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土豆悖论

The Potato Paradox

这里是Vsauce频道!
Vsauce!
我是凯文
Kevin here.
科罗拉多土豆甲虫
The Colorado potato beetle,
1811年在落基山脉第一次被无意中发现时
first observed innocently eating native plants
正在吃一种当地植物
in the Rocky Mountains in 1811,
当原产于南美洲的土豆
went crazy when potatoes,
被引进到美国时 它们疯狂地爱上了它
native to South America, were introduced to the U.S.
这些甲虫似乎在说
These beetles were like,
“哇 土豆太美味了” 它们说的对
“ Wow potatoes are delicious ” The beetles were right.
但它们对土豆的狂热对于作物们来说是灾难性的
But their potato-hunger is so devastating to crops,
整个消灭害虫的宣传活动
entire propaganda campaigns were
从第二次世界大战开始
launched in World War II and again
在冷战期间 传闻中央情报局
during The Cold War claiming that the CIA was dropping
在德国和欧洲东部等地留下这些“美国臭虫”
the “ American Bug ” in places like Germany and Eastern Europe
以一种生物入侵的形式
as a form of insect warfare.
这些科罗拉多土豆甲虫成为了土豆的最大克星
The Colorado potato beetle has been a majorpotato problem.
但是土豆不会是矛盾的 是吧?
But potatoes have never been paradoxical,right?
错 接下来进入:
Wrong. ENTER:
土豆悖论
THE POTATO PARADOX.
是这样的
It goes like this:
你得到100磅土豆 但是他们的99%重量都属于水
say you ’ ve got 100 pounds of potatoes and 99 % of their weight is water.
而剩余的1%是固体土豆物质 也就是淀粉
The other 1 % of their weight is solid potato stuff — starches,
蛋白质 果胶和矿物质 类似的物质
proteins, pectins, minerals, that kind of stuff.
当你放它们过夜 它们会变干一点
You leave them out overnight and they dry out a little bit.
当你醒来 它们只有98%的水分
When you wake up, they’re only 98 % water,
这会使得它的固体物质变成2%
that would make 2 % of it solid.
所以现在你那袋土豆有多重?
So, how much does your sack of spuds weigh now?
当你思考这一点时
While you think about it,
让我们来用些真正的土豆 而不是那些想象的
let’s get real for a second with real potatoes, not paradoxical ones.
所以 真正的土豆里79%是水的质量
So, real potatoes are 79% water by weight.
我可以把它转化成100克
So I cut this to exactly 100 grams,
这意味着里面有79克水
which means this 79 grams of water.
看起来很解渴
Looks thirst quenching.
79%已经很多了 但有更多水分的食物
79% is a lot, but we can go higher.
西瓜每100克里91%是水
Per 100 grams, Watermelon is 91% water.
但是什么还比西瓜水分更多呢?
But what’s more water than watermelon?
生菜
Lettuce.
生菜几乎达到95%的水分
Lettuce is almost 95% water.
意味着 生菜做沙拉只比做汤多了那5%
Meaning, salad is 5% away from being soup.
回到悖论…也许一个很棒的点子可以解释
Back to our paradox… probably a good idea to get back to that.
也许会弄坏天平
Probably broke the scale.
好了 我们有100磅这样的土豆
Anyway, we have 100 pounds of paradox potatoes,
水的百分比降低1%一夜
and the percentage of water weight goes down by 1% overnight
所以它们的重量会是99磅
so their weight today would be 99 pounds.
一个普遍认为的答案
A common answer.
也是一个好的答案
And a good one.
如果是“好的答案” 意味着
If by”good” you mean…
错误的
WRONG
实际上在经过细微的改变后 你的土豆变成了50磅
After this tiny change, your sack of spuds would actually weigh 50 pounds.
组成部分变动了1% 使得它的质量变成了一半
The 1% shift in composition cuts its weight in HALF.
怎样得到?
How?
最简单的方法来形象化答案就是 这些土豆
Well, the easiest way to visualize the solution is with potatoes.
100个
100 of them.
