“Death Note: L, Anonymity & Eluding Entropy”, 2011-05-04 (; backlinks):
Applied Computer Science: On Murder Considered As STEM Field—using information theory to quantify the magnitude of Light Yagami’s mistakes in Death Note and considering fixes
In the manga Death Note, the protagonist Light Yagami is given the supernatural weapon “Death Note” which can kill anyone on demand, and begins using it to reshape the world. The genius detective L attempts to track him down with analysis and trickery, and ultimately succeeds. Death Note is almost a thought-experiment-given the perfect murder weapon, how can you screw up anyway? I consider the various steps of L’s process from the perspective of computer security, cryptography, and information theory, to quantify Light’s initial anonymity and how L gradually de-anonymizes him, and consider which mistake was the largest as follows:
Light’s fundamental mistake is to kill in ways unrelated to his goal.
Killing through heart attacks does not just make him visible early on, but the deaths reveals that his assassination method is impossibly precise and something profoundly anomalous is going on. L has been tipped off that Kira exists. Whatever the bogus justification may be, this is a major victory for his opponents. (To deter criminals and villains, it is not necessary for there to be a globally-known single anomalous or supernatural killer, when it would be equally effective to arrange for all the killings to be done naturalistically by ordinary mechanisms such as third parties/police/judiciary or used indirectly as parallel construction to crack cases.)
Worse, the deaths are non-random in other ways—they tend to occur at particular times!
Just the scheduling of deaths cost Light 6 bits of anonymity
Light’s third mistake was reacting to the blatant provocation of Lind L. Tailor.
Taking the bait let L narrow his target down to 1⁄3 the original Japanese population, for a gain of ~1.6 bits.
Light’s fourth mistake was to use confidential police information stolen using his policeman father’s credentials.
This mistake was the largest in bits lost. This mistake cost him 11 bits of anonymity; in other words, this mistake cost him twice what his scheduling cost him and almost 8 times the murder of Tailor!
Killing Ray Penbar and the FBI team.
If we assume Penbar was tasked 200 leads out of the 10,000, then murdering him and the fiancee dropped Light just 6 bits or a little over half the fourth mistake and comparable to the original scheduling mistake.
Endgame: At this point in the plot, L resorts to direct measures and enters Light’s life directly, enrolling at the university, with Light unable to perfectly play the role of innocent under intense in-person surveillance.
From that point on, Light is screwed as he is now playing a deadly game of “Mafia” with L & the investigative team. He frittered away >25 bits of anonymity and then L intuited the rest and suspected him all along.
Finally, I suggest how Light could have most effectively employed the Death Note and limited his loss of anonymity. In an appendix, I discuss the maximum amount of information leakage possible from using a Death Note as a communication device.
(Note: This essay assumes a familiarity with the early plot of Death Note and Light Yagami. If you are unfamiliar with DN, see my Death Note Ending essay or consult Wikipedia or read the DN rules.)