Can you solve the Big Bang riddle? - James Tanton

譯者: Yi Hsuan Hung 審譯者: Man Chun Ma

It’s moments after the Big Bang and... wow, you’re still reeling.

這是大爆炸之後的片刻…… 哇，你還在暈眩中!

You’re a particle of matter, amidst a chaotic stew of forces,

你是一顆物質粒子，

fusion, and annihilation.

身處力量、融合和湮滅的混亂中。

If you’re lucky and avoid being destroyed by antimatter,

你如果很幸運沒被反粒子破壞，

you'll be the seed of a future galaxy.

你就成為了未來星系中的種子。

You gravitate towards a ring of particles that have devised a game.

你被一個巧妙設計過的粒子環所吸引。

A friendly gluon explains:

有個親切的膠子跟你說:

there are an equal number of matter and antimatter particles.

這裡有相同數量的物質和反物質粒子。

At the blow of a cosmic whistle,

在宇宙的一聲令下，

every particle of matter with a particle of antimatter to its immediate right

每個物質粒子會與其 右邊的反物質粒子合併，

will merge with that anitparticle to—poof!— both annihilate.

噗！兩者都湮滅。

The circle will tighten to make a smaller circle,

圓圈變緊，形成一個較小的圈圈，

and the process will repeat until just one particle of matter remains.

然後過程一直重複， 直到只剩下一個物質粒子。

They’d been waiting for someone like you, as with a perfectly balanced setup,

他們一直在等待像你這樣的人， 因爲在這完美平衡的設定裡，

no one would be left in the end.

最終沒有人會存活下來。

As guest of honor, they’ll let you choose where to insert yourself into the ring.

作為貴賓，他們會讓你 選擇進入圓環的位置。

What spot should you choose to make sure you’re the last particle standing?

你要選定哪個位置，才能確保 自己最後存活下來?

Pause here if you want to figure it out for yourself.

如果你想自己想通， 先在這按下暫停吧!

Explanation in 3

解釋倒數三秒

Explanation in 2

倒數兩秒

Explanation in 1

倒數一秒

A general strategy can’t rely on knowing what the circle looks like.

大家都知道不能依靠 圓圈的樣子制定策略。

But we can rely on how it should end: with you as the last particle standing.

但我們可以思考遊戲如何結束： 把你當作最後一個粒子。

Let's start there and work backwards.

我們從這往回推算。

Just before this, there were also some matter/antimatter pairs.

在此之前，還有一些 成對的物質及反物質。

Here’s 3 for the sake of example.

這裡有三對當作示範，

This right away suggests a strategy.

這立即顯示了一種策略。

You can simulate annihilations in any circle

您可以通過標記所有相鄰粒子對

by marking all pairs of adjacent particles,

來模擬任何圓圈中的湮滅，

then the newly adjacent pairs, and so on, to reach this final set.

然後是下一組相鄰的對， 依此類推，到最後一組。

If you map them back to the original circle,

如果你把它們映射回原來的圓圈，

standing to the immediate left of those final matter particles

站在最終物質粒子的左側

or the immediate right of final antiparticles

或是最終反粒子的右側，

means you’ll reach this endgame state and survive.

你就能走到遊戲終局並生存下來。

So here are the safe spots in all three given circles.

而這些就是三個圓圈中的所有安全點。

You find a good position and experience the bittersweet radiance

你就找個好位置， 看着你的新朋友們互相抵消，

of your new friends pairing off and becoming pure energy.

變成純粹的能量，然後你 獨自感受這苦中帶甜的滋味。

You’re soon left alone.

你很快又一個人了。

But wait a minute!

但等一下！

Today’s the big day.

今天是個特別的日子。

You’re an intelligent creature of matter amidst a chaotic crowd of alien races.

你是一群混亂的外星種族中的 一個智慧物質生物。

Every hundred million years,

每億年，

sentient species of the galaxy send emissaries to the core

銀河系中的智慧生物們 派遣使者前往星球核心

to pay tribute to the galactic seed you’re all descended from.

