A quick disclosure before you wander down this rabbit hole. Matti asked me look into the scene below and discuss the possibility and likeliness of such a series of events being plausible, before inevitably concluding with ’Yeah.. but no’.
I haven’t watched Death Note in about five years, but I’m a physicist by trade, and have worked a lot in science outreach, so have ended up becoming Matti’s go to for ’Is this science bonked or not?’. I’ve also spent enough of my life online that I have picked up a certain set of skills that make dinner party conversations with me rather awkward. So anyway, enjoy.
I haven’t watched Death Note in about five years, but I’m a physicist by trade, and have worked a lot in science outreach, so have ended up becoming Matti’s go to for ’Is this science bonked or not?’. I’ve also spent enough of my life online that I have picked up a certain set of skills that make dinner party conversations with me rather awkward. So anyway, enjoy.
Death Note Matsuda's Handstand on a Balcony Leap Scene (Ep 19: Matsuda)
So let us begin by discussing the elephant in the room: the plan is really quite stupid.
A fundamental aspect of any plan is that it can’t be dependent on many independent occurrences happening in the sequence that is desired, for it to be successful. If you watch through the scene with a healthy level of scrutiny and cynicism then you notice that with a few significant changes in the behaviour of various actors within the plot, the outcome would have been very different.
A fundamental aspect of any plan is that it can’t be dependent on many independent occurrences happening in the sequence that is desired, for it to be successful. If you watch through the scene with a healthy level of scrutiny and cynicism then you notice that with a few significant changes in the behaviour of various actors within the plot, the outcome would have been very different.
 | You could argue that the people in the room are very predictable, or that the masterminds behind this plan had thought it through so well that they knew exactly what would happen, but I’ve struggled to get three friends to meet at the pub at the right time and that involved significantly less props. I don’t remember the exact context of this event, but they must have been an easier way to do it, and one that had at least one built in contingency. But we’ll get back to my nitpicking later, let’s go through some of the physical events that happen. There’s the fall, the catch, the thrown weight, the fake body, and the removal of the body. |
| We’ll start with the initial fall, because, well, it’s where the plan really takes off. We’ll get to the possible issues with this actual plan in a bit, but let’s focus on the physics of what is going on. To be successful in landing on the mattress below, he needs to fall with almost no horizontal deviation. The overhand of the mattress below is marginal at best, and this is a necessary feature (as I’ll address later) for the plan to work at all. Falling with only a vertical component is difficult, as any horizontal motion you gain will continue until you are able to correct it in some manner. This isn’t as easy as it sounds. At low speeds your behaviour in free fall is similar to that of an astronaut on the ISS. Because there is no base for you to push against any movement you do will generally have minimal impact on your actual location, and instead will just cause you to rotate around the centre of mass. |  |
This can seem a little counter-intuitive at first because it goes against our normal day to day experiences with motion and mechanics. When we want to go forward we just ’go forward’ and usually lean ourselves forward slightly, but we are actually pushing back against the ground to launch ourselves forward. We don’t really consider this about our movements, because we do it all so instinctively.
When people are thrown in zero gravity environment, like vomit comet flights, they usually flail around and try to swim through the air. This is exceptionally inefficient because you can’t swim in air. (Start at 2:20 in the video below.)
When people are thrown in zero gravity environment, like vomit comet flights, they usually flail around and try to swim through the air. This is exceptionally inefficient because you can’t swim in air. (Start at 2:20 in the video below.)
So to be entirely factual, you can kind of swim through air, but you need to going quick enough (or in windy enough conditions) that you can divert the air around you to guide yourself.
However, the few feet fallen between balconies is not enough time to even get close to the right speed. So unless a strong gust blew him suddenly back into the building, he has got to fall almost straight down. Which is a lot harder than it seems even with all the caveats of caution that we have looked at above.
Firstly, the last point of anchorage was the balcony ledge, upon which he made himself fall off of to the right. As a result his momentum is heading away from the building already. From where he is it is possible for him to fall vertically, but it is just very unlikely. His stance before ’slipping’ is nearly completely upright, so his centre of gravity is very high. That point is also very far from the pivot point, so is able to move a great distance horizontal with only a slight lean over the edge, and once set in motion they’ll be very little to correct it.
This is a fundamental issue when trying to on to an that is not below you, but instead below the object you are hanging off of. If you watch some trying to swing to a balcony from the one above you’ll notice that is actually very awkward to do.
However, the few feet fallen between balconies is not enough time to even get close to the right speed. So unless a strong gust blew him suddenly back into the building, he has got to fall almost straight down. Which is a lot harder than it seems even with all the caveats of caution that we have looked at above.
