30Jul

what-if:流萤之星

时间: 2016-7-30 分类: 涨姿势拓视野 作者: XD

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语言:   大陆 港澳 台湾

引用元:http://what-if.xkcd.com/151/


 

Sun Bug

流萤之星

what-if:流萤之星

 

How many fireflies would it take to match the brightness of the Sun?

Luke Doty

要多少只萤火虫发出的光能和太阳一样亮?

卢克 多蒂

 

Not that many! I mean, it’s definitely one of those gigantic numbers with lots of zeroes, but in the grand scheme of things, there aren’t as many zeroes as you might expect.

没有那么多!我的意思是,这当然是一个有着很多零的巨大的数字,但是这个数字看上去没有你想像中的那么多零。

 

what-if:流萤之星

There are two numbers: “zero” and “anything that overflows your data type.”

有两个数字:“零”和“从你定义的数据类型中溢出的东西”

 

Our first question: Where does firefly light even come from?

那么问题来了:萤火虫的光从那里来的?

 

Fireflies may look like they’re full of glow-in-the-dark goo, but the light they give off actually comes from a thin layer on their surface.[1]Lots of insects have glowing surface patches, and some of those patches have been studied carefully to calculate their brightness.A 1928 paper on beetles called “headlight bugs”[2] found that their glowing patches, which were a little over a square millimeter in area, emitted about 0.0006 lumens of light.Fireflies have luminous organs (bright patches) that are about the same size as those of headlight bugs,[3] and their organs tend to have a similar peak brightness per area, so this figure is a good guess for the brightness of a firefly’s lantern.

萤火虫的肚子看起来像是装满会在黑暗中发光的胶水,但实际上这些光来自于其表面的一层薄薄的发光层[1]。有许多的昆虫有这种发光层,它们当中的一些甚至进化出了测量亮度的能力。 一篇1928年的论文里介绍了一种叫“大灯甲虫”[2]的会发光的甲虫,它的一平方毫米多的发光器能发出约0.0006流明的光。萤火虫的发光器面积大概和“大灯甲虫”的差不多[3],它们的发光器的峰值亮度也差别不大,所以这个数值应该是萤火虫灯亮度的一个不错的估计值。

 

Firefly lights aren’t “always-on.” They blink on and off, with patterns that vary from species to species and situation to situation. These flashes carry information, some of which you can decode using this delightful chart.[4]

萤火虫的光并不是一直亮的,它们是不断闪烁的,不同种类,不同情况下,他们闪烁的模式不尽相同。这些闪烁携带着信息,一些情况下,你可以使用这张“愉快的表格”来对这些信息进行解码。[4]

 

what-if:流萤之星

I don’t know why I find that chart so satisfying, but I do. It’s like that chart of sand grain sizes in article #83.

我不知道为什么当我找到这张表时会感到一本满足,但我就是很满足。就像我在#83期里找到的那张沙子大小的图表。

 

To get the brightest light, let’s assume we’re using a species with a mostly-on duty cycle—like a headlight bug. How does its 0.0006-lumen light output compare to the Sun?

为了得到最亮的光,假设我们找到一种物种,像“大灯甲虫”一样常亮的萤火虫。怎样用其0.0006流明的光与日争辉?

(原文用的是高占空比:mostly-on duty cycle,这里解释成常亮,便于理解。)

 

The Sun’s brightness is 3.8×10^28 lumens, so by simple division, it would take 3×10^31 of those fireflies to emit the same amount of light. That’s a surprisingly small number; adult fireflies weigh about 20 milligrams, which means 3×10^31 fireflies would only weigh about a third as much as Jupiter and 1/3000th as much as the Sun.

太阳的亮度为3.8×10^28流明,通过简单的除法,我们知道需要3×10^31只萤火虫同时发光才能达到太阳光的强度。这个数小的令人惊讶;成年萤火虫重约20毫克,这意味着3×10^31只萤火虫也就大约三分之一的木星重量或者1/3000的太阳重量。

 

In other words, per pound, fireflies are brighter than the Sun. Even though bioluminescence is millions of times less efficient than the Sun’s fusion-powered glow, the Sun can’t afford to be as bright because it has to last billions of times longer.[5]

换句话说,尽管生物发光的效率是太阳核聚变发光效率百万分之一,但是每磅萤火虫的亮度比太阳还亮。太阳不能这么亮的原因是它要持续燃烧几百亿年。[5]

 

But wait! A mass of fireflies that big would run into problems. Besides the obvious problems with gathering that many animals in one place, the fireflies would block each others’ light. The inner fireflies would be hidden behind the outer ones, and the total brightness would be limited.[6]

但是,桥豆麻袋,除了那个老生常谈的如何把那么多的动物聚集到一块的问题,这么一大团萤火虫还会导致另一个大问题:萤火虫会阻挡其他萤火虫发出的光。里面的萤火虫发出的光会被外面的挡住,所以总的亮度会被限制住。

 

what-if:流萤之星

8 ball, corner pocket.

