Science in Manga - The Make-Believe Science of "Spiral - Bonds of Reasoning"

imgSpiral - Suiri no Kizuna, also known as Spiral - Bonds of Reasoning, is a popular detective manga by Kyou Shirodaira (writer) and Eita Mizuno (art) that was published in Square Enix's Monthly Shounen Gangan (the manga ended its run in September 2005), and later adapted into a 25 episode anime series, which aired on TV every Tuesday.

The hero in Spiral is Ayumu Narumi, a genius detective high school boy who uses his powers of reasoning to solve—with ease—problems that seem unbelievably difficult. In the story this hero goes around trying to find his long-lost brother by solving riddles that his brother has left behind... but wait a minute, there seem to be many deductions and actions in this manga that will never happen in the real world. Tsuredure Thoughts has written an article on the science found in Spiral, below is a translation of the article, so un-suspend your suspended disbelief as we tease out the make-believe science that is shown in Spiral - Bonds of Reasoning.

Science Fiction Spiral - The Make-Believe Science of "Spiral - Bonds of Reasoning"
- Did they really calculate things as far as they do in the story?

Phenomenon No. 1: The Falling Key that Disobeys the Law of Inertia

Maybe there were people who pointed out the mistake in their heart, maybe I'm mentioning something that's been already mentioned, but I just have to write about this one. For a key, which is thrown from the window of a train crossing over a bridge, to be caught by someone standing under the bridge... is, no matter how hard you think about it, impossible.

This phenomenon happens in the climactic scene where Ayumu, who is forced to wear a time bomb around his neck, catches the key to unlock the bomb. I didn't feel it was so strange when I first read it in the manga, but when I watched the same scene in the anime, I almost spilt my tea. Why is the key falling straight down!?

The correct falling angle should look like this. (Drawn by Tsuyukusa-san, supervised by Asaki-san)


- The object will launch at the described location above as long as "the plane flies in one direction at a constant speed" and "outside factors other than gravity and inertia (such as influence of the wind) are ignored."

- The object dropped will move at the same horizontal speed as the plane; on the other hand, it will move faster vertically because of acceleration due to gravity. Thus, the object will draw a curve and fall.

For this reason, it is impossible for the key to fall into the hands of our hero when it is dropped from a train passing directly over him. The children who take the anime seriously might learn from this false information on how gravity and inertia work. The producers of the show should be more careful about how these things works.

Bonus Comment

imgSome Last Words on the Law of Inertia:

Since I have written this piece it has been pointed out that I too had made mistakes regarding the science of the falling key. The law of inertia can be defined as "A moving object will continue to move, a motionless object will continue to remain motionless." Actually, this is about as much as I knew about inertia.

The thing that is a bit difficult to grasp is the way a key falls when it's dropped from a plane mid-flight. Since it was in a plane that mid-flight, during which everything in the plane - both humans and keys - are also moving. To the passengers on the plane everything is stationary as they sit in their seats, but to someone looking up at the plane from the ground, the passengers are moving just as fast as the plane. (Actually, a person standing on the earth is, strictly speaking, also moving very fast, what with the earth rotating as it does.)

An object on something that is moving fall to earth due to gravity, but it will fall in such a way that the remaining influence of the plane causes it to fall at an angle.

It should be noted that this all happens in a very short amount of time. Because of the changing acceleration due to the gravitational force, the vertical velocity of an object will change. The velocity will be determined by G (acceleration due to gravity), T (time, in seconds) and D (distance). In the graph, the purple arrow indicates speed in relation to time.

In the above explanation it might have been better to say that "something was caught in gravity." It can be implicitly understood that the length of the red arrow shows the relationship of rate of acceleration and time.

In other words: Gravitational force (F) = M (mass) times A (acceleration due to gravity)

Phenomenon No. 2: Calculating the Point where the Key will Land

imgRight, so we have just seen how an object dropped from a moving plane will fall at an angle. Based on the law of inertia, the scene where the hero catches the key also seems unrealistic. The faster a vehicle is moving, the more difficult it becomes to accurately drop an object at a designated target. Even for the professionals, dropping emergency supplies to disaster victims from a helicopter needs a lot of skill. Of course, emergency workers drop big things, objects that are bigger than a box. In our hero's case, the object is not that much bigger than a key – it is a key!