噢噢噢哦哦 不不
OHHHH NO NO…
现在有100个土豆了
So here are 100 potatoes.
你必须抱住你的土豆 让它们知道你在乎
You must hug your potatoes so that they know that you care.
这个被涂成太空银色的土豆
This one painted potato, a lovely space age silver,
代表一开始的1%的土豆固体
is the 1 % of solid potato matter that we start with.
剩下99%是水
The other 99 represent the water.
当土豆变干
When the potatoes dry out,
固体物质数量不变
the amount of solid matter doesn ’ t change.
只有水消失
Only the water goes away.
如果我们去掉1单位水 我们现在就有99磅
So, if we remove ONE unit of water we now have 99 pounds
物质了 其中一磅是干的
of stuff, 1 of which is dry,
98磅是水 所以
98 of which are water. So,
让我们开始在这里做一些计算
let’s just do a little calculation here.
98除以99是98% 但还有0.9898989
98 out of 99 is 98%… but.989899.
我们不想要这些小数点后的数字
We don ’ t want all those point 9 things,
我们只要98%
we just want 98 percent.
好吧 这里太多水了
Okay, so that’s too much water.
我们又移去一个水
Let ’ s just remove another water, alright,
所以现在98磅中有97磅是水
so now we have 97 out of the 98 pounds here are water.
97除以98…
So, we’ll do 97 out of 98 and…
98.979591836%
98.979591836%.
太多了
That’s too much.
太多水了
It’s just too much water.
必须得有更好的办法
There’s got to be a better way.
但有个问题
Here ’ s the problem:
水的百分比下降很慢因为每个单位水去掉后
This is lowering really slowly because for every unit of water that dries away,
整个土豆物质含量也减少
the total amount that’s left ALSOgoes down.
看看我们需要拿走多少
To see how many we need to take away,
让我们看看最终结果
let ’ s look at the final result.
不好意思 土豆
Excuse me, potatoes.
好的 我们从这里开始
Okay, here’s what we’ve got going on here.
好了
Alright.
我们需要减去多少水
So we need to reduce how much water we
不是98也不是97…而是49
have not to 98 or 97… but to 49.
这是因为:
And here’s why:
我们有98%是水 2%是固体
So we have 98 % water, 2 % solid,
但我们只有一个单位固体
but we only have 1 solid unit.
让我们把2变成1
So let’s turn that 2 into a 1.
所以我们用2除以2 然后我们得到1
So, we’ll divide 2 by 2 and we get 1.
我们再对98做同样的运算
So we ’ ve got to do the same thing now to our 98,
将98除以2 等于49
so we ’ll divide 98 by 2 and that equals 49.
所以49加1等于50 50磅就是答案
So 49 plus 1 equals 50, and 50 pounds is the answer.
所以我们除去这么多代表水的土豆
So, we’ve got to get rid of SO MANY water potatoes.
我不知道有多少剩下
I don ’ t know how many are left,
但是应该是49份水和1份固体物质
but it should be 49 waters and 1 solid.
49除以50正是98%
And 49 divided by 50 is exactly 98%.
我们做到了
We did it!
这就是答案
That’s the answer.
土豆悖论得到
The potato paradox comes
每次当有两样东西
into play every time there are two items
其中一样浓度加倍时
and the concentration of one doubles.
这需要另一个物质的量减少
That requires the other one ’ s size to be reduced
到总量的一半
by half of the whole,
不管是增加1% 或是增加0.0001%
whether it’s doubling from 1% or.00001%.
又或是10%
Or 10%.
叫你的朋友解决这个问题 看他们怎么说
Ask your friends to solve this problem and see what they say.
很多时候
Most of the time,
我们第一反应是认为它不会变化很多
our first response is to assume that not much has changed
因为1%这么小
since 1% is so small.
这不是羞愧的事
This isn’t something to be ashamed of —
我们大脑有能像这样比较数字的能力:
our brains evolved to compare quantities like this:
有一只南方猛犸和五个人
there’s one wooly mammoth and there’s five of us.
