Can you solve the time traveling car riddle? - Dan Finkel

639,325 views ・ 2023-07-06

TED-Ed


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翻译人员: Ryan Qiao 校对人员: Yip Yan Yeung
00:06
Your time traveling has caused a few issues with the space-time continuum,
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你的时间旅行 给时空连续体造成了一些问题。
00:11
like your old high school bully, Riff, now ruling the future with an iron fist.
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比如, 你以前高中里的恶霸,里弗,
现在正用铁腕统治着未来。
00:16
You and the professor have driven your hovering DeLorean back to the past
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你和教授
驾着德罗宁悬浮跑车 回到了过去,
00:20
to undo your own meddling.
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来撤销你之前的干预。
00:22
But shortly after you fix your mistakes,
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可你们刚修复了错误,
00:25
another DeLorean appears and crashes into yours.
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另一辆德罗宁出现, 撞上了你们那辆。
00:28
Out step older versions of you and the professor,
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走出来的是 一个更年长版本的你和教授。
00:32
who apparently had the same idea from somewhere else in the timeline.
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显然,来自时间线上另一处的他们 和你们有同样的计划。
00:36
The professors panic and explain that the universe could collapse
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教授们惊慌失措地解释说, 宇宙可能会坍缩,
00:40
now that you’re both in the same time and place.
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因为你们正同处于 同一个时间和地点。
00:43
The only hope is to merge the time streams by having each version of you
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现在唯一的希望是
通过让每个版本的你们 同时穿越回到各自家中
00:48
simultaneously time travel home.
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来合并时间流。
00:51
You both have plenty of fuel,
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你们各自有充足的燃料,
00:53
but the crash broke your chrono-stabilizing gyroscopes
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但你们各自的 时间稳定陀螺仪都因撞车损坏了。
00:57
and your cars can only time travel under very specific circumstances.
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而你们的车都只有在
满足了以下特殊条件时 才能进行时间旅行。
01:02
Each of you will need to drive a mile south, then a mile east,
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你们需要分别 驱车向南行驶一英里,
然后向东行驶一英里,
01:06
and then a mile north to get the gyroscopes into temporal alignment.
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再然后向北一英里 以使陀螺仪进入时间对准状态。
01:11
That would be easy,
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这本来不难,
01:12
except each calibration requires placing a portable time gate
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但每次校准都需要 在你们的起点
01:17
at your starting point,
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放置便携式时间门,
01:18
then driving into it at the precise end of your three mile drive without it moving.
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然后在三英里的驱车行程 结束的那一刻
准确地驶入它而不让其移动。
01:25
Not only that, but your two time gates must be placed at least 100 miles apart
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不仅如此,你们的两个时间门 必须相距至少 100 英里,
01:31
so their signals don’t interfere.
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以避免信号干扰。
01:34
In other words, you need to find two different locations where you can drive
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换句话说,你们需要找到两个 不同的地点,同时满足
01:38
a mile south, a mile east, and then a mile north
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向南一英里,向东一英里, 然后向北一英里后
01:42
and end up exactly where you started.
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能最终回到出发点。
01:45
The professors are about to show you where you can do this when they vanish,
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教授们正要说到 你们在哪里出发能做到这些,
却突然消失了。
01:49
becoming victims of the collapsing timeline.
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他们成了时间线坍缩中的受害者。
01:52
It’s up to you now:
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现在轮到你们决定了:
01:53
where can you place the time gates?
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你该在哪里放置时间门?
01:55
Pause here to figure it out yourself. Answer in 3
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[请暂停一下,思考答案。] [答案揭晓倒计时:3]
01:58
Answer in 2
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[2]
02:01
Answer in 1
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[1]
02:03
If the earth were flat, there would be no way to solve this riddle.
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如果地球是平的, 我们就没法解开这个谜题。
02:07
What you need is some way to use the sphericalness of the planet,
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我们需要利用地球的球形特性,
02:12
some of its notable features,
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它的一些显著特征,
02:14
and the fact that lines of latitude aren’t really lines— they’re circles.