In the scene, the hero's sidekick, Hiyono-chan (usually a girl who is a bit wishy-washy), is on the train that is passing over the bridge. She spots where Ayumu is as soon as the train starts to make its way quickly across the bridge. How is it that she is able to drop the key directly to Ayumu? In a matter of seconds she apparently calculates the angle of the key as it would fall, taking into account the speed of the train, and drops the key so that it reaches its intended target.

In the case of airplanes making their emergency drops, the drop site is often not where the crew would calculate it to be: outside factors such as unforeseen drafts of winds can blow the emergency supplies off target.

Here is the problem with the scene: Say the train is going at 60 km/h. For the key to be dropped to its target accurately, it must be released before the train is over the intended target. At the speed of 60 km/h, the key will fall 16.6 meters per second. It will take 5 seconds for the key to fall from the train to its target. Hiyono-chan will have to drop the key 83.35 meters before the train reaches the spot over where Ayumu is standing for him to be able to catch the key.

Even for a person, let alone a girl like Hiyono, to try to use their own strength and wrist power to throw the key to a target would still be difficult due to the opposing force exerted by the train. It is impossible.

In the scene, the Ayumu successfully catches the key in his hand. This act would have required a phenomenal amount of calculation. Hiyono is able to estimate to the correct centimeter and to the correct split second where and when she has to drop the key to Ayumu? Oh, and there is the river too. The wind tends to pick up near rivers and other open areas, so it is natural to assume that a wind might be blowing. So Hiyono must calculate what impact of the interference from the wind. If the wind is strong, there is a chance it may blow the key into the river. Oh no!

If our hero Ayumu is able to calculate all these equations, can he send some signal to Hiyono up on the train as to when and where she should drop the key? Maybe Ayumu is not human? He seems more like Fatima, that hero from that "other manga."

If Ayumu's success is due to luck, then I think he should give up his detective work at once and become a gambler. He would also be able to find that long lost missing brother of his by going with his intuition.

*Beware: Don't try to replicate this experiment and go leaning out of train's windows throwing things down to the ground. It's dangerous.

Conclusion: The Scientific Way a Key would Fall

imgLet me explain how Hiyono-chan should have dropped the key in order to save our hero Ayumu, rather than putting his life in danger by dropping the key directly above him while on a moving train:

In order to counter the wind from blowing the key in a different direction and to make Ayumu Narumi, who is down under the railway bridge, notice the key, Hiyono should have attached something big to the key. Doing this it would have been easier to calculate where the key would fall. As soon as Hiyono realized from the train Ayumu's predicament, she should have without delay used all of her skill to attach the key to her bag, then she should have taken off her school uniform jacket, attached it to the handle of her bag, which would have made a simple parachute.

I am sure you have seen on TV when people were dropping an object from a high place, they usually attach a parachute to the object to help slacken the speed of descent. A jacket attached to the bag would act in a similar way, allowing the bag to hit the ground without causing any key-shattering shock. This is the way to drop the key; it is not so unnatural or unbelievable.

Saying this, I hope I have conveyed my feelings to the makers of Spiral - Bonds of Reasoning. I hope they understand that they should take into consideration how things should realistically happen. I beg of them to not let the impossible happen, like the key being caught below when thrown from a moving train high above. Please.

Phenomenon No. 3: Regarding the Mysterious Explosives Attached to Ayumu's Neck

There is another scene that I would like to poke my academic finger at: the mysterious "Key-Shaped" item. The key that is dropped to our hero resembles a typical key that one would use to open the front door to a house. I admire the hero for calmly catching the key, inserting it into the bomb attached to his neck that is just about to explode, but do you think an explosive device such as the one attached to Ayumu's neck would really be turned off by an ordinary front-door-opening-type key?

