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[Assistant] And we know that to define this process, it seems to be enough to define beta.


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[Assistant] Right? So okay, beta is here. And the only question is...


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[Assistant] Right? So this is an actual definition. Uh, the only question is, okay, if I can make sense of some statements about this process,


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[Assistant] It must be increasing, right, because here in discrete it's just a counting process. It counts the number of intersections. I mean, if I can make this picture in a sense clearer. Okay, so let us make a simple computation. Let us fix some epsilon and take the function bt squared plus epsilon squared.


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[Assistant] And apply the ETA formula to here, to this function. Uh, okay.


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[Assistant] Is that, and maybe it should be one half.


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[Assistant] Uh, lala. If it should be one half. Uh, nope, it should not. I think this is correct.


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[Assistant] Okay, so, what does it, what does it say?


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[Assistant] Okay, you can just write if the Brownian motion was started from zero, so you just write, uh, that this is epsilon plus


[User] Please transcribe this text

[Assistant] This is actually an increasing process.


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[Assistant] Well, now you have a straightforward idea, just pass to the limit when epsilon tends to 0.


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[Assistant] And here, okay, some increasing process.


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[Assistant] So there is a discussion of that in exercises, I mean in the last exercises sheet.


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[Assistant] But basically, okay, there is some technicalities just to prove, okay, there is a convergence and there is some limiting process.


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[Assistant] And, uh, again, in exercises, it's rather easy to see, I mean, it's fairly easy to see that, uh,


[User] Please transcribe this text

[Assistant] BT does not vanish on this interval. I mean, the analogy is here, again. So, I mean, here,


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[Assistant] Okay, it's clear, but here you can't, I mean in continuum, you can't just deduce it from the definition. It's not fair. So, at the end of the day, so what you have, what we have, is an increasing process LT node.


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[Assistant] Uh, which is constant on any interval.


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[Assistant] Uh, which is free of zeros of bt. And else it satisfies some properties.


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[Assistant] Okay, good. And then, so this is A. Then B. Again, this is an exercise.


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[Assistant] That, uh, this is actually can be reconstructed.


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[Assistant] This discussion already happened a month ago. It's not totally obvious, but here there is a way to prove it. And in particular it means that BT again can be reconstructed.


[User] Please transcribe this text

[Assistant] Uh, nope, not at all because, okay, that's the other way around. When BT moves,


[User] Please transcribe this text

[Assistant] No, this is just unrelated. When BT moves, this is constant.


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[Assistant] So here this process would be.


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[Assistant] No, this is not a variation. It's a sort of counting zeroes of bt. So that's something deeper.


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[Assistant] Uh, well, you have, you have like four items and exercises on all that. And let me now conclude the first half of today's lecture.


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[Assistant] Uh, well, just think again about this, I mean, the formula which is, uh, which is basically here. So let me rewrite.


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[Assistant] In a sense it was a definition of our LT node, but in fact there is another way here in exercises to define it. Okay, let's think about this for a while.


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[Assistant] And, uh, well, it quite reminds me of the formula which I just erased. Right? So, so...


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[Assistant] And here is now a term which replaces the second derivative.


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[Assistant] The second derivative was, what is the second derivative? The second derivative is the delta function.


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[Assistant] One can go, I mean, one can push this route further.


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[Assistant] And uhm, define not only the local time at zero, but the local time.


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[Assistant] Let me state it in a more formal way. Uh, so the claim is that for any, basically for any continuous


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[Assistant] There exists a family of processes LTE, increasing processes.


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[Assistant] So for this, I should write just the local time.


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[Assistant] So, this is some formula that must be thought about as a generalization of this formula. So, and it holds for any...


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[Assistant] Convex function, basically a difference of two.


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[Assistant] So if you have a convex function of f, or convex function of a single real variable, like an absolute value, or some of them, it's differentiable.


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[Assistant] Everywhere if you think about left derivatives or right derivatives. So this is the left derivative.


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[Assistant] And then the second derivative is a measure on r.


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[Assistant] So the claim is that you can always, for any semi-Martingale, and there is one half of course lost, uh, the claim is that for any, for any continuous semi-Martingale, you can do basically the same as we did for the Brownian motion at level 0. So there are increasing processes which are called, uh, local times.


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[Assistant] And you can write a generalization of the formula in this setup.


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[Assistant] Basically, the computation, the computation here, uh, proves another theorem by Levy, which I already mentioned.


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[Assistant] Starting from zero, uh, the process, the processes,


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[Assistant] And the process absolute value bt, bt node has the same distributions, has the same distributions.


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[Assistant] Thinking about the same Brownian motion, I mean, what we need is that two distributions are equal. Just think about beta


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[Assistant] Instead of, instead of B in the left hand side. So just think about...


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[Assistant] Distributed in the same way as, uh,


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[Assistant] That's what. Here I should put...


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[Assistant] Okay, let me check what exactly, just supremum of minus beta.


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[Assistant] And what I claim is that


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[Assistant] Uh, to figure it out, uh, what I'm saying is, uh,


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[Assistant] Is, uh, basically, yes, so what I'm saying.


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[Assistant] That this is the same as LT node, then I'm done. Because, right, I have this formula which relates BT and LT node.


[User] Please transcribe this text

[Assistant] If I prove that this is equal to that, then the first parts can side automatically, because I know what is the Brownian, what is the absolute value of the Brownian motion.


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[Assistant] Uh, so this is BT minus LT node. Uh, so this is the only part I need to check. And for this part I know


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[Assistant] Okay, LT node, this is an increasing process. In particular, I know that this is a supreme node over 0T ALICE node.


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[Assistant] Like this. And for, for each particular time s, I know that Ls


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[Assistant] Cannot be, I mean, it's strictly, it's greater or equal that minus, so this is minus bc.


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[Assistant] That Ls is at least minus bs, right? So this is at least, oh, is at least, yes, minus bs.


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[Assistant] Just because the difference of two is something non-negative. And to prove the opposite, uh, just say, okay,


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[Assistant] To prove the opposite, just say, okay, at the given time t, let me just consider the last time before this when bs was zero. Consider.


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[Assistant] And after that time we know that LT node did not change.


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[Assistant] Because it doesn't change on intervals free of zeros of bs. Okay.


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[Assistant] Uh, not extremely clear, just sort of an exercise to complete the picture. So, uh, what you should do is, I said, so I explained, I explained one inequality. The other inequality, just consider the last zero before t and check.


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[Assistant] It comes into, into equality. Then you know that two components coincide, and then you deduce that actually the first components coincide.


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[Assistant] Well, I don't know. In this strange color what's written is that we have bt and beta t defined on the same filtration.


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[Assistant] Moreover, this small guy is a function of the big guy. And, uh,


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[Assistant] Note that nevertheless, the filtration generated by beta is strictly less than the filtration generated by B, because this is a function of the absolute value of B. So this is something non-trivial happens, and this is not, not as simple as in the discrete coordinate.


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[Assistant] Okay, that's it for the first half. Let us have ten minutes break.


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[Assistant] Good. Uh, let us continue and this is the second half of the paragraph announced last time. So that's...


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[Assistant] After renumeration, resplitting, uh, this is called Dubin's Schwarz.


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[Assistant] Let this be a local martingale.


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[Assistant] And for simplicity, let us assume that the quadratic variation of this guy tends to infinity almost surely.


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[Assistant] So this is a random increasing process, so let us assume, uh, it tends to infinity.


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[Assistant] Actually, okay, let me comment on this.


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[Assistant] In a minute, actually, this is not of big importance. The claim is that, then,


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[Assistant] Randomly reparameterized Brownian motions. Okay?


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[Assistant] So there are two remarks. And the first remark is...


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[Assistant] A stupid one. Just a sort of a warning. The filtration, the S.


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[Assistant] So we had a process, it was defined on some filtration, and this Brownian motion, it lives somewhere, I mean, in the, in another space, here. Okay?


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[Assistant] But then what happens, so if with positive probability this limit is finite, uh, in a sense it means that here,


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[Assistant] I mean, on the Brownian motion side, what you have is a Brownian motion only until up some stopping time.


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[Assistant] And then to, to make the claim, uh, the claim correct,


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[Assistant] of probability spaces. So in this theorem this beta


[User] Please transcribe this text

[Assistant] Will be defined on the same probability space as m.


[User] Please transcribe this text

[Assistant] Is enlarging the probability space.


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[Assistant] So here it's going to be the same. You would like to have a full Brownian motion, okay? Maybe this Meritingale was just trivial, right? It was just constant zero. Not a very...


[User] Please transcribe this text

[Assistant] Interesting example. Bit boring. And the probability space was trivial.


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[Assistant] This is very straightforward. Though there is one subtle point, uh, we'll see it in a minute.


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[Assistant] So let us denote, I mean, this parameterization. So I'm going to denote this stop in time. Okay.


