Shadowing Practice: This is Crazy - Learn English Speaking with Video
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190 sentences
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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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Vocabulary and speaking notes for this lesson
This speaking lesson is built on the video “This is Crazy”. The speaker keeps coming back to these words: exponential, polynomial, hypothesis, solve, complete. This video has 190 sentences and 2263 words to shadow. The speech runs for 11:26. The speaker talks fast, about 198 words per minute, so expect linked and reduced sounds. 84% of the words are among the 3,000 most common in English; the rest is worth studying before you start.
Key vocabulary in this video
15 words from the video worth learning, with pronunciation and meaning:
| Word | Pronunciation | Meaning |
|---|---|---|
| solve verb | /sɒlv/ | To find an answer or solution to a problem or question; to work out. |
| hypothesis noun | /haɪˈpɒθɪsɪs/ | A tentative conjecture explaining an observation, phenomenon or scientific problem and that can be tested by further observation, investigation, or… |
| variable adjective | [ˈvæɹ.i.ə.bl̩] | Able to vary or be varied. |
| satisfy verb | /ˈsætɪsfaɪ/ | To be enough (for) |
| scientist noun | /ˈsaɪəntəst/ | One whose activities make use of the scientific method to answer questions regarding the measurable universe. A scientist may be involved in original research… |
| equation noun | /ɪˈkweɪ.ʒən/ | The act or process of equating two or more things, or the state of those things being equal (that is, identical). |
| verify verb | /ˈvɛɹɪfaɪ/ | To substantiate or prove the truth of something. |
| encryption noun | /ɪnˈkɹɪpʃən/ | The process of obscuring information to make it unreadable without special knowledge, key files, or passwords. |
| discovery noun | /dɪˈskʌv.ɹi/ | Something discovered. |
| formula noun | /ˈfɔː.mjʊ.lə/ | Any mathematical rule expressed symbolically. |
| potentially adverb | /pəˈtɛnʃ(ə)li/ | In a manner showing much potential; with the possibility of happening in a given way. |
| announce verb | /əˈnaʊn(t)s/ | To give public notice of, especially for the first time; to make known. |
| mathematics noun | /mæθ(.ə)ˈmæt.ɪks/ | An abstract representational system studying numbers, shapes, structures, quantitative change and relationships between them. |
| fold verb | /ˈfəʊld/ | To bend (any thin material, such as paper) over so that it comes in contact with itself. |
| quantum noun | /ˈkwɑntəm/ | The total amount of something; quantity. |
Phrasal verbs you will hear
| Word | Meaning |
|---|---|
| figure out verb | To come to understand; to discover or find a solution; to deduce. |
| check out verb | To record the departure or withdrawal of someone or something (such as guests, employees, books, etc.). |
| fall apart verb | To disintegrate, to break into pieces. |
| go back to verb | To stem from; to originate in. |
| open up verb | To open. |
| pick up verb | To lift; to grasp and raise. |
| start off verb | To begin. |
| take down verb | To remove something from a wall or similar vertical surface to which it is fixed. |
Sentences worth repeating
Short, complete lines from the video that you can reuse in everyday conversation:
- 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.
Grammar in this video
The structures the speaker uses most, with the exact words from the video:
| Structure | In the video |
|---|---|
| Passive voice be + past participle — the focus is on what happens, not who does it | was naturally intrigued · are solved · is broken |
| Present perfect have/has + past participle — a past action that still matters now | has done · have proved · have satisfied |
| Relative clauses who / which + clause — extra information about a person or thing | GrokBot, which is · exponential, which is · time, which means |
Pronunciation to watch
The speaker uses 27 contractions and reduced forms, such as don't, we're, can't. Say them the short way, as you hear them.
- The “th” sounds: hypothesis /haɪˈpɒθɪsɪs/, mathematics /mæθ(.ə)ˈmæt.ɪks/, smooth /smuːð/, nonetheless /ˌnʌnðəˈlɛs/, algorithm /ˈælɡəɹɪðm̩/
- The “sh” and “zh” sounds: equation /ɪˈkweɪ.ʒən/, encryption /ɪnˈkɹɪpʃən/, potentially /pəˈtɛnʃ(ə)li/, completion /kəmˈpliː.ʃən/, sheer /ʃɪɚ/
- Long words — get the stress right: hypothesis /haɪˈpɒθɪsɪs/, potentially /pəˈtɛnʃ(ə)li/, mathematics /mæθ(.ə)ˈmæt.ɪks/, naturally /ˈnæt͡ʃ.(ə.)ɹə.li/, fundamental /ˌfʌn.dəˈmɛn.təl/
How to practise with this video
- Listen to the whole video once without speaking and note the words you do not know.
- Start at 0.75× speed, shadow it sentence by sentence, then go back to normal speed once it feels easy.
- Record yourself and compare with the original, paying attention to words like solve, hypothesis, variable.
What is the Shadowing Technique?
Shadowing is a science-backed language learning technique originally developed for professional interpreter training and popularized by polyglot Dr. Alexander Arguelles. The method is simple but powerful: you listen to native English audio and immediately repeat it out loud — like a shadow following the speaker with just a 1–2 second delay. Unlike passive listening or grammar drills, shadowing forces your brain and mouth muscles to simultaneously process and reproduce real speech patterns. Research shows it significantly improves pronunciation accuracy, intonation, rhythm, connected speech, listening comprehension, and speaking fluency — making it one of the most effective methods for IELTS Speaking preparation and real-world English communication.