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

625,588 views ・ 2023-07-06

TED-Ed


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譯者: Lilian Chiu 審譯者: 穎君 紀
00:06
Your time traveling has caused a few issues with the space-time continuum,
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你的時間旅行導致 時空的連續性出了點問題。
00:11
like your old high school bully, Riff, now ruling the future with an iron fist.
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比如你以前高中的惡霸瑞夫 現在用鐵腕在統治未來。
00:16
You and the professor have driven your hovering DeLorean back to the past
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你和教授開著你的懸浮 迪羅倫汽車回到過去,
00:20
to undo your own meddling.
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打算還原你所造成的干預。
00:22
But shortly after you fix your mistakes,
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但就在你修正了你的錯誤後不久,
00:25
another DeLorean appears and crashes into yours.
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另一台迪羅倫汽車出現, 並和你的車相撞。
00:28
Out step older versions of you and the professor,
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從那台車走出來的 是年長的你與教授,
00:32
who apparently had the same idea from somewhere else in the timeline.
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很顯然,他們來自某個時點, 因為同樣的想法而回到過去。
00:36
The professors panic and explain that the universe could collapse
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教授們很驚恐,解釋說 宇宙可能會崩壞,
00:40
now that you’re both in the same time and place.
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因為你們現在身處在 同樣的時間與地點。
00:43
The only hope is to merge the time streams by having each version of you
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唯一的希望就是把時間流合併,
做法是讓不同版本的你 同時做時間旅行返家。
00:48
simultaneously time travel home.
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00:51
You both have plenty of fuel,
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你們的燃料都很充足,
00:53
but the crash broke your chrono-stabilizing gyroscopes
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但時間穩定陀螺儀在相撞時損壞了,
00:57
and your cars can only time travel under very specific circumstances.
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且你們的車只能在非常 特定的情況下做時間旅行。
01:02
Each of you will need to drive a mile south, then a mile east,
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你們各自都需要往南行駛一英里,
再往東行駛一英里, 再往北行駛一英里,
01:06
and then a mile north to get the gyroscopes into temporal alignment.
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才能讓陀螺儀的時間同步。
01:11
That would be easy,
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困難之處在於凡是做校準時
01:12
except each calibration requires placing a portable time gate
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都需要將可攜式的時間之門 放置在你的起點上,
01:17
at your starting point,
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01:18
then driving into it at the precise end of your three mile drive without it moving.
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接著,剛好在你行駛完 三英里路時穿過時間之門,
門的位置不能移動。
01:25
Not only that, but your two time gates must be placed at least 100 miles apart
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不僅如此,這兩扇時間之門 至少要相距一百英里,
01:31
so their signals don’t interfere.
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訊號才不會相互干擾。
01:34
In other words, you need to find two different locations where you can drive
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換言之,你們必須 找到兩個不同的地點,
讓你們可以向南行駛一英里, 向東一英里,再向北一英里,
01:38
a mile south, a mile east, and then a mile north
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01:42
and end up exactly where you started.
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結束時剛好回到起點。
01:45
The professors are about to show you where you can do this when they vanish,
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教授們正打算要向你們說明 在哪裡可以做到時,
他們卻消失了,成了 時間線崩壞的受害者。
01:49
becoming victims of the collapsing timeline.
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01:52
It’s up to you now:
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現在只能靠你們了, 時間之門能放在哪裡?
01:53
where can you place the time gates?
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01:55
Pause here to figure it out yourself. Answer in 3
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若想自行解題,在此暫停。 答案即將公佈:三。
01:58
Answer in 2
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答案即將公佈:二。
02:01
Answer in 1
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答案即將公佈:一。
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,這個謎題就無解。
02:07
What you need is some way to use the sphericalness of the planet,
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你需要想辦法利用地球的球形特性、
02:12
some of its notable features,
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它的一些顯著特徵,
02:14
and the fact that lines of latitude aren’t really lines— they’re circles.
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以及緯線其實不是直線 而是圓圈這項事實。
02:19
The equator is the biggest of these circles, but it doesn’t do much for you,
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赤道是最大的緯線圓圈。
但這點對你幫助不大,
02:24
and you can’t even go south from the South Pole.
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且從南極點出發還無法再向南行駛。
02:27
But let's try the North Pole.
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但,咱們來試試北極點。
02:29
When you go a mile south, you'll be on a circle that runs east west.
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當你向南行駛一英里,
你會處在一個東西向的圓圈上。
02:33
After a mile east, you’re still on that same circle,
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向東行駛一英里之後, 你還是在同一個圓圈上,
02:37
so the final mile north brings you back to your starting point.
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所以最後向北行駛一英里 就能讓你回到起點。
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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一扇門搞定了, 但第二扇門該放在哪裡?
02:46
Well, the nice thing about circles is that if you travel on them far enough,
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圓圈有一個好處,那就是 如果你沿著它走且走得夠遠,
02:50
you come back to where you started.
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就會回到起點。
02:52
If there were a circle that had a circumference of one mile,
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如果有一個圓圈的圓周是一英里,
02:56
that would work marvelously.
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那就完全行得通了。
02:58
You could drive south a mile to reach it, make the one mile rotation east,
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你可以向南行駛一英里到達 這個圓圈,再向東旋轉一圈。
03:02
then go north a mile to return to where you started.
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接著向北行駛一英里, 回到你的起點。
03:05
Such a circle does exist just north of the South Pole.
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這種圓圈確實存在, 就在南極點的北邊一點點。
03:10
To find your starting point,
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要找到起點,
03:11
you can use the standard formula for the circumference of a circle.
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你可以運用計算圓周的標準方程式。
03:15
If you wanted to be absolutely precise,
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如果你想百分之百精確,
03:18
you could use an equation that takes into account
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你可以在方程式中納入 地球球形表面的考量。
03:20
the roughly spherical shape of the Earth.
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03:23
But an area this small is so close to being flat
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但這麼小的區域,幾乎是平面的,
03:26
that the standard formula gives a solution within a fraction of an inch
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用標準方程式得到的解答
和實際距離誤差不會超過一英吋。
03:30
of the actual distance.
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03:32
A circle with a one mile circumference has a radius of just under 0.16 miles,
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圓周一英里的圓圈,
半徑略低於零點一六英里,
03:39
so any point on the circle one mile north of that
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所以在距離它一英里外的 圓圈上,任何一點
03:42
will be suitable for your time gate.
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都適合放置時間之門。
03:45
In fact, there are other answers too:
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事實上,還有其他答案:
03:47
start a little further south,
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從更南一點的位置開始,
03:49
and you could travel east around the Earth twice, three times, or more!
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你可以向東繞地球兩圈、三圈,更多圈!
03:54
In theory, there are infinite possible starting points,
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理論上可行的起點有無限多個,
03:57
but the circles get so tight that they aren't actually practical to drive.
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但圓圈太小時,汽車就無法行駛。
04:01
Everything’s getting a little weird
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當你抵達你的起點時, 一切開始變得有點怪異。
04:04
by the time you reach your starting points.
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04:06
You drop the time gates, sync up with your doppelgänger,
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你放置好時間之門, 和你的分身進行同步,
04:09
and slam down the pedal.
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猛力踩下油門。
04:11
You both reach 88mph just as you complete your three mile circuits,
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你們兩人在完成三英里繞行時, 時速都達到每小時八十八英里,
04:16
merge the timelines, and save the universe.
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將時間線合併,拯救了宇宙。
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