The bomb in the story is a time bomb that explodes after a certain amount of time. It is to be expected that the bomb should contain at least some kind of explosive materials, a clock, and some kind of ignition device as well as countless wires. With such a complicated device, a key is used to turn it off. I can't really say I am an expert on the intricacies of bombs, I just wonder: is it possible for a bomb to be that small and efficient?

In the both manga version and the anime version of Spiral, the bomb is a collar-sized neck-ring. It has enough firepower to blow the head off whoever it is attached to.

The graph here shows what the bomb looks like:


This explosive device seems to be able to withstand strong vibration, as it is robust enough to allow its wearer to run around without setting it off. Moreover, since Ayumu does not try to destroy it while it is on his neck, it can be inferred that it is a tough metallic cased bomb, made from a metallic substance that cannot be easily destroyed. It can't be ruled out that our hero, who does have a strange personality, is just trying to play strange detective games by seeing if he can catch a dropped key rather than just trying to physically remove the bomb himself.

It seems possible that there would be enough explosive material inside this metal-cased collar-shaped bomb to blow off a person's head (if anyone is a bomb expert please let me know if this is possible). When the key has been turned in the bomb, the wires connecting the clock to the detonator are disabled, and the time bomb timer is stopped, thus stopping the bomb from exploding.

Ok then, here is the problem: Is it possible that such a small and intricate device could be produced?

Asking this question earns the following chilly answer.

"A device of this size can be produced using plastic explosive materials. A matchbox filled with plastic explosives has the power to blow up a restaurant and all the customers in it. Plastic explosives are not like your everyday plastic materials. They are made from combinations of chemicals called Composition C-4 (C-4 explosives and semtex). Mixing trinimethylenetrinitroamino with oil based chemicals such as nitrotoluene, nitrocellulose, G-nitrotuluene, trinitrotoluene, octagen, hexogen, wax will produce plastic explosives."

It is common for terrorists to use plastic explosives when they plan to set off timed explosions. If a small amount of plastic explosives will be able to cause death of those around it, then it is possible that a sufficient amount of "plastic explosives and composition C-4" could be packed into a smallish collar shaped bomb.

Phenomenon No. 4: The Bomber Who Doesn't Take Cover as the Bomb is about to Explode

imgWait! There is one more loophole in the story. There is a scene where the villainess is standing near the hero, and taunting him. As the villain who made this intricate bomb, she should know the destructive power of the plastic explosives, then why does she stand within range of the bomb to taunt Ayumu? The evil nemesis is so careless that she could get caught in the explosion and be killed herself.

In this scene, the bomber is calmly standing a few meters from Ayumu as the bomb counts down to detonating. If the bomb explodes, the bad guy will most certainly be caught in the explosion. The villainess does not seem to think that a person with a bomb about to explode on his neck would be desperate enough to run toward her and take her to the next world with him. However, there is a possibility that the villainess is crazy enough not to care if she too is blown up into smithereens.

A plastic explosive bomb can destroy a lot of things within its range. A bomb the mere size of a matchbox can destroy a restaurant. Even plastic explosives the size of a grain of rice could probably cause damage too.

imgA person should not be leisurely standing so close to someone who has an extremely dangerous bomb attached to his neck. By the way, the villainess is holding a stuffed toy with a bomb in it, which she made by herself. It's wonderful. It seems anyone can make this kind of bomb out of gunpowder used in fireworks, which only scratches its victim even if detonated in close-range.

I think it would be a great idea if the villainess was to be portrayed holding a fluffy toy that she has managed to make into a bomb, in this situation there would have been gunpowder (the same that is used in fireworks), and the villainess would thus be able to stand at any distance from the victim with only the chance of being slightly grazed from the explosion.

Closing Words

I don't hate detective stories in manga and novels. I have followed Spiral - Bonds of Reasoning since it was first serialized. However, some things that happen in Spiral can not happen in the real world. I feel that it is poor and feeble of the author to include such tricks and mistakes so prominently in the story. It is something that seems to have been done without too much consideration.