8球,底洞。

 

Since the only light that matters is the light at the surface, we could imagine arranging the fireflies in a hollow sphere, with their lanterns pointing outward. Or, to make thing simpler, we could imagine a single giant firefly. How big would it need to be?

由于萤火虫的发光器是在肚子的表面,我们可以将萤火虫肚子朝外,排列成一个萤火虫空心球。或者更简单,我们可以假设一个巨型萤火虫。这只巨型萤火虫该有多大呢?

 

what-if:流萤之星

tickle tickle tickle

摸 摸 摸

 

Since we know our firefly will need to give off about 3×10^31 times as much light as a normal firefly, it will need a glowing patch 3×10^31 times larger. Since surface area is proportional to length squared, our firefly will have a body length √3×10^31=5×10^15 times longer than a normal firefly, which would make it about the size of the Solar System.

因为我们需要的萤火虫能发出比正常萤火虫高出约3×10^31倍的光,所以它需要一个比正常萤火虫大3×10^31倍的发光器。由于面积和长度的平方成正比, 这只萤火虫的体长要比正常的萤火虫长√3×10^31= 5×10^15倍,这大概有太阳系那么大。

 

what-if:流萤之星

Technically, Pluto is an arachnid.

科学上讲,冥王星应该属于蛛形纲。

(这里在玩冥王星的梗,就像蜘蛛不属于昆虫,但多数人会认为蜘蛛是昆虫)

 

Since mass is proportional to length cubed, our firefly would weigh (3×10^31)32=1.6×10^47 times as much as a normal firefly, which works out to about half as much as the entire Milky Way galaxy.

由于质量与长度的立方成正比,这只萤火虫的重量大概是普通萤火虫质量的(3×10^31)^3/2=1.6×10^47倍,这大概是半个银河系的质量。

 

Such a firefly would immediately collapse under its own weight and become a black hole. In fact, given the distribution of galaxies in our universe, there’s an upper limit to how large black holes can grow, and this firefly would be bigger than that limit. That means our firefly would become the largest black hole in the universe. It would give off a lot of light as it devoured our galaxy, and then, eventually, it would give off none at all.

这只萤火虫在自身重力的作用下,会立刻坍缩成一个黑洞。事实上,根据宇宙中星系的分布情况,我们能推测出黑洞质量是有一个上限的,而这只萤火虫已经突破这一上限了。这就意味着这只萤火虫将成为宇宙中最大的黑洞。它会释放出大量的光,吞噬掉银河系,最终,它将归于寂静。

 

Black holes last a long time, but they eventually evaporate through Hawking radiation. When the black hole era of our universe comes to an end, black holes will evaporate one by one, with the smallest evaporating faster. Since our firefly’s black hole would be the largest one in the universe, it would be the last to evaporate—a final outpost of irregularity in a universe fading toward heat death.

黑洞会存在很长时间,但他们最终会通过霍金辐射蒸发。当宇宙的黑洞纪元趋于结束,黑洞会一个接一个的蒸发掉,小黑洞蒸发的更快。由于萤火虫黑洞是宇宙中最大的一个黑洞,它会是最后一个蒸发的,成为宇宙热寂前的最后一座秩序存在的纪念碑。

(宇宙热寂说:是猜想宇宙终极命运的一种假说。根据热力学第二定律,作为一个“孤立”的系统,宇宙的熵会随着时间的流逝而增加,由有序向无序,当宇宙的熵达到最大值时,宇宙中的其他有效能量已经全数转化为热能,所有物质温度达到热平衡。)

 

We should probably add that to the identification chart, just in case.

以防万一,我们应将这个加入到年表里。

 

what-if:流萤之星

There’s some stuff before but it’s not important.

虽然之前还有些东西,但那不重要啦


[1]You can see some diagrams of the organs here and here.

[1]你可以在这里这里看到这些器官的图片。 

[2]Such a great name.

