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哪个星球是超级玛丽的世界? – 译学馆
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哪个星球是超级玛丽的世界?

What Planet Is Super Mario World? | Space Time | PBS Digital Studios

超级玛丽能跳的比吃了兴奋剂的袋鼠还高
Super Mario can jump higher than a kangaroo on steroids,
他是如何做到的呢?
but how does he do that?
有没有真实的星球
And is there any real-life planet
能让你跳的像超级玛丽一样高么?
where you could jump like Mario?
我的名字是盖布,这里是“时空”
My name is Gabe, and this is ‘Space Time.’
[音乐播放]
[MUSIC PLAYING]
那么我们怎么理解马里奥疯狂的跳跃能力?
So how can we understand Mario’s crazy jumping ability?
让我们从重力怎样影响运动开始说起
Let’s start with how gravity affects motion,
它对于跳跃的影响是巨大的
because that a huge effect on jumping.
在地球上,一个物体直线上升
Now on Earth, an object rising straight upward
它的每秒的速度将会每秒减少9.8米
will lose 9.8 meters per second of its speed each second.
同样,一个下落的物体将会获得每秒940米
Likewise, a falling object will gain 940 meters per second
的额外速度
of extra speed each second.
为了简练,我们把9.8四舍五入成10
For simplicity, let’s round the 9.8 to 10.
那么,把一个球扔出窗户
So, drop a ball out a window.
一秒后,它以每秒十米的速度下降
One second later, it’s moving at 10 meters per second.
两秒后,每秒20米
Two seconds later, 20 meters per second.
3秒后,30米,以此类推。
Three seconds later, 30, and so forth.
现在来看质量和形状的无关性
Now mass and shape are irrelevant.
如果你不考虑场景中的空气阻力
If you took air resistance out of the picture,
鮑泽和蘑菇在上升慢慢下降
Bowser and a mushroom would slow down when rising
或加速下落都会保持一致的速度
or speed up when falling in lockstep.
这个比率,大约每秒递增每秒10米速度
That rate, around 10 meters per second per second,
或每秒10米的平方,
or 10 meters per second squared, is
叫做重力引起的加速度
called the acceleration due to gravity,
或叫地球表面重力。
or the surface gravity of Earth.
这个经常用小写字母 g 表示
And it’s usually denoted by lowercase letter g.
现在来看星球表面重力对
Now a planet’s surface gravity has a huge effect
你在那个世界能跳多高的巨大影响
on how high you can jump on that world.
举个低重力的例子
Low gravity, for instance, is why
就是为什么宇航员穿着沉重的太空服在月球上还能跳的那么高
astronauts in heavy spacesuits could jump so high on the moon.
在任何一个星球,g值有一个简单的对应关系
But on any given planet, there’s a simple relationship
在你从星球表面跳跃中能达到的最高度
between its g value, the maximum height you reach during a jump
和跳跃过程中
from the surface of that planet, and the amount
达到高度花费的时间之间
of time it takes you to reach that height.
g等于两倍高除以
g equals twice the height divided
上升时间的平方
by the square of the rise time.
如果你对这个方程的出处感兴趣
If you’re interested in where that formula comes from,
你可以查看这个详情的链接
you can check out the link in the description.
让我们用这个方程去测量g
But we’re going to use the formula to measure g
在这个超级玛丽的世界里
on ‘Super Mario World.’
我们全部要做的就是马里奥一次跳跃的时间
All we need to do is time one of Mario’s jumps
来测量跳得高度
and measure the height of that jump.
我们用一个简单的跑表来测量时间
Time, we can measure with a simple stopwatch.
我们用马里奥本身当尺子来测量他跳得高度
Jump height, we can measure by using Mario himself as a ruler.
关心因特网研究,你能发现
Careful internet research, which you can also find
详细的介绍,爆料马里奥的官方身高是
in the description, reveals that Mario’s official stature is
1.55米,或大约5英尺1英寸高。
1.55 meters, or about 5’1′ tall.
现在我们做这个实验的一个简单版本
Now I did a crude version of this experiment
用游戏“超级玛丽世界”,它运行在超级任天堂
with ‘Super Mario World’ on a Super Nintendo Entertainment
系统上,大约出版于1991年。
System circa 1991.
