Pratique du Shadowing: This is Crazy - Apprendre l'anglais à l'oral avec la vidéo
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190 phrases
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The exponential time hypothesis is false.
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This is completely f*ing insane.
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OpenAI has done it again.
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They are now releasing even more proofs.
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When will the proof stop?
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We are announcing three new discoveries in mathematics, computer science, and physics about harmonic analysis, complexity theory, and quantum field theory.
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That's right, you heard it here.
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They are releasing a proof about my boy, computer scientist.
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And as somewhat of a computer scientist myself, I was naturally intrigued.
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And learning that the exponential time hypothesis is false means
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that we could fundamentally be entering into an era in which all modern diseases are solved in relatively short amount of computation,
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and it also means that all encryption is broken and everything you enjoy is completely gone and society collapses.
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So we have to talk about this.
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I'll help you understand it.
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Okay.
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As again, as a computer scientist myself, be glad to walk you through what is NP complete,
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what this all means, what is the exponential time hypothesis, and what does this actually mean?
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Should you be worried?
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Is P equal NP?
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But before we do, a quick thank you to the sponsor.
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I have to say one of my favorite parts of this AI revolution is GrokBot.
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And that is because so many little tedious tasks are now me just going,
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hey, can you update my calendar with all my kids' upcoming soccer games for this tournament?
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Or, hey, put milk on my list for things to pick up.
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And with the ability to add custom MCPs, you could actually add any of your applications and be able to sync with it.
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So GrokBot allows me to effectively control my life and just take out all the tedium.
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Honestly, kind of feels like the promise of AI that we kept on hearing
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that it's gonna make our life better because this actually makes life better.
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And my wife is much happier now that I'm a little bit more organized.
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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.
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I feel like they're thinking of me when they made that.
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I'm very, very, very happy.
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All right, so OpenAI is back at it again.
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This time, people are freaking out for a different reason.
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It's not for the purity of math that they're losing everybody on.
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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.
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Now, with this announcement, they actually announced three big discoveries.
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The first one for local smoothing of the Kakeya conjecture.
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The third for the existence of quantum chromodynamics and completions of the standard model.
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But it's the middle one.
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It's the middle one we're going to talk about, okay?
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The exponential time hypothesis.
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Now, to understand the exponential time hypothesis, you need to understand this very small Boolean expression right here.
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A or B or C.
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This is called a 3SAT problem.
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There's three variables in a group
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and we need to see what values of all the variables need to be to be able to satisfy this.
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So if we just simply set all of them to false, it would be false.
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But if we just set any one of them to be true, then we have satisfied that Boolean expression.
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We have found something that makes it true.
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And in this case, we just set C to true.
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But let's make it a little bit harder.
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Let's add one more group.
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So now we have two sets of three.
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This is still a three -sat problem.
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We have A or B or C and we have not a
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or d or e so now we have five variables a through e so
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if we were to kind of guess well what would satisfy
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this we would actually have to start guessing okay is all
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of them false satisfied no how about one of them true d true e
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and d true how about c true yes okay c is true
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this works awesome we now have satisfied this equation but notice
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that it took quite a few more guesses to get somewhere also just a side note the fact
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that this actually is the same it's the same thing
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that made them both true that's just an anomaly just okay don't think about it too hard all right
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so let's add actually a third one in here notice
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that we have not see in the third one f
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and g so that that puts our total variables all the way up to g
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or seven so now when we're checking notice
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that this takes a lot longer we have a lot more guesses like this would take us a
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while to figure out
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if you were doing this by hand you would have to do a bit of guessing
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but lo and behold we got it we were able to get the answer after
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so many guesses but you can see something here.
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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.
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Now this is kind of like the fundamental premise of the exponential time hypothesis.
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This hypothesis is super important because if it is true, then P does not equal NP.
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But right now, it hasn't been proven to be actually true.
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It's only a hypothesis.
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And the basic of the hypothesis is that the growth of the 3SAT problem is effectively bounded exponentially, like 2 to the n.