[2]虫如其名 

[3]See this paper on some common American fireflies.

[3]这篇论文介绍了一些常见的美国萤火虫。 

[4]You can also use LEDs to mess with firefly patterns, which feels strangely invasive.

[4]你可以用LED来干扰萤火虫的闪烁模式,看上去还蛮带感的。 

[5]If you like Fermi problems—and silly equations—there’s an interesting route you can take to this answer without doing any research on fireflies or the Sun at all. Instead, you can just plug this equation into Wolfram|Alpha: (5 billion years / (4 hours/day * 3 months)) / (1% * (speed of light)^2 / (3200 calories/pound)).

Let’s walk through it: The first half—the numerator—is a guess for the ratio between how long the Sun has to keep glowing compared to how long a firefly does. I took a wild guess that fireflies have to light up for a few hours each night for one summer, while the Sun has to last another five billion years. The second half—the denominator—is a guess as to the ratio between the stored energy in a pound of firefly vs a pound of star. Nuclear fusion converts about 1% of the input matter to energy, so from E=mc2, the stored energy is c2 kg/kg, whereas animal matter (say, butter) is about 3,200 food calories per pound. The result should tell us the ratio between a firefly’s brightness per pound and the Sun’s. And the answer we get says that the fireflies are a few thousand times brighter—which is roughly what we got from working through it the other way!

It’s true that we got lucky with some of our guesses, but since we made errors in both directions, they tended to cancel out. This kind of thing works more often than it seems like it should!

[5]如果你喜欢费米估算这种蠢蠢的问题,这里有个不需要你去研究萤火虫和太阳的有趣方案:你只要在Wolfram|Alpha 里输入这个方程:(50亿年 / (4 小时/天 * 3 个月)) / (1% * (光速)^2 / (3200 卡路里/磅)).

让我们来分析一下:上半部分,即分子表示的是太阳发光时间与萤火虫发光时间比率的估计值。我大致猜测萤火虫一个夏天也就每天晚上亮那么几个小时,而太阳则会再持续发光50亿年。下半部分,即分母表示的是对每磅萤火虫储存的能量和每磅恒星储存能量比值的估计值。核聚变大概会将1%的聚变材料变成能量,根据E=mc^2,每公斤物质储存c^2焦耳的能量;而动物的储能物质(如黄油)每磅大约有3200卡路里的能量。通过这个问题的答案,我们就能知道每磅萤火虫亮度与每磅太阳亮度的比率。结果是萤火虫的亮度大概是太阳亮度的几千倍(3940),这个结果和我们之前得到的结果大致相同。

的确,我们得到这个结果是有些幸运的成分在里面的,因为我们在两边的估算都有些误差,而这些误差正好相互抵消了。这种似是而非的事情其实经常发生。 

[6]But the light from the core fireflies wouldn’t just vanish. After bouncing around a few times, it would be absorbed by neighboring fireflies, which would get warmer. This is sort of like how radiation makes its way out of the Sun’s core—but in the case of the fireflies, they’d die from the heat before the process got very far.

[6]但是这些从核心发出的光不会就这样消失的,经过几次反射后,它会被周围的萤火虫吸收掉,最终变成了热。这其实和太阳核心热辐射有点类似,但是不一样的是,萤火虫在能够继续辐射这种能量前就已经热死了。


 

XD:屁股吸的人憔悴。


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已有 9 条评论 新浪微博
  1. 匿名

    这么一本正经的胡说八道我居然还看完了。

    2016年10月22日 21:15来自移动端 回复
  2. 蓝蓝的天空

    名称释得生动形象

    2016年8月4日 17:02来自移动端 回复
  3. 匿名

    字太多,不想看……密密麻麻,恐惧症!

    2016年8月4日 02:03来自移动端 回复
  4. 777

    一脸蒙b( ゚∀。)

    2016年8月3日 12:22来自移动端 回复
  5. S0001

    什么?!蜘蛛不是昆虫?!

    2016年8月2日 10:51 回复
  6. 這已經不算科普文章了,而是傷人san值的廢文((+_+))

    2016年7月31日 09:52来自移动端 回复
  7. CupcakeWOW

    這一本道得好有趣 XD

    2016年7月31日 01:28 回复
  8. CharaSpe

    看完了。 支持一下

    2016年7月31日 00:08来自iPhone 回复
  9. r13l

    我……居然……看……完……了……………………

    2016年7月30日 22:032 回复
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