enough calories in the mole planet to support the Earth's current population for 30 billion years). Normally, when organic matter decomposes, it releases much of that energy as heat. But throughout the majority of the planet's interior, the pressure would be over 100 megapascals, which is high enough to kill all bacteria and sterilize the mole remains-leaving no microorganisms to break down the mole tissue.
鼴鼠星說白了就是一個大肉球，其中蘊含着巨大的能量（鼴鼠星所含的卡路里足夠目前全世界人口吃上300億年）。一般來說，有機物被微生物分解時，會以熱量的形式釋放出大部分蘊藏的能量。但鼴鼠星大部分內核的壓強在100兆帕以上，這麼高的壓強足以殺死任何細菌，並把鼴鼠的屍體都蒸熟。這樣鼴鼠體內就不存在可以分解鼴鼠肉的微生物了。Closer to the surface, where the pressure would be lower, there would be another obstacle to decomposition-the interior of a mole planet would be low in oxygen. Without oxygen, the usual decomposition couldn't happen, and the only bacteria that would be able to break down the moles would be those that don't require oxygen. While inefficient, this anaerobic decomposition can unlock quite a bit of heat. If continued unchecked, it would heat the planet to a boil.
在接近表面的地方，壓強沒有這麼高，但還需要面臨另一個難題：鼴鼠星的內部含氧量非常低。沒有氧氣，普通的分解過程將無法發生，只有那些厭氧菌才能在這種條件下繼續分解。雖然厭氧分解效率很低，但這個過程仍會釋放大量熱量。這股熱量最終會把整個星球都變成一個大蒸籠。But the decomposition would be self-limiting. Few bacteria can survive at temperatures above about 60°C, so as the temperature went up, the bacteria would die off, and the decomposition would slow. Throughout the planet, the mole bodies would gradually break down into kerogen, a mush of organic matter that would-if the planet were hotter-eventually form oil.
但分解產物又會反過來限制分解的繼續進行。很少有細菌能在超過60℃的環境裏存活，因而隨着溫度的上升，細菌逐漸死去，分解進程也就慢慢停滯下來。整個星球的鼴鼠屍體會漸漸變成富含有機質的油母巖。如果星球的溫度繼續升高的話，它們最終會變成石油。The outer surface of the planet would radiate heat into space and freeze. Because the moles form a literal fur coat, when frozen they would insulate the interior of the planet and slow the loss of heat to space. However, the flow of heat in the liquid interior would be dominated by convection. Plumes of hot meat and bubbles of trapped gases like methane-along with the air from the lungs of the deceased moles-would periodically rise through the mole crust and erupt volcanically from the surface, a geyser of death blasting mole bodies free of the planet.
鼴鼠星的外表面會向外輻射熱量並凍結起來，冰凍的外殼就像給整個星球穿了一件毛大衣一樣，會把星球內部和外太空隔絕開來，因而會減緩熱量向外太空流失的速度。然而在液體內部，熱傳遞的主要形式爲對流，滾燙的肉漿和像甲烷（以及死去的鼴鼠肺中的空氣）這樣被困在其中的氣體形成的氣泡會在鼴鼠星的地殼裏週期性地翻滾上來，從地表猛烈噴發出來並形成"死亡"間歇泉，將無數鼴鼠的屍體拋射出鼴鼠星球。Eventually, after centuries or millennia of turmoil, the planet would calm and cool enough that it would begin to freeze all the way through. The deep interior would be under such high pressure that as it cooled, the water would crystallize out into exotic forms of ice such as ice III and ice V, and eventually ice II and ice IX.4
在經過數百萬年的動盪之後，鼴鼠星開始慢慢停息下來，溫度也低到整個星球都開始冰凍起來。此時由於鼴鼠星內部深處的壓強如此之大，以至於在冷卻的過程中，水結晶成了奇特的冰III和冰V形態，最終這些冰塊都會變成冰II和冰IX形態。All told, this is a pretty bleak picture. Fortunately, there's a better approach.
總而言之，這個故事的結局相當淒涼。不過好在有一個更好的結局。I don't have any reliable numbers for global mole population (or small mammal biomass in general), but we'll take a shot in the dark and estimate that there are at least a few dozen mice, rats, voles, and other small mammals for every human.
我手上沒有全球鼴鼠數量（或者小型哺乳生物的總體生物質量）的可靠的數字，但我們不妨認爲小鼠、大鼠、田鼠以及其他小型哺乳動物的數量約爲世界總人口的幾十倍There might be a billion habitable planets in our galaxy. If we colonized them, we'd certainly bring mice and rats with us. If just one in a hundred were populated with small mammals in numbers similar to Earth's, after a few million years-not long, in evolutionary time-the total number that have ever lived would surpass Avogadro's number.
10億顆宜居星球。如果我們將來去殖民這些星球，幾乎一定會帶着一些小鼠或大鼠。如果這些星球中有百分之一住着和地球上數目相當的小型哺乳生物，那麼幾百萬年後（相對於整個宇宙的進化史來說已經很短了），所有曾經存活的這些小生物的個數將會超過阿伏伽德羅常數。If you want a mole of moles, build a spaceship.
所以如果你想要有一摩爾的鼴鼠，得先造一艘宇宙飛船。"One mole" is close to the number of atoms in a gram of hydrogen. It's also, by chance, a decent ballpark guess for the number of grains of sand on Earth.
一立方英里約等於4π/3立方千米，因而半徑爲X千米的球的體積和邊長爲X英里的立方體的體積幾乎一樣。英文mole的兩個含義分別是摩爾（計量單位）、鼴鼠。That's a neat coincidence I've never noticed before - a cubic mile happens to be almost exactly 3π cubic kilometers, so a sphere with a radius of X kilometers has the same volume as a cube that's X miles on each side.
這裏有一個我以前從來沒注意到的巧合：一摩爾的數量接近於一克氫中所含的氫原子數。地球上所有的沙粒的數目也恰好很接近這個數字。No relation.
相互之間沒有關係。