Firstly, the last point of anchorage was the balcony ledge, upon which he made himself fall off of to the right. As a result his momentum is heading away from the building already. From where he is it is possible for him to fall vertically, but it is just very unlikely. His stance before ’slipping’ is nearly completely upright, so his centre of gravity is very high. That point is also very far from the pivot point, so is able to move a great distance horizontal with only a slight lean over the edge, and once set in motion they’ll be very little to correct it.
This is a fundamental issue when trying to on to an that is not below you, but instead below the object you are hanging off of. If you watch some trying to swing to a balcony from the one above you’ll notice that is actually very awkward to do.
The basic principles of mechanics make the very first part quite difficult, but we won’t write it off as impossible, because it is technically possible, just bloody awkward.
| So now we get to the next part which poses some problems: the mattress landing. We have to assume that he is able to land on the mattress, but even landing on it isn’t a sure sign of success. To illustrate this, I want you to go to your bedroom and lift your mattress over your head. Don’t worry, I’ll wait for you to come back. It actually doesn’t matter when you have gone to get your mattress because the mental image of you struggling to lift is enough to amuse me, because as you would realise if you *had* attempted to lift the mattress, they’re really bendy. Way too bendy to actually be reliable to do what the video shows. We see our daring protagonist land on the propped up mattress comfortably, and head into the room swiftly. There are a multitude of ways that this part of the plan could backfire horribly. If any of you engaged in the typical childlike behaviours of the youthful, you may have jumped on your, or more likely your parents, bed. However, if you have ever tried to repeat this as an adult you may have realised that beds are actually quite crap for bouncing on. If you apply any significant force to a mattress you just depress to the point where you are either resting on springs or leaning on the surface beneath. This is going to be a lot worse when you have the mattress resting on single points or edges. When the mattress is propped on an edge (like in the scene) then most of the mattress can bend or morph to accommodate the new uninvited guest, but the part resting on the ledge can’t. So the force applied here just crushes the mattress against the edge, so where there was a one a nice cushion separating you from smashing your ribs against the ledge, there is now just a few centimetres of incompressible fabric. In other words, it’s going to hurt like hell. |  The Manga  The Likely Reality |
Some of you may be shouting about ’crumple zones’ or *impulses*. Firstly, well done for listening during your science lessons. Secondly, you’re still wrong. Sorry.
Impulse is the change of momentum of an object, and cannot be changed for a given interaction. Momentum is simply to the mass of an object, multiplied by its velocity. So for a set object at a set velocity, coming to a rest, the momentum change is always going to be the same, so the impulse will be constant. But the force acting on that object is related to the time taken for the momentum change to happen. Impulse is usually denoted by a J (don’t ask why) and is defined as
Impulse is the change of momentum of an object, and cannot be changed for a given interaction. Momentum is simply to the mass of an object, multiplied by its velocity. So for a set object at a set velocity, coming to a rest, the momentum change is always going to be the same, so the impulse will be constant. But the force acting on that object is related to the time taken for the momentum change to happen. Impulse is usually denoted by a J (don’t ask why) and is defined as
But for more simple cases we can simplify it to:
The first method is more thorough and can deal with more complex and interesting cases, but the second method is more applicable to every day examples. So working with the second equation let’s posit some numbers so we can illustrate our point. Let’s say you weigh 100kg and you’re travelling at 20ms-1 your momentum will be 2000Ns. If you, upon hitting the mattress, are going from that speed to rest your momentum change, or impulse, will be 2000Ns (as when you are not moving your velocity is zero so your momentum is also zero). The force you, the object feel, can now be found from the above equation for impulse, but we need to know the time over which it takes for you to stop. In a world without mattresses the time taken to stop is extremely short. If we assume that it takes 0.1 seconds to stop, then we have
This number is pretty high, and is like being rocked by a heavyweight boxers punch over your entire body. It’s not guaranteed to kill you, but it is like falling from a five story building, so unlikely to go well. But if we to simply extend the time it to stop by a factor of 5 (so it now takes half a second to stop) the force would drastically reduce to 4000N. Which would feel more equivalent to falling off a 2 foot high table (or around 70cm). An uncomfortable experience, and you can still break bones or damage your dignity, but significantly less likely to kill you.
But the ability of a mattress to replicate this increase of time to stop is highly suspicious, especially given the fall to that point. We have to take a few liberties because working out what exactly is going on in terms of precise numbers is not easy, but if we go for assumptions that make the events more likely, it looks like the fall is about two floors. This means that by the time he hits the mattress he is travelling at about 11ms-1. If we give him a weight of about 60kg then the force he experiences upon stopping at the mattress is a minimum of 3300N (but more likely nearing toward 6000N). This isn’t too bad as we showed earlier it was like falling off a table, but that was based on falling off a table onto a relatively flat floor. Here, we’re not.