向萬物之源銀河種子致敬。

Each of the 27,182 attendees

27,182 名與會者中的每一個

has brought a cube of matter and a cube of antimatter.

都帶了一個物質和一個反物質立方體。

Except you: you’ve been chosen to represent your famed ancestor

除了你。你已經被選中 代表你著名的祖先

and reenact its moment of choice.

並重演它精彩的選擇時刻。

Everyone places their matter and antimatter cubes in a ring.

每個人都將他們的物質 和反物質立方體放在一個環中。

Your job: pick a spot to stand where you won’t be annihilated.

你的目的是選擇一個 你不會被殲滅的地方。

The ring is too large to simulate annihilations like before,

環太大了，因此 無法像以前那樣模擬湮滅，

but you have a programmable device you can point at spots between cubes.

但你有一個可寫程式的裝置， 你可以指向立方體之間的點。

The device can detect the full sequence of cubes around the circle,

該設備可以檢測 圓形周圍的完整立方體序列，

count cubes of each type, perform arithmetic,

計算每種類型的立方體， 進行演算，

and carry out simple logical commands.

並執行簡單的邏輯命令。

How do you program your device to identify safe spots?

你會怎麼寫程式以識別安全點？

Pause to figure it out for yourself. Answer in 3

如果你想自己搞清楚，按下暫停 解答倒數三秒。

Answer in 2

倒數兩秒。

Answer in 1

倒數一秒。

Let’s go back to our earlier approach:

讓我們回到前面提到的方法，

running time backwards starting from you alone,

時光倒流，從你是一個人開始，

then a sequence of pairs of cubes.

然後是一系列成對的立方體。

A second step back produces more pairs nestled between existing cubes.

再往回推，產生更多 位於現有立方體之間的對。

As does the next, and the next, each adding nestled pairs

就像下一對，再下一對， 每個都添加一對，

like a Russian doll of fundamental particles.

像是基本粒子版本的俄羅斯娃娃。

A pair never forms around an existing cube because only adjacent cubes annihilate.

一對永不在現有立方體旁形成， 因為只有相鄰的立方體會湮滅。

Your survival depends on the matter particles to your right

你的生存取決於你右邊的物質粒子，

buffering you from antimatter.

它把你和反物質隔開。

We can mathematically model this idea with a sum, starting with your +1.

我們可以從你的 +1 開始， 用總和對這個進行數學建模。

For instance, this would be +1+1-1+1-1.

例如，這將是 +1+1-1+1-1。

From your perspective, no matter how far you look,

從你的角度來看，無論你看多遠，

this sum will be positive.

總和都是正數。

Considering how we introduced pairs, this makes sense—

考慮到我們是如何引入配對的， 這是說得通的:

each inserted plus was immediately followed by a minus.

每個插入的加號緊跟一個減號。

If we examine the starting position of any other matter cube,

如果我們檢查任何 其他物質立方體的起始位置，

its sum will eventually hit zero.

最後總和都會歸零。

The moment that happens marks its exact annihilation partner.

發生的那一刻表示著 它的確切殲滅夥伴。

Again, our introduction of pairs reflects this;

同樣，配對的引入反映了這一點:

nestled pairs only delay the inevitable for the outer cubes.

嵌套的對只會延遲外部立方體 不可避免的消亡。

We can now program the device.

我們現在可以寫出程式了。

Start a running sum with +1, representing you,

用 +1 開始一個連續的總和， 代表你，

and scan around the circle.

然後繞圈掃描。

For each matter cube, add one,

對於每個物質立方體，加一，

and for each antimatter cube, subtract one.

對於每個反物質立方體，減一。

If all 54,364 cubes have been scanned

如果掃描了 所有 54,364 個立方體

without the sum ever hitting 0,

而總和未達到 0，

that spot is safe.

則該位置是安全的。

Nothing left to do but enjoy the fireworks.

剩下要做的就是 享受煙火吧!