シャドーイング練習: This is Crazy - 動画で英語スピーキングを学ぶ

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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

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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

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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

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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

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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.

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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,

151

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

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that we are sub exponential there's a chance

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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

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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

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and this is not the complete picture

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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

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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.

174

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.

179

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

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

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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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このレッスンの語彙とスピーキングのポイント

このスピーキングレッスンは、動画「This is Crazy」を教材にしています。繰り返し出てくる語は次のとおりです：exponential, polynomial, hypothesis, solve, complete。この動画には、シャドーイング用の文が190文、単語が2263語あります。音声の長さは11:26です。話す速さは速く、1分あたり約198語です。音のつながりや弱く発音される音が多くなります。単語の84%は英語の頻出3,000語に含まれます。残りは練習の前に確認しておきましょう。

この動画の重要語彙

動画に出てくる覚えておきたい単語15語を、発音と意味つきで紹介します。

単語	発音	意味
solve 動詞	/sɒlv/	解決する
hypothesis 名詞	/haɪˈpɒθɪsɪs/	仮説
variable 形容詞	[ˈvæɹ.i.ə.bl̩]	可変, 変えられる
satisfy 動詞	/ˈsætɪsfaɪ/	満たす
scientist 名詞	/ˈsaɪəntəst/	科学者
equation 名詞	/ɪˈkweɪ.ʒən/	方程式
encryption 名詞	/ɪnˈkɹɪpʃən/	暗号化
discovery 名詞	/dɪˈskʌv.ɹi/	発見
formula 名詞	/ˈfɔː.mjʊ.lə/	公式, 定式
announce 動詞	/əˈnaʊn(t)s/	発表する, 知らせる
mathematics 名詞	/mæθ(.ə)ˈmæt.ɪks/	数学
fold 動詞	/ˈfəʊld/	折る, 畳む
quantum 名詞	/ˈkwɑntəm/	量
salesman 名詞		店員, セールスマン
naturally 副詞	/ˈnæt͡ʃ.(ə.)ɹə.li/	勿論

動画に出てくる句動詞

単語	意味
check out 動詞	試験する, 検査する
pick up 動詞	拾う, 拾い上げる
take out 動詞	取り出す

繰り返し練習したい文

動画に出てくる短く完結した文です。日常会話でそのまま使えます。

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.

この動画の文法

話し手がよく使っている文型を、動画の実際の表現とともに紹介します。

文型	動画での表現
受動態 be + 過去分詞 — 誰がするかより、何が起きるかに焦点を当てる	was naturally intrigued · are solved · is broken
現在完了形 have/has + 過去分詞 — 過去の出来事が今も関係している	has done · have proved · have satisfied
関係詞節 who / which + 節 — 人や物について情報を加える	GrokBot, which is · exponential, which is · time, which means

注意したい発音

話し手はdon't, we're, can'tなど、短縮形や弱形を27回使っています。聞こえたとおりの短い形で発音しましょう。

「th」の音: hypothesis /haɪˈpɒθɪsɪs/, mathematics /mæθ(.ə)ˈmæt.ɪks/, smooth /smuːð/, nonetheless /ˌnʌnðəˈlɛs/, algorithm /ˈælɡəɹɪðm̩/
「sh」と「zh」の音: equation /ɪˈkweɪ.ʒən/, encryption /ɪnˈkɹɪpʃən/, potentially /pəˈtɛnʃ(ə)li/, completion /kəmˈpliː.ʃən/, sheer /ʃɪɚ/
長い単語（アクセントの位置に注意）: hypothesis /haɪˈpɒθɪsɪs/, potentially /pəˈtɛnʃ(ə)li/, mathematics /mæθ(.ə)ˈmæt.ɪks/, naturally /ˈnæt͡ʃ.(ə.)ɹə.li/, fundamental /ˌfʌn.dəˈmɛn.təl/

日本語話者が苦手な音：

/r/ と /l/ の区別 — /l/ は舌先を歯茎につけ、/r/ はどこにもつけない: variable [ˈvæɹ.i.ə.bl̩], naturally /ˈnæt͡ʃ.(ə.)ɹə.li/, greatly /ˈɡɹeɪ̯t.li/, linear /ˈlɪn.i.əɹ/, algorithm /ˈælɡəɹɪðm̩/
/v/ — /b/ にならないように、上の歯を下唇に当てる: solve /sɒlv/, variable [ˈvæɹ.i.ə.bl̩], verify /ˈvɛɹɪfaɪ/, discovery /dɪˈskʌv.ɹi/, clever /ˈklɛv.ɚ/
/f/ — 「フ」ではなく、上の歯と下唇で出す: satisfy /ˈsætɪsfaɪ/, verify /ˈvɛɹɪfaɪ/, formula /ˈfɔː.mjʊ.lə/, fold /ˈfəʊld/, refer /ɹɪˈfɜː/

この動画での練習方法

まず声を出さずに動画を最後まで聞き、知らない単語をメモします。
まず0.75倍速で一文ずつシャドーイングし、慣れてきたら通常の速度に戻します。
自分の声を録音して元の音声と比べます。solve, hypothesis, variableなどの単語に特に注意しましょう。

シャドーイングとは？英語上達に効果的な理由

シャドーイング（Shadowing）は、もともとプロの通訳者養成プログラムで開発された言語学習法で、多言語習得者として知られるDr. Alexander Arguelles によって広く普及されました。方法はシンプルですが非常に効果的：ネイティブスピーカーの英語を聞きながら、1〜2秒の遅延で声に出してすぐに繰り返す——まるで「影（shadow）」のように話者を追いかけます。文法ドリルや受動的なリスニングと異なり、シャドーイングは脳と口の筋肉が同時にリアルタイムで英語を処理・再現することを強制します。研究により、発音精度、抑揚、リズム、連音、リスニング力、そして会話の流暢さが大幅に向上することが確認されています。IELTSスピーキング対策や自然な英語コミュニケーションを目指す方に特におすすめです。

シャドーイングのやり方: ステップ別の完全ガイドを読む →

シャドーイング練習: This is Crazy - 動画で英語スピーキングを学ぶ

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