Death Note: L, Anonymity & Eluding Entropy

http://www.gwern.net/Death%20Note%20Anonymity

by simonbrown • 14 years ago

233 42 14 years ago

hardy263• 14 years ago

As a curiosity, how many bits were gained (rather than lost) when the second and third characters obtaining a death note were entered? (female and male respectively)

Do the bits of entropy add on, or does it not matter at all?

gwern4• 14 years ago

Depends on the assumptions you make, I think. If we make the assumption that #2 and #3 obtained Death Notes at a known time, then any observations before then still pin down #1 - if there are kills at morning Japan-time, that serves to pin him down to Japan, etc.

But once #2 and #3 become equally active, now any evidence like that serves to narrow down the propositions 'any of #1, #2, #3 are in Japan', so if someone asked you what's the odds that #2 lives in Japan, you would only have 1/3 the evidence you did before - because any kill linked to Japan would only have 1/3 chance of having been #2. If a kill is made using information from a rural Iowan newspaper with circulation of 100, well, all you know is that any of 1/2/3 had access to it (and maybe all 3!). And so on.

(In bit terms, if there were 4 Death Note users, then any observation has 1/4 the power it did, or 1/2^2; similarly, if there were 16 users, or 32 users... Once you established someone was a Death Note user you would still need to do that many more bits of work to figure out which Death Note user you want.)

gburt• 14 years ago

Can anyone explain what is going on here? Edit: to clarify, I honestly have no idea what I'm reading: the title piqued my interest, but then it became... I'm really not sure.

AznHisoka• 14 years ago

It's about an anime named Death Note where the main character(named Light) finds a notebook (dubbed death note), and has the ability to kill anyone if he writes their name in the book. Noone knows he has it, but someone names "L" is hired to find out, and eventually traces the deaths to Light.

Lockyy3• 14 years ago

Manga adapted into an anime and movie(s) to be pedantic.

bdg• 14 years ago

Japanese TV show and comic book about a school boy who writes names into a notebook given to him by an angel of death. Writing names in a notebook kills them.

I'm not sure why it's on hacker news-- so I called them tv shows and comic books to offend the otaku.

jamesaguilar• 14 years ago

At the top there are a few links to required reading before you can understand the article.

Eliezer• 14 years ago

So now if criminals found only in widely available public sources begin dying of heart disease and cancer at correctly distributed but far-above-average rates, L will know that it's somebody who read this article - possibly Gwern himself! Even if this article hadn't been published, such clever use of the Death Note would certainly point to someone with high IQ and possibly involved in the cryptographic community...

gwern4• 14 years ago

Well, all I can say is I don't remember writing this! Whomever did so must be one clever fellow though, and I'd be happy to assist anyone in trying to catch him...

ufo• 14 years ago

I hate to be pedantic, but mistake #1 misses the point a bit. While the serial killer doesn't want to be found, he certainly wants to be known.

evincarofautumn• 14 years ago

Agreed. It is interesting, though, to consider just how many bits of identifying information you must sacrifice in order to make your existence known while securing your anonymity. Also, considering Light’s ultimate goal was world domination, he would’ve had to make strategic anonymity sacrifices all along regardless. I say his first mistake was just jumping the gun with insufficient research.

Shaanie2• 14 years ago

Absolutely. I think a somewhat easier way for him to gain world domination would've been to start with another country than his own. If he could find a way to obtain information about another country's criminals without being exposed, it would probably be easier to first take over that country and then expand it from there.

Lockyy3• 14 years ago

Whilst it was a mistake in leading to his capture I must agree, he wanted it to be known he existed. It was the entire point, scare people into not being evil.

Cushman• 14 years ago

If you really want to scare people, you should make every cause of death "Batman". Or maybe "space laser".

glimcat• 14 years ago

"Death by ironic circumstances. Time of death chosen from within the allowed range such that hazards to bystanders are minimized, then such that irony is maximized, then randomly."

Solving for maxima in the Law of Universal Perversity should do it.

gwern4• 14 years ago

The death has to be possible; Light tests out the limits early and finds IIRC that if you specify an imprisoned criminal dies outside the prison, the Death Note just gives up and kills them normally or something like that. 'Batman' and 'space laser' are right out, as is making criminals solve NP-hard or Halting problems.

Splines• 14 years ago

Sort of reminds me of the board game "Scotland Yard". It'd be interesting to see if an analysis with a mathematical bent would yield some tips for playing the game.

throwaway15213• 14 years ago

How much can you trust each bit of information you gained though? For example, it might be very possible that Light could be intentionally waking up at the middle of the night to do his killings. In which case you would've ruled out japan, which then ruins your subsequent analysis which is all somewhat based on him being in japan. Verifying every bit of information gained or even assigning a probability to how much you can trust it seems to be a hard problem.

ZenPsycho• 14 years ago

I think this is handled by bayesian logic.

Natsu3• 14 years ago

The show itself used quite a few very interesting methods to do it. Basically, L played a lot of hunches and won big several times.

The part about the time of day was found out long after L had narrowed things down to a small region of Japan by provoking Light into killing someone who appeared on a "worldwide" broadcast that was actually only broadcast in Light's prefecture. The time of day part was actually used to hypothesize that Light was a student, whereupon the pattern changed to show people killed every hour of the day. And L saw through that by assuming (correctly) that Light had access to police data. It seemed like he was always watching Light's reactions to his moves, rather than the moves themselves.

Probably one of the most clever traps of all was after they met in person, when L was able to trap Light by getting evidence that Light knew something he should have no way of knowing at all by means of false evidence. He played it off as Light being too dumb to figure out the riddle, but the only reason he couldn't solve it was because he thought the answer was impossible (and he shouldn't have known that).

