If Pacific Rim Followed Its Own Math, The Kaiju Would Have Won

By Kyle Hill | March 25, 2014 10:00 am
Click to enkaijunate

Click to enkaijunate

In the microscopic serenity of a test tube, bacteria multiply exponentially. Given enough food and space, the population will quickly double itself every few days or even hours. High school biology students might remember the math that goes along with this growth—something in the form of P=ert (like the shampoo, professors urge students to remember). Interdimensional monsters from the film Pacific Rim invade Earth in much the same way.

In Pacific Rim, kaiju researcher Hermann Gottlieb is quoted as saying:

In the beginning the Kaiju attacks was spaced by twenty-four weeks, then twelve, then six, then every two weeks. The last one in Sydney…was a week. In four days, we could be seeing the Kaiju every eight hours until they are coming every four minutes.

Gottlieb’s timeframe of a looming apocalypse has the numbers he needs to predict when the next kaiju will emerge from the “breach.” We can do the same. Unfortunately, even giving Gottlieb the benefit of the doubt, the data doesn’t make any sense.

In the quote from Gottlieb, we learn that when kaiju first started appearing, the time between each “event” was half that of the previous interlude—24 weeks becomes 12 becomes 6. Then, most likely for dramatic effect, he skips ahead to where monsters are emerging from the sea every four minutes. If you assume the exponential shortening of time between events, like how bacteria grow (only in reverse), you get something like this:

EmergenceThe graph above shows just how quickly the number of days between attacks shortens as a function of each emergence. For example, the fifth kaiju to stomp onto land would arrive only 11 days after the fourth kaiju, which itself emerged three weeks after the third. Again, this mimics the relentless growth of bacteria. Both bacteria and the kaiju follow exponential equations—in this case y=336e-0.693x. That math hides a tremendously terrifying kaiju emergence rate.

Imagine a checkerboard with standard checker pieces. On the first square you place one checker, half an inch tall. Following exponential growth, on the second square of the checkerboard you place two checkers, now a total of one inch tall. On the third square you place four checkers, on the fourth you place eight, and so on until you reach the 64th square. Simply following exponential growth, the height of the checkers on the 64th square should be about 73 trillion miles—almost twelve and a half light years up into space, well past our Sun and a few stars.

Kaiju emergence, based on what the film says, is a bit different. Instead of doubling the kaiju population every so often, the time between emergences is like the checkers in reverse. You start with a large amount of time between attacks and before you know it there is a “Category 5” kaiju appearing every few nanoseconds. In short, if Gottlieb is on the right track with his math, things get apocalyptic pretty quickly. But how long would humanity have?

Adding up all the time between kaiju attacks, assuming that having a kaiju appear every minute or less is certain doom, the Jaegers would have about 11 months before all hell broke lose. This is where the data and the film start disagreeing.

According to the scholarly nerds who run wikis like this, the time between the first kaiju attack and the last (when the breach was sealed with a nuclear detonation) was 11 years. If you follow the math once more, the time between kaiju attacks after 11 years of emerging would be far less than the Planck time–possibly the smallest amount of time we could ever measure. Also, during that 11 years there were 46 confirmed kaiju attacks, while the math says less than 20 emergences would spell extinction.

At least the novelization and official canon material of Pacific Rim are consistent in their disregard for their own mathematics. In an analysis of kaiju attack frequency over at Nerdometrics, the author catalogued all explicitly stated kaiju attacks and the time between them. He was expecting to find something similar to what I calculated—a simple and elegant exponential curve. Instead, he found this:

The real mathSo, looking at the attacks individually, we don’t see anything even close to the math laid out by Gottlieb so forcefully in the movie. Pacific Rim still makes a good argument for cancelling the apocalypse quickly—if kaiju really were emerging like bacteria divide there would be a huge problem. But apparently the film is conflicted on how much of a problem emergence really is.

