跟讀練習: This is Crazy - 通過影片學習英語口語

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The exponential time hypothesis is false.

This is completely f*ing insane.

OpenAI has done it again.

They are now releasing even more proofs.

When will the proof stop?

We are announcing three new discoveries in mathematics, computer science, and physics about harmonic analysis, complexity theory, and quantum field theory.

That's right, you heard it here.

They are releasing a proof about my boy, computer scientist.

And as somewhat of a computer scientist myself, I was naturally intrigued.

And learning that the exponential time hypothesis is false means

that we could fundamentally be entering into an era in which all modern diseases are solved in relatively short amount of computation,

and it also means that all encryption is broken and everything you enjoy is completely gone and society collapses.

So we have to talk about this.

I'll help you understand it.

Okay.

As again, as a computer scientist myself, be glad to walk you through what is NP complete,

what this all means, what is the exponential time hypothesis, and what does this actually mean?

Should you be worried?

Is P equal NP?

But before we do, a quick thank you to the sponsor.

I have to say one of my favorite parts of this AI revolution is GrokBot.

And that is because so many little tedious tasks are now me just going,

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Or, hey, put milk on my list for things to pick up.

And with the ability to add custom MCPs, you could actually add any of your applications and be able to sync with it.

So GrokBot allows me to effectively control my life and just take out all the tedium.

Honestly, kind of feels like the promise of AI that we kept on hearing

that it's gonna make our life better because this actually makes life better.

And my wife is much happier now that I'm a little bit more organized.

So if you'd like to support the channel, go check out GrokBot, which is available on the web, desktop applications, and on mobile, Android included.

I feel like they're thinking of me when they made that.

I'm very, very, very happy.

All right, so OpenAI is back at it again.

This time, people are freaking out for a different reason.

It's not for the purity of math that they're losing everybody on.

In fact, it's for something a little bit different, because if what they have proved is correct, it is a step towards P equaling NP.

Now, with this announcement, they actually announced three big discoveries.

The first one for local smoothing of the Kakeya conjecture.

The third for the existence of quantum chromodynamics and completions of the standard model.

But it's the middle one.

It's the middle one we're going to talk about, okay?

The exponential time hypothesis.

Now, to understand the exponential time hypothesis, you need to understand this very small Boolean expression right here.

A or B or C.

This is called a 3SAT problem.

There's three variables in a group

and we need to see what values of all the variables need to be to be able to satisfy this.

So if we just simply set all of them to false, it would be false.

But if we just set any one of them to be true, then we have satisfied that Boolean expression.

We have found something that makes it true.

And in this case, we just set C to true.

But let's make it a little bit harder.

Let's add one more group.

So now we have two sets of three.

This is still a three -sat problem.

We have A or B or C and we have not a

or d or e so now we have five variables a through e so

if we were to kind of guess well what would satisfy

this we would actually have to start guessing okay is all

of them false satisfied no how about one of them true d true e

and d true how about c true yes okay c is true

this works awesome we now have satisfied this equation but notice

that it took quite a few more guesses to get somewhere also just a side note the fact

that this actually is the same it's the same thing

that made them both true that's just an anomaly just okay don't think about it too hard all right

so let's add actually a third one in here notice

that we have not see in the third one f

and g so that that puts our total variables all the way up to g

or seven so now when we're checking notice

that this takes a lot longer we have a lot more guesses like this would take us a

while to figure out

if you were doing this by hand you would have to do a bit of guessing

but lo and behold we got it we were able to get the answer after

so many guesses but you can see something here.

Every time we add a new group, and more specifically, every time we add a new variable, this requires a much larger amount of checking.

Now this is kind of like the fundamental premise of the exponential time hypothesis.

This hypothesis is super important because if it is true, then P does not equal NP.

But right now, it hasn't been proven to be actually true.

It's only a hypothesis.

And the basic of the hypothesis is that the growth of the 3SAT problem is effectively bounded exponentially, like 2 to the n.

Now, there are some improvements on the algorithms,

and people have been able to kind of reduce that base down to 1 .3 with clever programming tricks,

but that still is 1 .3 to the n.

To put this into perspective, I'm going to give a very special number.

Just go with it for a second.

1 .3 to the 2500.

This right here is more atoms than in the known universe.

So you can see that even with that much smaller base, when you get to so many of these, it becomes impossible to actually compute.

Like we don't have the computation ever to be able to solve this.

But what OpenAI just did is they found an equation that they were able to solve that looks like this,

two to the N divided by the squirt of the log of N.

And this takes it from being exponential to being sub -exponential, which is exactly what ETH said, nope, that cannot happen.

I put my foot on the ground.

We will not have non -exponentials here.

No, well, we actually have sub -exponentials.

Now, this is not polynomial time.

This is still exponential time, but it's sub -exponential because this does grow with the growth of n, which makes n smaller.

So the growth is just not quite the same.

If you remember my last equation, that 1 .3 to the 2 ,500, you can see right here that has greatly reduced it.