Lockyy3• 14 years ago

One problem with the article I realised earlier was that it described the broadcast to Kanto as a gamble because it wasn't broadcast anywhere else, which is wrong. It was broadcast in each region one after another to find out which region it was in. It wasn't a gamble at all, it was a very clever way of finding out where Kira was watching from.

buu7004• 14 years ago

It's kind of funny that you posted this now, because at the moment I'm actually hacking on the last level of Stripe's Capture the Flag with Low of Solipsism, L's theme, Kira's theme, Near's theme, and Zetsubou Billy looping in the background.

As a side note, has anyone else considered the possibility that it's entirely possible that Light could have simply set up a server which would schedule his victims' deaths for a certain randomised time, then at that time pull up an image of them on X and print their name on one page of the death note which was set up to be indefinitely recycled within the same printer?

At that point it'd have been trivial for him to set up a simple password-protected REST interface which would accept POST requests of victims' names/pictures, and he could have even done all his future recruiting through Tor without taking the risk of using physical mail (and eventually facilitating the recruitment of a local "Kira" in every country, possibly vetting through social media comment histories in a similar fashion to the way he evaluated Mikami).

This setup wouldn't necessarily have been possible, but the wording of the Death Note looks like it might have allowed for it (contingent on how strictly it defined "mind"). At the very least, printing through electronic media would have been worth an experiment.

Assuming the server were reasonably secure, and he'd taken appropriate steps to scale as time passed, the very fact of all that ink on one page would have made it completely illegible, and thus inconclusive evidence. Then, he could have just performed any Kira actions from a virtual machine with an encrypted filesystem, eventually ceasing any direct killings as his army increased in size. It would have scaled beautifully, and he'd have been almost perfectly anonymous.

To put the icing on the cake, if he didn't want to put in so much grunt work, he could have simply configured his server to automatically hook into every well-maintained reputable public listing of convicted violent criminals (as well as listings like the website of America's Most Wanted) and then forgotten about the whole thing. And hell, if the whole thing is automated, why not just put in a line of code that marks each death as being at the hands of the most likely intelligence agency? It would have achieved the same chilling effect ("OMG THE CIA IS KILLING EVERY CRIMINAL IN THE WORLD NOW!"), and thus the same goal, without even realistically risking his own livelihood.

sidww2• 14 years ago

But he wanted the world to know that there was a Kira. His ambition was to be the God of the world. He could anonymously send instructions to the world to do what he wanted only if people knew there was a Kira.

buu7004• 14 years ago

Yeah, that would be a strong disincentive to frame the CIA, since his goal morphed pretty early on from fixing the world to becoming a god. For a more prudent and altruistic death note user, that particular strategy could have fit well into the automation idea.

archangel_one2• 14 years ago

As I recall, part of the rules of the Death Note was that the user has to picture the face of the victim as they write the name, so they have to have a name and a face to kill. I assume a printer doesn't manage to do that, although I do suspect at times that some printers are fairly malevolent.

buu7004• 14 years ago

".. would accept POST requests of victims' names/pictures ... at that time pull up an image of them on X and print their name on one page of the death note ..." (emphasis added)

Like I said, this depends on a bit of a loose definition of "mind", so it might not have worked at all.

Here is the exact wording of the rule in question: "This note will not take effect unless the writer has the person’s face in their mind when writing his/her name. Therefore, people sharing the same name will not be affected."

It specifically appeals to the (somewhat hazy) concept of mind, which would imply the prerequisite of some sort of sentience. However, the rules are not absolute, but rather based on Ryuk's imperfect interpretation (Ryuk didn't know a priori how certain experiments would turn out, like writing causes of death before names with the FBI agents); thus, the use of "mind" itself isn't so important, as it merely implies that Ryuk's experience is limited to sentient beings, which should be obvious.

In other words, there isn't any way to know whether a death note could be used in this way without testing it on a "real" death note (or having the authors write canonical material on it).

noonespecial• 14 years ago

E-gads, Brain, brilliant! Wait. No. All of the printers I've ever administered would have one of those postscript errors where they print randomly forever and end up killing everyone on earth.

buu7004• 14 years ago

Haha, well, there's no way that would work anyway unless the postscript error caused X to open a Web browser and search for images of us too.

Tichy• 14 years ago

I have recently thought about a possible future where everybody could kill everybody else anonymously. No idea how that would play out - probably with extinction?

I think technology could provide such a future, for example something like those tiny poison drones in the movie Dune.

Or maybe it will be possible to genetically engineer a virus to just kill one specific person - kind of like Stuxnet was targeted at one specific factory...

mikecane2• 14 years ago

See the Twilight Zone episode or Matheson's story: http://en.wikipedia.org/wiki/Button,_Button_%28The_Twilight_...

mikecane2• 14 years ago

I thought the article was brilliant. I stopped watching the series Numb3rs early on, so I wonder if it ever really covered real math like that?

ff0066mote2• 14 years ago

Just a note to the author:

I'm getting a lot of [Math Processing Errors] when I view your article: http://imgur.com/PSeMX I haven't looked at the source to see what was going on, so it might be that I'm blocking flash or something.

Otherwise, it was great! :) Thanks for a fun read!

gwern4• 14 years ago

No, it's all done via MathJax/JavaScript. That should be cross-browser without any issues, I thought.

ff0066mote2• 14 years ago

Well, no worries. I was on a school computer with an outdated version of Chrome.

Death Note: L, Anonymity & Eluding Entropy

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