I should just say as well that I don't find the mix of love comedy and murder so funny. As the intro song should go, "Ho ho ho, that's the way of criminal gangs, Spiral."

It seems your destiny might be to be sent to the juvenile correctional institution. I apologize for this comment but it is all I have left to say.

Original Article: Tsuredure Thoughts
Translated by: Franky L.
Edited by: ocean and Gage


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throwing things from trains

There is one advantage to be had when throwing something from a train (as compared to an airplane), namely the relatively low speed of the train. A trained baseball pitcher can throw at speeds up to 100 mph; logically a person could throw a small object such as a key at a speed roughly equal to the speed of the train, especially if the train is moving 60 mph or less. If one was to lean out of the window, and throw an object towards the rear of the train, the two velocities would cancel out and the object would drop straight down. Of course, this requires both knowing the speed of the train and having excellent control of one's throwing speed.

But in this case, the person

But in this case, the person throwing the key is a little girl. She may be smart, but it's doubtful that she'll be able to throw the key at such a speed that it'll cancel out the momentum created by the train.

I think i know the reason...

For Phenomenon No. 4, i think i know why the bomber is so close to ayumu. i think she did day, in the comic series, that the bomb is not all that powerful like you have stated in Phenomenon No. 3. She emphasised that the bomb will only be strong enough to bomb ayumu's head off. Does this answer your question?
PS. This is only a story and not real. I think we should just go along with what the stories say. I mean, this is not real. Wouldn't we be more happy if we follow what they say dumbly? There should be a time which we should be smart and a time which we should be dumb. However, i appreciate your analysis. I, too, agree to your analysis. =1

For me it looks kind of

For me it looks kind of "mission impossible". she couldn't throw the key that good they wanna make us believe :)

Mm. Fun post. On the nature

Mm. Fun post. On the nature of bombs and the usage of C4.
C4 explodes when excited. Its unstable properties make it a very powerful explosive. For the C4 to blow a man's head off, not a sizeable chunk is needed; since exciting the separation of molecules that leads to the explosion requires only about the same voltage of a car battery, this could be achieved assuming that the young man has a neck diameter of at least eight inches Why eight? Well, it seems like the minimum requirement for a chunk of C4 potent enough to rip his head clean off through metal he was too lazy to remove--although C4 also perfectly explains why he wouldn't try a bandsaw or a welder--in case he cut a wire and sent a charge through.)
Merely interrupting the timed charge would be enough, although there is one other problem--the diffusion of C4 around the ring.
You see, a chunk of C4 is sufficient enough to remove a person's head because it explodes at once, creating force. There is a law in calculus, translating over to physics, which suggests that force can be equally distributed.
Chemical reactions don't really work that way. A minor explosion throughout the ring in sequence probably would cause enough trauma to break his neck and kill him (for it takes little pressure to break a human neck) but removing his head is a bit much.
Bombs, sadly, just don't work that way. Unless she put nails in there--then the force might be able to do it. Probably not, though.

Good job once again, haha.

Good job once again, haha. Gravity doesn't seem to be that powerful in the Spiral world. Once the key falls, it should accelerate in the X-direction due to gravity, which means it be speeding up. From what I can see, the key seems to fall slow enough for the main protagonist to not feel any force from the key as the key's final momentum apparently halts to a zero. Unless he caught the key horizontally or the ribbon acted as a parachute, it should hurt, and he shouldn't look that pretty. XDD

Oh god, even a little kid was able to gather up the material for a C4, shows how desperate people are for money.

1) about the key, there was

1) about the key, there was a huge ribbon attached to it, making air resistance greater, and therefore making it drop straighter. Also, Ayumu has great hand-eye coordination, making it easier for him to snatch it out of the air.
2) only with the use of gasoline or something similar would the radius of the explosion extend to 3 meters, mentioned in the manga. in the picture, she is clearly more than 3 meters away, and he does not have gasoline.

yes i agree that it would be difficult to calculate where the key would land, but as for the bomb, i must say that there is no loophole in the manga there.