We’re falling backwards onto a sharp edge. That force instead of being spread across the whole body is being focused directly across his back. Once again working on rough estimations, if we say the area of impact is about 0.006m2 (60cm is the width of his back, and the thickness of the ledge at impact is about a centimetre because his coming down on it at an angle) than the force per square metre climbs drastically 550,000Nm-2. That’s the kind of force
that snaps bones and spinal columns pretty swiftly.
But the ability of a mattress to replicate this increase of time to stop is highly suspicious, especially given the fall to that point. We have to take a few liberties because working out what exactly is going on in terms of precise numbers is not easy, but if we go for assumptions that make the events more likely, it looks like the fall is about two floors. This means that by the time he hits the mattress he is travelling at about 11ms-1. If we give him a weight of about 60kg then the force he experiences upon stopping at the mattress is a minimum of 3300N (but more likely nearing toward 6000N). This isn’t too bad as we showed earlier it was like falling off a table, but that was based on falling off a table onto a relatively flat floor. Here, we’re not.
We’re falling backwards onto a sharp edge. That force instead of being spread across the whole body is being focused directly across his back. Once again working on rough estimations, if we say the area of impact is about 0.006m2 (60cm is the width of his back, and the thickness of the ledge at impact is about a centimetre because his coming down on it at an angle) than the force per square metre climbs drastically 550,000Nm-2. That’s the kind of force
that snaps bones and spinal columns pretty swiftly.
Death Note Ep 19 - Touta Matsuda on the mattress, where he's landed without injury. Soichiro Yagami looks on.
What we are reliant on for this part to work is that the super thick mattress used isn’t like most mattresses, but instead is incredibly springy and cushioning, and able to absorb the entirety of the force, without dislodging or sliding, and without bending backwards over the edge (throwing our unlucky chap to the fate he seems destined for anyway).
I suppose it is possible, and I have just been experiencing awful mattresses, but it is demanding a lot from us to expect mattresses to behave like they do in TV, rather than how they do in real life.
So we are now down to the final part of the ruse, the fake throw and body. I’m including these two acts together because the problems with both are linked together. The initial part is how long it will take for someone falling to hit the ground. Once again, we are going off assumptions, but they will illustrate the problem even if we are off by a floor or two.
From my guesstimates it looks like the mattress is two floors below the party, and the ground is 5 floors below the mattress. With a height of seven floors we get an approximate height of the fall of about 21m (a storey is about 3m), and due to a series of equations called the suvat equations we can work out how long it would take to fall that distance.
I suppose it is possible, and I have just been experiencing awful mattresses, but it is demanding a lot from us to expect mattresses to behave like they do in TV, rather than how they do in real life.
So we are now down to the final part of the ruse, the fake throw and body. I’m including these two acts together because the problems with both are linked together. The initial part is how long it will take for someone falling to hit the ground. Once again, we are going off assumptions, but they will illustrate the problem even if we are off by a floor or two.
From my guesstimates it looks like the mattress is two floors below the party, and the ground is 5 floors below the mattress. With a height of seven floors we get an approximate height of the fall of about 21m (a storey is about 3m), and due to a series of equations called the suvat equations we can work out how long it would take to fall that distance.
For reasons that are best left unexplained, s is the distance, u is the initial velocity, a is the acceleration, and t is the time. In our case we know most of these values already. As we have said before s is about 21m, u is zero because he initially starts at rest (yes, that weird daredevil feat is classified as rest in this case, physics is odd), and a is just the gravitational acceleration due to the earth, which is 9.81ms-2. So we can rearrange this all to find an equation for t
But that isn’t what happens here, instead the bag is thrown when he hits the mattress. If we assume the best case scenario, that the bag is thrown the moment he hits the mattress, then we instead have two equations that must be added together (one for the 6m fall, and another for the 15m fall). This gives a time to fall of a little over 2.8s. You may say that 0.8 of a second is too small for us to notice, but you would be surprisingly wrong (and it should be noted that the reality of the scene was the bag was thrown after he hit the mattress which would just increase the number).
Humans have a surprisingly good instinct for how things behave in Newtonian physics. It is the physics of every day motion.
When your friend is running across a field and you hurl a ball towards them you have instinctively solve a bunch of equations simultaneously to calculate where your friend will be, the trajectory of the ball, how long the ball will travel for, so where to aim for the intersection of friend and ball. Your brain is amazingly good at instinctively understanding how bodies behave at speeds and masses familiar to us, so when something happens within these ranges that feels wrong we notice very quickly. When the wannabe acrobat tumbled off the edge the people would have instinctively expected him to hit the ground at a certain time.
There would obviously be a margin of error, but the actual noise would come after they had begun to feel that disaster had been avoided. They wouldn’t know it immediately, but something about it would bother them, and would niggle at them. This could be avoided if the next part, which is too have some human juice surrounding the body.