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[Assistant] This is of some importance, I mean, strictly greater instead of, instead of say greater or equal. Why? Because it might happen that our Mercingale MT is constant for some period.


[User] Please transcribe this text

[Assistant] Okay, like in this boring example. It's just a constant. But it might happen, okay, this is a random process.


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[Assistant] And again, there is some random set of intervals where it's used constantly.


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[Assistant] And then the claim is that, well, not the claim. Just a remark. Note that this mapping is right continuous.


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[Assistant] Here is a sample of quadratic variation.


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[Assistant] And on this picture, I already claimed something, so quadratic variation is an increasing process.


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[Assistant] Essentially, it's going to be a lemma that these intervals are the same intervals as here. But right now, okay, this is s.


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[Assistant] Well, what I'm saying is that, similarly, let us define tau s-minus, which is basically here.


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[Assistant] Provided some lemma holes, so.


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[Assistant] The set of all intervals.


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[Assistant] Is the set of the intervals.


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[Assistant] Such that the quadratic variation doesn't cross.


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[Assistant] Both are random sets of intervals. Okay?


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[Assistant] Uh, then, uh, what I would like to say is that basically there is nothing, nothing to do. So then we null from lemma.


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[Assistant] Right, because we know it's both left continuous and right continuous.


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[Assistant] For each stop in time there is a sigma algebra of everything that happens before. So, okay, this is filtration. And if you are careful with measure theoretical issues, this is actually complete filtration.


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[Assistant] Because of right continuity. Because of the definition of this tau plus. And, uh, well, moreover,


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[Assistant] Uh, Mertingale, local Mertingale, I mean, MT was a local Mertingale. Moreover, we know that there's the expectation of


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[Assistant] In this trigger. Uh, just because, what can be, what can be the problem? The problem can, could be only if beta is very big. The beta and this quadratic variation is very big. So, uh, just say, alright, this is essentially,


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[Assistant] Apply. Optional stopping tool.


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[Assistant] And then what you see is, okay, the expectation of


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[Assistant] Some mess here, let me repeat what I would like to say formally. So formally I would like to say not this. Excuse me.


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[Assistant] I would like to say that not beta s, but m, c,


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[Assistant] Min, tau, S+, is a true martian.


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[Assistant] And moreover, we know that not only this guy is a true martingale, but also it's square.


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[Assistant] Because this is again, if we know that the quadratic variation is bounded, then we know that we can, I mean,


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[Assistant] We know that this is a true martingale and this is a true martingale. And so we can apply optional stopping to the second, too.


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[Assistant] Plus. And basically that's it.


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[Assistant] Uh, well, okay. This means that the expectation of beta


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[Assistant] Oh la la, la la la la la la, and nobody corrects me.


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[Assistant] Okay, here, of course, this is also incorrect. I mean, I don't know anything about the quadratic variation of this martingale. So let us do it slowly. Okay, it was a martingale. I introduced a change of time. Right?


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[Assistant] To write this, I should write quadratic variation here, not the time itself.


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[Assistant] Right? I mean, this is a stupid statement. It cannot be true, I mean, it should be m squared minus its quadratic variation, right? And this is not the quadratic variation.


[User] Please transcribe this text

[Assistant] Okay, so it must be quadratic variation there. It must be quadratic variation here.


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[Assistant] What I say, okay, this is trivial because just by our definition it means that, okay, the expectation will be the s squared minus s.


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[Assistant] Okay, as often the difficulty is that, there is absolutely nothing deep here.


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[Assistant] And because of that it's very hard to, to, to proceed.


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[Assistant] Okay, maybe just in words. The message is that, okay, if you have a merging game.


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[Assistant] And you reparameterize it by stopping times. You still have a Mertingale. This is what optional stopping says. And the same happens with quadratic variations.


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[Assistant] The only fact is that now, instead of the quadratic variation, you have just S. This is the definition of our stopping times.


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[Assistant] Again, there is nothing deep, so first there's a set of intervals. What I'm saying is that due to continuity, continuity of processes,


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[Assistant] It is enough to check the statement for a fixed interval.


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[Assistant] You can interchange almost surely and the set of all the intervals because you can take the countable set of intervals and that's enough. Okay? And then for this, this is a trivial claim. Why? Just note that


[User] Please transcribe this text

[Assistant] Okay, another, something another, very simple. So first, note that


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[Assistant] This is obvious because we have a construction of the quadratic variation as a limit of squares of increments. So if all the increments are zeros, then this increment is zero.


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[Assistant] And, uh, for the other side, uh, just say okay.


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[Assistant] I'm Technica, let's see, introducing Martin Gale and see...


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[Assistant] Which has no, I mean, which does nothing until time u, and then starts growing, right? So, if u is small, uh, minus mu.


[User] Please transcribe this text

[Assistant] If u is small, then, uh, minus mt. Uh, minus other way around.


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[Assistant] If u is small, if t is small, then this is t and this is t. This is zero. And then it starts growing when t exceeds u.


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[Assistant] And then say, uh, okay, the quadratic variation is,


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[Assistant] This is an increment of the Mersenne-Dale series. This is a difference of two quadratic variations. And let


[User] Please transcribe this text

[Assistant] Let us introduce a stop in time, t epsilon, which is by definition the infimum of all t such that n and t exceeds epsilon.


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[Assistant] And then say, okay, we know that the expectation of


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[Assistant] On sub-subset of our probability space. Then the martingale does not change along this interval on this subset. Okay? So formally, what I should write is that for any, uh, okay, let me just try to reproduce it.


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[Assistant] What I put is n on the right end, and it is of course the expectation of n v mean z epsilon.


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[Assistant] Nothing happened. So what is, what is the role of T epsilon? This is a cutoff to use, I mean, to work with true martingales. If I'm on the event A, then T epsilon exceeds V, I mean.


[User] Please transcribe this text

[Assistant] On this interval, the quadratic variation does not grow, so it starts growing later. So this is that. And this is the expectation, uh, well this is...


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[Assistant] Obviously less than expectation of.


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[Assistant] Does the square of the martingale stop there? And this is the expectation of the quadratic variation stopped at this time. And this is less than epsilon.


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[Assistant] I mean, some trivial estimates, but again, in words, what is the point? The point is that we know that the expectation of the square of the Mertingale is the expectation of the quadratic variation. So if we know that on some subset quadratic variation does not grow, it should tell us that


[User] Please transcribe this text

[Assistant] The conditional expectation on this subset of N squared is zero.


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[Assistant] Okay, here is, is the formal proof. So you see that this guy is less than epsilon and then you send epsilon to zero.


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[Assistant] So, again this lemma is here.


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[Assistant] Well, it is something to do, but it boils down to the identity, the expectation of the square. Mercingale is the expectation of its quadratic variation.


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[Assistant] Okay, so, uh, this is the theorem.


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[Assistant] And, uh, the last piece for today.


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[Assistant] Which is of the very much same spirit. So imagine now that we are in 2D. And let


[User] Please transcribe this text

[Assistant] We have the two-dimensional Brownian motion.


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[Assistant] Uh, do I need a notation for this point? Start with that.


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[Assistant] Some point in the domain. Here it is.


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[Assistant] Constant is too boring. So I do not assume it is one to one. Just any analytic function in this, in this domain. Okay? So it maps.


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[Assistant] And maybe let us assume that it is analytic and continuous up to boundary.


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[Assistant] Okay, for simplicity, let it be continuous up to boundary.


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[Assistant] You can always slightly shrink your domain if needed. I mean, this is not, not a big price. And this is an exit time.


[User] Please transcribe this text

[Assistant] And then what I'm saying is that, okay, if you think about the,


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[Assistant] What you see is another trajectory of the Brownian motion. Then.


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[Assistant] There exists a Brownian motion bs, beta s.


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[Assistant] Distribute it in the same way as, uh,


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[Assistant] Integral zero, see?


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[Assistant] What should be the variable? It can be s, r.


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[Assistant] So, this is a very much spirit. What I have here is again a Brownian motion, but with a reparameterized time. And here...


[User] Please transcribe this text

[Assistant] Is the explicit formula for this reparameterization. That's the message of this here.


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[Assistant] I see some trajectory of another Brownian motion in the right hand plane, uh, well, probably until some time.


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[Assistant] Remark, imagine that you actually have a conformal mate. Imagine.


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[Assistant] Okay, it is analytic and one for one.


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[Assistant] Some domain there, this is path. Then you can apply this theorem in both directions.


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[Assistant] If I just think about the geometric trajectory of the two-dimensional Brownian motion, then the picture I see here, distribution of trajectories, is exactly the picture I see there, in terms of distributions of the trajectories.


[User] Please transcribe this text

[Assistant] In particular, all the quantities, all the quantities of a sort like, what is the probability that we hit some space in this domain, okay, here and there, up to conformal transform.


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[Assistant] I should say that's it. So, let us make it, but... Let...


