Thursday, June 28, 2012

Physicist Contributes Equation Central to Upcoming Spider-man Film

On July 3, one of the summer's hottest blockbusters – The Amazing Spider-man – will hit theaters across the country. There's a lot more to the film than A-listers and special effects, however. Physics and quantitative biology are apparently "at the center of a few major plot points in the film," according to the University of Minnesota.

University of Minnesota physics professor Jim Kakalios instilled some physics in the film by adapting a special equation for the filmmakers to use. Called the "decay rate algorithm," the equation referenced several times in the movie "relates to cell regeneration and human mortality," Kakalios said in a video released today.

But the decay rate algorithm isn't simply a figment of Kakalios' imagination. In fact, it has been adapted from a frequently cited equation connecting the likelihood of death with age: the Gompertz Law.

The Gompertz law, named for the 19th century actuary and mathematician Benjamin Gompertz, predicts that humans have an exponentially increasing likelihood of dying as they age after reaching their early 20s. Eventually, the chance of death approaches 100 percent around the age of 122, the final age of the oldest confirmed person in history.

The probability of dying on the y-axis (1=dead), and age on the x-axis. This curve was developed using data for Swedish men. Image courtesy Dietrich Stauffer via his arXiv article.

The law works surprisingly well, even for other species. Quantitative biologists and actuaries have built upon this law throughout the years, and Kakalios added some of this knowledge for the decay rate algorithm used in Spiderman.

In addition to the newer research included in the algorithm, Kakalios added what he called "some mathematical glitter," to lend the algorithm some more visual complexity.

A version of the decay rate algorithm used in the film. Don't ask me what all of the variables represent because I simply don't know.

Because the Gompertz law (or variations of it) has matched empirical data well, Kakalios' colleague Boris Shklovskii developed a very simple theory for why it works so well. Essentially, Shklovskii suggests that mutant cells increase exponentially with age, and immune cells increasingly develop a lower likelihood of fighting off these mutant cells.

The model certainly doesn't account for all causes of death, but it's interesting to consider regardless. You can see his short paper on arXiv.org.

Kakalios explains this theory more fully in the video below, and he explains his other contributions to the upcoming Spider-man film. In addition to contributing the decay rate algorithm, Kakalios gave the filmmakers background information on tensile strength needed for Peter Parker's wrist-flung spider webs.

There's some audio problems with the video (Kakalios can only be heard in the left speaker). I'll update the video if the University of Minnesota uploads a new one.

Kakalios served as a science adviser for the spiderman film as a part of The Science and Entertainment Exchange, which pairs practicing scientists with filmmakers in an effort to make TV shows and films more scientifically accurate and realistic.

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4 comments:

  1. Thanks for the great write up. I deliberately added terms (per the film makers request) to the expression that had no explicit meaning, as I did not want the equation to be the actual Gompertz formula or any other related expression. After all, there is no equation that will describe a transformation into a giant green lizard!

    And the video has sound on one channel and music on the other. My family tells me that voice is bad enough that one does not need to hear it in stereo!

    And it's Kakalios, by the way. Not the first time its been mis-spelled and won't be the last!

    Your Friendly Neighborhood Physics Professor,

    Jim

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  2. Thanks for you comment, Jim. I apologize for misspelling your name in the second half of the post! I think I've changed all of the misspellings, but please let me know if I missed anything.

    -Brian

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  3. Hey Jim, quick question. Did you add in the kappa and sigma? Do they have anything to do with the Kappa Sigma Fraternity? Thanks!

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  4. This is brilliant...i find it so intriguing i have been reading about it two days now yea.

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