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以及一个事实: 纬线不是真正的直线,
而是圆。
02:19
The equator is the biggest of these circles, but it doesn’t do much for you,
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赤道是其中最大的圆, 但这对我们帮助不大。
02:24
and you can’t even go south from the South Pole.
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而至于南极点, 我们根本不能从那里再向南走。
02:27
But let's try the North Pole.
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但让我们尝试一下北极点。
02:29
When you go a mile south, you'll be on a circle that runs east west.
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当你向南行驶一英里后, 你将位于一个东西向的圆上。
02:33
After a mile east, you’re still on that same circle,
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再向东行驶一英里后, 你仍然在同一个圆上,
02:37
so the final mile north brings you back to your starting point.
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所以最后一英里向北行驶 会将你带回到出发点。
02:41
Perfect.
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完美。
02:42
That’s one gate down, but where should you place the second?
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第一个门成功了, 但第二个应该放在哪里呢?
02:46
Well, the nice thing about circles is that if you travel on them far enough,
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圆的一个好处在于, 如果你在上面行驶足够远,
02:50
you come back to where you started.
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你会回到出发点。
02:52
If there were a circle that had a circumference of one mile,
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如果有一个周长为一英里的圆,
02:56
that would work marvelously.
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那将完美解决我们的问题。
02:58
You could drive south a mile to reach it, make the one mile rotation east,
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你可以驱车向南行驶一英里, 到达这个圆,
然后向东行驶一英里,刚好一圈,
03:02
then go north a mile to return to where you started.
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最后向北行驶一英里, 回到出发点。
03:05
Such a circle does exist just north of the South Pole.
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符合我们要求的圆 可以在南极点以北一些找到。
03:10
To find your starting point,
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要找到你的起点,
03:11
you can use the standard formula for the circumference of a circle.
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你可以用圆周长的标准公式计算。
03:15
If you wanted to be absolutely precise,
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如果你想要非常精确,
03:18
you could use an equation that takes into account
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那你可以用一个考虑到
03:20
the roughly spherical shape of the Earth.
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地球的不规则球体形状的公式。
03:23
But an area this small is so close to being flat
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但我们考虑的这么小一片区域 几乎是平的。
03:26
that the standard formula gives a solution within a fraction of an inch
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所以标准公式给出的答案 和实际距离相差
03:30
of the actual distance.
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不及一英寸之几分。
03:32
A circle with a one mile circumference has a radius of just under 0.16 miles,
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一个周长为一英里的圆圈的半径 略小于 0.16 英里,
03:39
so any point on the circle one mile north of that
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所以在距离这个圆上任意一点 以北一英里的地方
03:42
will be suitable for your time gate.
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都可以放置你的时间门。
03:45
In fact, there are other answers too:
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实际上,还有其他的答案:
03:47
start a little further south,
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从更南端一些出发,
03:49
and you could travel east around the Earth twice, three times, or more!
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你可以绕地球上向东行驶两圈, 三圈,甚至更多!
03:54
In theory, there are infinite possible starting points,
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理论上来讲, 存在着无数个满足条件的起点。
03:57
but the circles get so tight that they aren't actually practical to drive.
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但当这些圆变得太小, 在实际操作中会无法驾车通过。
04:01
Everything’s getting a little weird
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当你们到达各自的起点时,
04:04
by the time you reach your starting points.
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一切正变得越来越奇怪。
04:06
You drop the time gates, sync up with your doppelgänger,
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你和另一个你同步, 分别放置好了时间门,
04:09
and slam down the pedal.
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然后同时猛踩油门。
04:11
You both reach 88mph just as you complete your three mile circuits,
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你们各自完成三英里行驶时, 都达到了 88 迈的速度,
04:16
merge the timelines, and save the universe.
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合并时间线, 拯救了宇宙。
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