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[Assistant] Right? Because it's an analytic function and it's real part imaginary, a harmonic function. So, because of that I know that dbc and dbc are local merges.


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[Assistant] We solved this example, I mean, this is true in any RD. Okay? Okay, let us now...


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[Assistant] Compute. Uuuh, what is D?


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[Assistant] Okay, what I should do? First there are some, uh, diffusion terms. So what are them?


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[Assistant] Bt1 is the first component. Plus, uuuh prime.


[User] Please transcribe this text

[Assistant] Some second derivatives, so what are the second derivatives?


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[Assistant] Well, this is, I should take another derivative in x of that. Right, so what's that?


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[Assistant] See, and there is no one half because it's killed in data for, in datas for.


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[Assistant] And what you see is u' squared, u' squared, so this is f' squared. So all together.


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[Assistant] Everson is computed at this point. V check.


[User] Please transcribe this text

[Assistant] Similarly, if you, if you do exactly the same computation for the second function, you see something dv in some local martingale part, plus the same drift.


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[Assistant] Uh, is, uh, v prime x. So what's written is actually u prime x squared plus v prime x squared. So this is f prime squared.


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[Assistant] Yeah, well, anyway, this is just a computation. I mean, if the claim is true, which we heard many times, right, then it must work.


[User] Please transcribe this text

[Assistant] There's just no, no way, uh, for this to break down.


[User] Please transcribe this text

[Assistant] Okay, good. Now what I'm saying is that, okay, I have now two local martingales, and, uh, what I know is that the quadratic variation of the first is given by the integral of that, the quadratic variation of the second is given by the integral of that, and the bracket is zero.


[User] Please transcribe this text

[Assistant] And now this is exactly the same situation as we had in the previous theorem.


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[Assistant] So what we will see is that, okay, now there are two martingales, uh,


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[Assistant] Of course, it should be said that there is absolutely no surprise in this result. So.


[User] Please transcribe this text

[Assistant] As we know that the harmonic function, I mean any harmonic function of the two-dimensional Brownian motion is a Mersingale. So it's a huge amount of information, right? Probably it's enough to reconstruct


[User] Please transcribe this text

[Assistant] It should be enough to claim that trajectories of the Brownian motion is also conformally invariant. And, uh,


[User] Please transcribe this text

[Assistant] Uh, maybe the last remark on the blackboard. Just an example.


[User] Please transcribe this text

[Assistant] So here it was, it was a conformal mapping, but actually,


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[Assistant] To have something interesting, I mean, it's often useful to consider not one-to-one mappings, but something more general.


[User] Please transcribe this text

[Assistant] Here we have the full plane, and here we have


[User] Please transcribe this text

[Assistant] So what I'm drawing is that the horizontal line, horizontal lines on the left picture, they,


[User] Please transcribe this text

[Assistant] Then I'll raise the right picture and, uh,


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[Assistant] Impressionistic style. Okay, if it was here or that. It's another color, so on so forth.


[User] Please transcribe this text

[Assistant] Exactly the response to wheezing round.


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[Assistant] The number of full turns, for instance, you make until something happens, then on the left hand side, this is a much easier question.


[User] Please transcribe this text

[Assistant] So, it's just an idea that of course there are many, many conformal transforms. And what the last theorem claims...


[User] Please transcribe this text

[Assistant] Of the Brownian motion in 3D, which can be used to compute quantities. Right? Clear?


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[Assistant] Okay, good. And let me then, I'll then conclude by sort of a general, general remark, so we still have one more lecture.


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[Assistant] And then we have two, somehow two.


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[Assistant] Different worlds. The first is lattices, random walks, something like that. The second is continuous limit.


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[Assistant] And in the continuous limit what we now constructed is the Brownian motion and we now have tools to compute things for that.


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[Assistant] Right? What is the advantage? The advantage in continuum is that there are much more symmetries. Much many symmetries. And this allows to perform computations.


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[Assistant] So that's exactly similar to, for instance, usual integration.


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[Assistant] So integrals are about sums, right? So it's about computing sums. But the number of tools, the toolbox in continuum,


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[Assistant] It's much larger because you can perform change of variables, you can do integration by parse. Okay, this is already indiscreet, but.


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[Assistant] You know, it's just, it's just very useful language. This is exactly the same.


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[Assistant] On the other hand, what is also very good to have in mind is that when we speak about some phenomenon in continuum,


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[Assistant] It might be always very helpful to have a sort of a discrete cartoon.


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[Assistant] That's what I tried to show you in the first half, when it was a discrete cartoon for the local type, that there is some complicated concept.


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[Assistant] So I just wrote this integral of sine bdb. What's that?


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[Assistant] Is there any signs of this?


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[Assistant] All issues of such kind, uh, might be simpler to understand.


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[Assistant] Well, okay, that's morally the same story happens with the models we are trying to investigate, uh, in our research. I mean, so we have some models on lattices or something like that, we have some conjectures for their limits, and we try to make this correspondence work.


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[Assistant] Try to prove that indeed this converse to that. Try to infer quantities in continuum. What are the natural quantities in continuum from thinking about what are natural quantities in discrete.


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[Assistant] Okay, that's a sort of a philosophical comment, sorry for this, and that's it for today.


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[Assistant] 是的,我想要按摩,我最近肌肉十分酸痛。


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[Assistant] 不过你如果今天购买十次的话,只需付八千元。


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[Assistant] 我有听过,不过从没试过。 泰式按摩是什么?


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[Assistant] 我需要做臉部保養並諮詢一下美容師的意見。


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[Assistant] 你们有做脸部保养吗?价钱大概多少?


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[Assistant] Lian bu qīn jié hòu, wǒ huì bāng nǐ chú qù liǎn shàng lǎo hòà de jiǎo zhí.


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[Assistant] 你的指甲看起来非常健康又漂亮。你要上指甲油吗?


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[Assistant] 我不知道要选哪一个颜色,哪个颜色适合我。


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[Assistant] Today we will work on writing. In the first two lessons we learned how to build an essay and then how to make it better with extra details. Today we will look at some new photos and practice some more. So grab your notebook and pencil and let's get started.


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[Assistant] This is a city park. There are many people in the park today.


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[Assistant] Behind them there is a boy and a girl chasing a brown dog. They look really happy.


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[Assistant] There is one lonely boy sitting on the dock. He is playing with a small toy boat. I think he is sad. Hmm.


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[Assistant] Here is your picture. I will give you four minutes to write your essay. After four minutes, I will write an example for you to check yours. You can post your paragraph in the comments section of the video and I will check it for you. So go ahead and start.


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[Assistant] There is a mother and her two children under the birdhouse. They are on a picnic. They are having fun feeding the geese. In the middle there are four kids playing soccer. The goalie is scared to try and catch the ball. The boy that kicked the ball hopes it will score. It's an exciting game.


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[Assistant] This looks like a city bus. There are lots of students from the school riding the bus today. I think they are going home.


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[Assistant] In the first row, there are two boys sitting together. I don't think they are friends. The boy on the left looks uncomfortable. The boy to the right is sitting too close. There is also a boy sitting behind them.


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[Assistant] There it is, there it is, that's a great guess. I mean, that's a great guess, but completely wrong. And I'll tell you why. If you're looking at the clues, ray of light, there's a singer that we all know.


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[Assistant] There also had a song, Frozen, of the same name. And little known fact, I used to run into Madonna like almost every other day at hot yoga in Sherman Oaks. Oh my god, you have never experienced life unless you have done a downward dog with Madonna. So!


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[Assistant] Oh, I'm glad you asked. There was like a tiger on the bed. I mean, there was like a, a king. She would, you know, Tiger King. Everyone knows her from Big Cat Rescue. You know, what do I think it is? Who? Carole Baskin. I think it's Carole Baskin. What? What is wrong with you people? Stay, well, stay with me.


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[Assistant] I'm a warrior. I'm a fighter. I fight for my clues. You know, I just always believe in myself, even when no one else does. So in the clue package, there was so much gold. There were gold medals in that house. There was water in that house and just stay with me.


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[Assistant] One and one for Michael Phelps. Hey, Michael Phelps is the buster rhymes of his day in swimming.


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[Assistant] This honestly reminds me of my favorite singing comedy duo. They're in all the Christopher Guest movies. There was a Rose in the package and the last name of the family in their most recent show is Rose. So I think this is Eugene Levy and Catherine O'Hara.


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[Assistant] Thank you, Nick, but now, I honestly can't get my head out of this being an Olympic gold medalist. In the clue package, there's so much gold in that house. Michael Phelps holds the record for the most ever gold medals. There's no reason that this can't be Michael Phelps.


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[Assistant] So Dennis, this plant here is called ocotillo. These leaves might make you upchuck, lose moisture, and get sick. So we're gonna go for the flowers. There you go. So go ahead and try one of those. Chew that and tell me what you think of it.


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[Assistant] There's a little bit of honey in there, a little floral, a little bit of orange. The only bad taste you might get if there's an ant in there. Crazy ants taste like rotten blue cheese.