100

Now, this is still completely not even computable

101

that number is just gigantic we're not going to be able to solve

102

that in my lifetime but as you can see it's significantly reduced

103

and this means is there a path to continuing to reduce

104

this are we just starting the walking of reducing this now this may sound a little bit familiar

105

because if you just remember a few weeks ago on october 6th

106

when open ai dropped like 372 different uh proofs

107

or was it i can't remember what it was doesn't really matter it was a lot of proofs.

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One of them was about integer multiplication.

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The integer multiplication started off as being this like barely in just the tiniest improvement of all time.

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And then over the course of the next couple weeks, you started seeing improvement and improvement and improvement.

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So is this going to be another one of those cases

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where it starts off with just barely a little bit of an improvement

113

that just leads to a deluge of huge improvements on this running time?

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Are we going to see something like p does not equal np

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now you're probably asking

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i don't know what p equal does not equal np even means what is the implication

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this is where all the scary stuff actually happens because

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if this starts to improve a whole bunch

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and we open up new doors

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and we eventually get this all the way down into polynomial time

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this will just upend society yes p equals np will make things kind of crazy for us okay

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so we have to talk about p equals np

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because this is the big question because

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if p equals np we are all screwed

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and we are also in a super great world where we could cure cancer

126

it's the craziest world we could ever possibly live in

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and this is why there exists a set of problems called

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np problems non -deterministic polynomial problems these problems have a very special condition on them

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they can be verified in polynomial time this is really important

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so when we go back to this i can look at this one right here and go like this.

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Okay, that one's true.

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That one's true because not zero.

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And that one's true.

134

Boom.

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I just verified with my eyeballs a problem that is super hard, that is exponentially difficult to solve for,

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but I can verify it in linear time.

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It's super easy to see if something's right, super hard to determine the problem.

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Inside of NP, there's a set of problems called P.

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And now this is the big question.

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Is all the problems in NPP or is just some of them?

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P means that they are solvable in polynomial time.

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See, then there's one other group of problems we'd like to call NP -hard.

143

Now, this is kind of a funny one.

144

It has a really funny name to it because you're like, oh, well, why aren't all the problems inside of NP?

145

It's called NP -hard.

146

Well, what they mean is that they're at least as hard as every other problem inside of NP.

147

And so this little intersection right here is a very special class of problems we like to refer to as NP -complete.

148

NP -complete problems are NP hard problems that are verifiable in polynomial time.

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This problem is NP complete.

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Now, NP complete has this really special property, which every problem that is NP complete, you can represent by any other problem that's NP complete,

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meaning that the traveling salesman can actually be represented as a three SAT problem.

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That is why I showed you this little formula over here,

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because 2500 is the size of the United States being represented as a three SAT formula solving the traveling salesman

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which means it takes forever to solve we can't solve

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this even with the best stuff the best computers in the universe can't solve

156

that problem right now but here's the thing with that paper showing

157

that exponential time hypothesis is in fact false

158

that we are sub exponential there's a chance

159

that we could keep on figuring out how to reduce it into polynomial time

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and that's where things get crazy and the reason why is

161

that once one of these problems become polynomial time all of these problems become polynomial time by the sheer nature

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that they are the hardest of all the problems within np

163

now where this gets really really bad is think of rsa rsa

164

which of course is like how you do public key encryption there's like many versions of this

165

and this is not the complete picture

166

but just go with me here effectively there's two prime numbers that are multiplied together and then you get this public key.

167

that anybody can look at and it's completely fine

168

because they don't know how to get these private keys from this public one.

169

Yes, I know there's an inverted matrix involved in all of this.

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We're not going to talk about it.

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Just don't worry about that, okay?

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Just keep it simple.

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So that means these private keys, to be able to find those, you have to do something called integer factorization.

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And that turns out to be a really hard problem.

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Not an NP hard problem, but a very hard problem inside of NP because we can validate that in polynomial time,

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but we cannot solve for it in polynomial time.

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And since exponential time hypothesis is now false and we are now sub -exponential, if this does improve and go to polynomial,

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that means we can crack RSA in polynomial time, which means powerful computers would be able to break encryption across the internet.

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This also goes for like SHA -256.

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This also goes for HMAC.

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This goes for pseudo -random number generators.

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It goes for blockchain, which awesome.

183

Love to see that last one get taken down

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but nonetheless everything would kind of fall apart

185

but there's also protein folding turns out protein folding is in fact going to be an NP complete problem

186

so if we could change that we could potentially do research what would take decades

187

or hundreds of years you could potentially do in like a year

188

you would even be able to solve sudokus in polynomial time now

189

that would be a crazy world right I mean solving sudokus okay that's getting a little too fanciful the name

190

Is the NP a gin?