或者我们需要多少食物
Or, how much food do we need
来维持家庭活过凛冬
to keep the family surviving through the winter?
评估相对的比例是一种抽象的能力
Evaluating concentrations is more abstract and
不是一种关乎生死存亡
not usually a life-or-death issue that
自然选择会在演化中有所影响的能力
natural selection would play a role in shaping.
不像其他有名的悖论 例如像时间旅行之类的
Unlike other famous paradoxes, time travel ones for example,
土豆悖论是个
the POTATO paradox is a
真实 真…实… 的悖论
VERIDICAL *VE-RI-DI-CAL* paradox,
意味着它有我们都能同意并且证明它正确的答案
which means it has a TRUE solution we can all agree on and prove,
但是尽管如此结果依旧让人惊讶
but is nonetheless surprising.
所以土豆悖论不是一个基于
So, the potato paradox is a kind of paradox not built on
误解 不可能的事或是推测的悖论 相反
misunderstandings or impossibilities or speculation but instead,
它是一个能让我们了解大脑如何工作的理论
is one that really teases out how the mind works.
现在如果你不介意的话
Now if you ’ ll excuse me,
我有一个很棒的土豆玩偶 可以变成一个土豆人
I have a vintage potato toy to turn into a potato man
在他丢失1%的水分
before he loses 1% of his water composition
和他一半的体重前
and half his weight.
同以往一样 谢谢观看
And as always – thanks for watching.
Vsauce
一开始的超棒的土豆悖论动画
The awesome potato paradox animation at the beginning of this video was created by
由视觉特效师埃里克兰格莱用AE制作的
VFX wizard Eric Langlay using After Effects.
如果你想要学习如何做酷炫的视觉特效
If you want to learn how to do cool visual effects,
这里有很多的课程 在Skillshare社区
there are dozens of courses just on After Effects over at Skillshare.
并且他们请来了这方面的专家
And they’re taught by experts who really know what they’re doing,
所以你会学到东西
so you’ll really learn what you’re doing,
无论你是否需要了解这些基础知识
whether you need to know the basics
噢小心
OH, LOOK OUT
你只要想学这些新的技能
or you just want to learn some new techniques.
我认为我们都能一直运用些新技能
Which, I think we all can always use some new techniques.
Skillshare的年度订阅费算下来
An annual Skillshare subscription is less
一个月少于10美元 并且前1000人
than ten bucks a month and the first one thousand
使用视频简介最上方的推广链接
people to use the promo link at the top
将会获得他们
of this video ’ s description will get their
前两个月只需99美分的机会
first two months for just 99 cents,
比这个土豆的价钱更便宜
which is less than this potato cost me.
我会给这个家伙一个手臂 或者手
And I would give this guy an arm… or a hand…
我猜它有了手臂 但是手 坏了
I guess he has an arm, but the hand, it’sbroken.
这个东西有60岁
Listen, this thing is 60 years old.
这很神奇…好吧 让我们看看 如果它…不
It’s amazing that it… ok, let’s seeif it… doesn’t.
如果把它立起来的话 它能保持住吗
What if it stood… will this hold it?
它可以立得住吗?
WILL THIS HOLD IT?
它可以!
IT HOLDS IT!
这个土豆人以一个土豆的形态生存着呼吸着
The Potato Man lives and breathes in a potato stand.
我不是想要押韵 但它的确押韵
I didn’t mean for that to rhyme, but itdid.
现在我们来看这个东西
Let’s look at this thing for a second.
土豆先生大头滑稽脸套装 这是它的原文
Mr. Potato Head Funny Face kit, this was the original thing.
并且这个不只是有土豆
And it really wasn’t just for potatoes,
你可以看到你可以做辣椒 甜菜根 橘子 苹果…
you can see you can make peppers, beets, oranges, apples…
噢噢喔不!
OHHH NOOOOO!
这些都是将蔬菜拟人化
Really, it was all about turning vegetables into people,
让我认为是 一件我们都该支持的事
which I think is something we can all get behind.
*叹气* 我需要清理太多东西了
*sigh* I have so much to clean up.

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