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[Assistant] This is a striped-tailed scorpion. Look, he's trying to sting me. And I better be very careful. I better try to get that stinger off there. Because boy, he's gonna give me a full dose of venom.


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[Assistant] So let's cook it up by a fire later if we're lucky enough to make it by twirling sticks together, which is no easy thing.


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[Assistant] How about we learn some desert foods that maybe you could have eaten during your ordeal?


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[Assistant] And that scorpion, we'll watch as it turns color and maybe shrivels a bit. And how do you know when this is cooked? It's kinda like a shrimp, right? Where it's translucent, it's gonna go to pink. No sushi here. We're gonna overcook it. Just in case there are intestinal parasites and such.


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[Assistant] Sweet. So hey guys, I think the scorpion's been in there long enough. So what we're gonna do is section it up. Do you fancy a tail, a head, a claw? What do you like? You know what, I'll do the tail. It's hot.


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[Assistant] Picture in the head, best part. Alright, bottoms up. Enjoy, Dennis.


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[Assistant] Chapter 1 The Body 1999 A group of five climbers


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[Assistant] Move slowly across the north face of Everest.


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[Assistant] One of them sees something strange on the rocks below him, something whiter than the snow. Carefully, he climbs down towards it. Then he calls his friends on his radio. Come down here, he says. Look at this. Coming closer, they see it is the dead body of a climber.


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[Assistant] The wind has blown some of the clothes from the body and the skin is clean and white like new stone. In the icy cold it looks like the body of a man who died a few days ago.


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[Assistant] But the bits of clothes that are still on the body are old, brown and grey.


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[Assistant] Nothing like the brightly coloured clothes that modern climbers wear. The body is lying face down. Above the head, the fingers of one hand are dug into the icy ground.


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[Assistant] One leg is broken in two places below the knee, and the other leg is lying over it. The body looks strong and healthy, they think, like the body of a runner or dancer. The climbers photograph the body carefully. Then, very gently, they touch the dead man's clothes, the hobnail boots, the trousers and shirt made of wool.


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[Assistant] How little he was wearing, they think, on this icy cold mountain.


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[Assistant] I walk out on the street in Seattle with more clothing than he had on, one of them says. Yet here they are.


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[Assistant] At 8,155 meters on Mount Everest, the highest mountain in the world. Who is this man? He can only be one of two people, they think. But which one? Then, they find a name inside his shirt.


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[Assistant] George Lee Mallory, it says. But who is George Lee Mallory? Why are these climbers so interested in him? How did he die? And what happened to him before he died? Where is his friend, Andrew Irvine? And the most important question of all, was this man, George Mallory,


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[Assistant] The first man to reach the summit of Everest.


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[Assistant] Chapter 2. Dangers. The climbers do not stay long with the body.


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[Assistant] Because Mount Everest is one of the most dangerous places in the world.


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[Assistant] At four thousand meters, it is harder still. And at five thousand meters, most people begin to feel ill. They get headaches, feel tired, and breathe quickly all the time, like someone who has run a long way. In 1921, when Mallory first went to Everest,


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[Assistant] No one had climbed a mountain higher than 7500 meters. And many people did not think it was possible. If climbers don't have enough oxygen,


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[Assistant] They'll be too tired to climb, they said.


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[Assistant] And they won't be able to think clearly either. So they will make stupid mistakes, forget to eat and drink, or talk to people who are not there. Perhaps they'll die. But the need for oxygen is not the only problem on Everest. There is also the weather. Almost every week


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[Assistant] There are winds of a hundred or even two hundred kilometres per hour. It is difficult to walk or even stand up in these winds.


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[Assistant] The wind can blow climbers off the edge of the mountain, thousands of meters to the valley below.


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[Assistant] Climbers sometimes sit in their tents for days, unable to sleep because of the noise.


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[Assistant] And afraid that the wind will blow their tents away. And then there is the cold.


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[Assistant] Temperatures on Everest often fall below minus 20 degrees Celsius. But the wind makes that feel much colder. But before anyone can climb Everest, they have to get there. Tibet, in China, is to the north of Everest. And Nepal is to the south. And, until 1950,


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[Assistant] Nepal refused to let any foreign climbers enter their country.


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[Assistant] So the earliest climbers, like Mallory and Irvine, had to get to Everest from the north, through Tibet. And that was not easy at all.


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[Assistant] Chapter 3 Through Tibet to Everest 1921


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[Assistant] Until the early 19th century, nobody in the West knew about Mount Everest. People in Tibet knew, of course. They called it Chomolungma, goddess mother of the world. And to people in Nepal, it was Sagamatha, goddess of the sky.


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[Assistant] But no one in Tibet or Nepal had ever climbed the mountain.


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[Assistant] They thought that was a very strange idea.


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[Assistant] And no foreign person had ever been so far into the Himalayas.


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[Assistant] But in the 1830s, a British soldier, called George Everest, was making maps in North India.


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[Assistant] He made the first maps of the Himalayas and measured the height of some of the mountains.


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[Assistant] But Everest finished his work in 1843 and he never saw Chomolungma.


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[Assistant] The first British man to see the mountain was Everest's friend, Andrew Waugh.


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[Assistant] In 1852, Radhanath Sikdar, who worked for war,


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[Assistant] War said that this was the highest mountain in the world.


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[Assistant] He gave it the name of his old friend, George Everest in 1865.


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[Assistant] But very few British people were able to enter Tibet or Nepal at that time. So it was not until 1921 that the first British expedition


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[Assistant] Went to see if it was possible to climb the mountain. There were nine British climbers on this expedition, and one of them was George Mallory.


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[Assistant] To get to Everest, the climbers had to walk 500 kilometers through Tibet. Their Tibetan porters carried everything they needed. Food, tents, clothes, cameras, and climbing equipment. It was a long, difficult journey, which took a month. They were always climbing. At first, through river valleys with tall trees.


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[Assistant] Colorful flowers and birds. Then,


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[Assistant] On to a wide stony place where nothing grew. There was no sound except the wind. And all the time, the air was becoming thinner.


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[Assistant] The climbers walked past Tibetan villages high up on the sides of mountains and came to Rongbuk, the highest monastery in the world.


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[Assistant] Was to go up the East Wrong Book Glacier.


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[Assistant] From there, they planned to climb to the North Coal.


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[Assistant] A small, flat place on the north ridge of Everest. By this time, it was late in the year, and the winds were getting stronger. They had not planned to get to the summit this year, but only to look for a way up.


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[Assistant] But on the 23rd of September, 1921, Mallory, with two other climbers and three porters,


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[Assistant] When they reach the snow ridge of the North Coal, the next day, they could see the summit, one thousand eight hundred meters above them. But at seven thousand meters, it was difficult to breathe, and they moved slowly.


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[Assistant] And they could hardly stand up in the strong, icy winds. They would have to go down and come back next year.


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[Assistant] Chapter 4, The First Attempt, 1922. In 1922, a larger expedition returned. They brought oxygen with them this time, but the equipment was very heavy, and it did not always work.


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[Assistant] Many of the climbers wanted to climb the mountain on their own, if possible without help. So climbing with oxygen was not popular with most of the climbers.


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[Assistant] Four climbers set out on the first summit attempt. Mallory, Moorshead, Norton and Somerville. With five porters.


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[Assistant] They left camp four on the north col at seven a.m. There was a terrible cold wind and the climbers moved slowly.


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[Assistant] Cutting steps in the snow for the porters behind them.


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[Assistant] They hoped to reach 8,230 meters that day.


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[Assistant] They were too cold and tired to go on. They found a place for Camp 5 and the porters left their loads here and went back down.


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[Assistant] They had to melt snow over a small cooker, which took a long time. Next morning, Morsehead was ill.


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[Assistant] So Mallory, Norton and Somerville set out at 8am, leaving Moor's Head alone in the tent. They moved slowly.


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[Assistant] Stopping after every few steps to rest and breathe.


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[Assistant] As they climbed, their hobnail boots slipped dangerously on the stones and rocks.


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[Assistant] In the thin air, they felt tired.


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[Assistant] More tired than any of them had ever felt before. At 2 p.m., they reached 8,227 meters.


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[Assistant] They were the Australian, George Finch, a Gurkha called Tejbir Bhura, and Geoffrey Bruce, a young man who had never climbed before. Unlike the first group, Finch and Bruce liked using oxygen. They made a new Camp 5, 150 meters higher than Mallory's. But then they were caught in a storm.


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[Assistant] To 8,323 meters. But here, Bruce became exhausted and had to be helped down. Because the oxygen had been so successful, Mallory, Somerville, and a third climber, called Colin Crawford, decided to make another attempt, this time with oxygen.


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[Assistant] But while they were climbing across a snow slope, there was a sudden avalanche. Everyone was buried under the snow.