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Now, there are some improvements on the algorithms,
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and people have been able to kind of reduce that base down to 1 .3 with clever programming tricks,
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but that still is 1 .3 to the n.
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To put this into perspective, I'm going to give a very special number.
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Just go with it for a second.
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1 .3 to the 2500.
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This right here is more atoms than in the known universe.
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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.
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Like we don't have the computation ever to be able to solve this.
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But what OpenAI just did is they found an equation that they were able to solve that looks like this,
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two to the N divided by the squirt of the log of N.
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And this takes it from being exponential to being sub -exponential, which is exactly what ETH said, nope, that cannot happen.
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I put my foot on the ground.
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We will not have non -exponentials here.
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No, well, we actually have sub -exponentials.
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Now, this is not polynomial time.
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This is still exponential time, but it's sub -exponential because this does grow with the growth of n, which makes n smaller.
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So the growth is just not quite the same.
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If you remember my last equation, that 1 .3 to the 2 ,500, you can see right here that has greatly reduced it.
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Now, this is still completely not even computable
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that number is just gigantic we're not going to be able to solve
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that in my lifetime but as you can see it's significantly reduced
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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
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because if you just remember a few weeks ago on october 6th
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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.
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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.
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It has a really funny name to it because you're like, oh, well, why aren't all the problems inside of NP?
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It's called NP -hard.
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Well, what they mean is that they're at least as hard as every other problem inside of NP.
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And so this little intersection right here is a very special class of problems we like to refer to as NP -complete.
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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
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that problem right now but here's the thing with that paper showing
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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
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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
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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.
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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.
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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.
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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
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or hundreds of years you could potentially do in like a year
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you would even be able to solve sudokus in polynomial time now
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that would be a crazy world right I mean solving sudokus okay that's getting a little too fanciful the name
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Is the NP a gin?
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Vocabulaire et conseils d’expression pour cette leçon
Cette leçon d’expression orale s’appuie sur la vidéo « This is Crazy ». Les mots qui reviennent le plus souvent : exponential, polynomial, hypothesis, solve, complete. Cette vidéo contient 190 phrases et 2263 mots à répéter en shadowing. La partie parlée dure 11:26. Le locuteur parle vite, environ 198 mots par minute : attendez-vous à des liaisons et à des sons réduits. 84 % des mots font partie des 3 000 mots les plus courants en anglais ; le reste mérite d’être vu avant de commencer.
Vocabulaire clé de cette vidéo
15 mots de la vidéo à retenir, avec leur prononciation et leur sens :
| Mot | Prononciation | Sens |
|---|---|---|
| solve verbe | /sɒlv/ | résoudre, régler |
| hypothesis nom | /haɪˈpɒθɪsɪs/ | hypothèse |
| variable adjectif | [ˈvæɹ.i.ə.bl̩] | variable |
| satisfy verbe | /ˈsætɪsfaɪ/ | satisfaire |
| scientist nom | /ˈsaɪəntəst/ | scientifique, savant |
| equation nom | /ɪˈkweɪ.ʒən/ | équation |
| verify verbe | /ˈvɛɹɪfaɪ/ | vérifier |
| encryption nom | /ɪnˈkɹɪpʃən/ | chiffrement |
| discovery nom | /dɪˈskʌv.ɹi/ | découverte |
| formula nom | /ˈfɔː.mjʊ.lə/ | formule |
| potentially adverbe | /pəˈtɛnʃ(ə)li/ | potentiellement |
| announce verbe | /əˈnaʊn(t)s/ | annoncer |
| mathematics nom | /mæθ(.ə)ˈmæt.ɪks/ | mathématiques |
| fold verbe | /ˈfəʊld/ | plier |
| quantum nom | /ˈkwɑntəm/ | quantité |
Les verbes à particule que vous entendrez
| Mot | Sens |
|---|---|
| figure out verbe | cerner |
| check out verbe | mater, regarder |
| fall apart verbe | tomber en morceaux |
| open up verbe | ouvrir |
| pick up verbe | soulever |
| take down verbe | décrocher |
| take out verbe | supprimer, sortir |
| turn out verbe | se finir, se terminer |
Des phrases à répéter
Des phrases courtes et complètes de la vidéo, à réutiliser dans la conversation de tous les jours :
- 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.