我让马里奥在上面做正规跳跃,不做旋转跳,
I had Mario do regular jumps in place, not the spin jumps,
并且我们使用胶带标记出他帽子顶端的位置
and I used to some tape to mark where the top of his hat
在跳跃最高点和跳跃前
was at the apex of the jump and before the jump.
我发现它跳跃的高度大约是二又四分之一个马里奥
I found it that he jumped about two and a quarter Marios.
乘上他的身高1.55米
Multiply that by his height of 1.55 meters,
你得到了他跳的高度
and you find that his jump height
是接近3又1/2米
is almost 3 and 1/2 meters.
计算跳跃的时间很难,尽管,因为它
Timing the jump is trickier, though, because it
发生的很快。
happened so fast.
我最后成功记录了15次跳跃时间,
I ended up timing 15 successive jumps,
除以15得到一次跳跃上下的时间
dividing that by 15 to get the up-and-down time for one jump,
并且除以2得到到达最高点的时间
and then dividing that by 2 to get the time to reach the apex.
我的计算结果是大约0.3秒从开始到最高点的时间
My result is about 0.3 seconds from launch to apex.
现在,让我们把这些数带入方程。
Now, let’s put these numbers into the formula from before.
如果我们设置高为3.5,时间是0.3秒,
If we set h to 3.5 meters and t to 0.3 seconds,
我们得到最终的g值在每秒78米平方左右
we get a final g value of around 78 meters per second per
或叫接近8个地球g
second, or almost 8 Earth g’s.
这意味着“超级玛丽世界”有大约8倍
That means ‘Super Mario World’ has about eight times
的地球表面重力。
the surface gravity of Earth.
现在,作为它的计算结果,其他人
Now, as it turns out, other people
做测量,有过更复杂的版本
have done more sophisticated versions of these measurements
使用的是任天堂模拟器,屏幕截图
using Nintendo emulators, screen capture
程序,和目前数学软件
programs, and actual mathematical software.
他们的计算结果有些不一样
Their results show some variation,
但也在5和10个地球g之间,
but all give surface gravities of between 5 and 10 Earth g’s,
坚持用我的粗糙计算
which is consistent with my crude calculation.
此外,他们用了很多的细节分析
Moreover, their more detailed analyses
确认超级玛丽遵守重力的法则,
confirm that ‘Super Mario World’ respects the rules of gravity,
意味着马里奥的速度变成了一个稳定的比率
meaning Mario’s speed does indeed change at a steady rate
不论是跳起或下落,所以我们的测量方法
whenever he jumps or falls, so that our method of measuring
g方程是适用的
g’s should be kosher.
并且在“超级玛丽世界”的g值的下线更大,比
And the bottom line is that g is bigger on Super Mario World
地球上更大,那么实际比较弱的重力并不是
than on Earth, so that weaker gravity is not in fact
关键因素,即使马里奥跳跃那么勇猛。
the key to Mario’s jumping prowess.
那什么才是关键?
What is it?
变态的腿力。
Crazy leg strength.
类似,超人的腿力
Like, superhuman leg strength.
记住,“超级玛丽世界”的重力是8倍强于
Remember, gravity is eight times stronger on Super Mario World
地球的重力,然而马里奥却跳的那么高
than it is on Earth, yet Mario jumps much higher
比我们在地球上能跳的更高。
than we can on Earth.
那么他起跳的速度必须很快。
So his takeoff speed must be really big.
多快呢?
How big?
如果马里奥在地球上,他的起跳速度必须
If Mario were on Earth, he would have a takeoff speed
超过每小时50英里并且能跳28米远
of over 50 miles an hour and be able to jump about 28 meters,
也就是90步远。
or over 90 feet.
也就是说马里奥能跨越洛克菲勒中心的
That means Mario could hurdle the Rockefeller Center
圣诞树,还有富余。
Christmas tree with room to spare.
马里奥跳的高度让人类难以置信。
So it’s highly implausible that Mario is even human.
并且不仅仅是跳跃的效果。
And not just because of the jumping.
在一个八倍地球表面重力的星球上,
On a planet with eight times Earth’s surface gravity,
你的血液也是八倍的重。
your blood is eight times as heavy.