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[Assistant] All the climbers and seven porters managed to climb out. But seven porters were killed. It was clear that Everest had won. This time.


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[Assistant] Chapter 5, Saving the Porters, 1924.


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[Assistant] The British climbers returned in April 1924. This time, they planned to succeed. Edward Norton


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[Assistant] The porters carried equipment up to Camps 1 and 2 on the Wrong Book and East Wrong Book glaciers.


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[Assistant] One woman carried her two year old child on top of an 18 kilogram load.


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[Assistant] From 5,300 meters to 6,000 meters. Then she carried her child back down and offered to go up again. The next part was harder.


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[Assistant] On a cold stormy day, Mallory, Irvine, and two other climbers set out with 20 porters.


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[Assistant] To carry equipment from base camp to camp three. But the weather was terrible.


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[Assistant] A strong wind blew down off the mountain straight into their faces. The ice on the glacier was as clear and hard as glass. There were not enough tents at Camp 2, so some of the porters slept outside. Next morning, they went on to Camp 3.


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[Assistant] But here, it was even colder than before. That night, the temperature fell to minus 29 degrees Celsius.


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[Assistant] The strong, icy wind blew into the tents all night.


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[Assistant] So everyone inside the tents was covered with snow.


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[Assistant] The storm blew for two more days. Many of the porters lay in their tents, not caring about life or death. At last, the storm ended.


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[Assistant] On the 15th of May, all the climbers and porters went down the valley to the Wrong Book Monastery, where the chief monk said prayers for them. Next day, the wind had gone, and the sky was clear and blue. The climbers returned to Camp 3,


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[Assistant] Then, they started to climb up the steep ice wall to the north col, to make camp four. And, once again, things went wrong.


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[Assistant] The ice was covered with new snow after the storm. There were many crevasses, deep holes in the ice, which were difficult to see under the snow.


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[Assistant] This was the place where seven porters had died in 1922. This time, four people set out. Mallory, Norton, Odell, and Lapka Tsering. They climbed carefully, cutting steps in the snow. They crossed several deep crevasses. Then, just below the North Coal, they came to a steep slope


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[Assistant] About a hundred meters high. It was a dangerous place.


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[Assistant] The slope was covered with new soft snow At the foot of the slope was a wall of ice


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[Assistant] Falling hundreds of meters to the valley below. Mallory climbed slowly up the slope, while Norton and Odell held him from below on a rope. After half an hour, they reached the top and found a place for Camp Four. But all the climbers were tired. On the way down,


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[Assistant] The snow suddenly collapsed under Mallory's feet and he fell into a crevasse. Only his ice axe across the top of the crevasse saved him. No one had seen him fall. He looked up at the sky, then down into the deep blue hole below him. One mistake here could mean death.


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[Assistant] He pulled his tired body up the ice wall and out onto the snow. When the climbers got back to Camp 3, they were all exhausted. Their heads ached, and they coughed all night in the thin, cold air. Next day, three more climbers, Somerville, Irvine, and Hazard,


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[Assistant] And the temperature fell to minus 31 degrees Celsius. The exhausted porters shivered in their tents. All next day, Norton, in camp three, waited for them to come down. At last, he saw them coming. Black dots on the snow.


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[Assistant] But only eight porters and Hazard arrived at Camp 3. Four porters had turned back, afraid that they would fall. So now, four porters were alone at Camp 4, and more and more snow was falling.


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[Assistant] Making the steep slope more dangerous than ever. Without help from the climbers, the porters would die. All the climbers were tired and ill. Mallory and Somerville had bad throats and were coughing badly. It snowed heavily all night. But next morning


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[Assistant] Norton, Mallory and Somerville.


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[Assistant] Climbed slowly up towards camp four. It was difficult, dangerous work. They reached the snow slope and called out to the porters above them in words like these. Are you alive? the climbers asked. Can you walk? Yes, sir, a porter answered. But we're afraid.


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[Assistant] It's too dangerous. If we slip, we'll fall and die. If you stay there, you'll die of cold, Norton said. Wait there. We're coming to get you. Very carefully.


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[Assistant] Somerville climbed across the steep slope towards the four porters. He had a rope round his waist. Mallory and Norton held the rope from below to keep Somerville safe. But when he was five metres away from the porters, Somerville reached the end of the rope. What do I do now? he thought. We have no more rope.


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[Assistant] And it will soon be dark. Come across! He called out to the porters. It's not far. Carefully. One at a time.


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[Assistant] The first two porters reached Somerville safely. Then they climbed past him, holding the rope towards Norton and Mallory. Somerville looked at the last two porters. Come on, he said. It's not difficult, one at a time. But the porters were afraid and both started together. A second later,


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[Assistant] They slipped and fell. They slid past Somerville down the slope, towards the valley, thousands of meters below. But then, a few meters from the edge of the slope, they stopped. Don't move, Somerville said. Just wait for me.


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[Assistant] Somerville climbed down until he could just reach the men with his other hand. He pulled up the first man, then the second.


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[Assistant] They climbed along the rope to Mallory and Norton.


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[Assistant] Somerville tied the rope round his waist again and climbed back after them. Even now they were not safe. It was nearly dark and a long way above Camp 3. One of the porters, Namkir, could not use his hands because he had bad frostbite. But at last they reached Camp 3.


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[Assistant] Where two more climbers, Noel and Adele, were waiting with warm food. All the climbers were exhausted.


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[Assistant] Mallory and Somerville could not stop coughing, and Norton's feet hurt badly.


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[Assistant] Helping the four porters had made them very, very tired. And they were nowhere near the summit of Everest. Slowly, they went down to Camp One. They needed time to rest and to decide what to do next.


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[Assistant] Chapter 6 Somerville and Norton 1924


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[Assistant] Norton decided that two pairs of climbers would try to reach the summit without oxygen.


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[Assistant] Mallory and Geoffrey Bruce would go first.


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[Assistant] And Norton and Somerville would follow the next day.


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[Assistant] The climbers would find a place for Camp 5 above 7,600 meters. And for Camp 6.


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[Assistant] At 8,231 meters, Adele and Irvine would go up to Camp 4 to help the climbers when they came down. On the 1st of June, Mallory and Bruce climbed up to Camp 4 with nine porters. The next day was clear and sunny, but above the North Coal


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[Assistant] They met a terrible icy wind. It was difficult to stand. Hardly possible to walk.


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[Assistant] Only five porters continued with Mallory and Bruce.


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[Assistant] They found a place for two small tents on a steep slope.


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[Assistant] All that night, they shivered in their sleeping bags.


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[Assistant] Only one porter was able to go on. Sadly, they decided to come down. As they went down, they passed Norton and Somerville, with four more porters coming up. These men reached Camp 5 and spent a better night there. The wind was less strong, and they managed to cook, eat, and sleep.


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[Assistant] And in the thin air, with no oxygen, it was difficult to move.


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[Assistant] Three porters, Napu Yishay, Lapka Chedi, and Semchumbi, were ready to go on. They climbed on.


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[Assistant] Up to 8,170 metres, higher than any man had been before. Here, at 1.30pm, they put up one tiny tent, Camp 6. Then, the porters went down to the North Coal.


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[Assistant] While Norton and Somerville got ready for the night. As it grew dark, they wondered


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[Assistant] Can a man sleep without oxygen at this height? Yes. It was the best night since I left Camp One, Norton wrote.


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[Assistant] So at 6.45 next morning, the two men set out for the summit.


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[Assistant] They climbed slowly, taking three or four breaths for every step. They stayed a little below the ridge to keep out of the wind. But in the shadow of the mountain, out of the sun, it was very cold. Norton shivered all the time, and he was having trouble with his eyes. Somerville coughed a lot.


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[Assistant] And his bad throat made it difficult to breathe.


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[Assistant] By midday, they were at 8,536 meters. The view was wonderful.


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[Assistant] They were above the clouds with a sea of mountains below them. But Somerville was exhausted. His throat was worse. He could hardly breathe. So Norton went on alone.


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[Assistant] He was moving more and more slowly on a steep slope like the roof of a house. There were large stones and soft snow under his feet. It was easy to fall. And below him


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[Assistant] 2,743 meters straight down, in the thin, clear air, was the East Rhongboog Glacier and Camp 3. He looked up.


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[Assistant] He was about 275 meters below the summit, but they were vertical meters, meters measured up the mountain, not along it. But he was tired and moving very slowly and his eyes were getting worse. Sometimes he saw two ice axes in his hand, not one.


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[Assistant] He knew that it was possible. He could get to the summit. But he could not get back.


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[Assistant] Norton was nearer the summit than any man before him.


