Can you solve the Big Bang riddle? - James Tanton

翻译人员: Yuwei Wu 校对人员: Helen Chang

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

这是宇宙大爆炸后不久… 哇，你还在晕眩。

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

你是一个物质的粒子， 身处一团混杂着力、

fusion, and annihilation.

聚变和湮灭的混沌之中。

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

如果你足够幸运， 避免被反物质摧毁，

you'll be the seed of a future galaxy.

你将成为未来星系的种子。

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

你被一圈设计游戏的粒子吸引。

A friendly gluon explains:

一个友好的胶子解释道:

there are an equal number of matter and antimatter particles.

物质和反物质粒子的数量是相等的

At the blow of a cosmic whistle,

随着宇宙哨声的吹响，

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

每个物质粒子的右边 都有一个反物质粒子，

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

将与那个反粒子融合在一起，然后

噗！两者都湮灭了。

The circle will tighten to make a smaller circle,

这个圆会变紧， 形成一个更小的圆，

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

这个过程会不断重复， 直到只剩下一个物质粒子。

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

他们一直在等着像你这样的粒子， 因为有了完美的平衡，

no one would be left in the end.

最后就没有任何剩余。

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

作为主宾，他们会让你自己选择 插入圈的哪个位置。

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

你应该选择哪个点来确保 你是最后一个站着的粒子?

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

如果您想自己解出，在此处暂停。

Explanation in 3

三秒后解答

Explanation in 2

两秒后解答

Explanation in 1

一秒后解答

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

一般的策略不能依赖于 知道圆圈是什么样子的。

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

但我们可以依赖于它应该如何结束: 那就是你是最后一个粒子。

Let's start there and work backwards.

让我们从这里开始，然后往回推。

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

在此之前， 也有一些物质/反物质的双对。

Here’s 3 for the sake of example.

这里用3举个例子。

This right away suggests a strategy.

这就提出了一种策略。

You can simulate annihilations in any circle

你可以通过标记所有相邻粒子对 来模拟任何圆中的湮灭，

by marking all pairs of adjacent particles,

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

然后再标记新的相邻粒子对，

以此类推，最终得到这一组。

If you map them back to the original circle,

如果你把它们映射回最初的圆圈，

standing to the immediate left of those final matter particles

站在最后物质粒子的左边

or the immediate right of final antiparticles

或最后反粒子的右边，

means you’ll reach this endgame state and survive.

就意味着你会到达最后并存活下来。

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

这是三个圈的安全点。

You find a good position and experience the bittersweet radiance

你找到了一个不错的位置，并体验到

新朋友们结对并成为纯粹能量的 苦乐参半的光芒。

of your new friends pairing off and becoming pure energy.

You’re soon left alone.

你很快就被剩下了。

But wait a minute!

但是等一下!

Today’s the big day.

今天是个大日子。

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

在一群混乱的外星种族中， 你是一种智慧的物质生物。

Every hundred million years,

每过一亿年，

sentient species of the galaxy send emissaries to the core

星系中有知觉的物种就会派 遣使者到星系核心

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

向你们的后代致敬。

Each of the 27,182 attendees

27,182名与会者

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

每人带来了一个物质立方体 和一个反物质立方体。

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

除了你：你被选中来代表 你著名的祖先，

and reenact its moment of choice.

重现那个被选择的时刻。

Everyone places their matter and antimatter cubes in a ring.

每个人都把他们的物质 和反物质立方体放在一个环里。

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

你的任务是： 选一个站在你不会被消灭的地方。

The ring is too large to simulate annihilations like before,

这个环太大了， 不能像以前那样模拟湮灭，

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

但你有一个可编程的设备， 你可以指向立方体之间的点。

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

该设备可以检测 圆形周围的完整立方体序列，

count cubes of each type, perform arithmetic,

计算每种类型的立方体，执行算术，

and carry out simple logical commands.

并执行简单的逻辑命令。

How do you program your device to identify safe spots?

你如何对你的设备进行编程 以识别安全地点?

Pause to figure it out for yourself. Answer in 3

停下来自己想想。 3秒后解答

Answer in 2

2秒后解答

Answer in 1

1秒后解答

Let’s go back to our earlier approach:

让我们回到我们之前的思路：

running time backwards starting from you alone,

从你一个人开始逆向运行时间，

then a sequence of pairs of cubes.

然后是一系列的立方体。

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

再退一步，就会在现有的 立方体之间产生更多对。

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

每一个都是如此， 每个都增加了一对嵌套，

like a Russian doll of fundamental particles.

每一个都像俄罗斯的基本粒子套娃。

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

一对不会在一个存在的立方体周围形成， 因为只有相邻的立方体才会湮灭。

Your survival depends on the matter particles to your right

你的生存取决于你右边的物质粒子

buffering you from antimatter.

在反物质中对你的缓冲。

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

我们可以用加法来建立 这个想法的数学模型，从+1开始。

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

例如，这会是 +1+1-1+1-1。

From your perspective, no matter how far you look,

从你的角度来看， 无论你看得多远，

this sum will be positive.

这个总和都是正的。

Considering how we introduced pairs, this makes sense—

考虑到我们是如何引入对的， 这是有意义的—

each inserted plus was immediately followed by a minus.

每个插入的加号后面 紧跟着一个减号。

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

如果我们检查任何其他 物质立方体的起始位置，

its sum will eventually hit zero.

它的总和最终将为零。

The moment that happens marks its exact annihilation partner.

发生的那一刻标志着它的毁灭伙伴。

Again, our introduction of pairs reflects this;

我们对配对的介绍再次反映了这一点;

nestled pairs only delay the inevitable for the outer cubes.

依偎在一起的成对只会推迟外部 立方体不可避免的命运。

We can now program the device.

我们现在可以对设备进行编程。

Start a running sum with +1, representing you,

用+1表示你，开始加，

and scan around the circle.

然后扫描这个圆。

For each matter cube, add one,

每个物质立方体加一，

and for each antimatter cube, subtract one.

每个反物质立方体减一。

If all 54,364 cubes have been scanned

如果所有的54,364个 立方体都被扫描过，

without the sum ever hitting 0,

而总和没有达到0，

that spot is safe.

那么这个点是安全的。

Nothing left to do but enjoy the fireworks.

剩下的就是欣赏烟花， 其他什么也不用做。