La grammaire de cette vidéo
Les structures que le locuteur utilise le plus, avec les mots exacts de la vidéo :
| Structure | Dans la vidéo |
|---|---|
| Voix passive be + participe passé — l’accent est mis sur ce qui arrive, pas sur qui le fait | was naturally intrigued · are solved · is broken |
| Present perfect have/has + participe passé — une action passée qui compte encore maintenant | has done · have proved · have satisfied |
| Propositions relatives who / which + proposition — une précision sur une personne ou une chose | GrokBot, which is · exponential, which is · time, which means |
Prononciation à surveiller
Le locuteur utilise 27 contractions et formes réduites, comme don't, we're, can't. Prononcez-les sous leur forme courte, telles que vous les entendez.
- Les sons « th »: hypothesis /haɪˈpɒθɪsɪs/, mathematics /mæθ(.ə)ˈmæt.ɪks/, smooth /smuːð/, nonetheless /ˌnʌnðəˈlɛs/, algorithm /ˈælɡəɹɪðm̩/
- Les sons « sh » et « zh »: equation /ɪˈkweɪ.ʒən/, encryption /ɪnˈkɹɪpʃən/, potentially /pəˈtɛnʃ(ə)li/, completion /kəmˈpliː.ʃən/, sheer /ʃɪɚ/
- Mots longs — placez bien l’accent: hypothesis /haɪˈpɒθɪsɪs/, potentially /pəˈtɛnʃ(ə)li/, mathematics /mæθ(.ə)ˈmæt.ɪks/, naturally /ˈnæt͡ʃ.(ə.)ɹə.li/, fundamental /ˌfʌn.dəˈmɛn.təl/
Les sons difficiles pour les francophones :
- /h/ — il se souffle, il n’est pas muet: hypothesis /haɪˈpɒθɪsɪs/, behold /bɪˈhəʊld/, harmonic /hɑɹˈmɑnɪk/
- /tʃ/ et /dʒ/ — à ne pas adoucir en « ch » et « j »: naturally /ˈnæt͡ʃ.(ə.)ɹə.li/, generator /ˈdʒɛnəɹeɪtə(ɹ)/, gigantic /d͡ʒaɪˈɡæntɪk/, exponential /ˌɛk.spəˈnɛn.t͡ʃəl/, integer /ˈɪn.tɪ.d͡ʒə(ɹ)/
- /r/ anglais — langue recourbée, sans frotter la gorge: variable [ˈvæɹ.i.ə.bl̩], verify /ˈvɛɹɪfaɪ/, encryption /ɪnˈkɹɪpʃən/, discovery /dɪˈskʌv.ɹi/, naturally /ˈnæt͡ʃ.(ə.)ɹə.li/
Comment s’entraîner avec cette vidéo
- Écoutez la vidéo en entier une fois sans parler et notez les mots que vous ne connaissez pas.
- Commencez à la vitesse 0,75×, répétez phrase par phrase, puis revenez à la vitesse normale quand cela devient facile.
- Enregistrez-vous et comparez avec l’original, en faisant attention à des mots comme solve, hypothesis, variable.
Qu'est-ce que la technique du Shadowing ?
Le Shadowing est une technique d'apprentissage des langues fondée sur la science, développée à l'origine pour la formation des interprètes professionnels. Le principe est simple mais puissant : vous écoutez de l'anglais natif et le répétez immédiatement à voix haute — comme une ombre suivant le locuteur avec un décalage de 1 à 2 secondes. Les recherches montrent une amélioration significative de la précision de la prononciation, de l'intonation, du rythme, des liaisons, de la compréhension orale et de la fluidité.