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[Assistant] He decided to turn back towards Somerville. It was the right thing to do. Halfway down to Camp 5, Somerville stopped. There was something in his throat. For nearly a minute, he could not breathe at all. Then, he coughed up a ball of blood and could breathe again. When they reached Camp 4,


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[Assistant] Norton could not see at all. Chapter seven, Mallory and Irvine, 1924. But to Norton's surprise, there were two more climbers at Camp Four, Mallory and Irvine. Mallory had decided to try again, with oxygen this time. Irvine was young,


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[Assistant] But he understood the oxygen equipment better than anyone. So Mallory decided to climb with him. On the 6th of June, they set out for Camp 5. Eight porters carried food and oxygen. Next day, they went on to Camp 6 with four porters. There,


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[Assistant] Asking him to wait at camp four the next evening. The weather was fine, he said. But the oxygen was very heavy to carry.


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[Assistant] Adele was climbing alone, without oxygen.


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[Assistant] He spent the night at Camp 5 and then climbed up towards Camp 6.


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[Assistant] At 7,900 meters, he found some very old rocks. Studying rocks was Odell's job, and the rocks that he found showed him that Everest had once been under the sea.


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[Assistant] At twelve-fifty p.m., the clouds cleared above him, and he could see the summit ridge of Everest. High on the ridge, he saw


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[Assistant] Two tiny black dots moving on the snow. They climbed quickly to the top of a rock step near the summit. Then the clouds came back and they disappeared. It was Mallory and Irvine climbing strongly towards the summit. But Odell thought they were a little late.


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[Assistant] Was there enough time for them to get to the summit and then down to Camp 6 that night? He climbed up to Camp 6 and left some food for them in the tent. Then he climbed higher towards the summit, calling out for them. But no one answered. He wondered what to do. He wanted to stay.


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[Assistant] But the tiny tent at Camp 6 was too small for three men. So, at 4.30pm, he went down. By 7pm, he was in Camp 4. The next day was the 9th of June. Odell was worried. When he looked up the mountain, he could see the tents of Camps 5 and 6, but nothing


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[Assistant] And nobody was moving. So Odell with two porters climbed up again to Camp 5. There was a strong wind all night. The porters shivered in their tent. And next morning they refused to move. So Odell went on alone up to Camp 6.


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[Assistant] But no one was there. The tent was closed. The food was still there. Mallory and Irvine had disappeared.


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[Assistant] For two hours, Odell climbed on, above Camp 6, towards the summit. What was he thinking? Mallory and Irvine were probably dead. But perhaps, just perhaps, one of them was still alive, badly injured up there. Perhaps he could see something, or find something,


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[Assistant] He put them on the snow in the shape of a T. It was a message to the others, far below, that Mallory and Irvine were dead. But what happened to them?


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[Assistant] Did they reach the summit before they died? Or did they turn back, like Norton and Somerville? No one knows. When Odell last saw them,


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[Assistant] It was already 12.50 in the afternoon. But they were moving quickly, he said. So perhaps they went on to the summit.


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[Assistant] And then were too tired to find Camp Six before dark. Perhaps in the darkness one of them fell and the other died trying to help him. Perhaps they both fell together. Or perhaps with no more oxygen


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[Assistant] They were just too cold and tired to move anymore and lay down in the snow to sleep. It was 75 years before some of these questions were answered.


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[Assistant] Western climbers could no longer enter Tibet, but they could enter Nepal.


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[Assistant] Went to the southern side of Everest, for the first time.


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[Assistant] And in 1952 a Swiss climber called Raymond Lambert made an attempt on the summit with Tenzing Norgay.


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[Assistant] Tenzing was one of the Sherpa people of Nepal who are excellent climbers and know the mountains well.


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[Assistant] Together Lambert and Tenzing almost reached the summit. But their oxygen equipment was not working well.


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[Assistant] The Norton had gone in 1924. They turned back.


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[Assistant] In 1953, John Hunt came to Kathmandu, the capital of Nepal, with a large British expedition. Tenzing Norgay joined them here.


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[Assistant] And the expedition set out for Tiangboche, a monastery south of Everest. The walk took 17 days.


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[Assistant] They were joined by two New Zealand climbers, Edmund Hillary and George Low.


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[Assistant] The climbers spent three weeks at base camp.


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[Assistant] Getting used to the thin mountain air.


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[Assistant] Was to find a way up the Kumbu icefall onto the Kumbu glacier.


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[Assistant] The Khumbu Glacier is a slow moving river of ice, and the Khumbu Icefall


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[Assistant] Is a large wall of broken ice.


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[Assistant] This icefall is over 300 meters high.


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[Assistant] Six times higher than Niagara Falls. And the ice in it moves very slowly all the time.


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[Assistant] There are pieces of ice as big as houses which could fall on the climbers' heads at any moment.


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[Assistant] There are avalanches of ice that could kill a man in a second.


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[Assistant] Terrible crevasses go hundreds of meters down into the blue-green darkness under the climbers' feet. Sometimes the climbers heard ice moving far below them. The climbers and sherpas


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[Assistant] Carried loads of over 18 kilograms up this difficult route.


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[Assistant] They made Camp 2 halfway up the icefall.


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[Assistant] And camp three, at the top of the ice form.


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[Assistant] They climbed up the glacier to Camp 4.


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[Assistant] The next big problem was to climb the Lotse Face to the South Col. High above Camp 5 is the Mountain of Lotse, 8,500 meters. To the left of Lotse is the South Col of Everest.


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[Assistant] The first 600 meters of the Lotzi face is a steep slope of ice. The Lotzi glacier.


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[Assistant] This ice is very difficult to climb with many ice walls and deep crevasses.


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[Assistant] For eleven long days, the New Zealander George Lowe and the Sherpa Anulu


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[Assistant] Fought their way up this wall of ice. All the way they cut steps in the ice.


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[Assistant] And fixed ropes for the others to follow them.


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[Assistant] They made Camp 6 at 7010 meters. And Camp 7.


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[Assistant] But on the 21st of May, Anoulu and Wilfred Noyce


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[Assistant] Finally managed to cross the difficult snow slope.


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[Assistant] And seventeen Sherpas followed them up to the South Col.


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[Assistant] The Sherpas had only a cup of tea for breakfast at Camp 7 after a long, cold night. They were carrying loads of 22 kilograms with no oxygen. At the South Col, they made Camp 8. Then, the same day, they went down again to Camp 4. They had climbed


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[Assistant] For 10 hours with no food or drink all day.


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[Assistant] But Camp 8 on the South Coal was ready at last. Now the attempt on the summit could begin.


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[Assistant] The first two summit climbers, Tom Baudillon and Charles Evans,


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[Assistant] Set out from camp four to the south coal. John Hunt and two Sherpas went with them carrying heavy loads. Using oxygen,


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[Assistant] The three British men reached the col first, but they were very tired. And when they took off their oxygen equipment, they could not think clearly. It took them over an hour.


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[Assistant] Then John Hunt and the Sherpa Denamgiel set out to climb higher. They both had oxygen and were carrying about 20 kilograms. They moved very slowly and Bordelon and Evans soon came past them. Hunt and Denamgiel both had problems with their oxygen. Sometimes ice


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[Assistant] Stopped it working, and it was very difficult to breathe.


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[Assistant] On they went, more and more slowly.


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[Assistant] At 8,338 meters, Hunt and Anamgyal could go no further. They put down their loads and turned back. When they reached the South Coal, they could hardly walk.


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[Assistant] This was their one chance to get to the top. But was it safe? Or would they die? Like Mallory and Irvine before them. They stood and looked and thought. Evans had already had trouble with his oxygen. Baudelon had fixed it.


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[Assistant] They thought it would take three hours to reach the summit.


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[Assistant] And they would have to climb down another 900 meters without oxygen to Camp 8. It was too far. So sadly they turned back, but it was the right thing to do. The wind grew stronger and clouds came up. It was difficult to find the way. They were very tired.


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[Assistant] And several times, they slipped on the way down.


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[Assistant] At one point, Evans slipped and fell.


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[Assistant] He slid past Boodylon like a bullet and pulled him off his feet. A moment later, they were both.


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[Assistant] Sliding down the snow towards the glacier, thousands of feet below.


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[Assistant] Quickly, Bordelon turned onto his face and dug his ice axe into the snow. The ice axe stopped them, but they had nearly died.


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[Assistant] Was this what happened to Mallory and Irvine 29 years earlier? They wondered. A sudden fall on the way down and no one to help? It could happen so easily. When they reached Camp 8, they were exhausted. Their faces were covered with ice and they could hardly walk.


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[Assistant] They look like strangers from another planet. John Hunt said.


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[Assistant] But they had climbed higher than any man before them.


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[Assistant] Chapter 10. On Top of the World. 1953. Hillary and Tenzing were already at Camp 8, together with John Hunt, Danamgel, and Ang Timber. Gregory and Lo were there too, with three more Sherpas. But the weather was bad.


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[Assistant] A terrible wind blew straight across the South Col, and the temperature


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[Assistant] Hoping that the wind would not blow them away.


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[Assistant] Bordelon and Evans were exhausted. Three of the Sherpas were ill.