Gottlieb insists that numbers are “as close as we get to the handwriting of God.” God gave you some bad information, Hermann



Further Reading:

Pacific Rim Physics (Part 1): A Rocket Punch is a Boeing 747 to the Face

Pacific Rim Physics (Part 2): In a Nuclear Explosion Bubble at the Bottom of the Ocean

Image Credits:

Pacific Rim poster by toybot studios

Kaiju attack graph via Nerdometrics

CATEGORIZED UNDER: Space & Physics, top posts
  • Tom Diggs

    Maybe they’re just k selected with a small carrying capacity. I’m guessing that their emergence rate must be connected to population size somehow, and given that they are so huge, their k is likely small.

  • Otto66

    Dr. Geiszler continues to question Dr. Gottlieb’s science through out most of the movie. Y’all just provided proof.

  • http://avangionq.stumbleupon.com/ AvangionQ

    Most action movies replay the cliche trope of the underdog hero or team scoring an unlikely upset win just before the closing credits.

  • SilverX2

    the problem with this is you assume that each time span lasted only one rotation: 1 event then the next one is 24 then the next one is 12, when in reality it was actually the more events then you account for, based on the number of kills each jaeger had.

  • Alex

    Gottlieb does sound like he’s implying the relationship between attacks laid out here but technically you could also read it as there were years and years of an attack every 24 weeks, then at some point it dropped to years of an attack every 16 weeks, etc. (and now it’s speeding up for whatever reason). Also there’d be a limit to how fast kaiju can emerge from the breach so they’d never be able to come through on a nanosecond basis. Love these kind of articles!

  • ObeyMyBrain

    Yeah, the quote from Gottlieb does not say that, “when kaiju first started appearing, the time between each “event” was half that of the previous interlude.” it says, “In the beginning the Kaiju attacks was spaced by twenty-four weeks, then twelve, then six, then every two weeks.”

    Then every two weeks means a Kaiju would appear, two weeks go by and another Kaiju would appear and then another two weeks for the next and so on. Otherwise the entire war would be over in less than a year rather than eleven.

  • OutPastPluto

    My problem with the entire sequence of events is that they didn’t erect a field of nuclear landmines from the start. Nevermind the math of the sequence.

    • moozh

      Or use the F (friendly) sword from day one… instead of throwing each other around like it’s a wrestling match!

  • Octocubist_Theologian

    Math is the least of Pacific Rim’s problems.

  • Negroponte

    Just putting my two cents, but if I recall correctly, the frequency of the attacks was altered at some point, I think after the guy connected his mind to them (I’m not sure). Gottlieb treated the progression as a recent discovery, one would imagine if he has been studying them since the beginning, he would have come to this conclusion much earlier. So the progression, as I understand, doesn’t begin until at some point along the way. I know the quote says “in the beginning”, but I think the quote is wrong (or I am). I also noticed, he doesn’t quite say each attack happens at this progression. It could be a different progression, where maybe a few attacks happened every 24 weeks, then it changed to to 12, then after say 7 attacks, it dropped to 6. The progression would be entirely different in that case, looking more like the second graph.

  • sakusakusakura_nyo

    All you really need is a bird kaiju and a shark kaiju to team up, then the giant robots wouldn’t stand a chance.

  • Betty Rose

    i love to spend a lot of time with my children in the half term and weekends. and sometimes its not all about going out and spending money. a day in making up a funny story and acting it out is one idea for great fun literacy activities! also, writing about what they did on there last holiday and the bits they most enjoyed! tey could write a letter to a family member or friend or help write out the shopping list. this gets your child used to different types or writing and different words and spellings.


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About Kyle Hill

Kyle Hill is a science writer and communicator who specializes in finding the secret science in your favorite fandom. His work has appeared in Wired, The Boston Globe, Scientific American, Popular Science, Slate, and more. He is a TV correspondent for Al Jazeera America's science and technology show TechKnow and a columnist for Skeptical Inquirer magazine. Find his stream of nerdery on Twitter: @Sci_Phile Email him at sciencebasedlife [at] gmail [dot] com.


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