现在来看,一个人类的心脏不能供血到大脑,
Now, a human heart couldn’t pump that up to the brain,
那作为一个实际的意大利水管更工将失去意识和死亡。
so an actual Italian plumber would be unconscious or dead.
那么在人类的词汇里,至少,
So in terms of human physiology, at least,
“超级玛丽”成为一个不现实的名词。
‘Super Mario’ gets a realism fail.
但是超级玛丽世界本身是什么样子呢?
But what about Super Mario World itself?
有哪个真实行星有这么大的g?
Do any real-life planets have that large a g?
好吧,g在任何一个星球都是确定的
Well, g on a given planet is determined
是被星球的质量和半径所决定的。
by a combination of that planet’s mass and its radius.
你可以用下面的公式来计算,
You can compute it with the following formula,
用地球的质量和半径作为参考。
using Earth’s mass and radius as a reference.
在那些主要的石头大家伙里面找找——就
What you find is that all the major rocky bodies– that
是说月亮,火星,金星,水星——他们每一个
means the moon, Mars, Venus, Mercury– all of them
都比地球g值更小。
have smaller g values than Earth does.
那些巨大的气体行星,像天王星,海王星和土星,
The gas giant planets, like Uranus, Neptune, and Saturn,
没有固体的表面可以去站立,
don’t have solid surfaces to stand on, per se,
但是我们只对比这个g值
but just for comparison, the g values
他们和地球的差距也都在15%以内。
they would have are all within 15% or so of Earth.
甚至在木星上,g也只有地球的2又1/2倍
Even on Jupiter, g is only 2 and 1/2 times or so Earth’s value.
所以很明显超级玛丽世界不在我们太阳系。
So Super Mario World is clearly not in our solar system.
对比太阳系外的行星
Comparisons to planets outside the solar system
是很困难的,因为天文学家
are trickier, because astronomers
不能很好的评估质量和
don’t have good estimates of both mass
半径尤其对于大多数系外行星。
and radius for most exoplanets.
系外行星,官方有一个列表
exoplanets.org has a table where you
你能从那里搜索出一些,已经能评估
can search through the ones for which we can estimate
表面重力的星球,并且找到你
the surface gravity, and you find
需要的那些数值,几倍地球g值的
those with values that are many times Earth g’s are
都是那些气体构成的大家伙。
thought to be gas giants.
实际上,更大的g值是可能
In fact, g values this large would more likely
出现在很多星星上的。
occur on stars.
现在,尽管仍然有用,
Now, though the jury is still out,
大多数星球的构成
most models of planet formation also
很难满足两个条件
suggest that it’s hard to have both
一个是高g值另一个是实体表面。
a high g and a solid surface.
那究竟哪个行星是超级玛丽世界?
So what planet is Super Mario World?
对,一个行星要有实体表面
Well, a planet with a solid surface
让马里奥可以像在游戏里那样跳跃
where Mario could jump exactly the way he does in the game
这是不可能存在的,至少在我们的宇宙里是不可能的。
is unlikely to exist, at least in our universe.
现在我们假设超级玛丽世界
Now I suppose Super Mario World could
存在一个平台在那些大型气体星球的边上。
be a platform at the edge of some gas giant.
但这个平台是怎么固定的呢?
But then what’s holding up the platform?
也许是金刚干的?
Donkey Kong?
记得,你要自己尝试实践
Remember, you could try this experiment
这些困难的测量,就像我这样。
yourself, even with rough measurements like mine.
知道有多强的重力真的很酷
It’d actually be cool to know how strong gravity is
你可以找些老版本的超级玛丽,或者其他什么游戏
in older versions of ‘Super Mario’ games, or in other games
都可以。
altogether.
如果你找到,尤其是如果你
If you find out, and especially if you
找到游戏虚拟重力对应的真实行星,
find a game that mimics the gravity of any actual planet,
请发评论告诉我。
please let me know in the comments,
附上你的测量方法。
along with your measurements.
我会报导任何有趣的发现
I’ll report any interesting discoveries
在“时空”节目的下一章里。
on the next episode of ‘Space Time.’
嗨,如果你喜欢空间知识,请订阅我们吧。
And hey, if you like space stuff, please subscribe.
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[MUSIC PLAYING]

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