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[Assistant] And hunt, like Ang Temba and Anamgyal.


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[Assistant] So Evans, John Hunt, and Anamgyal helped him and Angtember down to Camp 7. Gregory, Lowe, and three Sherpas spent another night at Camp 8 with Hillary and Tenzing. On the morning of the 28th of May, the wind began to fall.


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[Assistant] Hillary and Tenzing got ready to set out. Gregory and Lo's job was to start first and make Camp Nine somewhere below the South Summit.


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[Assistant] But two of their three Sherpas were ill, so Lo, Gregory, and Angnima carried everything between them.


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[Assistant] They carried about 18 kilograms each.


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[Assistant] Hillary and Tenzing followed at 10am, carrying about 22kg each.


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[Assistant] At 8,338 meters, they found the loads which Hunt and Anamgyal had left, and picked them up too. Now, they were carrying 27 kilograms each. At 2.30 p.m., they found a small place for Camp 9.


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[Assistant] Gregory, Lo, and Angnima dropped their loads and went down. Hillary and Tenzing put up their tent and crawled inside. The wind was very strong.


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[Assistant] And they were afraid the tent would blow away.


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[Assistant] The temperature fell to minus 27 degrees celsius. But by 4am, the wind had stopped and the sky cleared.


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[Assistant] When they opened the tent door in the early morning sun,


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[Assistant] They could see the monastery at Thiang Boche.


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[Assistant] 4878 meters below, where the monks were getting out of bed. They melted snow for a warm drink, and checked the oxygen equipment carefully. Tenzing had worn his boots all night, but Hillary had taken his off, and they were as hard as ice. He had to heat them over the small cooker,


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[Assistant] To make them soft. At six thirty a.m., they set out. And by nine a.m., they reached the South Summit. They sat down and studied the summit ridge carefully. It looked frightening, Hillary thought. The snow cornices to the right were very dangerous.


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[Assistant] Two thousand five hundred meters above the valley below. And the rocks on the left looked very difficult too. But the snow just above the rocks looked better. Perhaps it was possible to climb there. As soon as they stepped onto the snow, they were happy. It was good, hard snow.


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[Assistant] So cutting steps in it was easy, but it was still very dangerous. One slip and they could fall thousands of meters. Hillary went first, cutting steps in the snow. Behind him,


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[Assistant] Tenzing put the rope around his ice axe and dug it into the snow to keep them safe. Then Hillary stopped and Tenzing went first, cutting steps. First one man, then the other.


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[Assistant] Several times their oxygen stopped working and they found it hard to breathe. But each time they fixed it and went on. As the sun rose, they felt warmer. To my surprise, I was enjoying the climb, Hillary said later. The weather was still fine and they could see the tents of Camp Four


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[Assistant] Two thousand four hundred and thirty-nine meters below. But halfway up the ridge, they met a problem. They reached a rock wall, seventeen meters high.


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[Assistant] It looked difficult and dangerous to climb. On the left, it was clean rock.


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[Assistant] The wind had blown a cornice of hard snow against it. Hillary pushed his boot into a hole between the rock and the snow. He began to climb with his back to the rock, hoping that the snow did not move. At last he reached the top of the wall and Tenzing followed him up.


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[Assistant] Now, there were just 220 vertical meters to go. Slowly, cutting steps in the snow, they climbed on. Even with oxygen,


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[Assistant] They had to take two or three breaths after every step.


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[Assistant] Each time they thought they had reached the summit, they saw another one higher. They were both tired. The ridge seemed never-ending, Hillary wrote later. But then, quite suddenly, it did end. They looked around and realized they could not go any higher.


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[Assistant] It was 11.30 a.m., and they had reached the summit of Everest. They shook hands and threw their arms round each other. Hillary took out a camera and took a picture, the picture, of Tenzing on top of Everest, the highest man in the world. On his ice axe,


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[Assistant] Tenzing had the flags of Great Britain, Nepal, India, and the United Nations. Hillary took pictures of the view, north, south, east, and west.


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[Assistant] Tenzing made a small hole in the snow. In it, he put some sweets, a pencil, which his daughter had given him, and the flags from the ice axe. Hillary made a hole too, and put a small crucifix in there. They gave these things to the mountain Chomolungva, goddess mother of the world.


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[Assistant] They were on top of the world.


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[Assistant] But were they really the first men who had ever been there?


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[Assistant] Hillary and Tenzing searched to see if Mallory and Irvine had left anything up there 29 years ago. They found nothing, but that was not surprising. Every few days, there is new snow on the mountain. Every month,


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[Assistant] Winds of over 150 kilometers per hour blow across the top of Everest, adding more snow, burying what was there before. After 15 minutes, they turned back. They needed to get down before they used all the oxygen. They went carefully.


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[Assistant] It would be stupid to have an accident now. An hour later, they were at the South Summit. By evening, they were with George Lowe at the South Coll. Next day, they were down at Camp Four.


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[Assistant] Only two men had reached the summit. One from New Zealand, one from Nepal. But everyone in the expedition was happy.


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[Assistant] They had done something no one had ever done before.


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[Assistant] But each man in the expedition had needed the help of all the others.


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[Assistant] Many hundreds of men and women have climbed Everest, most of them in large expeditions.


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[Assistant] Some groups have been very large indeed. In 1975,


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[Assistant] A Chinese expedition with 400 people.


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[Assistant] Managed to send nine climbers to the summit. They left a small metal tripod there, fixed to the rock. In 1985, a Norwegian expedition sent 17 people to the top.


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[Assistant] All these climbers, like Hillary and Tenzing, needed the help of many others.


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[Assistant] Almost all of them used oxygen too. People have climbed Everest from the south, north, and west.


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[Assistant] But the first climber to climb the mountain all alone, with no oxygen at all, was Reinhold Messner. In 1978, two climbers, Reinhold Messner and Peter Haberler, joined


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[Assistant] A large German-Austrian expedition climbing from Nepal. Most of the expedition were using oxygen but Messner and Habela decided to climb without it. After


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[Assistant] The success of Hillary and Tenzing in 1953 using oxygen, Messner said, the whole world


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[Assistant] Norton climbed to 8,575 meters with no oxygen. So, Messner thought, perhaps it is possible


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[Assistant] To climb two hundred and seventy-three metres more. He tried twice. The first time,


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[Assistant] He reached the south col with two sherpas, but they were caught in a terrible storm. Their tent nearly collapsed in the wind, and they spent two nights without eating or drinking before they came down. But a few days later, Messner tried again with Peter Hebbeler, and in ten hours,


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[Assistant] They climbed from the south col to the summit, with no oxygen at all. But back at the south col, they were very ill. Hubbler had a terrible headache.


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[Assistant] Messner had taken off his goggles to make a film, and the bright snow had hurt his eyes. Just like Norton in 1924, he lay in his tent all night, unable to see anything. The two men needed help.


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[Assistant] Two years later, in 1980, Messner began a new attempt. This time, he went through Tibet.


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[Assistant] Like Norton and Mallory in 1924.


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[Assistant] But Messner did not take a lot of heavy equipment and hundreds of porters. He just went with his girlfriend, Nina, and two Chinese people came with them to show them the way.


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[Assistant] They started at the same place as the British Base Camp in 1924. Then, with three yaks, they climbed to Camp 3, at 6,500 metres, on the East Wrong Book Glacier.


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[Assistant] Then the two Chinese went back to base camp, while Nina and Messner stayed at Camp 3 for 10 days, getting used to the height. On the 24th of July, Messner climbed to the North Col at 7,000 meters. But he felt very tired, and there was too much soft snow. So,


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[Assistant] He and Nina returned to base camp and spent three weeks


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[Assistant] Walking and climbing above 5,000 meters. Each day they grew stronger and breathed more easily in the thin mountain air. On the 15th of August they returned to Camp 3, and on the 17th of August


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[Assistant] Messner climbed up to the North Col again, much faster than before. Now he was ready, he thought. He came down to Camp 3 to sleep. That night he ate and drank and slept for a while. Then he got up, dressed carefully,


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[Assistant] And packed his rucksack with everything he needed. Food for a wheat, a small cooker, tent, sleeping bag, camera. He had a head torch to see in the dark, two ski sticks, crampons, and a strong, light ice axe.


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[Assistant] He touched Nina's face gently with his lips and stepped out of the tent into the night. I shall be thinking of you, she said sleepily. Bye bye. Bye bye. The words came out of the night and then he was gone.


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[Assistant] An hour later, he nearly died.


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[Assistant] The snow suddenly collapsed under his feet and he fell into a crevasse. His head torch went out and everything was dark.


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[Assistant] He had decided not to take a radio with him. Now he was frightened. He could see nothing, and it was not possible to call for help. Then the torch came on again. He was standing on a snow bridge, about one meter square, above a deep black hole. He looked round.