Humans have a surprisingly good instinct for how things behave in Newtonian physics. It is the physics of every day motion.
When your friend is running across a field and you hurl a ball towards them you have instinctively solve a bunch of equations simultaneously to calculate where your friend will be, the trajectory of the ball, how long the ball will travel for, so where to aim for the intersection of friend and ball. Your brain is amazingly good at instinctively understanding how bodies behave at speeds and masses familiar to us, so when something happens within these ranges that feels wrong we notice very quickly. When the wannabe acrobat tumbled off the edge the people would have instinctively expected him to hit the ground at a certain time.
There would obviously be a margin of error, but the actual noise would come after they had begun to feel that disaster had been avoided. They wouldn’t know it immediately, but something about it would bother them, and would niggle at them. This could be avoided if the next part, which is too have some human juice surrounding the body.
Death Note's Aiber stands in (well sprawls in) as Matsuda's
supposed corpse for the viewing of Yotsuba executives. Wedy stands by
ready to scream as if witness to the fall and thud.
I don’t recommend looking up pictures of people who committed suicide by jumping off of great heights, but the person rarely looks all that pleasant afterwards. There are cases (the picture known as ’The Most Beautiful Suicide’ is a notable example) where the person looks relatively normal, but these are usually from when the impact was cushioned in a way that wasn’t enough to prevent death but was enough to stop the body being damaged.
There is usually some blood, some contortions of the limbs (that have broken or bent in inhuman ways), and in the most unpleasant of cases the head has cracked violently. These are pretty nasty aspects, but not beyond what you would expect the supposed mastermind of this act to know, and given the stakes these men have in deaths, they would probably know of this too.
They probably wouldn’t immediately call the whole act bullshit, but just like the extended fall time, it would continue to bother them and haunt them for reasons they can’t quite understand. They would probably at first assume it is because it was such an odd and ’tragic’ act, but those little errors, those disjointed continuities, they would begin to become more and more obvious to them.
Unless these men are truly the idiots that L assumes them to be (which I doubt because their supposed positions of seniority), someone would become suspicious of something, and seeing as they seemingly wanted him dead (once again, the narrative context is a little lost on me) I doubt that once they were rumblings that it could have been staged, it would be harder to put it back in Pandora’s box again.
There is usually some blood, some contortions of the limbs (that have broken or bent in inhuman ways), and in the most unpleasant of cases the head has cracked violently. These are pretty nasty aspects, but not beyond what you would expect the supposed mastermind of this act to know, and given the stakes these men have in deaths, they would probably know of this too.
They probably wouldn’t immediately call the whole act bullshit, but just like the extended fall time, it would continue to bother them and haunt them for reasons they can’t quite understand. They would probably at first assume it is because it was such an odd and ’tragic’ act, but those little errors, those disjointed continuities, they would begin to become more and more obvious to them.
Unless these men are truly the idiots that L assumes them to be (which I doubt because their supposed positions of seniority), someone would become suspicious of something, and seeing as they seemingly wanted him dead (once again, the narrative context is a little lost on me) I doubt that once they were rumblings that it could have been staged, it would be harder to put it back in Pandora’s box again.
Matsuda's Mattress Rescue: Implausible, but not Impossible
So after looking through the mechanics of the act it becomes obvious that the whole thing is possible, but decreasingly plausible.
They are so many little parts of it that either require the world to be more favourable than it usually is, and for those in the room to not notice any inconsistencies with the normal reality of such a large fall.
But the problem with the whole thing is that it fundamentally requires every single person in the room to act exactly as L predicts them to.
All it takes is for one person to run to the edge of the balcony, one person to attempt to physically remove him from his foolish feats, or one person to look down a little too soon and see a mattress poking out.
A good plan does not require that everything go an exact way for it to work, it just requires a few key events to ensure the course of fate runs the way you desire. The fundamental reason this plan would not work in the real world is because people like L think they can control everything but forget that humans have an amazing ability to go off script.
They are so many little parts of it that either require the world to be more favourable than it usually is, and for those in the room to not notice any inconsistencies with the normal reality of such a large fall.
But the problem with the whole thing is that it fundamentally requires every single person in the room to act exactly as L predicts them to.
All it takes is for one person to run to the edge of the balcony, one person to attempt to physically remove him from his foolish feats, or one person to look down a little too soon and see a mattress poking out.
A good plan does not require that everything go an exact way for it to work, it just requires a few key events to ensure the course of fate runs the way you desire. The fundamental reason this plan would not work in the real world is because people like L think they can control everything but forget that humans have an amazing ability to go off script.
Read more from Liam Dodd Physicist at his own website, where he's also linked the article published here.