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本課的詞彙與口語要點

這節口語課以影片“This is Crazy”為素材。影片中反覆出現的詞有：exponential, polynomial, hypothesis, solve, complete。這段影片共有 190 個句子、2263 個單詞可供跟讀。講話部分時長為 11:26。說話人語速較快，每分鐘約 198 個詞，會出現較多連讀和弱讀。 84% 的單詞屬於英語最常用的 3,000 詞，其餘的詞建議在練習前先學一下。

影片中的重點詞彙

影片中 15 個值得學習的單詞，附發音和釋義：

單詞	發音	釋義
solve 動詞	/sɒlv/	解決 /解決
hypothesis 名詞	/haɪˈpɒθɪsɪs/	假說 /假說, 假設 /假設
satisfy 動詞	/ˈsætɪsfaɪ/	滿足 /滿足
scientist 名詞	/ˈsaɪəntəst/	科學家 /科學家
equation 名詞	/ɪˈkweɪ.ʒən/	方程式, 方程
verify 動詞	/ˈvɛɹɪfaɪ/	校驗 /校驗, 驗證 /驗證
encryption 名詞	/ɪnˈkɹɪpʃən/	加密
discovery 名詞	/dɪˈskʌv.ɹi/	發現 /發現
formula 名詞	/ˈfɔː.mjʊ.lə/	公式
announce 動詞	/əˈnaʊn(t)s/	通告, 公佈
mathematics 名詞	/mæθ(.ə)ˈmæt.ɪks/	數學 /數學, 算學 /算學
fold 動詞	/ˈfəʊld/	摺 /折, 折疊 /摺疊
quantum 名詞	/ˈkwɑntəm/	量
salesman 名詞		售貨員 /售貨員, 推銷員 /推銷員
soccer 名詞	/ˈsɑk.ɚ/	足球, 蹴球

影片中出現的短語動詞

單詞	釋義
figure out 動詞	弄清楚
check out 動詞	退房
pick up 動詞	拾取, 撿 /撿
take out 動詞	取出
turn out 動詞	原來 /原來

值得反覆跟讀的句子

影片中簡短而完整的句子，可以直接用在日常對話裡：

That's right, you heard it here.
I'll help you understand it.
Should you be worried?
I'm very, very, very happy.
Let's add one more group.

影片中的語法

說話人最常用的結構，並附上影片中的原話：

結構	影片中的用法
被動語態 be + 過去分詞 — 強調發生了什麼，而不是誰做的	was naturally intrigued · are solved · is broken
現在完成時 have/has + 過去分詞 — 過去發生但與現在仍有關聯的事	has done · have proved · have satisfied
定語從句 who / which + 從句 — 補充說明人或事物	GrokBot, which is · exponential, which is · time, which means

需要注意的發音

說話人用了 27 次縮略和弱讀形式，例如 don't, we're, can't。請按聽到的簡短形式來說。

“th” 音: hypothesis /haɪˈpɒθɪsɪs/, mathematics /mæθ(.ə)ˈmæt.ɪks/, smooth /smuːð/, nonetheless /ˌnʌnðəˈlɛs/, algorithm /ˈælɡəɹɪðm̩/
“sh” 和 “zh” 音: equation /ɪˈkweɪ.ʒən/, encryption /ɪnˈkɹɪpʃən/, potentially /pəˈtɛnʃ(ə)li/, completion /kəmˈpliː.ʃən/, sheer /ʃɪɚ/
長單詞——注意重音位置: hypothesis /haɪˈpɒθɪsɪs/, potentially /pəˈtɛnʃ(ə)li/, mathematics /mæθ(.ə)ˈmæt.ɪks/, naturally /ˈnæt͡ʃ.(ə.)ɹə.li/, fundamental /ˌfʌn.dəˈmɛn.təl/

中文母語者容易讀錯的音：

/v/ — 不要讀成 /w/，上齒輕觸下唇: solve /sɒlv/, variable [ˈvæɹ.i.ə.bl̩], verify /ˈvɛɹɪfaɪ/, discovery /dɪˈskʌv.ɹi/, clever /ˈklɛv.ɚ/
詞尾子音 — 要讀清楚，後面不要加母音: solve /sɒlv/, hypothesis /haɪˈpɒθɪsɪs/, scientist /ˈsaɪəntəst/, announce /əˈnaʊn(t)s/, mathematics /mæθ(.ə)ˈmæt.ɪks/
/r/ 和 /l/ 的區別: variable [ˈvæɹ.i.ə.bl̩], naturally /ˈnæt͡ʃ.(ə.)ɹə.li/, greatly /ˈɡɹeɪ̯t.li/, linear /ˈlɪn.i.əɹ/, algorithm /ˈælɡəɹɪðm̩/

如何用這段影片練習

先完整聽一遍影片，不要開口，記下不認識的單詞。
先用 0.75 倍速逐句跟讀，熟練之後再回到正常速度。
錄下自己的聲音並與原聲對比，特別注意 solve, hypothesis, satisfy 這類單詞。

什麼是跟讀法？

跟讀法 (Shadowing) 是一種有科學依據的語言學習技巧，最初開發用於專業口譯員的培訓，並由多語言者Alexander Arguelles博士普及。這個方法簡單而強大：您在聽英語母語原聲的同時立即大聲重複——就像是一個延遲1-2秒緊跟說話者的影子。與被動聽力或語法練習不同，跟讀法強迫您的大腦和口腔肌肉同時處理並模模擬實的講話模式。研究表明它能顯著提高發音準確性，語調，節奏，連讀，聽力理解和口語流利度——使其成為雅思口語備考和真實英語交流最有效的方法之一。

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跟讀練習: This is Crazy - 通過影片學習英語口語

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