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[Assistant] There was a small ice ridge to the left, going up, but to climb that, he needed crampons on his boots, and his crampons were in his rucksack. Very carefully, he got them out and put them on. Carefully, he reached forward across the crevasse with his arms, then


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[Assistant] As the sun came out, the clouds and mountains turned from dark blue to yellow and then pink. There was good hard snow under his feet. He climbed quickly, taking 50 steps, then resting, then taking 50 more. The ski sticks made climbing easier. As he climbed,


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[Assistant] Messner thought about Mallory and Irvine. They had come the same way up the mountain long ago. They had oxygen, but their clothes and equipment were much heavier than Messner's. Mallory and Irvine had no light tents and sleeping bags, no crampons, no ski sticks.


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[Assistant] But when Odell last saw them, they were high up on the north ridge.


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[Assistant] Two tiny black dots on the snow going strongly. Did they reach the summit? he wondered. Or did they die before that? Far below him, Nina stood outside the tent.


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[Assistant] Watching Messner climb higher and higher. To her,


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[Assistant] He was now a tiny black dot on the snow. I would like to climb with him, she wrote in her diary. One day, perhaps, I tell myself, the further he is from me, the stronger becomes my love. By nine a.m.


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[Assistant] Messner was at 7,360 meters. He was tired and had to rest every 30 steps.


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[Assistant] Up here, the thin, dry air had only one third as much oxygen as at sea level. His throat hurt, and for long moments he could think of nothing but breathing.


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[Assistant] Still a bit more. You can do it, he told himself. What you climb today, you won't have to climb tomorrow. At last, at 7,800 meters, high up on the north ridge, he decided to stop. The view from here was wonderful.


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[Assistant] Some of the highest mountains in the Himalayas were below him.


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[Assistant] And 1,300 meters below.


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[Assistant] He could see the tiny red dot of Nina's tent.


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[Assistant] He took a long, long time to put up his tent. Again and again, the wind almost blew it away.


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[Assistant] He held it down with his ski sticks and ice axe. Then he pushed his rucksack inside and crawled in after it. But he could not rest. To get water


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[Assistant] He had to melt snow with his small stove.


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[Assistant] His throat hurt, but he had to make himself drink. He was not hungry, but he had to cook and make himself eat. And that night a storm came up.


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[Assistant] The temperature fell to minus 20 degrees Celsius. Winds of over 80 kilometers per hour tried to blow the tent off the mountain. Next morning, the wind had fallen, but Messner felt terribly tired. For an hour, he lay in his tent, half asleep, unable to move. Every small thing,


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[Assistant] Making a drink, eating, putting on his boots was hard work. He had to argue with himself. You must go on, he told himself. Then, a minute later, why don't I go down? But he knew the answer to that. I wanted to make the climb. I still want to.


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[Assistant] He took the tent down and packed his rucksack. The sky was blue. The sun was shining. But as he set out the clouds and wind came back. His legs were tired.


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[Assistant] There was too much new snow on the ridge.


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[Assistant] So, he moved down onto the rocky north face, the same way that Norton had gone, also without oxygen.


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[Assistant] The rocks sloped steeply like the roof on a church. It was very quiet. But Messner began to hear voices. Is that somebody talking nearby? He wondered. Is somebody there? I believe I hear voices. Perhaps it is Mallory and Irvine.


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[Assistant] He was at 8,220 meters. He was too tired to go on anymore.


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[Assistant] He could only take ten steps now before resting.


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[Assistant] He found a flat piece of snow above a large rock and put up his tent there. He took a picture of the tent, then got inside his sleeping bag. Again, he had to melt snow to get water. And it was difficult to sleep. Even when he was resting in the tent,


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[Assistant] His heart was beating a hundred times a minute. Next morning, he could see little. He was in the clouds. Should he go on or wait? He wondered. No, he thought. He couldn't wait. It's now or never. Either or. I must either go up or go down.


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[Assistant] He decided to leave the tent and rucksack behind. He put the camera in his pocket, picked up his ice axe, and set out. It was harder to climb without the ski sticks. He was afraid that he would fall.


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[Assistant] So he often climbed on hands and knees. As he climbed up to the ridge it became steeper.


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[Assistant] Often he dug his ice axe into the snow above his head and lay on his face resting.


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[Assistant] For three hours, he crawled slowly along the ridge. His dry throat felt like wood. Where is the summit? He wondered. He could see almost nothing. Then, suddenly, the cloud cleared.


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[Assistant] And he could see right down to the glacier in the valley. He took a few photos, then the cloud came back. Where is the summit? He wondered. At most, it can only be another ten meters up to the top. He crawled on, always upwards. Then, suddenly, there it was. The metal tripod


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[Assistant] Messner had seen it before in 1978. Now he took hold of it like an old friend. He had done it. He was on top of the world with nothing above him but sky. He sat down like a stone. All he wanted to do was rest.


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[Assistant] But it was after three o'clock. He could not stay here in the dark. Slowly, he got up. He took a few photos. Then, at four o'clock, he turned to go. I must get back down, he thought. Half an hour too late means the end of me. On the way down, he started coughing badly.


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[Assistant] He lay in his sleeping bag like a dead man, but he could not sleep. He melted a little snow to drink, but ate nothing. Next morning he left the tent where it was, carrying the ski sticks and rucksack.


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[Assistant] He came down the mountain like a man walking in his sleep. Twice he slipped and fell. Each time he turned on his face and dug his ice axe into the snow. Then suddenly on the glacier, he saw Nina standing in front of him. Resting on his ski sticks, he looked at her.


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[Assistant] Was she really there? Yes, she was. Reinhold, how are you? She said. She ran towards him. Messner fell to his knees. He was crying. Nina held him in her arms. Everything's okay, Reinhold, she said. You are all right. The camp is over there.


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[Assistant] Where are all my friends? He asked. I'm your friend. I'm here, Reinhold. Don't worry. We're going to our camp now. Yes. Where is the camp actually? He asked. Over there. She took his rucksack and led him to the camp.


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[Assistant] Here, she gave him food and drink and let him sleep.


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[Assistant] Had climbed the highest mountain in the world, all alone, with no oxygen. But the mountain had beaten him too. They both won this fight, the mountain and the man.


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[Assistant] Chapter 12, The Final Question.


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[Assistant] By 1999, many people, both men and women, had climbed Everest. They came from the USA, India, China, Japan, Italy, and many more countries. One climber, Goran Krop, from Sweden, rode his bicycle to Everest, climbed the mountain,


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[Assistant] Without oxygen and rode home again. But still.


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[Assistant] Nobody had found an answer to the question.


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[Assistant] What happened to Mallory and Irvine? A climber called Jochen Hemleb


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[Assistant] Became interested in this problem in 1988 He studied the problem for years.


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[Assistant] Climbing up behind Mallory and Irvine towards Camp 6.


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[Assistant] And Odell could see the summit ridge of Everest above him. High up on the ridge


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[Assistant] He saw two tiny black dots moving on the snow. They were moving quickly.


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[Assistant] He saw them climb a rock step on the ridge. Then the clouds came back and they disappeared.


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[Assistant] But it is only about 250 vertical meters from the summit. And the third step is even closer. So the first question is, which of the three steps were Mallory and Irvine climbing when Adele last saw them? In 1924,


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[Assistant] Odell said it was the rock step at a very short distance from the base of the final pyramid. And both of them climbed quickly to the top of it. It is difficult to climb the second step, but much easier to climb the third step. And the first step is quite a long distance from the summit.


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[Assistant] So at 12.50 p.m., Mallory and Irvine were probably at either the second step or the third step, only a very short distance from the summit. If that is right, did they stop there? Probably not. All the difficult parts of the climb


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[Assistant] He probably saw them climb the first step, much further from the summit. Reinhold Messner agrees. Mallory did not climb the second step, he says. Odell saw them on the first step. So who is right? And how can we know? In 1933,


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[Assistant] A British climber found Irvine's ice axe.


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[Assistant] At 8460 meters. Just below the first step.


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[Assistant] But why was it there? Did he put it down or drop it in an accident? And did this happen on the way up or the way down? No one knows. In 1960, a Chinese climber found an old wooden tent post and rope


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[Assistant] Like those used in 1924, just below the second step. And in 1979, a Japanese climber met another Chinese climber, Wang Hongbao, on the mountain and heard a strange story. Four years earlier, Wang said he had found a body


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[Assistant] An English dead near the Chinese Camp 6 at 8,100 meters.


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[Assistant] Jochen Hemleb was part of an expedition that set out to find some answers. From Tibet,


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[Assistant] They climbed slowly up the East Wrong Book Glacier to Camp 5, just under the North East Ridge. At 7,900 metres, one climber, Andy Paulitz,


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[Assistant] You are really close to them at that point, he said.


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[Assistant] It took a lot of photographs and video film to make this clear.


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[Assistant] The five climbers reached Camp 6 near the place where Wang Hongbao had seen the English dead. On the 1st of May, 1999, they set out to find the body again.